text stringlengths 644 10k |
|---|
hapter 3. An indifference curve represents all market baskets that give the consumer the same level of utility. If U* is a fixed utility level, the indifference curve that corresponds to that utility level is given by In §3.5, we show that the marginal rate of substitution is equal to the ratio of the marginal utilities of the two goods being consumed. U(X, Y) = U* As the market baskets are changed by adding small amounts of X and subtracting small amounts of Y, the total change in utility must equal zero. Therefore, MUX(X, Y)dX + MUY(X, Y)dY = dU* = 0 (A4.7) 152 PART 2 • Producers, Consumers, and Competitive Markets Rearranging, -dY/dX = MUX(X, Y)/MUY(X, Y) = MRSXY (A4.8) where MRSXY represents the individual’s marginal rate of substitution of X for Y. Because the left-hand side of (A4.8) represents the negative of the slope of the indifference curve, it follows that at the point of tangency, the individual’s marginal rate of substitution (which trades off goods while keeping utility constant) is equal to the individual’s ratio of marginal utilities, which in turn is equal to the ratio of the prices of the two goods, from (A4.6).3 When the individual indifference curves are convex, the tangency of the indifference curve to the budget line solves the consumer ’s optimization problem. This principle was illustrated by Figure 3.13 (page 86) in Chapter 3. Marginal Utility of Income Whatever the form of the utility function, the Lagrange multiplier represents the extra utility generated when the budget constraint is relaxed—in this case by adding one dollar to the budget. To show how the principle works, we differentiate the utility function U(X, Y) totally with respect to I: dU/dI = MUX(X, Y)(dX/dI) + MUY(X, Y)(dY/dI) (A4.9) Because any increment in income must be divided between the two goods, it follows that dI = PXdX + PYdY (A4.10) Substituting from (A4.5) into (A4.9), we get dU/dI = lPX(dX/dI) + lPY(dY/dI) = l(PXdX + PYdY)/dI (A4.11) and substituting (A4.10) into (A4.11), we get dU/dI = l(PXdX + PYdY)/(PXdX + PYdY) = l (A4.12) Thus the Lagrange multiplier is the extra utility that results from an extra dollar of income. Going back to our original analysis of the conditions for utility maximization, we see from equation (A4.5) that maximization requires the utility obtained from the consumption of every good, per dollar spent on that good, to be equal to the marginal utility of an additional dollar of income. If this were not the case, utility could be increased by spending more on the good with the higher ratio of marginal utility to price and less on the other good. 3We implicitly assume that the “second-order conditions” for a utility maximum hold. The consumer, therefore, is maximizing rather than minimizing utility. The convexity condition is sufficient for the second-order conditions to be satisfied. In mathematical terms, the condition is that d(MRS)/dX 6 0 or that dY2/dX2 7 0 where - dY/dX is the slope of the indifference curve. Remember: diminishing marginal utility is not sufficient to ensure that indifference curves are convex. CHAPTER 4 • Individual and Market Demand 153 An Example In general, the three equations in (A4.4) can be solved to determine the three unknowns X, Y, and as a function of the two prices and income. Substitution for then allows us to solve for the demand for each of the two goods in terms of income and the prices of the two commodities. This principle can be most easily seen in terms of an example. A frequently used utility function is the Cobb-Douglas utility function, which can be represented in two forms: U(X, Y) = a log(X) + (1 - a) log(Y) and U(X, Y) = XaY1 - a For the purposes of demand theory, these two forms are equivalent because they both yield the identical demand functions for goods X and Y. We will derive the demand functions for the first form and leave the second as an exercise for the student. To find the demand functions for X and Y, given the usual budget constraint, we first write the Lagrangian: = a log(X) + (1 - a)log(Y) - l(PXX + PYY - I) Now differentiating with respect to X, Y, and and setting the derivatives equal to zero, we obtain 0 /0X = a/X - lPX = 0 0 /0Y = (1 - a)/Y - lPY = 0 0 /0l = PXX + PYY - I = 0 The first two conditions imply that PXX = a/l PYY = (1 - a)/l (A4.13) (A4.14) Combining these expressions with the last condition (the budget constraint) gives us a/l + (1 - a)/l - I = 0 or = 1/I. Now we can substitute this expression for back into (A4.13) and (A4.14) to obtain the demand functions: X = (a/PX)I Y = [(1 - a)/PY]I In this example, the demand for each good depends only on the price of that good and on income, not on the price of the other good. Thus, the cross-price elasticities of demand are 0. • Cobb-Douglas utility function Utility function U(X,Y ) = XaY 1 −a, where X and Y are two goods and a is a constant. In §2.4, we explain that the cross-price elasticity of demand refers to the percentage change in the quantity demanded of one good that results from a 1-percent increase in the price of another good. 154 PART 2 • Producers, Consumers, and Competitive Markets • duality Alternative way of looking at the consumer’s utility maximization decision: Rather than choosing the highest indifference curve, given a budget constraint, the consumer chooses the lowest budget line that touches a given indifference curve. = $1, PY We can also use this example to review the meaning of Lagrange multipliers. To do so, let’s substitute specific values for each of the parameters in the problem. Let a = 1/2, PX = $2, and I = $100. In this case, the choices that maximize utility are X = 50 and Y = 25. Also note that = 1/100. The Lagrange multiplier tells us that if an additional dollar of income were available to the consumer, the level of utility achieved would increase by 1/100. This conclusion is relatively easy to check. With an income of $101, the maximizing choices of the two goods are X = 50.5 and Y = 25.25. A bit of arithmetic tells us that the original level of utility is 3.565 and the new level of utility 3.575. As we can see, the additional dollar of income has indeed increased utility by .01, or 1/100. Duality in Consumer Theory There are two different ways of looking at the consumer’s optimization decision. The optimum choice of X and Y can be analyzed not only as the problem of choosing the highest indifference curve—the maximum value of U( )—that touches the budget line, but also as the problem of choosing the lowest budget line—the minimum budget expenditure—that touches a given indifference curve. We use the term duality to refer to these two perspectives. To see how this principle works, consider the following dual consumer optimization problem: the problem of minimizing the cost of achieving a particular level of utility: subject to the constraint that Minimize PXX + PYY U(X, Y) = U* The corresponding Lagrangian is given by = PXX + PYY - μ(U(X, Y) - U*) (A4.15) where μ is the Lagrange multiplier. Differentiating with respect to X, Y, and μ and setting the derivatives equal to zero, we find the following necessary conditions for expenditure minimization: and PX PY - μMUX(X, Y) = 0 - μMUY(X, Y) = 0 U(X, Y) = U* By solving the first two equations, and recalling (A4.5), we see that μ = [PX/MUX(X, Y)] = [PY/MUY(X, Y)] = 1/l Because it is also true that MUX(X, Y)/MUY(X, Y) = MRSXY = PX/PY CHAPTER 4 • Individual and Market Demand 155 the cost-minimizing choice of X and Y must occur at the point of tangency of the budget line and the indifference curve that generates utility U*. Because this is the same point that maximized utility in our original problem, the dual expenditure- minimization problem yields the same demand functions that are obtained from the direct utility-maximization problem. To see how the dual approach works, let’s reconsider our Cobb-Douglas example. The algebra is somewhat easier to follow if we use the exponential form of the Cobb-Douglas utility function, U(X, Y) = XaY1 - a. In this case, the Lagrangian is given by = PXX + PYY - μ[XaY1 - a - U*] (A4.16) Differentiating with respect to X, Y, and μ and equating to zero, we obtain PX PY = μ aU*/X = μ(1 - a)U*/Y Multiplying the first equation by X and the second by Y and adding, we get PXX + PYY = μU* First, we let I be the cost-minimizing expenditure (if the individual did not spend all of his income to get utility level U*, U* would not have maximized utility in the original problem). Then it follows that μ = I/U*. Substituting in the equations above, we obtain X = aI/PX and Y = (1 - a)I/PY These are the same demand functions that we obtained before. Income and Substitution Effects The demand function tells us how any individual’s utility-maximizing choices respond to changes in both income and the prices of goods. It is important, however, to distinguish that portion of any price change that involves movement along an indifference curve from that portion which involves movement to a different indifference curve (and therefore a change in purchasing power). To make this distinction, we consider what happens to the demand for good X when the price of X changes. As we explained in Section 4.2, the change in demand can be divided into a substitution effect (the change in quantity demanded when the level of utility is fixed) and an income effect (the change in the quantity demanded with the level of utility changing but the relative price of good X unchanged). We denote the change in X that results from a unit change in the price of X, holding utility constant, by 0X/0PX|U = U* Thus the total change in the quantity demanded of X resulting from a unit change in PX is dX/dPX = 0X/0PX|U = U* + (0X/0I)(0I/0PX) (A4.17) In §4.2, the effect of a price change is divided into an income effect and a substitution effect. 156 PART 2 • Producers, Consumers, and Competitive Markets The first term on the right side of equation (A4.17) is the substitution effect (because utility is fixed); |
the second term is the income effect (because income increases). From the consumer’s budget constraint, I = PXX + PYY, we know by differen- tiation that 0I/0PX = X (A4.18) Suppose for the moment that the consumer owned goods X and Y. In that case, equation (A4.18) would tell us that when the price of good X increases by $1, the amount of income that the consumer can obtain by selling the good increases by $X. In our theory of consumer behavior, however, the consumer does not own the good. As a result, equation (A4.18) tells us how much additional income the consumer would need in order to be as well off after the price change as he or she was before. For this reason, it is customary to write the income effect as negative (reflecting a loss of purchasing power) rather than as a positive. Equation (A4.17) then appears as follows: dX/dPX = 0X/0PX|U = U* - X(0X/0I) (A4.19) In this new form, called the Slutsky equation, the first term represents the substitution effect: the change in demand for good X obtained by keeping utility fixed. The second term is the income effect: the change in purchasing power resulting from the price change times the change in demand resulting from a change in purchasing power. An alternative way to decompose a price change into substitution and income effects, which is usually attributed to John Hicks, does not involve indifference curves. In Figure A4.1, the consumer initially chooses market basket A on budget line RS. Suppose that after the price of food falls (and the • Slutsky equation Formula for decomposing the effects of a price change into substitution and income effects. R Clothing (units per month) ′ R A B FIGURE A4.1 HICKSIAN SUBSTITUTION EFFECT The individual initially consumes market basket A. A decrease in the price of food shifts the budget line from RS to RT. If a sufficient amount of income is taken away to make the individual no better off than he or she was at A, two conditions must be met: The new market basket chosen must lie on line segment BT' of budget line R' T' (which intersects RS to the right of A), and the quantity of food consumed must be greater than at A. S ′ T T Food (units per month) CHAPTER 4 • Individual and Market Demand 157 budget line moves to RT), we take away enough income so that the individual is no better off (and no worse off) than he was before. To do so, we draw a budget line parallel to RT. If the budget line passed through A, the consumer would be at least as satisfied as he was before the price change: He still has the option to purchase market basket A if he wishes. According to the Hicksian substitution effect, therefore, the budget line that leaves him equally well off must be a line such as R’T’, which is parallel to RT and which intersects RS at a point B below and to the right of point A. Revealed preference tells us that the newly chosen market basket must lie on line segment BT'. Why? Because all market baskets on line segment R' B could have been chosen but were not when the original budget line was RS. (Recall that the consumer preferred basket A to any other feasible market basket.) Now note that all points on line segment BT' involve more food consumption than does basket A. It follows that the quantity of food demanded increases whenever there is a decrease in the price of food with utility held constant. This negative substitution effect holds for all price changes and does not rely on the assumption of convexity of indifference curves that we made in Section 3.1 (page 69). • Hicksian substitution effect Alternative to the Slutsky equation for decomposing price changes without recourse to indifference curves. In §3.1, we explain that an indifference curve is convex if the marginal rate of substitution diminishes as we move down along the curve. In §3.4, we explain how information about consumer preferences is revealed through the consumption choices that consumers make. EXERCISES 1. Which of the following utility functions are consistent with convex indifference curves and which are not? a. U(X, Y) = 2X + 5Y b. U(X, Y) = (XY).5 c. U(X, Y) = Min (X, Y), where Min is the minimum of the two values of X and Y. 2. Show that the two utility functions given below generate identical demand functions for goods X and Y: a. U(X, Y) = log(X) + log(Y) b. U(X, Y) = (XY).5 3. Assume that a utility function is given by Min(X, Y), as in Exercise 1(c). What is the Slutsky equation that decomposes the change in the demand for X in response to a change in its price? What is the income effect? What is the substitution effect? 4. Sharon has the following utility function: U(X, Y) = 1X + 1Y where X is her consumption of candy bars, with price = $1, and Y is her consumption of espressos, with = $3. PX PY a. Derive Sharon’s demand for candy bars and espresso. b. Assume that her income I = $100. How many candy bars and how many espressos will Sharon consume? c. What is the marginal utility of income? 5. Maurice has the following utility function: U(X, Y) = 20X + 80Y - X2 - 2Y2 where X is his consumption of CDs with a price of $1 and Y is his consumption of movie videos, with a rental price of $2. He plans to spend $41 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize Maurice’s utility. This page intentionally left blank C H A P T E R 5 Uncertainty and Consumer Behavior So far, we have assumed that prices, incomes, and other variables are known with certainty. However, many of the choices that people make involve considerable uncertainty. Most people, for example, borrow to finance large purchases, such as a house or a college education, and plan to pay for them out of future income. But for most of us, future incomes are uncertain. Our earnings can go up or down; we can be promoted or demoted, or even lose our jobs. And if we delay buying a house or investing in a college education, we risk price increases that could make such purchases less affordable. How should we take these uncertainties into account when making major consumption or investment decisions? Sometimes we must choose how much risk to bear. What, for example, should you do with your savings? Should you invest your money in something safe, such as a savings account, or something riskier but potentially more lucrative, such as the stock market? Another example is the choice of a job or career. Is it better to work for a large, stable company with job security but slim chance for advancement, or is it better to join (or form) a new venture that offers less job security but more opportunity for advancement? To answer such questions, we must examine the ways that people can compare and choose among risky alternatives. We will do this by taking the following steps: 1. In order to compare the riskiness of alternative choices, we need to quantify risk. We therefore begin this chapter by discussing measures of risk. 2. We will examine people’s preferences toward risk. Most people find risk undesirable, but some people find it more undesirable than others. 3. We will see how people can sometimes reduce or eliminate risk. Sometimes risk can be reduced by diversification, by buying insurance, or by investing in additional information. 4. In some situations, people must choose the amount of risk they wish to bear. A good example is investing in stocks or bonds. We will see that such investments involve trade-offs between the monetary gain that one can expect and the riskiness of that gain. 5. Sometimes demand for a good is driven partly or entirely by speculation—people buy the good because they think its price will rise.1 Describing Risk 160 5.2 Preferences Toward Risk 165 5.3 Reducing Risk 170 *5.4 The Demand for Risky Assets 176 5.5 Bubbles 185 5.6 Behavioral Economics 189 .1 Deterring Crime 164 5.2 Business Executives and the Choice of Risk 169 5.3 The Value of Title Insurance When Buying a House 173 5.4 The Value of Information in an Online Consumer Electronics Market 175 5.5 Doctors, Patients, and the Value of Information 175 5.6 Investing in the Stock Market 183 5.7 The Housing Price Bubble (I) 186 5.8 The Housing Price Bubble (II) 188 5.9 Selling a House 192 5.10 New York City Taxicab Drivers 196 159 160 PART 2 • Producers, Consumers, and Competitive Markets • probability Likelihood that a given outcome will occur. We will see how this can lead to a bubble, where more and more people, convinced that the price will keep rising, buy the good and push its price up further—until eventually the bubble bursts and the price plummets. In a world of uncertainty, individual behavior may sometimes seem unpredictable, even irrational, and perhaps contrary to the basic assumptions of consumer theory. In the final section of this chapter, we offer an overview of the flourishing field of behavioral economics, which, by introducing important ideas from psychology, has broadened and enriched the study of microeconomics. 5.1 Describing Risk To describe risk quantitatively, we begin by listing all the possible outcomes of a particular action or event, as well as the likelihood that each outcome will occur.1 Suppose, for example, that you are considering investing in a company that explores for offshore oil. If the exploration effort is successful, the company’s stock will increase from $30 to $40 per share; if not, the price will fall to $20 per share. Thus there are two possible future outcomes: a $40-per-share price and a $20-per-share price. Probability Probability is the likelihood that a given outcome will occur. In our example, the probability that the oil exploration project will be successful might be 1/4 and the probability that it is unsuccessful 3/4. (Note that the probabilities for all possible events must add up to 1.) Our interpretation of probability can depend on the nature of the uncertain event, on the beliefs of the people involved, or both. One objective interpretation of probability relies on the frequency with which certain events tend to |
occur. Suppose we know that of the last 100 offshore oil explorations, 25 have succeeded and 75 failed. In that case, the probability of success of 1/4 is objective because it is based directly on the frequency of similar experiences. But what if there are no similar past experiences to help measure probability? In such instances, objective measures of probability cannot be deduced and more subjective measures are needed. Subjective probability is the perception that an outcome will occur. This perception may be based on a person’s judgment or experience, but not necessarily on the frequency with which a particular outcome has actually occurred in the past. When probabilities are subjectively determined, different people may attach different probabilities to different outcomes and thereby make different choices. For example, if the search for oil were to take place in an area where no previous searches had ever occurred, I might attach a higher subjective probability than you to the chance that the project will succeed: Perhaps I know more about the project or I have a better understanding of the oil business and can therefore make better use of our common information. Either different information or different abilities to process the same information can cause subjective probabilities to vary among individuals. 1Some people distinguish between uncertainty and risk along the lines suggested some 60 years ago by economist Frank Knight. Uncertainty can refer to situations in which many outcomes are possible but the likelihood of each is unknown. Risk then refers to situations in which we can list all possible outcomes and know the likelihood of each occurring. In this chapter, we will always refer to risky situations, but will simplify the discussion by using uncertainty and risk interchangeably. Regardless of the interpretation of probability, it is used in calculating two important measures that help us describe and compare risky choices. One measure tells us the expected value and the other the variability of the possible outcomes. CHAPTER 5 • Uncertainty and Consumer Behavior 161 Expected Value The expected value associated with an uncertain situation is a weighted average of the payoffs or values associated with all possible outcomes. The probabilities of each outcome are used as weights. Thus the expected value measures the central tendency—the payoff or value that we would expect on average. Our offshore oil exploration example had two possible outcomes: Success yields a payoff of $40 per share, failure a payoff of $20 per share. Denoting “probability of” by Pr, we express the expected value in this case as • expected value Probabilityweighted average of the payoffs associated with all possible outcomes. • payoff Value associated with a possible outcome. Expected value = Pr(success)($40/share) + Pr(failure)($20/share) = (1/4)($40/share) + (3/4)($20/share) = $25/share More generally, if there are two possible outcomes having payoffs X1 and X2 and if the probabilities of each outcome are given by Pr1 and Pr2, then the expected value is E(X) = Pr1X1 + Pr2X2 When there are n possible outcomes, the expected value becomes E(X) = Pr1X1 + Pr2X2 + c + PrnXn Variability Variability is the extent to which the possible outcomes of an uncertain situation differ. To see why variability is important, suppose you are choosing between two part-time summer sales jobs that have the same expected income ($1500). The first job is based entirely on commission—the income earned depends on how much you sell. There are two equally likely payoffs for this job: $2000 for a successful sales effort and $1000 for one that is less successful. The second job is salaried. It is very likely (.99 probability) that you will earn $1510, but there is a .01 probability that the company will go out of business, in which case you would earn only $510 in severance pay. Table 5.1 summarizes these possible outcomes, their payoffs, and their probabilities. Note that these two jobs have the same expected income. For Job 1, expected income is .5($2000) .5($1000) $1500; for Job 2, it is .99($1510) .01($510) $1500. However, the variability of the possible payoffs is different. We measure TABLE 5.1 INCOME FROM SALES JOBS OUTCOME 1 OUTCOME 2 PROBABILITY INCOME ($) PROBABILITY INCOME ($) EXPECTED INCOME ($) Job 1: Commission Job 2: Fixed Salary .5 .99 2000 1510 .5 .01 1000 510 1500 1500 • variability Extent to which possible outcomes of an uncertain event differ. 162 PART 2 • Producers, Consumers, and Competitive Markets TABLE 5.2 DEVIATIONS FROM EXPECTED INCOME ($) OUTCOME 1 DEVIATION OUTCOME 2 DEVIATION Job 1 Job 2 2000 1510 500 10 1000 510 −500 −990 • deviation Difference between expected payoff and actual payoff. • standard deviation Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values. variability by recognizing that large differences between actual and expected payoffs (whether positive or negative) imply greater risk. We call these differences deviations. Table 5.2 shows the deviations of the possible income from the expected income from each job. By themselves, deviations do not provide a measure of variability. Why? Because they are sometimes positive and sometimes negative, and as you can see from Table 5.2, the average of the probability-weighted deviations is always 0.2 To get around this problem, we square each deviation, yielding numbers that are always positive. We then measure variability by calculating the standard deviation: the square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected values.3 Table 5.3 shows the calculation of the standard deviation for our example. Note that the average of the squared deviations under Job 1 is given by .5($250,000) + .5($250,000) = $250,000 The standard deviation is therefore equal to the square root of $250,000, or $500. Likewise, the probability-weighted average of the squared deviations under Job 2 is .99($100) + .01($980,100) = $9900 The standard deviation is the square root of $9900, or $99.50. Thus the second job is much less risky than the first; the standard deviation of the incomes is much lower.4 The concept of standard deviation applies equally well when there are many outcomes rather than just two. Suppose, for example, that the first summer job yields incomes ranging from $1000 to $2000 in increments of $100 that are all equally likely. The second job yields incomes from $1300 to $1700 (again in increments of $100) that are also equally likely. Figure 5.1 shows the alternatives TABLE 5.3 CALCULATING VARIANCE ($) OUTCOME 1 2000 1510 DEVIATION SQUARED 250,000 100 OUTCOME 2 1000 510 DEVIATION SQUARED WEIGHTED AVERAGE DEVIATION SQUARED STANDARD DEVIATION 250,000 980,100 250,000 9900 500 99.50 Job 1 Job 2 2For Job 1, the average deviation is .5($500) .5(−$500) 0; for Job 2 it is .99($10) .01(−$990) 0. 3Another measure of variability, variance, is the square of the standard deviation. 4In general, when there are two outcomes with payoffs X1 and X2, occurring with probability Pr1 and Pr2, and E(X) is the expected value of the outcomes, the standard deviation is given by s, where s2 = Pr1[(X1 - E(X))2] + Pr2[(X2 - E(X))2] Probability 0.2 0.1 CHAPTER 5 • Uncertainty and Consumer Behavior 163 FIGURE 5.1 OUTCOME PROBABILITIES FOR TWO JOBS The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are flat because all outcomes are equally likely. Job 2 Job 1 $1000 $1500 $2000 Income graphically. (If there had been only two equally probable outcomes, then the figure would be drawn as two vertical lines, each with a height of 0.5.) You can see from Figure 5.1 that the first job is riskier than the second. The “spread” of possible payoffs for the first job is much greater than the spread for the second. As a result, the standard deviation of the payoffs associated with the first job is greater than that associated with the second. In this particular example, all payoffs are equally likely. Thus the curves describing the probabilities for each job are flat. In many cases, however, some payoffs are more likely than others. Figure 5.2 shows a situation in which the most extreme payoffs are the least likely. Again, the salary from Job 1 has a greater standard deviation. From this point on, we will use the standard deviation of payoffs to measure the degree of risk. Decision Making Suppose you are choosing between the two sales jobs described in our original example. Which job would you take? If you dislike risk, you will take the second job: It offers the same expected income as the first but with less risk. But suppose we add $100 to each of the payoffs in the first job, so that the expected payoff increases from $1500 to $1600. Table 5.4 gives the new earnings and the squared deviations. Probability 0.3 0.2 0.1 Job 2 Job 1 FIGURE 5.2 UNEQUAL PROBABILITY OUTCOMES The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are peaked because the extreme payoffs are less likely than those near the middle of the distribution. $1000 $1500 $2000 Income 164 PART 2 • Producers, Consumers, and Competitive Markets TABLE 5.4 INCOMES FROM SALES JOBS—MODIFIED ($) OUTCOME 1 Job 1 Job 2 2100 1510 DEVIATION SQUARED 250,000 100 OUTCOME 2 DEVIATION SQUARED EXPECTED INCOME STANDARD DEVIATION 1100 510 250,000 980,100 1600 1500 500 99.50 The two jobs can now be described as follows: Job 1: Job 2: Expected Income $1600 Expected Income $1500 Standard Deviation $500 Standard Deviation $99.50 Job 1 offers a higher expected income but is much riskier than Job 2. Which job is preferred depends on the individual. While an aggressive entrepreneur w |
ho doesn’t mind taking risks might choose Job 1, with the higher expected income and higher standard deviation, a more conservative person might choose the second job. People’s attitudes toward risk affect many of the decisions they make. In Example 5.1 we will see how attitudes toward risk affect people’s willingness to break the law, and how this has implications for the fines that should be set for various violations. Then in Section 5.2, we will further develop our theory of consumer choice by examining people’s risk preferences in greater detail. E XAM PLE 5.1 DETERRING CRIME Fines may be better than incarceration in deterring certain types of crimes, such as speeding, doubleparking, tax evasion, and air polluting.5 A person choosing to violate the law in these ways has good information and can reasonably be assumed to be behaving rationally. Other things being equal, the greater the fine, the more a potential criminal will be discouraged from committing the crime. For example, if it cost nothing to catch criminals, and if the crime imposed a calculable cost of $1000 on society, we might choose to catch all violations and impose a fine of $1000 on each. This practice would discourage people whose benefit from engaging in the activity was less than the $1000 fine. In practice, however, it is very costly to catch lawbreakers. Therefore, we save on administrative costs by imposing relatively high fines (which are no more costly to collect than low fines), while allocating resources so that only a fraction of the violators are apprehended. Thus the size of the fine that must be imposed to discourage criminal behavior depends on the attitudes toward risk of potential violators. Suppose that a city wants to deter people from double-parking. By double-parking, a typical resident saves $5 in terms of his own time for engaging in activities that are more pleasant than searching for a parking space. If it costs nothing to catch a double-parker, a fine of just over $5—say, $6— should be assessed every time he double-parks. This policy will ensure that the net benefit of double-parking (the $5 benefit less the $6 fine) would be less than zero. Our citizen will therefore choose to obey the law. In fact, all potential violators whose benefit was less than or equal to $5 would be discouraged, while a few whose benefit was greater than $5 (say, someone who double-parks because of an emergency) would violate the law. 5This discussion builds indirectly on Gary S. Becker, “Crime and Punishment: An Economic Approach,” Journal of Political Economy (March/April 1968): 169–217. See also A. Mitchell Polinsky and Steven Shavell, “The Optimal Tradeoff Between the Probability and the Magnitude of Fines,” American Economic Review 69 (December 1979): 880–91. CHAPTER 5 • Uncertainty and Consumer Behavior 165 In practice, it is too costly to catch all violators. Fortunately, it’s also unnecessary. The same deterrence effect can be obtained by assessing a fine of $50 and catching only one in ten violators (or perhaps a fine of $500 with a one-in-100 chance of being caught). In each case, the expected penalty is $5, i.e., [$50][.1] or [$500][.01]. A policy that combines a high fine and a low probability of apprehension is likely to reduce enforcement costs. This approach is especially effective if drivers don’t like to take risks. In our example, a $50 fine with a .1 probability of being caught might discourage most people from violating the law. We will examine attitudes toward risk in the next section. A new type of crime that has become a serious problem for music and movie producers is digital piracy; it is particularly difficult to catch and fines are rarely imposed. Nevertheless, fines that are levied are often very high. In 2009, a woman was fined $1.9 million for illegally downloading 24 songs. That amounts to a fine of $80,000 per song. 5.2 Preferences Toward Risk We used a job example to show how people might evaluate risky outcomes, but the principles apply equally well to other choices. In this section, we concentrate on consumer choices generally and on the utility that consumers obtain from choosing among risky alternatives. To simplify things, we’ll consider the utility that a consumer gets from his or her income—or, more appropriately, the market basket that the consumer’s income can buy. We now measure payoffs, therefore, in terms of utility rather than dollars. Figure 5.3 (a) shows how we can describe one woman’s preferences toward risk. The curve 0E, which gives her utility function, tells us the level of utility (on the vertical axis) that she can attain for each level of income (measured in thousands of dollars on the horizontal axis). The level of utility increases from 10 to 16 to 18 as income increases from $10,000 to $20,000 to $30,000. But note that marginal utility is diminishing, falling from 10 when income increases from 0 to $10,000, to 6 when income increases from $10,000 to $20,000, and to 2 when income increases from $20,000 to $30,000. Now suppose that our consumer has an income of $15,000 and is considering a new but risky sales job that will either double her income to $30,000 or cause it to fall to $10,000. Each possibility has a probability of .5. As Figure 5.3 (a) shows, the utility level associated with an income of $10,000 is 10 (at point A) and the utility level associated with an income of $30,000 is 18 (at E). The risky job must be compared with the current $15,000 job, for which the utility is 13.5 (at B). To evaluate the new job, she can calculate the expected value of the resulting income. Because we are measuring value in terms of her utility, we must calculate the expected utility E(u) that she can obtain. The expected utility is the sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur. In this case expected utility is E(u) = (1/2)u($10,000) + (1/2)u($30,000) = 0.5(10) + 0.5(18) = 14 The risky new job is thus preferred to the original job because the expected utility of 14 is greater than the original utility of 13.5. The old job involved no risk—it guaranteed an income of $15,000 and a utility level of 13.5. The new job is risky but offers both a higher expected income ($20,000) and, more importantly, a higher expected utility. If the woman wishes to increase her expected utility, she will take the risky job. In §3.1, we explained that a utility function assigns a level of utility to each possible market basket. In §3.5, marginal utility is described as the additional satisfaction obtained by consuming an additional amount of a good. • expected utility Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur. 166 PART 2 • Producers, Consumers, and Competitive Markets • risk averse Condition of preferring a certain income to a risky income with the same expected value. • risk neutral Condition of being indifferent between a certain income and an uncertain income with the same expected value. • risk loving Condition of preferring a risky income to a certain income with the same expected value. • risk premium Maximum amount of money that a riskaverse person will pay to avoid taking a risk. Different Preferences Toward Risk People differ in their willingness to bear risk. Some are risk averse, some risk loving, and some risk neutral. An individual who is risk averse prefers a certain given income to a risky income with the same expected value. (Such a person has a diminishing marginal utility of income.) Risk aversion is the most common attitude toward risk. To see that most people are risk averse most of the time, note that most people not only buy life insurance, health insurance, and car insurance, but also seek occupations with relatively stable wages. Figure 5.3 (a) applies to a woman who is risk averse. Suppose hypothetically that she can have either a certain income of $20,000, or a job yielding an income of $30,000 with probability .5 and an income of $10,000 with probability .5 (so that the expected income is also $20,000). As we saw, the expected utility of the uncertain income is 14—an average of the utility at point A(10) and the utility at E(18)—and is shown by F. Now we can compare the expected utility associated with the risky job to the utility generated if $20,000 were earned without risk. This latter utility level, 16, is given by D in Figure 5.3 (a). It is clearly greater than the expected utility of 14 associated with the risky job. For a risk-averse person, losses are more important (in terms of the change in utility) than gains. Again, this can be seen from Figure 5.3 (a). A $10,000 increase in income, from $20,000 to $30,000, generates an increase in utility of two units; a $10,000 decrease in income, from $20,000 to $10,000, creates a loss of utility of six units. A person who is risk neutral is indifferent between a certain income and an uncertain income with the same expected value. In Figure 5.3 (c) the utility associated with a job generating an income of either $10,000 or $30,000 with equal probability is 12, as is the utility of receiving a certain income of $20,000. As you can see from the figure, the marginal utility of income is constant for a risk-neutral person.6 Finally, an individual who is risk loving prefers an uncertain income to a certain one, even if the expected value of the uncertain income is less than that of the certain income. Figure 5.3 (b) shows this third possibility. In this case, the expected utility of an uncertain income, which will be either $10,000 with probability .5 or $30,000 with probability .5, is higher than the utility associated with a certain income of $20,000. Numerically, E(u) = .5u($10,000) + .5u($30,000) = .5(3) + .5(18) = 10.5 7 u($20,000) = 8 Of course, some people may be averse to some risks and act like risk lovers with respect to others. For example, many people purchase life insurance and are co |
nservative with respect to their choice of jobs, but still enjoy gambling. Some criminologists might describe criminals as risk lovers, especially if they commit crimes despite a high prospect of apprehension and punishment. Except for such special cases, however, few people are risk loving, at least with respect to major purchases or large amounts of income or wealth. RISK PREMIUM The risk premium is the maximum amount of money that a risk-averse person will pay to avoid taking a risk. In general, the magnitude 6Thus, when people are risk neutral, the income they earn can be used as an indicator of well-being. A government policy that doubles incomes would then also double their utility. At the same time, government policies that alter the risks that people face, without changing their expected incomes, would not affect their well-being. Risk neutrality allows a person to avoid the complications that might be associated with the effects of governmental actions on the riskiness of outcomes. CHAPTER 5 • Uncertainty and Consumer Behavior 167 of the risk premium depends on the risky alternatives that the person faces. To determine the risk premium, we have reproduced the utility function of Figure 5.3 (a) in Figure 5.4 and extended it to an income of $40,000. Recall that an expected utility of 14 is achieved by a woman who is going to take a risky job with an expected income of $20,000. This outcome is shown graphically by drawing a horizontal line to the vertical axis from point F, which bisects straight Utility 18 16 14 13.5 10 E C B D F A 0 10 15 16 20 30 Income ($1000) (a) Utility E E 18 12 6 0 C A 10 20 30 Income ($1000) (c) C A 10 20 30 Income ($1000) (b) Utility 18 8 3 0 FIGURE 5.3 RISK AVERSE, RISK LOVING, AND RISK NEUTRAL People differ in their preferences toward risk. In (a), a consumer’s marginal utility diminishes as income increases. The consumer is risk averse because she would prefer a certain income of $20,000 (with a utility of 16) to a gamble with a .5 probability of $10,000 and a .5 probability of $30,000 (and expected utility of 14). In (b), the consumer is risk loving: She would prefer the same gamble (with expected utility of 10.5) to the certain income (with a utility of 8). Finally, the consumer in (c) is risk neutral and indifferent between certain and uncertain events with the same expected income. 168 PART 2 • Producers, Consumers, and Competitive Markets Utility 20 18 14 10 G E C F A Risk Premium 10 16 20 30 40 Income ($1000) FIGURE 5.4 RISK PREMIUM The risk premium, CF, measures the amount of income that an individual would give up to leave her indifferent between a risky choice and a certain one. Here, the risk premium is $4000 because a certain income of $16,000 (at point C) gives her the same expected utility (14) as the uncertain income (a .5 probability of being at point A and a .5 probability of being at point E) that has an expected value of $20,000. line AE (thus representing an average of $10,000 and $30,000). But the utility level of 14 can also be achieved if the woman has a certain income of $16,000, as shown by dropping a vertical line from point C. Thus, the risk premium of $4000, given by line segment CF, is the amount of expected income ($20,000 minus $16,000) that she would give up in order to remain indifferent between the risky job and a hypothetical job that would pay her a certain income of $16,000. RISK AVERSION AND INCOME The extent of an individual’s risk aversion depends on the nature of the risk and on the person’s income. Other things being equal, risk-averse people prefer a smaller variability of outcomes. We saw that when there are two outcomes—an income of $10,000 and an income of $30,000—the risk premium is $4000. Now consider a second risky job, also illustrated in Figure 5.4. With this job, there is a .5 probability of receiving an income of $40,000, with a utility level of 20, and a .5 probability of getting an income of $0, with a utility level of 0. The expected income is again $20,000, but the expected utility is only 10: Expected utility = .5u($0) + .5u($40,000) = 0 + .5(20) = 10 Compared to a hypothetical job that pays $20,000 with certainty, the person holding this risky job gets 6 fewer units of expected utility: 10 rather than 16 units. At the same time, however, this person could also get 10 units of utility from a job that pays $10,000 with certainty. Thus the risk premium in this case is $10,000, because this person would be willing to give up $10,000 of her $20,000 expected income to avoid bearing the risk of an uncertain income. The greater the variability of income, the more the person would be willing to pay to avoid the risky situation. CHAPTER 5 • Uncertainty and Consumer Behavior 169 Expected income U3 U2 U1 Expected income U3 U2 U1 Standard deviation of income (a) Standard deviation of income (b) FIGURE 5.5 RISK AVERSION AND INDIFFERENCE CURVES Part (a) applies to a person who is highly risk averse: An increase in this individual’s standard deviation of income requires a large increase in expected income if he or she is to remain equally well off. Part (b) applies to a person who is only slightly risk averse: An increase in the standard deviation of income requires only a small increase in expected income if he or she is to remain equally well off. RISK AVERSION AND INDIFFERENCE CURVES We can also describe the extent of a person’s risk aversion in terms of indifference curves that relate expected income to the variability of income, where the latter is measured by the standard deviation. Figure 5.5 shows such indifference curves for two individuals, one who is highly risk averse and another who is only slightly risk averse. Each indifference curve shows the combinations of expected income and standard deviation of income that give the individual the same amount of utility. Observe that all of the indifference curves are upward sloping: Because risk is undesirable, the greater the amount of risk, the greater the expected income needed to make the individual equally well off. Figure 5.5 (a) describes an individual who is highly risk averse. Observe that in order to leave this person equally well off, an increase in the standard deviation of income requires a large increase in expected income. Figure 5.5 (b) applies to a slightly risk-averse person. In this case, a large increase in the standard deviation of income requires only a small increase in expected income. In §3.1, we define an indifference curve as all market baskets that generate the same level of satisfaction for a consumer. EXAM PLE 5.2 BUSINESS EXECUTIVES AND THE CHOICE OF RISK Are business executives more risk loving than most people? When they are presented with alternative strategies, some risky, some safe, which do they choose? In one study, 464 executives were asked to respond to a questionnaire describing risky situations that an individual might face as vice president of a hypothetical company.7 Respondents were presented with four risky events, each of which had a 7This example is based on Kenneth R. MacCrimmon and Donald A. Wehrung, “The Risk In-Basket,” Journal of Business 57 (1984): 367–87. 170 PART 2 • Producers, Consumers, and Competitive Markets given probability of a favorable and unfavorable outcome. The payoffs and probabilities were chosen so that each event had the same expected value. In increasing order of the risk involved (as measured by the difference between the favorable and unfavorable outcomes), the four items were: 1. A lawsuit involving a patent violation 2. A customer threatening to buy from a competitor 3. A union dispute 4. A joint venture with a competitor To gauge their willingness to take or avoid risks, researchers asked respondents a series of questions regarding business strategy. In one situation, they could pursue a risky strategy with the possibility of a high return right away or delay making a choice until the outcomes became more certain and the risk was reduced. In another situation, respondents could opt for an immediately risky but potentially profitable strategy that could lead to a promotion, or they could delegate the decision to someone else, which would protect their job but eliminate the promotion possibility. The study found that executives vary substantially in their preferences toward risk. Roughly 20 percent indicated that they were relatively risk neutral; 40 percent opted for the more risky alternatives; and 20 percent were clearly risk averse (20 percent did not respond). More importantly, executives (including those who chose risky alternatives) typically made efforts to reduce or eliminate risk, usually by delaying decisions and collecting more information. Some have argued that a cause of the financial crisis of 2008 was excessive risk-taking by bankers and Wall Street executives who could earn huge bonuses if their ventures succeeded but faced very little downside if the ventures failed. The U.S. Treasury Department’s Troubled Asset Relief Program (TARP) bailed out some of the banks, but so far has been unable to impose constraints on “unnecessary and excessive” risk-taking by banks’ executives. We will return to the use of indifference curves as a means of describing risk aversion in Section 5.4, where we discuss the demand for risky assets. First, however, we will turn to the ways in which an individual can reduce risk. 5.3 Reducing Risk As the recent growth in state lotteries shows, people sometimes choose risky alternatives that suggest risk-loving rather than risk-averse behavior. Most people, however, spend relatively small amounts on lottery tickets and casinos. When more important decisions are involved, they are generally risk averse. In this section, we describe three ways by which both consumers and businesses commonly reduce risks: diversification, insurance, and obtaining more information about choices and payoffs. Diversification Recall the old saying, “Don’t put all your eggs in one basket.” |
Ignoring this advice is unnecessarily risky: If your basket turns out to be a bad bet, all will be lost. Instead, you can reduce risk through diversification: allocating your resources to a variety of activities whose outcomes are not closely related. Suppose, for example, that you plan to take a part-time job selling appliances on a commission basis. You can decide to sell only air conditioners or only heaters, or you can spend half your time selling each. Of course, you can’t be sure how hot or cold the weather will be next year. How should you apportion your time in order to minimize the risk involved? Risk can be minimized by diversification—by allocating your time so that you sell two or more products (whose sales are not closely related) rather than a • diversification Practice of reducing risk by allocating resources to a variety of activities whose outcomes are not closely related. CHAPTER 5 • Uncertainty and Consumer Behavior 171 TABLE 5.5 INCOME FROM SALES OF APPLIANCES ($) HOT WEATHER COLD WEATHER Air conditioner sales Heater sales 30,000 12,000 12,000 30,000 single product. Suppose there is a 0.5 probability that it will be a relatively hot year, and a 0.5 probability that it will be cold. Table 5.5 gives the earnings that you can make selling air conditioners and heaters. If you sell only air conditioners or only heaters, your actual income will be either $12,000 or $30,000, but your expected income will be $21,000 (.5[$30,000] .5[$12,000]). But suppose you diversify by dividing your time evenly between the two products. In that case, your income will certainly be $21,000, regardless of the weather. If the weather is hot, you will earn $15,000 from air conditioner sales and $6000 from heater sales; if it is cold, you will earn $6000 from air conditioners and $15,000 from heaters. In this instance, diversification eliminates all risk. Of course, diversification is not always this easy. In our example, heater and air conditioner sales are negatively correlated variables—they tend to move in opposite directions; whenever sales of one are strong, sales of the other are weak. But the principle of diversification is a general one: As long as you can allocate your resources toward a variety of activities whose outcomes are not closely related, you can eliminate some risk. THE STOCK MARKET Diversification is especially important for people who invest in the stock market. On any given day, the price of an individual stock can go up or down by a large amount, but some stocks rise in price while others fall. An individual who invests all her money in a single stock (i.e., puts all her eggs in one basket) is therefore taking much more risk than necessary. Risk can be reduced—although not eliminated—by investing in a portfolio of ten or twenty different stocks. Likewise, you can diversify by buying shares in mutual funds: organizations that pool funds of individual investors to buy a large number of different stocks. There are thousands of mutual funds available today for both stocks and bonds. These funds are popular because they reduce risk through diversification and because their fees are typically much lower than the cost of assembling one’s own portfolio of stocks. In the case of the stock market, not all risk is diversifiable. Although some stocks go up in price when others go down, stock prices are to some extent positively correlated variables: They tend to move in the same direction in response to changes in economic conditions. For example, the onset of a severe recession, which is likely to reduce the profits of many companies, may be accompanied by a decline in the overall market. Even with a diversified portfolio of stocks, therefore, you still face some risk. Insurance We have seen that risk-averse people are willing to pay to avoid risk. In fact, if the cost of insurance is equal to the expected loss (e.g., a policy with an expected loss of $1000 will cost $1000), risk-averse people will buy enough insurance to recover fully from any financial losses they might suffer. • negatively correlated variables Variables having a tendency to move in opposite directions. • mutual fund Organization that pools funds of individual investors to buy a large number of different stocks or other financial assets. • positively correlated variables Variables having a tendency to move in the same direction. 172 PART 2 • Producers, Consumers, and Competitive Markets Why? The answer is implicit in our discussion of risk aversion. Buying insurance assures a person of having the same income whether or not there is a loss. Because the insurance cost is equal to the expected loss, this certain income is equal to the expected income from the risky situation. For a risk-averse consumer, the guarantee of the same income regardless of the outcome generates more utility than would be the case if that person had a high income when there was no loss and a low income when a loss occurred. To clarify this point, let’s suppose a homeowner faces a 10-percent probability that his house will be burglarized and he will suffer a $10,000 loss. Let’s assume he has $50,000 worth of property. Table 5.6 shows his wealth in two situations—with insurance costing $1000 and without insurance. Note that expected wealth is the same ($49,000) in both situations. The variability, however, is quite different. As the table shows, with no insurance the standard deviation of wealth is $3000; with insurance, it is 0. If there is no burglary, the uninsured homeowner gains $1000 relative to the insured homeowner. But with a burglary, the uninsured homeowner loses $9000 relative to the insured homeowner. Remember: for a risk-averse individual, losses count more (in terms of changes in utility) than gains. A risk-averse homeowner, therefore, will enjoy higher utility by purchasing insurance. THE LAW OF LARGE NUMBERS Consumers usually buy insurance from companies that specialize in selling it. Insurance companies are firms that offer insurance because they know that when they sell a large number of policies, they face relatively little risk. The ability to avoid risk by operating on a large scale is based on the law of large numbers, which tells us that although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted. For example, I may not be able to predict whether a coin toss will come out heads or tails, but I know that when many coins are flipped, approximately half will turn up heads and half tails. Likewise, if I am selling automobile insurance, I cannot predict whether a particular driver will have an accident, but I can be reasonably sure, judging from past experience, what fraction of a large group of drivers will have accidents. ACTUARIAL FAIRNESS By operating on a large scale, insurance companies can be sure that over a sufficiently large number of events, total premiums paid in will be equal to the total amount of money paid out. Let’s return to our burglary example. A man knows that there is a 10-percent probability that his house will be burgled; if it is, he will suffer a $10,000 loss. Prior to facing this risk, he calculates the expected loss to be $1000 (.10 $10,000). The risk involved is considerable, however, because there is a 10-percent probability of TABLE 5.6 THE DECISION TO INSURE ($) INSURANCE BURGLARY (PR .1) NO BURGLARY (PR .9) EXPECTED WEALTH STANDARD DEVIATION No Yes 40,000 49,000 50,000 49,000 49,000 49,000 3000 0 CHAPTER 5 • Uncertainty and Consumer Behavior 173 a large loss. Now suppose that 100 people are similarly situated and that all of them buy burglary insurance from the same company. Because they all face a 10-percent probability of a $10,000 loss, the insurance company might charge each of them a premium of $1000. This $1000 premium generates an insurance fund of $100,000 from which losses can be paid. The insurance company can rely on the law of large numbers, which holds that the expected loss to the 100 individuals as a whole is likely to be very close to $1000 each. The total payout, therefore, will be close to $100,000, and the company need not worry about losing more than that. When the insurance premium is equal to the expected payout, as in the example above, we say that the insurance is actuarially fair. But because they must cover administrative costs and make some profit, insurance companies typically charge premiums above expected losses. If there are a sufficient number of insurance companies to make the market competitive, these premiums will be close to actuarially fair levels. In some states, however, insurance premiums are regulated in order to protect consumers from “excessive” premiums. We will examine government regulation of markets in detail in Chapters 9 and 10 of this book. In recent years, some insurance companies have come to the view that catastrophic disasters such as earthquakes are so unique and unpredictable that they cannot be viewed as diversifiable risks. Indeed, as a result of losses from past disasters, these companies do not feel that they can determine actuarially fair insurance rates. In California, for example, the state itself has had to enter the insurance business to fill the gap created when private companies refused to sell earthquake insurance. The state-run pool offers less insurance coverage at higher rates than was previously offered by private insurers. • actuarially fair Characterizing a situation in which an insurance premium is equal to the expected payout. EXAM PLE 5.3 THE VALUE OF TITLE INSURANCE WHEN BUYING A HOUSE Suppose you are buying your first house. To close the sale, you will need a deed that gives you clear “title.” Without such a clear title, there is always a chance that the seller of the house is not its true owner. Of course, the seller could be engaging in fraud, but it is more likely that the seller is unaware of the exact nature of his or her ownership rights. For example, the owner may ha |
ve borrowed heavily, using the house as “collateral” for a loan. Or the property might carry with it a legal requirement that limits the use to which it may be put. Suppose you are willing to pay $300,000 for the house, but you believe there is a one-in-twenty chance that careful research will reveal that the seller does not actually own the property. The property would then be worth nothing. If there were no insurance available, a risk-neutral person would bid at most $285,000 for the property (.95[$300,000] + .05[0]). However, if you expect to tie up most of your assets in the house, you would probably be risk averse and, therefore, bid much less—say, $230,000. In situations such as this, it is clearly in the interest of the buyer to be sure that there is no risk of a lack of full ownership. The buyer does this by purchasing “title insurance.” The title insurance company researches the history of the property, checks to see whether any legal liabilities are attached to it, and generally assures itself that there is no ownership problem. The insurance company then agrees to bear any remaining risk that might exist. 174 PART 2 • Producers, Consumers, and Competitive Markets Because the title insurance company is a specialist in such insurance and can collect the relevant information relatively easily, the cost of title insurance is often less than the expected value of the loss involved. A fee of $1500 for title insurance is not unusual, even though the expected loss can be much higher. It is also in the interest of sellers to provide title insurance, because all but the most risk-loving buyers will pay much more for a house when it is insured than when it is not. In fact, most states require sellers to provide title insurance before a sale can be completed. In addition, because mortgage lenders are all concerned about such risks, they usually require new buyers to have title insurance before issuing a mortgage. • value of complete information Difference between the expected value of a choice when there is complete information and the expected value when information is incomplete. The Value of Information People often make decisions based on limited information. If more information were available, one could make better predictions and reduce risk. Because information is a valuable commodity, people will pay for it. The value of complete information is the difference between the expected value of a choice when there is complete information and the expected value when information is incomplete. To see how information can be valuable, suppose you manage a clothing store and must decide how many suits to order for the fall season. If you order 100 suits, your cost is $180 per suit. If you order only 50 suits, your cost increases to $200. You know that you will be selling suits for $300 each, but you are not sure how many you can sell. All suits not sold can be returned, but for only half of what you paid for them. Without additional information, you will act on your belief that there is a .5 probability that you will sell 100 suits and a .5 probability that you will sell 50. Table 5.7 gives the profit that you would earn in each of these two cases. Without additional information, you would choose to buy 100 suits if you were risk neutral, taking the chance that your profit might be either $12,000 or $1500. But if you were risk averse, you might buy 50 suits: In that case, you would know for sure that your profit would be $5000. With complete information, you can place the correct order regardless of future sales. If sales were going to be 50 and you ordered 50 suits, your profits would be $5000. If, on the other hand, sales were going to be 100 and you ordered 100 suits, your profits would be $12,000. Because both outcomes are equally likely, your expected profit with complete information would be $8500. The value of information is computed as Expected value with complete information: Less: Expected value with uncertainty (buy 100 suits): Equals: Value of complete information $8500 - 6750 $1750 Thus it is worth paying up to $1750 to obtain an accurate prediction of sales. Even though forecasting is inevitably imperfect, it may be worth investing in a marketing study that provides a reasonable forecast of next year’s sales. TABLE 5.7 PROFITS FROM SALES OF SUITS ($) SALES OF 50 SALES OF 100 EXPECTED PROFIT Buy 50 suits Buy 100 suits 5000 1500 5000 12,000 5000 6750 CHAPTER 5 • Uncertainty and Consumer Behavior 175 EXAM PLE 5.4 THE VALUE OF INFORMATION IN AN ONLINE CONSUMER ELECTRONICS MARKET Internet-based price comparison sites offer a valuable informational resource to consumers, as shown by a study of a leading price-comparison website, Shopper.com. Researchers studied price information provided to consumers on over 1,000 topselling electronics products for an 8-month period. They found that consumers saved about 16% when using this website versus shopping in the store, because the website significantly reduced the cost of finding the lowest priced product.8 The value of price comparison information is not the same for everyone and for every product. Competition matters. The study found that when only two firms list prices on Shopper.com, consumers save 11%. But the savings increase with the number of competitors, jumping to 20% when more than 30 companies list prices. One might think that the Internet will generate so much information about prices that only the lowestprice products will be sold in the long run, causing the value of such information to eventually decline to zero. So far, this has not been the case. There are fixed costs for parties to both transmit and to acquire information over the Internet. These include the costs of maintaining servers and the fees that sites such as Shopper.com charge to list prices at their sites. The result is that prices are likely to continue to vary widely as the Internet continues to grow and mature. You might think that more information is always a good thing. As the follow- ing example shows, however, that is not always the case. EXAM PLE 5.5 DOCTORS, PATIENTS, AND THE VALUE OF INFORMATION Suppose you were seriously ill and required major surgery. Assuming you wanted to get the best care possible, how would you go about choosing a surgeon and a hospital to provide that care? Many people would ask their friends or their primary-care physician for a recommendation. Although this might be helpful, a truly informed decision would probably require more detailed information. For example, how successful has a recommended surgeon and her affiliated hospital been in performing the particular operation that you need? How many of her patients have died or had serious complications from the operation, and how do these numbers compare with those for other surgeons and hospitals? This kind of information is likely to be difficult or impossible for most patients to obtain. Would patients be better off if detailed information about the performance records of doctors and hospitals were readily available? Not necessarily. More information is often, but not always, better. Interestingly in this case, access to performance information could actually lead to worse health outcomes. Why? Because access to such information would create two different incentives that would affect the behavior of both doctors and patients. First, it would allow patients to choose doctors with better performance records, which creates an incentive for doctors to perform better. That is a good thing. But second, it would encourage doctors to limit their practices to patients who are in relatively good health. The reason is that very old or very sick patients are more likely to have complications or die as a result of treatment; doctors who treat such patients are likely to have worse performance records (other factors being equal). To the extent that doctors would be judged according to performance, they would 8Michael Baye, John Morgan, and Patrick Scholten,” The Value of Information in an Online Electronics Market.”Journal of Public Policy and Marketing, vol. 22 (2003): 17–25. 176 PART 2 • Producers, Consumers, and Competitive Markets have an incentive to avoid treating very old or sick patients. As a result, such patients would find it difficult or impossible to obtain treatment. Whether more information is better depends on which effect dominates—the ability of patients to make more informed choices versus the incentive for doctors to avoid very sick patients. In a recent study, economists examined the impact of the mandatory “report cards” introduced in New York and Pennsylvania in the early 1990s to evaluate outcomes of coronary bypass surgeries.9 They analyzed hospital choices and outcomes for all elderly heart attack patients and patients receiving coronary bypass surgery in the United States from 1987 through 1994. By comparing trends in New York and Pennsylvania to the trends in other states, they could determine the effect of the increased information made possible by the availability of report cards. They found that although report cards improved matching of patients with hospitals and doctors, they also caused a shift in treatment from sicker patients towards healthier ones. Overall, this led to worse outcomes, especially among sicker patients. Thus the study concluded that report cards reduced welfare. The medical profession has responded to this problem to some extent. For example, in 2010, cardiac surgery programs across the country voluntarily reported the results of coronary-artery bypass grafting procedures. Each program was rated with one to three stars, but this time the ratings were “risk adjusted” to reduce the incentive for doctors to choose less risky patients. More information often improves welfare because it allows people to reduce risk and to take actions that might reduce the effect of bad outcomes. However, as this example makes clear, information can cause people to change their b |
ehavior in undesirable ways. We will discuss this issue further in Chapter 17. • asset Something that provides a flow of money or services to its owner. *5.4 The Demand for Risky Assets Most people are risk averse. Given a choice, they prefer fixed monthly incomes to those which, though equally large on average, fluctuate randomly from month to month. Yet many of these same people will invest all or part of their savings in stocks, bonds, and other assets that carry some risk. Why do riskaverse people invest in the stock market and thereby risk losing part or all of their investments?10 How do people decide how much risk to bear when making investments and planning for the future? To answer these questions, we must examine the demand for risky assets. Assets An asset is something that provides a flow of money or services to its owner. A home, an apartment building, a savings account, or shares of General Motors stock are all assets. A home, for example, provides a flow of housing services to its owner, and, if the owner did not wish to live there, could be rented out, thereby providing a monetary flow. Likewise, apartments can be rented out, providing a flow of rental income to the owner of the building. A savings account pays interest (usually every day or every month), which is usually reinvested in the account. 9David Dranove, Daniel Kessler, Mark McClennan, and Mark Satterthwaite, “Is More Information Better? The Effects of ’Report Cards’ on Health Care Providers,” Journal of Political Economy 3 (June 2003): 555–558. 10Most Americans have at least some money invested in stocks or other risky assets, though often indirectly. For example, many people who hold full-time jobs have shares in pension funds underwritten in part by their own salary contributions and in part by employer contributions. Usually such funds are partly invested in the stock market. CHAPTER 5 • Uncertainty and Consumer Behavior 177 The monetary flow that one receives from asset ownership can take the form of an explicit payment, such as the rental income from an apartment building: Every month, the landlord receives rent checks from the tenants. Another form of explicit payment is the dividend on shares of common stock: Every three months, the owner of a share of General Motors stock receives a quarterly dividend payment. But sometimes the monetary flow from ownership of an asset is implicit: It takes the form of an increase or decrease in the price or value of the asset. An increase in the value of an asset is a capital gain; a decrease is a capital loss. For example, as the population of a city grows, the value of an apartment building may increase. The owner of the building will then earn a capital gain beyond the rental income. The capital gain is unrealized until the building is sold because no money is actually received until then. There is, however, an implicit monetary flow because the building could be sold at any time. The monetary flow from owning General Motors stock is also partly implicit. The price of the stock changes from day to day, and each time it does, owners gain or lose. Risky and Riskless Assets A risky asset provides a monetary flow that is at least in part random. In other words, the monetary flow is not known with certainty in advance. A share of General Motors stock is an obvious example of a risky asset: You cannot know whether the price of the stock will rise or fall over time, nor can you even be sure that the company will continue to pay the same (or any) dividend per share. Although people often associate risk with the stock market, most other assets are also risky. An apartment building is one example. You cannot know how much land values will rise or fall, whether the building will be fully rented all the time, or even whether the tenants will pay their rents promptly. Corporate bonds are another example—the issuing corporation could go bankrupt and fail to pay bond owners their interest and principal. Even long-term U.S. government bonds that mature in 10 or 20 years are risky. Although it is highly unlikely that the federal government will go bankrupt, the rate of inflation could unexpectedly increase and make future interest payments and the eventual repayment of principal worth less in real terms, thereby reducing the value of the bonds. In contrast, a riskless (or risk-free) asset pays a monetary flow that is known with certainty. Short-term U.S. government bonds—called Treasury bills—are riskless, or almost riskless. Because they mature in a few months, there is very little risk from an unexpected increase in the rate of inflation. You can also be reasonably confident that the U.S. government will not default on the bond (i.e., refuse to pay back the holder when the bond comes due). Other examples of riskless or almost riskless assets include passbook savings accounts and shortterm certificates of deposit. • risky asset Asset that provides an uncertain flow of money or services to its owner. • riskless (or risk-free) asset Asset that provides a flow of money or services that is known with certainty. Asset Returns People buy and hold assets because of the monetary flows they provide. To compare assets with each other, it helps to think of this monetary flow relative to an asset’s price or value. The return on an asset is the total monetary flow it yields—including capital gains or losses—as a fraction of its price. For example, a bond worth $1000 today that pays out $100 this year (and every year) has a return of • return Total monetary flow of an asset as a fraction of its price. 178 PART 2 • Producers, Consumers, and Competitive Markets • real return Simple (or nominal) return on an asset, less the rate of inflation. • expected return Return that an asset should earn on average. • actual return Return that an asset earns. 10 percent.11 If an apartment building was worth $10 million last year, increased in value to $11 million this year, and also provided rental income (after expenses) of $0.5 million, it would have yielded a return of 15 percent over the past year. If a share of General Motors stock was worth $80 at the beginning of the year, fell to $72 by the end of the year, and paid a dividend of $4, it will have yielded a return of -5 percent (the dividend yield of 5 percent less the capital loss of 10 percent). When people invest their savings in stocks, bonds, land, or other assets, they usually hope to earn a return that exceeds the rate of inflation. Thus, by delaying consumption, they can buy more in the future than they can by spending all their income now. Consequently, we often express the return on an asset in real—i.e., inflation-adjusted—terms. The real return on an asset is its simple (or nominal) return less the rate of inflation. For example, with an annual inflation rate of 5 percent, our bond, apartment building, and share of GM stock have yielded real returns of 5 percent, 10 percent, and −10 percent, respectively. EXPECTED VERSUS ACTUAL RETURNS Because most assets are risky, an investor cannot know in advance what returns they will yield over the coming year. For example, our apartment building might have depreciated in value instead of appreciating, and the price of GM stock might have risen instead of fallen. However, we can still compare assets by looking at their expected returns. The expected return on an asset is the expected value of its return, i.e., the return that it should earn on average. In some years, an asset’s actual return may be much higher than its expected return and in some years much lower. Over a long period, however, the average return should be close to the expected return. Different assets have different expected returns. Table 5.8, for example, shows that while the expected real return of a U.S. Treasury bill has been less than 1 percent, the expected real return on a group of representative stocks on the New York Stock Exchange has been more than 9 percent.12 Why would anyone buy a Treasury bill when the expected return on stocks is so much higher? Because the demand for an asset depends not just on its expected return, but also on its risk: Although stocks have a higher expected return than Treasury bills, they also carry much more risk. One measure of risk, the standard deviation of the real annual return, is equal to 20.4 percent for common stocks, 8.3 percent for corporate bonds, and only 3.1 percent for U.S. Treasury bills. The numbers in Table 5.8 suggest that the higher the expected return on an investment, the greater the risk involved. Assuming that one’s investments are well diversified, this is indeed the case.13 As a result, the risk-averse investor must balance expected return against risk. We examine this trade-off in more detail in the next section. 11The price of a bond often changes during the course of a year. If the bond appreciates (or depreciates) in value during the year, its return will be greater (or less) than 10 percent. In addition, the definition of return given above should not be confused with the “internal rate of return,” which is sometimes used to compare monetary flows occurring over a period of time. We discuss other return measures in Chapter 15, when we deal with present discounted values. 12For some stocks, the expected return is higher, and for some it is lower. Stocks of smaller companies (e.g., some of those traded on the NASDAQ) have higher expected rates of return—and higher return standard deviations. 13It is nondiversifiable risk that matters. An individual stock may be very risky but still have a low expected return because most of the risk could be diversified away by holding a large number of such stocks. Nondiversifiable risk, which arises from the fact that individual stock prices are correlated with the overall stock market, is the risk that remains even if one holds a diversified portfolio of stocks. We discuss this point in detail in the context of the capital asset pricing model in Chapter 15 |
. CHAPTER 5 • Uncertainty and Consumer Behavior 179 TABLE 5.8 INVESTMENTS—RISK AND RETURN (1926–2010) AVERAGE RATE OF RETURN (%) AVERAGE REAL RATE OF RETURN (%) RISK (STANDARD DEVIATION) Common stocks (S&P 500) Long-term corporate bonds U.S. Treasury bills 11.9 6.2 3.7 8.7 3.3 0.7 20.4 8.3 3.1 Source: Ibbotson® SBBI® 2001 Classic Yearbook: Market results for Stocks, Bonds, Bills, and Inflation 1926–2010. © 2011 Morningstar. The Trade-Off Between Risk and Return Suppose a woman wants to invest her savings in two assets—Treasury bills, which are almost risk free, and a representative group of stocks. She must decide how much to invest in each asset. She might, for instance, invest only in Treasury bills, only in stocks, or in some combination of the two. As we will see, this problem is analogous to the consumer’s problem of allocating a budget between purchases of food and clothing. Let’s denote the risk-free return on the Treasury bill by Rf. Because the return is risk free, the expected and actual returns are the same. In addition, let the expected return from investing in the stock market be Rm and the actual return be rm. The actual return is risky. At the time of the investment decision, we know the set of possible outcomes and the likelihood of each, but we do not know what particular outcome will occur. The risky asset will have a higher expected return than the risk-free asset (Rm 7 Rf). Otherwise, risk-averse investors would buy only Treasury bills and no stocks would be sold. THE INVESTMENT PORTFOLIO To determine how much money the investor should put in each asset, let’s set b equal to the fraction of her savings placed in the stock market and (1 - b) the fraction used to purchase Treasury bills. The expected return on her total portfolio, Rp, is a weighted average of the expected return on the two assets:14 Rp = bRm + (1 - b)Rf (5.1) Suppose, for example, that Treasury bills pay 4 percent (Rf .04), the stock market’s expected return is 12 percent (Rm .12), and b 1/2. Then Rp 8 percent. How risky is this portfolio? One measure of riskiness is the standard deviation of its return. We will denote the standard deviation of the risky stock market investment by m. With some algebra, we can show that the standard deviation of the portfolio, p (with one risky and one risk-free asset) is the fraction 14The expected value of the sum of two variables is the sum of the expected values. Therefore Rp = E[brm] + E[(1 - b)Rf] = bE[rm] + (1 - b)Rf = bRm + (1 - b)Rf 180 PART 2 • Producers, Consumers, and Competitive Markets In §3.2 we explain how a budget line is determined from an individual’s income and the prices of the available goods. • Price of risk Extra risk that an investor must incur to enjoy a higher expected return. of the portfolio invested in the risky asset times the standard deviation of that asset:15 s p = bs m (5.2) The Investor’s Choice Problem We have still not determined how the investor should choose this fraction b. To do so, we must first show that she faces a risk-return trade-off analogous to a consumer’s budget line. To identify this trade-off, note that equation (5.1) for the expected return on the portfolio can be rewritten as Rp = Rf + b(Rm - Rf) Now, from equation (5.2) we see that b p/ m, so that Rp = Rf + (Rm - Rf) s m s p (5.3) RISK AND THE BUDGET LINE This equation is a budget line because it describes the trade-off between risk ( p) and expected return (Rp). Note that it is the equation for a straight line: Because Rm, Rf, and m are constants, the slope (Rm − Rf)/ m is a constant, as is the intercept, Rf. The equation says that the expected return on the portfolio Rp increases as the standard deviation of that return p increases. We call the slope of this budget line, (Rm − Rf)/ m, the price of risk, because it tells us how much extra risk an investor must incur to enjoy a higher expected return. The budget line is drawn in Figure 5.6. If our investor wants no risk, she can invest all her funds in Treasury bills (b 0) and earn an expected return Rf. To receive a higher expected return, she must incur some risk. For example, she could invest all her funds in stocks (b 1), earning an expected return Rm but incurring a standard deviation m. Or she might invest some fraction of her funds in each type of asset, earning an expected return somewhere between Rf and Rm and facing a standard deviation less than m but greater than zero. RISK AND INDIFFERENCE CURVES Figure 5.6 also shows the solution to the investor’s problem. Three indifference curves are drawn in the figure. Each curve describes combinations of risk and return that leave the investor equally satisfied. The curves are upward-sloping because risk is undesirable. Thus, with a greater amount of risk, it takes a greater expected return to make the investor equally well-off. Curve U3 yields the greatest amount of satisfaction and U1 the least amount: For a given amount of risk, the investor earns a higher expected return on U3 than on U2 and a higher expected return on U2 than on U1. 15To see why, we observe from footnote 4 that we can write the variance of the portfolio return as s p 2 = E[brm + (1 - b)Rf - Rp]2 Substituting equation (5.1) for the expected return on the portfolio, Rp, we have s p 2 = E[brm + (1 - b)Rf - bRm - (1 - b)Rf]2 = E[b(rm - Rm)]2 = b 2s m 2 Because the standard deviation of a random variable is the square root of its variance, s = bs m. p Expected return, Rp Rm R* Rf 0 CHAPTER 5 • Uncertainty and Consumer Behavior 181 U3 U2 U1 Budget Line σ* σ m Standard deviation of return, σ p FIGURE 5.6 CHOOSING BETWEEN RISK AND RETURN An investor is dividing her funds between two assets—Treasury bills, which are risk free, and stocks. The budget line describes the trade-off between the expected return and its riskiness, as measured by the standard deviation of the return. The slope of the budget line is (Rm− R f)/ m, which is the price of risk. Three indifference curves are drawn, each showing combinations of risk and return that leave an investor equally satisfied. The curves are upward-sloping because a risk-averse investor will require a higher expected return if she is to bear a greater amount of risk. The utility-maximizing investment portfolio is at the point where indifference curve U2 is tangent to the budget line. Of the three indifference curves, the investor would prefer to be on U3. This position, however, is not feasible, because U3 does not touch the budget line. Curve U1 is feasible, but the investor can do better. Like the consumer choosing quantities of food and clothing, our investor does best by choosing a combination of risk and return at the point where an indifference curve (in this case U2) is tangent to the budget line. At that point, the investor’s return has an expected value R* and a standard deviation *. Naturally, people differ in their attitudes toward risk. This fact is illustrated in Figure 5.7, which shows how two different investors choose their portfolios. Investor A is quite risk averse. Because his indifference curve UA is tangent to the budget line at a point of low risk, he will invest almost all of his funds in Treasury bills and earn an expected return RA just slightly larger than the riskfree return Rf. Investor B is less risk averse. She will invest most of her funds in stocks, and while the return on her portfolio will have a higher expected value RB, it will also have a higher standard deviation B. If Investor B has a sufficiently low level of risk aversion, she might buy stocks on margin: that is, she would borrow money from a brokerage firm in order 182 PART 2 • Producers, Consumers, and Competitive Markets Expected return, Rp UA UB FIGURE 5.7 THE CHOICES OF TWO DIFFERENT INVESTORS Investor A is highly risk averse. Because his portfolio will consist mostly of the risk-free asset, his expected return RA will be only slightly greater than the risk-free return. His risk A, however, will be small. Investor B is less risk averse. She will invest a large fraction of her funds in stocks. Although the expected return on her portfolio RB will be larger, it will also be riskier. Rm RB RA Rf Budget Line 0 σ A σ B σ m Standard deviation of return, σ p to invest more than she actually owns in the stock market. In effect, a person who buys stocks on margin holds a portfolio with more than 100 percent of the portfolio’s value invested in stocks. This situation is illustrated in Figure 5.8, which shows indifference curves for two investors. Investor A, who is relatively risk-averse, invests about half of his funds in stocks. Investor B, however, has an indifference curve that is relatively flat and tangent with the budget line at FIGURE 5.8 BUYING STOCKS ON MARGIN Because Investor A is risk averse, his portfolio contains a mixture of stocks and risk-free Treasury bills. Investor B, however, has a very low degree of risk aversion. Her indifference curve, UB, is tangent to the budget line at a point where the expected return and standard deviation for her portfolio exceed those for the stock market overall. This implies that she would like to invest more than 100 percent of her wealth in the stock market. She does so by buying stocks on margin—i.e., by borrowing from a brokerage firm to help finance her investment. RB Rm RA Rf 0 UA UB Budget Line σ A σ m σ B CHAPTER 5 • Uncertainty and Consumer Behavior 183 a point where the expected return on the portfolio exceeds the expected return on the stock market. In order to hold this portfolio, the investor must borrow money because she wants to invest more than 100 percent of her wealth in the stock market. Buying stocks on margin in this way is a form of leverage: the investor increases her expected return above that for the overall stock market, but at the cost of increased risk. In Chapters 3 and 4, we simplified the problem of consumer choice by assuming that the consumer had only two goods from which to choose— food and clothing. In the sam |
e spirit, we have simplified the investor ’s choice by limiting it to Treasury bills and stocks. The basic principles, however, would be the same if we had more assets (e.g., corporate bonds, land, and different types of stocks). Every investor faces a trade-off between risk and return.16 The degree of extra risk that each is willing to bear in order to earn a higher expected return depends on how risk averse he or she is. Less risk-averse investors tend to include a larger fraction of risky assets in their portfolios. EXAM PLE 5.6 INVESTING IN THE STOCK MARKET The 1990s witnessed a shift in the investing behavior of Americans. First, many people started investing in the stock market for the first time. In 1989, about 32 percent of families in the United States had part of their wealth invested in the stock market, either directly (by owning individual stocks) or indirectly (through mutual funds or pension plans invested in stocks). By 1998, that fraction had risen to 49 percent. In addition, the share of wealth invested in stocks increased from about 26 percent to about 54 percent during the same period.17 Much of this shift is attributable to younger investors. For those under the age of 35, participation in the stock market increased from about 22 percent in 1989 to about 41 percent in 1998. In most respects, household investing behavior has stabilized after the 1990s shift. The percent of families with investments in the stock market was 51.1% in 2007. However, older Americans have become much more active. By 2007, 40 percent of people over age 75 held stocks, up from 29 percent in 1998. Why have more people started investing in the stock market? One reason is the advent of online trading, which has made investing much easier. Another reason may be the considerable increase in stock prices that occurred during the late 1990s, driven in part by the so-called “dot com euphoria.” These increases may have convinced some investors that prices could only continue to rise in the future. As one analyst put it, “The market’s relentless seven-year climb, the popularity of mutual funds, the shift by employers to self-directed retirement plans, and the avalanche of do-it-yourself investment publications all have combined to create a nation of financial know-it-alls.”18 Figure 5.9 shows the dividend yield and price/ earnings (P/E) ratio for the S&P 500 (an index of stocks of 500 large corporations) over the period 16As mentioned earlier, what matters is nondiversifiable risk, because investors can eliminate diversifiable risk by holding many different stocks (e.g., via mutual funds). We discuss diversifiable versus nondiversifiable risk in Chapter 15. 17Data are from the Federal Reserve Bulletin, January 2000, and the Survey of Consumer Finances, 2011. 18“We’re All Bulls Here: Strong Market Makes Everybody an Expert,” Wall Street Journal, September 12, 1997. 184 PART 2 • Producers, Consumers, and Competitive Markets 50 45 40 35 30 25 20 15 10 5 o i t a R E / P Dividend Yield P/E Ratio 0 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 Year ) FIGURE 5.9 DIVIDEND YIELD AND P/E RATIO FOR S&P 500 The dividend yield for the S&P 500 (the annual dividend divided by the stock price) has fallen dramatically, while the price/earnings ratio (the stock price divided by the annual earningsper-share) rose from 1980 to 2002 and then dropped. 1970 to 2011. Observe that the dividend yield (the annual dividend divided by the stock price) fell from about 5 percent in 1980 to below 2 percent by 2000. Meanwhile, however, the price/ earnings ratio (the share price divided by annual earnings per share) increased from about 8 in 1980 to over 40 in 2002, before falling to around 20 between 2005 and 2007 and then increasing through 2011. In retrospect, the increase in the P/E ratio could only have occurred if investors believed that corporate profits would continue to grow rapidly in the coming decade. This suggests that in the late 1990s, many investors had a low degree of risk aversion, were quite optimistic about the economy, or both. Alternatively, some economists have argued that the run-up of stock prices during the 1990s was the result of “herd behavior,” in which investors rushed to get into the market after hearing of the successful experiences of others.19 The psychological motivations that explain herd behavior can help to explain stock market bubbles. However, they go far beyond the stock market. They also apply to the behavior of consumers and firm managers in a wide variety of settings. Such behavior cannot always be captured by the simplified assumptions that we have made up to this point about consumer choice. In the next section, we will discuss these aspects of behavior in detail, and we will see how the traditional models of Chapters 3 and 4 can be expanded to help us understand this behavior. 19See, for example, Robert Shiller, Irrational Exuberance, Princeton University Press, 2000. CHAPTER 5 • Uncertainty and Consumer Behavior 185 5.5 Bubbles During 1995 to 2000, the stock prices of many Internet companies rose sharply. What was behind these sharp price increases? One could argue—as many stock analysts, investment advisors, and ordinary investors did at the time—that these price increases were justified by fundamentals. Many people thought that the Internet’s potential was virtually unbounded, particularly as high-speed Internet access became more widely available. After all, more and more goods and services were being bought online through companies such as Amazon.com, Craigslist.org, Ticketmaster.com, Fandango. com, and a host of others. In addition, more and more people began to read the news online rather than buying physical newspapers and magazines, and more and more information became available online through sources like Google, Bing, Wikipedia, and WebMD. And as a result, companies began to shift more and more of their advertising from newspapers and television to the Internet. Yes, the Internet has certainly changed the way most of us live. (In fact, some of you may be reading the electronic version of this book, which you downloaded from the Pearson website and hopefully paid for!) But does that mean that any company with a name that ends in “.com” is sure to make high profits in the future? Probably not. And yet many investors (perhaps “speculators” is a better word) bought the stocks of Internet companies at very high prices, prices that were increasingly difficult to justify based on fundamentals, i.e., based on rational projections of future profitability. The result was the Internet bubble, an increase in the prices of Internet stocks based not on the fundamentals of business profitability, but instead on the belief that the prices of those stocks would keep going up. The bubble burst when people started to realize that the profitability of these companies was far from a sure thing, and that prices that go up can also come down. Bubbles are often the result of irrational behavior. People stop thinking straight. They buy something because the price has been going up, and they believe (perhaps encouraged by their friends) that the price will keep going up, so that making a profit is a sure thing. If you ask these people whether the price might at some point drop, they typically will answer “Yes, but I will sell before the price drops.” And if you push them further by asking how they will know when the price is about to drop, the answer might be “I’ll just know.” But, of course, most of the time they won’t know; they will sell after the price has dropped, and they will lose at least part of their investment. (There might be a silver lining—perhaps they will learn some economics from the experience.) Bubbles are often harmless in the sense that while people lose money, there is no lasting damage to the overall economy. But that is not always the case. The United States experienced a prolonged housing price bubble that burst in 2008, causing financial losses to large banks that had sold mortgages to home buyers who could not afford to make their monthly payments (but thought housing prices would keep rising). Some of these banks were given large government bailouts to keep them from going bankrupt, but many homeowners were less fortunate, and facing foreclosure, they lost their homes. By the end of 2008, the United States was in its worst recession since the Great Depression of the 1930s. The housing price bubble, far from harmless, was partly to blame for this. • bubble An increase in the price of a good based not on the fundamentals of demand or value, but instead on a belief that the price will keep going up. Recall from Section 4.3 that speculative demand is driven not by the direct benefits one obtains from owning or consuming a good but instead is driven by an expectation that the price of the good will increase. 186 PART 2 • Producers, Consumers, and Competitive Markets E XAM PLE 5.7 THE HOUSING PRICE BUBBLE (I) Starting around 1998, U.S. housing prices began rising sharply. Figure 5.10 shows the S&P/CaseShiller housing price index at the national level.20 From 1987 (when the Index was first published) to 1998, the index rose around 3 percent per year in nominal terms. (In real terms, i.e., net of inflation, the index dropped about 0.5 percent per year.) This was a normal rate of price increase, roughly commensurate with population and income growth and with inflation. But then prices started rising much more rapidly, with the index increasing about 10 percent per year until it reached its peak of 190 in 2006. During that 8-year period from 1998 to 2006, many people bought into the myth that housing was a sure-fire investment, and that prices could only keep going up. Many banks also bought into this myth and offered mortgages to people with incomes well below what it would take to make the monthly interest and principal payments over the long term. The demand for housing increased sharply, with so |
me people buying four or five houses under the assumption that they could “flip” them in a year and make a quick profit. This speculative demand served to push prices up further. However, in 2006 something funny happened. Prices stopped going up. In fact, during 2006, prices 190 170 150 130 110 90 70 50 Housing Price Index (nominal) Housing Price Index (real) 1987 1989 1991 1993 1995 1997 1999 Year 2001 2003 2005 2007 2009 2011 FIGURE 5.10 S&P/CASE-SHILLER HOUSING PRICE INDEX The Index shows the average home price in the United States at the national level. Note the increase in the index from 1998 to 2007, and then the sharp decline. 20The S&P/Case-Shiller index measures the change in housing prices by tracking repeat sales of single family homes in 20 cities across the United States. By comparing a home’s original sale price with its price in subsequent sales, the index is able to control for other variables (i.e., size, location, style) that might also lead to rising home prices. CHAPTER 5 • Uncertainty and Consumer Behavior 187 actually fell slightly (about 2 percent in nominal terms). Then, in 2007 prices started falling rapidly, and by 2008 it had become clear that the great housing boom was just a bubble, and the bubble had burst. From its peak in early 2006 through 2011, housing prices fell by over 33 percent in nominal terms. (In real terms they fell by nearly 40% percent.) And this drop is an average for the United States as a whole. In some states, such as Florida, Arizona, and Nevada, the bubble was far worse, with prices dropping by over 50 percent. The United States was not the only country to experience a housing price bubble. More or less the same thing happened in Europe. In Ireland, for example, a booming economy and increasing foreign investment—along with widespread speculation— pushed housing prices up 305% between 1995 and 2007 (641% between 1987 and 2007—both in nominal terms). After over a decade of above average growth, Ireland’s bubble burst. By 2010, housing prices had fallen over 28% from their 2007 peak. Spain and other European countries suffered similar fates, contributing to a worldwide debt crisis. Other apparent bubbles have yet to deflate. Many Chinese cities, including Shanghai and Beijing, have seen rapidly rising housing and land prices, with some apartments reportedly doubling in value in mere months.21 Informational Cascades Suppose you are considering investing in the stock of Ajax Corp., which is trading at $20 per share. Ajax is a biotech company that is working on a radically new approach to the treatment of chronic boredom (a disease that often afflicts students of economics). You find it difficult to evaluate the company’s prospects, but $20 seems like a reasonable price. But now you see the price is increasing—to $21, $22, then a jump to $25 per share. In fact, some friends of yours have just bought in at $25. Now the price reaches $30. Other investors must know something. Perhaps they consulted biochemists who can better evaluate the company’s prospects. So you decide to buy the stock at $30. You believe that positive information drove the actions of other investors, and you acted accordingly. Was buying the stock of Ajax at $30 a rational decision, or were you simply buying into a bubble? It might indeed be rational. After all, it is reasonable to expect that other investors tried to value the company as best they could and that their analyses might have been more thorough or better informed than yours. Thus the actions of other investors could well be informative and lead you to rationally adjust your own valuation of the company. Note that in this example, your investment decisions are based not on fundamental information that you have obtained (e.g., regarding the likelihood that Ajax’s R&D will be successful), but rather on the investment decisions of others. And note that you are implicitly assuming that: (i) these investment decisions of others are based on fundamental information that they have obtained; or (ii) these investment decisions of others are based on the investment decisions of others still, which are based on fundamental information that they have obtained; or (iii) these investment decisions of others are based on the investment decisions of others still, which in turn are based on the investment decisions of still more others, which are based on fundamental information that they obtained; or . . . etc., etc. You get the idea. Maybe the “others” at the end of the chain based their investment decisions on weak information that was no more informative than the information you started with when you began thinking about Ajax. In other 21Fearing a sudden collapse, the Chinese government took steps to curtail skyrocketing housing prices, tightening lending requirements and requiring purchasers to put more money down. See http://www.businessinsider.com/the-chinese-real-estate-bubble-is-the-most-obvious-bubbleever-2010-1#prices-are-way-out-of-whack-compared-to-global-standards-3. 188 PART 2 • Producers, Consumers, and Competitive Markets E XAM PLE 5.8 THE HOUSING PRICE BUBBLE (II) Informational cascades may help to explain the housing bubbles that occurred in the U.S. and other countries. For example, from 1999 to 2006, home prices in Miami nearly tripled. Would it have been completely irrational to buy real estate in Miami in 2006? In the years prior to 2006, some analysts projected large increases in the demand for housing in Miami and other parts of Florida, based in part on a growing number of aging retirees that want to move to someplace warm, and in part on an influx of immigrants with family or other roots in Miami. If other investors acted on the belief that these analysts had done their homework, investing might have been rational. Informational cascades may also help explain the housing bubbles that took place in other parts of the U.S., notably Arizona, Nevada, and California. (See Figure 5.11.) There, too, some analysts had projected large increases in demand. On the other hand, few analysts projected large demand increases in cities like Cleveland (not exactly a retirement paradise), and indeed such cities experienced little in the way of a bubble. Was it rational to buy real estate in Miami in 2006? Rational or not, investors should have known that considerable risk was involved in buying real estate there (or elsewhere in Florida, Arizona, Nevada, and California). Looking back, we now know that many of these investors lost their shirts (not to mention their homes). 500 450 400 350 300 250 200 150 100 50 1987 1989 1991 1993 1995 1997 1999 Year 2001 2003 2005 2007 2009 2011 Los Angeles Miami Las Vegas New York Cleveland FIGURE 5.11 S&P/CASE-SHILLER HOUSING PRICE INDEX FOR FIVE CITIES The Index shows the average home price for each of five cities (in nominal terms). For some cities, the housing bubble was much worse than for others. Los Angeles, Miami, and Las Vegas experienced some of the sharpest increases in home prices, and then starting in 2007, prices plummeted. Cleveland, on the other hand, largely avoided the bubble, with home prices increasing, and then falling, only moderately. CHAPTER 5 • Uncertainty and Consumer Behavior 189 words, your own investment decisions might be the result of an informational cascade—actions based on actions based on actions . . . , etc., driven by very limited fundamental information. The bubble that results from an informational cascade can in fact be rational in the sense that there is a basis for believing that investing in the bubble will yield a positive return. The reason is that if investors early in the chain indeed obtained positive information and based their decisions on that information, the expected gain to an investor down the chain will be positive.22 However, the risk involved will be considerable, and it is likely that at least some investors will underestimate that risk. • Informational cascade An assessment (e.g., of an investment opportunity) based in part on the actions of others, which in turn were based on the actions of others. 5.6 Behavioral Economics Recall that the basic theory of consumer demand is based on three assumptions: (1) consumers have clear preferences for some goods over others; (2) consumers face budget constraints; and (3) given their preferences, limited incomes, and the prices of different goods, consumers choose to buy combinations of goods that maximize their satisfaction (or utility). These assumptions, however, are not always realistic: Preferences are not always clear or might vary depending on the context in which choices are made, and consumer choices are not always utility-maximizing. Perhaps our understanding of consumer demand (as well as the decisions of firms) would be improved if we incorporated more realistic and detailed assumptions regarding human behavior. This has been the objective of the newly flourishing field of behavioral economics, which has broadened and enriched the study of microeconomics.23 We introduce this topic by highlighting some examples of consumer behavior that cannot be easily explained with the basic utility-maximizing assumptions that we have relied on so far: • There has just been a big snowstorm, so you stop at the hardware store to buy a snow shovel. You had expected to pay $20 for the shovel—the price that the store normally charges. However, you find that the store has suddenly raised the price to $40. Although you would expect a price increase because of the storm, you feel that a doubling of the price is unfair and that the store is trying to take advantage of you. Out of spite, you do not buy the shovel.24 • Tired of being snowed in at home you decide to take a vacation in the country. On the way, you stop at a highway restaurant for lunch. Even though you are unlikely to return to that restaurant, you believe that it is fair and 22For a reasonably simple example that makes this point (and an interesting discussi |
on), see S. Bikhchandani, D. Hirschleifer, and I. Welch, “Learning from the Behavior of Others: Conformity, Fads, and Informational Cascades,” 12 Journal of Economic Perspectives, (Summer 1998): 151–170. 23For more detailed discussion of the material presented in this section, see Stefano DellaVigna, “Psychology and Economics: Evidence from the Field,” Journal of Economic Literature 47(2), 2009: 315–372; Colin Camerer and George Loewenstein, “Behavioral Economics: Past, Present, Future,” in Colin Camerer, George Loewenstein, and Matthew Rabin (eds.), Advances in Behavioral Economics, Princeton University Press, 2003. 24This example is based on Daniel Kahneman, Jack Knetsch, and Richard Thaler, “Fairness as a Constraint on Profit Seeking: Entitlements in the Market,” American Economic Review 76 (September 1986): 728–741. 190 PART 2 • Producers, Consumers, and Competitive Markets appropriate to leave a 15-percent tip in appreciation of the good service that you received. • You buy this textbook from an Internet bookseller because the price is lower than the price at your local bookstore. However, you ignore the shipping cost when comparing prices. Each of these examples illustrates plausible behavior that cannot be explained by a model based solely on the basic assumptions described in Chapters 3 and 4. Instead, we need to draw on insights from psychology and sociology to augment our basic assumptions about consumer behavior. These insights will enable us to account for more complex consumer preferences, for the use of simple rules in decision-making, and for the difficulty that people often have in understanding the laws of probability. Adjustments to the standard model of consumer preferences and demand can be grouped into three categories: A tendency to value goods and services in part based on the setting one is in, a concern about the fairness of an economic transaction, and the use of simple rules of thumb as a way to cut through complex economic decisions. We examine each of these in turn. Reference Points and Consumer Preferences The standard model of consumer behavior assumes that consumers place unique values on the goods and services they purchase. However, psychologists and market research studies have found that perceived value depends in part on the setting in which the purchasing decision occurs. That setting creates a reference point on which preferences might be at least partly based. The reference point—the point from which the individual makes the consumption decision—can strongly affect that decision. Consider, for example, apartment prices in Pittsburgh and San Francisco. In Pittsburgh, the median monthly rent in 2006 for a two-bedroom apartment was about $650, while in San Francisco the rent for a similar apartment was $2,125. For someone accustomed to San Francisco housing prices, Pittsburgh might seem like a bargain. On the other hand, someone moving from Pittsburgh to San Francisco might feel “gouged”—thinking it unfair for housing to cost that much.25 In this example, the reference point is clearly different for long-time residents of Pittsburgh and San Francisco. Reference points can develop for many reasons: our past consumption of a good, our experience in a market, our expectation about how prices should behave, and even the context in which we consume a good. Reference points can strongly affect the way people approach economic decisions. Below we describe several different examples of reference points and the way they affect consumer behavior. • reference point The point from which an individual makes a consumption decision. • endowment effect Tendency of individuals to value an item more when they own it than when they do not. ENDOWMENT EFFECT A well-known example of a reference point is the endowment effect—the fact that individuals tend to value an item more when they happen to own it than when they do not. One way to think about this effect is to consider the gap between the price that a person is willing to pay for a good and the price at which she is willing to sell the same good to someone else. Our 25This example is based on Uri Simonsohn and George Loewenstein, “Mistake #37: The Effects of Previously Encountered Prices on Current Housing Demand,” The Economic Journal 116 (January 2006): 175–199. CHAPTER 5 • Uncertainty and Consumer Behavior 191 basic theory of consumer behavior says that this price should be the same, but many experiments suggest that is not what happens in practice.26 In one classroom experiment, half of the students chosen at random were given a free coffee mug with a market value of $5; the other half got nothing.27 Students with the mug were asked the price at which they would sell it back to the professor; the second group was asked the minimum amount of money that they would accept in lieu of a mug. The decision faced by both groups is similar but their reference points are different. For the first group, whose reference point was possession of a mug, the average selling price was $7. For the second group, which did not have a mug, the average amount desired in lieu of a mug was $3.50. This gap in prices shows that giving up the mug was perceived to be a greater “loss” to those who had one than the “gain” from obtaining a mug for those without one. This is an endowment effect—the mug was worth more to those people who already owned it. LOSS AVERSION The coffee mug experiment described above is also an example of loss aversion—the tendency of individuals to prefer avoiding losses over acquiring gains. The students who owned the mug and believed that its market value was indeed $5 were averse to selling it for less than $5 because doing so would have created a perceived loss. The fact that they had been given the mug for free, and thus would still have had an overall gain, didn’t matter as much. As another example of loss aversion, people are sometimes hesitant to sell stocks at a loss, even if they could invest the proceeds in other stocks that they think are better investments. Why? Because the original price paid for the stock—which turned out to be too high given the realities of the market—acts as a reference point, and people are averse to losses. (A $1000 loss on an investment seems to “hurt” more than the perceived benefit from a $1000 gain.) While there are a variety of circumstances in which endowment effects arise, we now know that these effects tend to disappear as consumers gain relevant experience. We would not expect to see stockbrokers or other investment professionals exhibit the loss aversion described above.28 FRAMING Preferences are also influenced by framing, which is another manifestation of reference points. Framing is a tendency to rely on the context in which a choice is described when making a decision. How choices are framed—the names they are given, the context in which they are described, and their appearance—can affect the choices that individuals make. Are you more likely to buy a skin cream whose package claims that is will “slow the aging process” or one that is described as “making you feel young again.” These products might be essentially identical except for their packaging. Yet, in the real world where information is sometimes limited and perspective matters, many individuals would prefer to buy the product that emphasizes youth. 26Experimental work such as this has been important to the development of behavioral economics. It is for this reason that the 2002 Nobel Prize in economics was shared by Vernon Smith, who did much of the pioneering work in the use of experiments to test economic theories. 27Daniel Kahneman, Jack L. Knetsch, and Richard H. Thaler, “Experimental Tests of the Endowment Effect and the Coase Theorem,” Journal of Political Economy 98, (December 1990): 1925–48. 28John A. List, “Does Market Experience Eliminate Market Anomalies?” Quarterly Journal of Economics 118 (January 2003): 41–71. • loss aversion Tendency for individuals to prefer avoiding losses over acquiring gains. • framing Tendency to rely on the context in which a choice is described when making a decision. 192 PART 2 • Producers, Consumers, and Competitive Markets E XAM PLE 5.9 SELLING A HOUSE Homeowners sometimes sell their homes because they have to relocate for a new job, because they want to be closer to (or farther from) the city in which they work, or because they want to move to a bigger or smaller house. So they put their home on the market. But at what price? The owners can usually get a good idea of what the house will sell for by looking at the selling prices of comparable houses, or by talking with a realtor. Often, however, the owners will set an asking price that is well above any realistic expectation of what the house can actually sell for. As a result, the house may stay on the market for many months before the owners grudgingly lower the price. During that time the owners have to continue to maintain the house and pay for taxes, utilities, and insurance. This seems irrational. Why not set an asking price closer to what the market will bear? The endowment effect is at work here. The homeowners view their house as special; their ownership has given them what they think is a special appreciation of its value—a value that may go beyond any price that the market will bear. If housing prices have been falling, loss aversion could also be at work. As we saw in Examples 5.7 and 5.8, U.S and European housing prices started falling around 2008, as the housing bubble deflated. As a result, some homeowners were affected by loss aversion when deciding on an asking price, especially if they bought their home at a time near the peak of the bubble. Selling the house turns a paper loss, which may not seem real, into a loss that is real. Averting that reality may serve to explain the reluctance of home owners to take that final step of selling their home. It is not surprising, therefore, to find that houses tend to stay on the marke |
t longer during economic downturns than in upturns. Fairness People sometimes do things because they think it is appropriate or fair to do so, even though there is no financial or other material benefit. Examples include charitable giving, volunteering time, or tipping in a restaurant. Fairness likewise affected consumer behavior in our example of buying a snow shovel. At first glance, our basic consumer theory does not appear to account for fairness. However, we can often modify our models of demand to account for the effects of fairness on consumer behavior. To see how, let’s return to our original snow shovel example. In that example, the market price of shovels was $20, but right after a snowstorm (which caused a shift in the demand curve), stores raised their price to $40. Some consumers, however, felt they were being unfairly gouged, and refused to buy a shovel. This is illustrated in Figure 5.12. Demand curve D1 applies during normal weather. Stores have been charging $20 for a shovel, and sell a total quantity of Q1 shovels per month (because many consumers buy shovels in anticipation of snow). In fact some people would have been willing to pay much more for a shovel (the upper part of the demand curve), but they don’t have to because the market price is $20. Then the snowstorm hits, and the demand curve shifts to the right. Had the price remained $20, the quantity demanded would have increased to Q2. But note that the new demand curve (D2) does not extend up as far as the old one. Many consumers might feel that an increase in price to, say, $25 is fair, but an increase much above that would be unfair gouging. Thus the new demand curve becomes very elastic at prices above $25, and no shovels can be sold at a price much above $30. Note how fairness comes in to play here. In normal weather, some consumers would have been willing to pay $30 or even $40 for a shovel. But they know that P $40 $25 $20 CHAPTER 5 • Uncertainty and Consumer Behavior 193 FIGURE 5.12 DEMAND FOR SNOW SHOVELS Demand curve D1 applies during normal weather. Stores have been charging $20 and sell Q1 shovels per month. When a snowstorm hits, the demand curve shifts to the right. Had the price remained $20, the quantity demanded would have increased to Q2. But the new demand curve (D2) does not extend up as far as the old one. Consumers view an increase in price to, say, $25 as fair, but an increase much above that as unfair gouging. The new demand curve is very elastic at prices above $25, and no shovels can be sold at a price much above $30. D1 Q2 Q1 D2 Q the price has always been $20, and they feel that a sharp increase in price after a snowstorm is unfair gouging and refuse to buy. Note also how we can modify standard demand curves to account for consumer attitudes towards fairness. Another example of fairness arises in the ultimatum game. Imagine that, under the following rules, you are offered a chance to divide 100 one-dollar bills with a stranger whom you will never meet again: You first propose a division of the money between you and the stranger. The stranger will respond by either accepting or rejecting your proposal. If he accepts, you each get the share that you proposed. If he rejects, you both get nothing. What should you do? Because more money means more utility, our basic theory provides a clear answer to this question. You should propose that you get $99 while the other person gets only $1. Moreover, the responder should be happy to accept this proposal, because $1 is more than he had before and more than he would get if he rejected your offer (in both cases zero). This is a beneficial deal for both of you. Yet most people facing this choice hesitate to make such an offer because they think it unfair, and many “strangers” would reject the offer. Why? The stranger might believe that because you both received the windfall opportunity to divide $100, a simple and fair division would be 50/50 or something close to that. Maybe the stranger will turn down the $1 offer to teach you that greediness is not appropriate behavior. Indeed, if you believe that the stranger will feel this way, it will be rational for you to offer a greater amount. In fact, when this game is played experimentally, typical sharing proposals range between 67/33 and 50/50, and such offers are normally accepted. The ultimatum game shows how fairness can affect economic decisions. Not surprisingly, fairness concerns can also affect negotiations between firms and their workers. A firm may offer a higher wage to employees because the managers believe that workers deserve a comfortable standard of living or because they want to foster a pleasant working environment. Moreover, workers who do 194 PART 2 • Producers, Consumers, and Competitive Markets not get a wage that they feel is fair may not put much effort into their work.29 (In Section 17.6, we will see that paying workers higher-than-market wages can also be explained by the “efficiency wage theory” of labor markets, in which fairness concerns do not apply.) Fairness also affects the ways in which firms set prices and can explain why firms can more easily raise prices in response to higher costs than to increases in demand.30 Fortunately, fairness concerns can be taken into account in the basic model of consumer behavior. If individuals moving to San Francisco believe that high apartment rents are unfair, their maximum willingness to pay for rental housing will be reduced. If a sufficient number of individuals feel this way, the resulting reduction in demand will lead to lower rental prices. Similarly, if enough workers do not feel that their wages are fair, there will be a reduction in the supply of labor, and wage rates will increase. Rules of Thumb and Biases in Decision Making Many economic (and everyday) decisions can be quite complex, especially if they involve choices about matters in which we have little experience. In such cases, people often resort to rule of thumb or other mental shortcuts to help them make decisions. In the tipping example, you took a mental shortcut when you decided to offer a 15-percent tip. The use of such rules of thumb, however, can introduce a bias into our economic decision making—something that our basic model does not allow.31 ANCHORING The mental rules that we use in making decisions frequently depend on both the context in which the decisions are made and the information available. For example, imagine that you just received a solicitation from a new local charity to make a donation. Rather than asking for a gift of any amount, the charity asks you to choose: $20, $50, $100, $250, or “other.” The purpose of these suggestions is to induce you to anchor your final donation. Anchoring refers to the impact that a suggested (perhaps unrelated) piece of information may have on your final decision. Rather than trying to decide precisely how much to donate—say $44.52—and not wanting to appear miserly, one might simply write a check for the next higher category—$50. Another individual wishing to make only a token donation of $10 might choose the lowest stated amount, $20. In both cases, anchoring can bias individual choices toward larger donations. Similarly, it’s no coincidence so many price tags end with the digits 95 or 99. Marketers understand that consumers tend to overemphasize the first digit of prices, and also to think in terms of price categories like “under $20” or “over $20.” Thus to the consumer, who may not be thinking too carefully, $19.95 seems much cheaper than $20.01. RULES OF THUMB A common way to economize on the effort involved in making decisions is to ignore seemingly unimportant pieces of information. 29For a general discussion of behavioral economics and the theory of wages and employment, see George Akerlof, “Behavioral Macroeconomics and Macroeconomic Behavior,” American Economic Review 92 (June 2002): 411–33. 30See, for example, Julio J. Rotemberg, “Fair Pricing,” NBER Working Paper No. W10915, 2004. 31For an introduction to this topic see Amos Tversky and Daniel Kahneman, “Judgment under Uncertainty: Heuristics and Biases,” Science 185 (September 1974): 1124–31. • anchoring Tendency to rely heavily on one prior (suggested) piece of information when making a decision. CHAPTER 5 • Uncertainty and Consumer Behavior 195 • law of small numbers Tendency to overstate the probability that a certain event will occur when faced with relatively little information. For example, goods purchased over the Internet often involve shipping costs. Although small, these costs should be included as part of the good’s final price when making a consumption decision. However, a recent study has shown that shipping costs are typically ignored by many consumers when deciding to buy things online. Their decisions are biased because they view the price of goods to be lower than they really are.32 Whereas depending on rules of thumb can introduce biases in decision making, it is important to understand that they do serve a useful purpose. Frequently, rules of thumb help to save time and effort and result in only small biases. Thus, they should not be dismissed outright. Consumers often face uncertainty when making decisions, and lack the understanding of probability to make those decisions optimally. (Consider the difficulty involved, for example, in calculating expected utility.) Consumers will often use rules of thumb when making decisions, but sometimes those rules of thumb can lead to strong biases. THE LAW OF SMALL NUMBERS People are sometimes prone to a bias called the law of small numbers: They tend to overstate the probability that certain events will occur when faced with relatively little information from recent memory. For example, many people tend to overstate the likelihood that they or someone they know will die in a plane crash or win the lottery. Recall the roulette player who bets on black after seeing red come up three times in a row: He has ignored the l |
aws of probability. Research has shown that investors in the stock market are often subject to a small-numbers bias, believing that high returns over the past few years are likely to be followed by more high returns over the next few years—thereby contributing to the kind of “herd behavior” that we discussed in the previous section. In this case, investors assess the likely payoff from investing by observing the market over a short period of time. In fact, one would have to study stock market returns for many decades in order to estimate accurately the expected return on equity investments. Similarly when people assess the likelihood that housing prices will rise based on several years of data, the resulting misperceptions can result in housing price bubbles.33 Although individuals may have some understanding of true probabilities (as when flipping a coin), complications arise when probabilities are unknown. For instance, few people have an idea about the probability that they or a friend will be in a car or airplane accident. In such cases, we form subjective probability assessments about such events. Our estimation of subjective probabilities may be close to true probabilities, but often they are not. Forming subjective probabilities is not always an easy task and people are generally prone to several biases in the process. For instance, when evaluating the likelihood of an event, the context in which the evaluation is made can be very important. If a tragedy such as a plane crash has occurred recently, many people will tend to overestimate the probability of it happening to them. Likewise, when a probability for a particular event is very, very small, many people simply ignore that possibility in their decision making. 32Tankim Hossain and John Morgan, “… Plus Shipping and Handling: Revenue (Non) Equivalence in Field Experiments on eBay,” Advances in Economic Analysis & Policy 6: 2 (2006). 33See Charles Himmelberg, Christopher Mayer, and Todd Sinai, “Assessing High House Prices: Bubbles, Fundamentals and Misperceptions,” Journal of Economic Perspectives 19 (Fall 2005): 67–92. 196 PART 2 • Producers, Consumers, and Competitive Markets Summing Up Where does this leave us? Should we dispense with the traditional consumer theory discussed in Chapters 3 and 4? Not at all. In fact, the basic theory that we learned up to now works quite well in many situations. It helps us to understand and evaluate the characteristics of consumer demand and to predict the impact on demand of changes in prices or incomes. Although it does not explain all consumer decisions, it sheds light on many of them. The developing field of behavioral economics tries to explain and to elaborate on those situations that are not well explained by the basic consumer model. If you continue to study economics, you will notice many cases in which economic models are not a perfect reflection of reality. Economists have to carefully decide, on a case-by-case basis, what features of the real world to include and what simplifying assumptions to make so that models are neither too complicated to study nor too simple to be useful. E XAM PLE 5.10 NEW YORK CITY TAXICAB DRIVERS Most cab drivers rent their taxicabs for a fixed daily fee from a company that owns a fleet of cars. They can then choose to drive the cab as little or as much as they want during a 12-hour period. As with many services, business is highly variable from day to day, depending on the weather, subway breakdowns, holidays, and so on. How do cabdrivers respond to these variations, many of which are largely unpredictable? In many cities, taxicab rates are fixed by regulation and do not change from day to day. However, on busy days drivers can earn a higher income because they do not have to spend as much time searching for riders. Traditional economic theory would predict that drivers will work longer hours on busy days than on slow days; an extra hour on a busy day might bring in $20, whereas an extra hour on a slow day might yield only $10. Does traditional theory explain the actual behavior of taxicab drivers? An interesting study analyzed actual taxicab trip records obtained from the New York Taxi and Limousine Commission for the spring of 1994.34 The daily fee to rent a taxi was then $76, and gasoline cost about $15 per day. Surprisingly, the researchers found that most drivers drive more hours on slow days and fewer hours on busy days. In other words, there is a negative relationship between the effective hourly wage and the number of hours worked each day; the higher the wage, the sooner the cabdrivers quit for the day. Behavioral economics can explain this result. Suppose that most taxicab drivers have an income target for each day. That target effectively serves as a reference point. Daily income targeting makes sense from a behavioral perspective. An income target provides a simple decision rule for drivers because they need only keep a record of their fares for the day. A daily target also helps drivers with potential self-control problems; without a target, a driver may choose to quit earlier on many days just to avoid the hassles of the job. The target in the 1994 study appeared to be about $150 per day. Still other studies challenge this “behavioral” explanation of behavior. A different study, also of New York City cab drivers who rented their taxis, concluded that the traditional economic model does indeed offer important insights into drivers’ 34Colin Camerer, Linda Babcock, George Loewenstein, and Richard Thaler, “Labor Supply of New York City Cabdrivers: One Day at a Time,” Quarterly Journal of Economics (May 1997): 404–41. See also, Henry S. Farber, “Reference-Dependent Preferences and Labor Supply: The Case of New York City Taxi Drivers,” American Economic Review 98 (2008): 1069–82. CHAPTER 5 • Uncertainty and Consumer Behavior 197 behavior.35 The study concluded that daily income had only a small effect on a driver’s decision as to when to quit for the day. Rather, the decision to stop appears to be based on the cumulative number of hours already worked that day and not on hitting a specific income target. What may soon become known as “the great taxicab driver debate” did not end here. A recent study sought to explain these two seemingly contradictory results. Reanalyzing the same taxicab trip records, the authors found that the traditional economic model goes a long way in explaining most workday decisions of taxicab drivers, but that a behavioral model that accounts for reference points and targeted goals (for income and hours) can do even better.36 If you are interested in learning more about the taxicab industry, you can look ahead to the examples in Chapters 8, 9, and 15. SUMMARY 1. Consumers and managers frequently make decisions in which there is uncertainty about the future. This uncertainty is characterized by the term risk, which applies when each of the possible outcomes and its probability of occurrence is known. 2. Consumers and investors are concerned about the expected value and the variability of uncertain outcomes. The expected value is a measure of the central tendency of the values of risky outcomes. Variability is frequently measured by the standard deviation of outcomes, which is the square root of the probabilityweighted average of the squares of the deviation from the expected value of each possible outcome. 3. Facing uncertain choices, consumers maximize their expected utility—an average of the utility associated with each outcome—with the associated probabilities serving as weights. 4. A person who would prefer a certain return of a given amount to a risky investment with the same expected return is risk averse. The maximum amount of money that a risk-averse person would pay to avoid taking a risk is called the risk premium. A person who is indifferent between a risky investment and the certain receipt of the expected return on that investment is risk neutral. A risk-loving consumer would prefer a risky investment with a given expected return to the certain receipt of that expected return. 5. Risk can be reduced by (a) diversification, (b) insur- ance, and (c) additional information. 6. The law of large numbers enables insurance companies to provide insurance for which the premiums paid equal the expected value of the losses being insured against. We call such insurance actuarially fair. 7. Consumer theory can be applied to decisions to invest in risky assets. The budget line reflects the price of risk, and consumers’ indifference curves reflect their attitudes toward risk. 8. Individual behavior sometimes seems unpredictable, even irrational, and contrary to the assumptions that underlie the basic model of consumer choice. The study of behavioral economics enriches consumer theory by accounting for reference points, endowment effects, anchoring, fairness considerations, and deviations from the laws of probability. QUESTIONS FOR REVIEW 1. What does it mean to say that a person is risk averse? Why are some people likely to be risk averse while others are risk lovers? 2. Why is the variance a better measure of variability than the range? 3. George has $5000 to invest in a mutual fund. The expected return on mutual fund A is 15 percent and the expected return on mutual fund B is 10 percent. Should George pick mutual fund A or fund B? 4. What does it mean for consumers to maximize expected utility? Can you think of a case in which a person might not maximize expected utility? 5. Why do people often want to insure fully against uncertain situations even when the premium paid exceeds the expected value of the loss being insured against? 6. Why is an insurance company likely to behave as if it were risk neutral even if its managers are risk-averse individuals? 35Henry S. Farber, “Is Tomorrow Another Day? The Labor Supply of New York City Cabdrivers,” Journal of Political Economy 113 (2005): 46–82. 36See Vincent P. Crawford and Juanjuan Meng, “New Yo |
rk City Cab Drivers’ Labor Supply Revisited: Reference-Dependent Preferences with Rational-Expectations Targets for Hours and Income,” American Economic Review, 101 (August 2011): 1912–1934. 198 PART 2 • Producers, Consumers, and Competitive Markets 7. When is it worth paying to obtain more information to 10. What is an endowment effect? Give an example of reduce uncertainty? such an effect. 8. How does the diversification of an investor’s portfolio avoid risk? 9. Why do some investors put a large portion of their portfolios into risky assets while others invest largely in risk-free alternatives? (Hint: Do the two investors receive exactly the same return on average? If so, why?) 11. Jennifer is shopping and sees an attractive shirt. However, the price of $50 is more than she is willing to pay. A few weeks later, she finds the same shirt on sale for $25 and buys it. When a friend offers her $50 for the shirt, she refuses to sell it. Explain Jennifer’s behavior. EXERCISES 1. Consider a lottery with three possible outcomes: • $125 will be received with probability .2 • $100 will be received with probability .3 • $50 will be received with probability .5 a. What is the expected value of the lottery? b. What is the variance of the outcomes? c. What would a risk-neutral person pay to play the lottery? 2. Suppose you have invested in a new computer company whose profitability depends on two factors: (1) whether the U.S. Congress passes a tariff raising the cost of Japanese computers and (2) whether the U.S. economy grows slowly or quickly. What are the four mutually exclusive states of the world that you should be concerned about? 3. Richard is deciding whether to buy a state lottery ticket. Each ticket costs $1, and the probability of winning payoffs is given as follows: PROBABILITY RETURN .4 .3 .3 $100 30 −30 What is the expected value of the uncertain investment? What is the variance? 5. You are an insurance agent who must write a policy for a new client named Sam. His company, Society for Creative Alternatives to Mayonnaise (SCAM), is working on a low-fat, low-cholesterol mayonnaise substitute for the sandwich-condiment industry. The sandwich industry will pay top dollar to the first inventor to patent such a mayonnaise substitute. Sam’s SCAM seems like a very risky proposition to you. You have calculated his possible returns table as follows: PROBABILITY RETURN PROBABILITY RETURN OUTCOME .5 .25 .2 .05 $0.00 $1.00 $2.00 $7.50 .999 .001 −$1,000,000 (he fails) $1,000,000,000 (he succeeds and sells his formula) a. What is the expected return of Sam’s project? What is the variance? a. What is the expected value of Richard’s payoff if he b. What is the most that Sam is willing to pay for buys a lottery ticket? What is the variance? insurance? Assume Sam is risk neutral. b. Richard’s nickname is “No-Risk Rick” because he is an extremely risk-averse individual. Would he buy the ticket? c. Richard has been given 1000 lottery tickets. Discuss how you would determine the smallest amount for which he would be willing to sell all 1000 tickets. d. In the long run, given the price of the lottery tickets and the probability/return table, what do you think the state would do about the lottery? 4. Suppose an investor is concerned about a business choice in which there are three prospects—the probability and returns are given below: c. Suppose you found out that the Japanese are on the verge of introducing their own mayonnaise substitute next month. Sam does not know this and has just turned down your final offer of $1000 for the insurance. Assume that Sam tells you SCAM is only six months away from perfecting its mayonnaise substitute and that you know what you know about the Japanese. Would you raise or lower your policy premium on any subsequent proposal to Sam? Based on his information, would Sam accept? 6. Suppose that Natasha’s utility function is given by u (I) = 110I, where I represents annual income in thousands of dollars. CHAPTER 5 • Uncertainty and Consumer Behavior 199 a. Is Natasha risk loving, risk neutral, or risk averse? Explain. b. Suppose that Natasha is currently earning an income of $40,000 (I 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a .6 probability of earning $44,000 and a .4 probability of earning $33,000. Should she take the new job? c. In (b), would Natasha be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance? (Hint: What is the risk premium?) 7. Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: PAYOFF $300 $250 $200 PROBABILITY (INVESTMENT A) PROBABILITY (INVESTMENT B) 0.10 0.80 0.10 0.30 0.40 0.30 a. Find the expected return and standard deviation of each investment. b. Jill has the utility function U 5I, where I denotes the payoff. Which investment will she choose? c. Ken has the utility function U = 5 1I. Which investment will he choose? d. Laura has the utility function U 5I2. Which invest- ment will she choose? 8. As the owner of a family farm whose wealth is $250,000, you must choose between sitting this season out and investing last year’s earnings ($200,000) in a safe money market fund paying 5.0 percent or planting summer corn. Planting costs $200,000, with a six-month time to harvest. If there is rain, planting summer corn will yield $500,000 in revenues at harvest. If there is a drought, planting will yield $50,000 in revenues. As a third choice, you can purchase AgriCorp drought-resistant summer corn at a cost of $250,000 that will yield $500,000 in revenues at harvest if there is rain, and $350,000 in revenues if there is a drought. You are risk averse, and your preference for family wealth (W) is specified by the relationship U(W) = 1W. The probability of a summer drought is 0.30, while the probability of summer rain is 0.70. Which of the three options should you choose? Explain. 9. Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences? 10. A city is considering how much to spend to hire people to monitor its parking meters. The following information is available to the city manager: • Hiring each meter monitor costs $10,000 per year. • With one monitoring person hired, the probability of a driver getting a ticket each time he or she parks illegally is equal to .25. • With two monitors, the probability of getting a ticket is .5; with three monitors, the probability is .75; and with four, it’s equal to 1. • With two monitors hired, the current fine for over- time parking is $20. a. Assume first that all drivers are risk neutral. What parking fine would you levy, and how many meter monitors would you hire (1, 2, 3, or 4) to achieve the current level of deterrence against illegal parking at the minimum cost? b. Now assume that drivers are highly risk averse. How would your answer to (a) change? c. (For discussion) What if drivers could insure themselves against the risk of parking fines? Would it make good public policy to permit such insurance? 11. A moderately risk-averse investor has 50 percent of her portfolio invested in stocks and 50 percent in riskfree Treasury bills. Show how each of the following events will affect the investor’s budget line and the proportion of stocks in her portfolio: a. The standard deviation of the return on the stock market increases, but the expected return on the stock market remains the same. b. The expected return on the stock market increases, but the standard deviation of the stock market remains the same. c. The return on risk-free Treasury bills increases. 12. Suppose there are two types of e-book consumers: 100 “standard” consumers with demand Q 20 P and 100 “rule of thumb” consumers who buy 10 e-books only if the price is less than $10. (Their demand curve is given by Q 10 if P 10 and Q 0 if P 10.) Draw the resulting total demand curve for e-books. How has the “rule of thumb” behavior affected the elasticity of total demand for e-books? This page intentionally left blank C H A P T E R 6 Production In the last three chapters, we focused on the demand side of the market—the preferences and behavior of consumers. Now we turn to the supply side and examine the behavior of producers. We will see how firms can produce efficiently and how their costs of production change with changes in both input prices and the level of output. We will also see that there are strong similarities between the optimizing decisions made by firms and those made by consumers. In other words, understanding consumer behavior will help us understand producer behavior. In this chapter and the next we discuss the theory of the firm, which describes how a firm makes cost-minimizing production decisions and how the firm’s resulting cost varies with its output. Our knowledge of production and cost will help us understand the characteristics of market supply. It will also prove useful for dealing with problems that arise regularly in business. To see this, just consider some of the problems often faced by a company like General Motors. How much assembly-line machinery and how much labor should it use in its new automobile plants? If it wants to increase production, should it hire more workers, construct new plants, or both? Does it make more sense for one automobile plant to produce different models, or should each model be manufactured in a separate plant? What should GM expect its costs to be during the coming year? How are these costs likely to change over time and be affected by the level of production? These questions apply not only to business firms but also to other producers of goods and services, such as governments and nonprofit |
agencies. The Production Decisions of a Firm In Chapters 3 and 4, we studied consumer behavior by breaking it down into three steps. First, we explained how to describe consumer preferences. Second, we accounted for the fact that consumers face budget constraints. Third, we saw how, given their preferences and budget constraints, consumers can choose combinations of goods to maximize their satisfaction. The production decisions of firms are analogous to the purchasing decisions of consumers, and can likewise be understood in three steps: 1. Production Technology: We need a practical way of describing how inputs (such as labor, capital, and raw materials) can be .1 Firms and Their Production Decisions 202 6.2 Production with One Variable Input (Labor) 206 6.3 Production with Two Variable Inputs 216 6.4 Returns to Scale 223 .1 A Production Function for Health Care 211 6.2 Malthus and the Food Crisis 212 6.3 Labor Productivity and the Standard of Living 215 6.4 A Production Function for Wheat 221 6.5 Returns to Scale in the Carpet Industry 225 201 202 PART 2 • Producers, Consumers, and Competitive Markets • theory of the firm Explanation of how a firm makes cost-minimizing production decisions and how its cost varies with its output. transformed into outputs (such as cars and televisions). Just as a consumer can reach a level of satisfaction from buying different combinations of goods, the firm can produce a particular level of output by using different combinations of inputs. For example, an electronics firm might produce 10,000 televisions per month by using a substantial amount of labor (e.g., workers assembling the televisions by hand) and very little capital, or by building a highly automated capital-intensive factory and using very little labor. 2. Cost Constraints: Firms must take into account the prices of labor, capital, and other inputs. Just as a consumer is constrained by a limited budget, the firm will be concerned about its cost of production. For example, the firm that produces 10,000 televisions per month will want to do so in a way that minimizes its total production cost, which is determined in part by the prices of the inputs it uses. 3. Input Choices: Given its production technology and the prices of labor, capital, and other inputs, the firm must choose how much of each input to use in producing its output. Just as a consumer takes account of the prices of different goods when deciding how much of each good to buy, the firm must take into account the prices of different inputs when deciding how much of each input to use. If our electronics firm operates in a country with low wage rates, it may decide to produce televisions by using a large amount of labor, thereby using very little capital. These three steps are the building blocks of the theory of the firm, and we will discuss them in detail in this chapter and the next. We will also address other important aspects of firm behavior. For example, assuming that the firm is always using a cost-minimizing combination of inputs, we will see how its total cost of production varies with the quantity it produces and how it can choose that quantity to maximize its profit. We begin this chapter by discussing the nature of the firm and asking why firms exist in the first place. Next, we explain how the firm’s production technology can be represented in the form of a production function—a compact description of how inputs are turned into output. We then use the production function to show how the firm’s output changes when just one of its inputs (labor) is varied, holding the other inputs fixed. Next, we turn to the more general case in which the firm can vary all of its inputs, and we show how the firm chooses a costminimizing combination of inputs to produce its output. We will be particularly concerned with the scale of the firm’s operation. Are there, for example, any technological advantages that make the firm more productive as its scale increases? 6.1 Firms and Their Production Decisions Firms as we know them today are a relatively new invention. Prior to the mid1800s, almost all production was done by farmers, craftsmen, individuals who wove cloth and made clothing, and merchants and traders who bought and sold various goods. This was true in the U.S., Europe, and everywhere else in the world. The concept of a firm—run by managers separate from the firm’s owners, and who hire and manage a large number of workers—did not even exist. Modern corporations emerged only in the latter part of the 19th century.1 1The classic history of the development of the modern corporation is Alfred Chandler, Jr., The Visible Hand: The Managerial Revolution in American Business, Cambridge: Harvard University Press, 1977. CHAPTER 6 • Production 203 Today we take firms for granted. It is hard for us to imagine the production of automobiles without large companies like Ford and Toyota, the production of oil and natural gas without companies like Exxon-Mobil and Shell, or even the production of breakfast cereal without companies like Kellogg and General Mills. But stop for a minute and ask yourself whether we really need firms to produce the goods and services that we consume regularly. This was the question raised by Ronald Coase in a famous 1937 article: If markets work so well in allocating resources, why do we need firms?2 Why Do Firms Exist? Do we really need firms to produce cars? Why couldn’t cars be produced by a collection of individuals who worked independently and contracted with each other when appropriate, rather than being employed by General Motors? Couldn’t some people design a car (for a fee), other people buy steel, rent the equipment needed to stamp the steel into the shapes called for in the design, and then do the stamping (also for negotiated fees), other people make steering wheels and radiators, still other people assemble the various parts, and so on, where again, every task would be performed for a negotiated fee? Or take another example: We—the authors of this book—work for universities, which are essentially firms that provide educational services along with research. We are paid monthly salaries and in return are expected to teach regularly (to students recruited by our “firms” and in classrooms the “firms” provide), do research and write (in the offices our “firms” give us), and carry out administrative tasks. Couldn’t we simply bypass the universities and offer our teaching services on an hourly basis in rented classrooms to students who show up and pay us, and likewise do research on a paid piecemeal basis? Do we really need colleges and universities with all their overhead costs? In principle, cars could indeed be produced by a large number of independent workers, and an education could be produced by a number of independent teachers. These independent workers would offer their services for negotiated fees, and those fees would be determined by market supply and demand. It shouldn’t take you long, however, to realize that such a system of production would be extremely inefficient. Think about how difficult it would be for independent workers to decide who will do what to produce cars, and negotiate the fees that each worker will charge for each task. And if there were any change in the design of the car, all of these tasks and fees would have to be renegotiated. For cars produced this way, the quality would likely be abysmal, and the cost astronomical. Firms offer a means of coordination that is extremely important and would be sorely missing if workers operated independently. Firms eliminate the need for every worker to negotiate every task that he or she will perform, and bargain over the fees that will be paid for those tasks. Firms can avoid this kind of bargaining by having managers that direct the production of salaried workers—they tell workers what to do and when to do it, and the workers (as well as the managers themselves) are simply paid a weekly or monthly salary. There is no guarantee, of course, that a firm will operate efficiently, and there are many examples of firms that operate very inefficiently. Managers cannot always monitor what workers are doing, and managers themselves sometimes make 2Ronald Coase, “The Nature of the Firm,” Economica (1937), Vol. 4: 386–405. Coase won a Nobel Prize in Economics in 1991. 204 PART 2 • Producers, Consumers, and Competitive Markets • factors of production Inputs into the production process (e.g., labor, capital, and materials). • production function Function showing the highest output that a firm can produce for every specified combination of inputs. decisions that are in their interest, but not in the firm’s best interest. As a result, the theory of the firm (and more broadly, organizational economics) has become an important area of microeconomic research. The theory has both positive aspects (explaining why managers and workers behave the way they do) and normative aspects (explaining how firms can be best organized so that they operate as efficiently as possible).3 We will discuss some aspects of the theory later in this book. At this point we simply stress that firms exist because they allow goods and services to be produced far more efficiently than would be possible without them. The Technology of Production What do firms do? We have seen that firms organize and coordinate the activities of large numbers of workers and managers. But to what purpose? At the most fundamental level, firms take inputs and turn them into outputs (or products). This production process, turning inputs into outputs, is the essence of what a firm does. Inputs, which are also called factors of production, include anything that the firm must use as part of the production process. In a bakery, for example, inputs include the labor of its workers; raw materials, such as flour and sugar; and the capital invested in its ovens, mixers, and other equipment needed to produce such outputs as bread, cakes, and p |
astries. As you can see, we can divide inputs into the broad categories of labor, materials, and capital, each of which might include more narrow subdivisions. Labor inputs include skilled workers (carpenters, engineers) and unskilled workers (agricultural workers), as well as the entrepreneurial efforts of the firm’s managers. Materials include steel, plastics, electricity, water, and any other goods that the firm buys and transforms into final products. Capital includes land, buildings, machinery and other equipment, as well as inventories. The Production Function Firms can turn inputs into outputs in a variety of ways, using various combinations of labor, materials, and capital. We can describe the relationship between the inputs into the production process and the resulting output by a production function. A production function indicates the highest output q that a firm can produce for every specified combination of inputs.4 Although in practice firms use a wide variety of inputs, we will keep our analysis simple by focusing on only two, labor L and capital K. We can then write the production function as q = F(K, L) (6.1) This equation relates the quantity of output to the quantities of the two inputs, capital and labor. For example, the production function might describe the number of personal computers that can be produced each year with a 10,000-squarefoot plant and a specific amount of assembly-line labor. Or it might describe the crop that a farmer can obtain using specific amounts of machinery and workers. It is important to keep in mind that inputs and outputs are flows. For example, our PC manufacturer uses a certain amount of labor each year to produce some number of computers over that year. Although it might own its plant and 3The literature on the theory of the firm is vast. One of the classics is Oliver Williamson, Markets and Hierarchies: Analysis and Antitrust Implications, New York: Free Press, 1975. (Williamson won a Nobel Prize for his work in 2009.) 4In this chapter and those that follow, we will use the variable q for the output of the firm, and Q for the output of the industry. CHAPTER 6 • Production 205 machinery, we can think of the firm as paying a cost for the use of that plant and machinery over the year. To simplify things, we will frequently ignore the reference to time and refer only to amounts of labor, capital, and output. Unless otherwise indicated, however, we mean the amount of labor and capital used each year and the amount of output produced each year. Because the production function allows inputs to be combined in varying proportions, output can be produced in many ways. For the production function in equation (6.1), this could mean using more capital and less labor, or vice versa. For example, wine can be produced in a labor-intensive way using many workers, or in a capital-intensive way using machines and only a few workers. Note that equation (6.1) applies to a given technology—that is, to a given state of knowledge about the various methods that might be used to transform inputs into outputs. As the technology becomes more advanced and the production function changes, a firm can obtain more output for a given set of inputs. For example, a new, faster assembly line may allow a hardware manufacturer to produce more high-speed computers in a given period of time. Production functions describe what is technically feasible when the firm operates efficiently—that is, when the firm uses each combination of inputs as effectively as possible. The presumption that production is always technically efficient need not always hold, but it is reasonable to expect that profit-seeking firms will not waste resources. The Short Run versus the Long Run It takes time for a firm to adjust its inputs to produce its product with differing amounts of labor and capital. A new factory must be planned and built, and machinery and other capital equipment must be ordered and delivered. Such activities can easily take a year or more to complete. As a result, if we are looking at production decisions over a short period of time, such as a month or two, the firm is unlikely to be able to substitute very much capital for labor. Because firms must consider whether or not inputs can be varied, and if they can, over what period of time, it is important to distinguish between the short and long run when analyzing production. The short run refers to a period of time in which the quantities of one or more factors of production cannot be changed. In other words, in the short run there is at least one factor that cannot be varied; such a factor is called a fixed input. The long run is the amount of time needed to make all inputs variable. As you might expect, the kinds of decisions that firms can make are very different in the short run than those made in the long run. In the short run, firms vary the intensity with which they utilize a given plant and machinery; in the long run, they vary the size of the plant. All fixed inputs in the short run represent the outcomes of previous long-run decisions based on estimates of what a firm could profitably produce and sell. There is no specific time period, such as one year, that separates the short run from the long run. Rather, one must distinguish them on a case-by-case basis. For example, the long run can be as brief as a day or two for a child’s lemonade stand or as long as five or ten years for a petrochemical producer or an automobile manufacturer. We will see that in the long run firms can vary the amounts of all their inputs to minimize the cost of production. Before treating this general case, however, we begin with an analysis of the short run, in which only one input to the production process can be varied. We assume that capital is the fixed input, and labor is variable. • short run Period of time in which quantities of one or more production factors cannot be changed. • fixed input Production factor that cannot be varied. • long run Amount of time needed to make all production inputs variable. 206 PART 2 • Producers, Consumers, and Competitive Markets 6.2 Production with One Variable Input (Labor) When deciding how much of a particular input to buy, a firm has to compare the benefit that will result with the cost of that input. Sometimes it is useful to look at the benefit and the cost on an incremental basis by focusing on the additional output that results from an incremental addition to an input. In other situations, it is useful to make the comparison on an average basis by considering the result of substantially increasing an input. We will look at benefits and costs in both ways. When capital is fixed but labor is variable, the only way the firm can produce more output is by increasing its labor input. Imagine, for example, that you are managing a clothing factory. Although you have a fixed amount of equipment, you can hire more or less labor to sew and to run the machines. You must decide how much labor to hire and how much clothing to produce. To make the decision, you will need to know how the amount of output q increases (if at all) as the input of labor L increases. Table 6.1 gives this information. The first three columns show the amount of output that can be produced in one month with different amounts of labor and capital fixed at 10 units. The first column shows the amount of labor, the second the fixed amount of capital, and the third total output. When labor input is zero, output is also zero. Output then increases as labor is increased up to an input of 8 units. Beyond that point, total output declines: Although initially each unit of labor can take greater and greater advantage of the existing machinery and plant, after a certain point, additional labor is no longer useful and indeed can be counterproductive. Five people can run an assembly line better than two, but ten people may get in one another’s way. Average and Marginal Products The contribution that labor makes to the production process can be described on both an average and a marginal (i.e., incremental) basis. The fourth column in Table 6.1 shows the average product of labor (APL ), which is the output per TABLE 6.1 PRODUCTION WITH ONE VARIABLE INPUT AMOUNT OF LABOR (L) AMOUNT OF CAPITAL (K ) TOTAL OUTPUT (q) AVERAGE PRODUCT (q/L) MARGINAL PRODUCT (q/L 10 10 10 10 10 10 10 10 10 10 10 10 0 10 30 60 80 95 108 112 112 108 100 — 10 15 20 20 19 18 16 14 12 10 — 10 20 30 20 15 13 4 0 4 8 • average product Output per unit of a particular input. CHAPTER 6 • Production 207 • marginal product Additional output produced as an input is increased by one unit. unit of labor input. The average product is calculated by dividing the total output q by the total input of labor L. The average product of labor measures the productivity of the firm’s workforce in terms of how much output each worker produces on average. In our example, the average product increases initially but falls when the labor input becomes greater than four. The fifth column of Table 6.1 shows the marginal product of labor (MPL). This is the additional output produced as the labor input is increased by 1 unit. For example, with capital fixed at 10 units, when the labor input increases from 2 to 3, total output increases from 30 to 60, creating an additional output of 30 (i.e., 60–30) units. The marginal product of labor can be written as q/L—in other words, the change in output q resulting from a 1-unit increase in labor input L. Remember that the marginal product of labor depends on the amount of capital used. If the capital input increased from 10 to 20, the marginal product of labor most likely would increase. Why? Because additional workers are likely to be more productive if they have more capital to use. Like the average product, the marginal product first increases then falls—in this case, after the third unit of labor. To summarize: Average product of labor = Output/labor input = q/L Marginal product of labor |
= Change in output/change in labor input = q/L The Slopes of the Product Curve Figure 6.1 plots the information contained in Table 6.1. (We have connected all the points in the figure with solid lines.) Figure 6.1 (a) shows that as labor is increased, output increases until it reaches the maximum output of 112; thereafter, it falls. The portion of the total output curve that is declining is drawn with a dashed line to denote that producing with more than eight workers is not economically rational; it can never be profitable to use additional amounts of a costly input to produce less output. Figure 6.1 (b) shows the average and marginal product curves. (The units on the vertical axis have changed from output per month to output per worker per month.) Note that the marginal product is positive as long as output is increasing, but becomes negative when output is decreasing. It is no coincidence that the marginal product curve crosses the horizontal axis of the graph at the point of maximum total product. This happens because adding a worker in a manner that slows production and decreases total output implies a negative marginal product for that worker. The average product and marginal product curves are closely related. When the marginal product is greater than the average product, the average product is increasing. This is the case for labor inputs up to 4 in Figure 6.1 (b). If the output of an additional worker is greater than the average output of each existing worker (i.e., the marginal product is greater than the average product), then adding the worker causes average output to rise. In Table 6.1, two workers produce 30 units of output, for an average product of 15 units per worker. Adding a third worker increases output by 30 units (to 60), which raises the average product from 15 to 20. Similarly, when the marginal product is less than the average product, the average product is decreasing. This is the case when the labor input is greater than 4 in Figure 6.1 (b). In Table 6.1, six workers produce 108 units of output, for an average product of 18. Adding a seventh worker contributes a marginal product of only 4 units (less than the average product), reducing the average product to 16. 208 PART 2 • Producers, Consumers, and Competitive Markets FIGURE 6.1 PRODUCTION WITH ONE VARIABLE INPUT The total product curve in (a) shows the output produced for different amounts of labor input. The average and marginal products in (b) can be obtained (using the data in Table 6.1) from the total product curve. At point A in (a), the marginal product is 20 because the tangent to the total product curve has a slope of 20. At point B in (a) the average product of labor is 20, which is the slope of the line from the origin to B. The average product of labor at point C in (a) is given by the slope of the line 0C. To the left of point E in (b), the marginal product is above the average product and the average is increasing; to the right of E, the marginal product is below the average product and the average is decreasing. As a result, E represents the point at which the average and marginal products are equal, when the average product reaches its maximum. Output per month 112 60 30 Output per worker per month 20 10 D C Total Product 10 Labor per Month E 0 1 2 3 4 5 (a) 6 (b) Average Product Marginal Product 7 8 9 10 Labor per month We have seen that the marginal product is above the average product when the average product is increasing and below the average product when the average product is decreasing. It follows, therefore, that the marginal product must equal the average product when the average product reaches its maximum. This happens at point E in Figure 6.1 (b). Why, in practice, should we expect the marginal product curve to rise and then fall? Think of a television assembly plant. Fewer than ten workers might be insufficient to operate the assembly line at all. Ten to fifteen workers might be able to run the assembly line, but not very efficiently. If adding a few more workers allowed the assembly line to operate much more efficiently, the marginal product of those workers would be very high. This added efficiency, however, might start to diminish once there were more than 20 workers. The marginal product of the twenty-second worker, for example, might still be very high (and above the average product), but not as high as the marginal product of the nineteenth or twentieth worker. The marginal product of the twenty-fifth worker might be lower still, perhaps equal to the average product. With 30 workers, adding one more worker would yield more output, but not very CHAPTER 6 • Production 209 much more (so that the marginal product, while positive, would be below the average product). Once there were more than 40 workers, additional workers would simply get in each other’s way and actually reduce output (so that the marginal product would be negative). The Average Product of Labor Curve The geometric relationship between the total product and the average and marginal product curves is shown in Figure 6.1 (a). The average product of labor is the total product divided by the quantity of labor input. At B, for example, the average product is equal to the output of 60 divided by the input of 3, or 20 units of output per unit of labor input. This ratio, however, is exactly the slope of the line running from the origin to B in Figure 6.1 (a). In general, the average product of labor is given by the slope of the line drawn from the origin to the corresponding point on the total product curve. The Marginal Product of Labor Curve As we have seen, the marginal product of labor is the change in the total product resulting from an increase of one unit of labor. At A, for example, the marginal product is 20 because the tangent to the total product curve has a slope of 20. In general, the marginal product of labor at a point is given by the slope of the total product at that point. We can see in Figure 6.1 (b) that the marginal product of labor increases initially, peaks at an input of 3, and then declines as we move up the total product curve to C and D. At D, when total output is maximized, the slope of the tangent to the total product curve is 0, as is the marginal product. Beyond that point, the marginal product becomes negative. THE RELATIONSHIP BETWEEN THE AVERAGE AND MARGINAL PRODUCTS Note the graphical relationship between average and marginal products in Figure 6.1 (a). At B, the marginal product of labor (the slope of the tangent to the total product curve at B—not shown explicitly) is greater than the average product (dashed line 0B). As a result, the average product of labor increases as we move from B to C. At C, the average and marginal products of labor are equal: While the average product is the slope of the line from the origin, 0C, the marginal product is the tangent to the total product curve at C (note the equality of the average and marginal products at point E in Figure 6.1 (b)). Finally, as we move beyond C toward D, the marginal product falls below the average product; you can check that the slope of the tangent to the total product curve at any point between C and D is lower than the slope of the line from the origin. The Law of Diminishing Marginal Returns A diminishing marginal product of labor (as well as a diminishing marginal product of other inputs) holds for most production processes. The law of diminishing marginal returns states that as the use of an input increases in equal increments (with other inputs fixed), a point will eventually be reached at which the resulting additions to output decrease. When the labor input is small (and capital is fixed), extra labor adds considerably to output, often because workers are allowed to devote themselves to specialized tasks. Eventually, however, the law of diminishing marginal returns applies: When there are too many workers, some workers become ineffective and the marginal product of labor falls. The law of diminishing marginal returns usually applies to the short run when at least one input is fixed. However, it can also apply to the long run. • law of diminishing marginal returns Principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease. 210 PART 2 • Producers, Consumers, and Competitive Markets Even though inputs are variable in the long run, a manager may still want to analyze production choices for which one or more inputs are unchanged. Suppose, for example, that only two plant sizes are feasible and that management must decide which to build. In that case, management would want to know when diminishing marginal returns will set in for each of the two options. Do not confuse the law of diminishing marginal returns with possible changes in the quality of labor as labor inputs are increased (as would likely occur, for example, if the most highly qualified laborers are hired first and the least qualified last). In our analysis of production, we have assumed that all labor inputs are of equal quality; diminishing marginal returns results from limitations on the use of other fixed inputs (e.g., machinery), not from declines in worker quality. In addition, do not confuse diminishing marginal returns with negative returns. The law of diminishing marginal returns describes a declining marginal product but not necessarily a negative one. The law of diminishing marginal returns applies to a given production technology. Over time, however, inventions and other improvements in technology may allow the entire total product curve in Figure 6.1 (a) to shift upward, so that more output can be produced with the same inputs. Figure 6.2 illustrates this principle. Initially the output curve is given by O1, but improvements in technology may allow the curve to shift upward, first to O2, and later to O3. Suppose, for example, that over time, as labor is increased in agricultural production, techno |
logical improvements are being made. These improvements might include genetically engineered pest-resistant seeds, more powerful and effective fertilizers, and better farm equipment. As a result, output changes from A (with an input of 6 on curve O1) to B (with an input of 7 on curve O2) to C (with an input of 8 on curve O3). The move from A to B to C relates an increase in labor input to an increase in output and makes it appear that there are no diminishing marginal returns when in fact there are. Indeed, the shifting of the total product curve suggests that there may be no negative long-run implications for economic growth. In fact, as FIGURE 6.2 THE EFFECT OF TECHNOLOGICAL IMPROVEMENT Labor productivity (output per unit of labor) can increase if there are improvements in technology, even though any given production process exhibits diminishing returns to labor. As we move from point A on curve O1 to B on curve O2 to C on curve O3 over time, labor productivity increases. Output per time period 100 50 C B A O3 O2 O1 10 Labor per time period we can see in Example 6.1, the failure to account for long-run improvements in technology led British economist Thomas Malthus wrongly to predict dire consequences from continued population growth. CHAPTER 6 • Production 211 EXAM PLE 6.1 A PRODUCTION FUNCTION FOR HEALTH CARE Expenditures on health care have increased rapidly in many countries. This is especially true in the United States, which has been spending 15% of its GDP on health care in recent years. But other countries also devote substantial resources to health care (e.g., 11% of GDP in France and Germany and 8% of GDP in Japan and the United Kingdom). Do these increased expenditures reflect increases in output or do they reflect inefficiencies in the production process? Figure 6.3 shows a production function for health care in the United States.5 The vertical axis utilizes one possible measure of health output, the average increase in life expectancy for the population. (Another measure of output might be reductions in the average numbers of heart attacks or strokes.) The horizontal axis measures thousands of dollars spent on health care inputs, which include expenditures on doctors, nurses, administrators, hospital equipment, and drugs. The production function represents C B D Increased Life Expectancy (years) 8 7 6 4 A FIGURE 6.3 A PRODUCTION FUNCTION FOR HEALTH CARE Additional expenditures on health care (inputs) increase life expectancy (output) along the production frontier. Points A, B, and C represent points at which inputs are efficiently utilized, although there are diminishing returns when moving from B to C. Point D is a point of input inefficiency. 0 10 30 50 Input Expenditures per person ($000) 5This example is based on Alan M. Garber and Jonathan Skinner, “Is American Health Care Uniquely Inefficient?” Journal of Economic Perspectives, Vol. 22, No. 4 (Fall 2008): 27–50. 212 PART 2 • Producers, Consumers, and Competitive Markets the maximum achievable health outcome for the population as a whole, as a function of the dollars spent per capita on health care inputs. Points on the production function such as A, B, and C are by construction inputs that are being used as efficiently as possible to produce output. Point D, which lies below the production function, is inefficient in that the health care inputs associated with D do not generate the maximum possible health output. Notice that the production function exhibits diminishing returns: it becomes relatively flat as more and more money is spent on health care. For example, the health output at point B is quite a bit higher than the output at point A since the marginal productivity of health care expenditures is high. Starting at point A, an additional $20,000 of health expenditures (from $10,000 to $30,000) increases life expectancy by 3 years. However, output at C is only slightly higher than the output at B, even though the difference in health inputs is large. In moving from B to C, an additional $20,000 of health expenditures increases life expectancy by only 1 year. Why is this? The answer is that given current medical technologies, additional expenditures on medical procedures and/or the use of newer drugs has only a minimal effect on life expectancy rates. Thus the marginal productivity of dollars expended on health has become less and less effective as the expenditure level increases. We can now see one possible explanation for the high level of health-care expenditures in the United States. The United States is relatively wealthy, and it is natural for consumer preferences to shift toward more health care as incomes grow, even as it becomes more and more expensive to obtain even modest increases in life expectancy. (Recall our discussion of health care choice in Example 3.4.) Thus, Americans may have been seeking better and bet- ter medical outcomes, but with limited success, given the shape of the health care production function. In other words, compared to other countries, the United States may be operating farther to the right along the flat portion of the health-care production function. There is another explanation, however. It may be that the production of health care in the United States is inefficient, i.e., higher medical outputs could be achieved with the same or similar input expenditures if those expenditures were more effectively utilized. In Figure 6.3, this is shown as a move from point D to point B; here with no additional expenditure life expectancy is increased by 1 year by using inputs more efficiently. A comparison of various measures of health and health care across a number of developed countries suggests that this may indeed be the case. First, only 28 percent of primary care physicians use electronic health records in the United States, compared to 89 percent in the United Kingdom and 98 percent in the Netherlands. Second, the percentage of chronically ill patients that did not pursue care, did not follow recommended treatments, or did not take fully recommended medications was 42 percent in the United States compared to 9 percent in the United Kingdom and 20 percent in Germany. Third, the billing, insurance, and credentialing system is more complex and burdensome in the United States than in many other countries, so the number of health care administrative personnel per capita is greater. Both explanations for U.S. health care spending probably have some validity. It is likely that the United States indeed suffers from inefficiency in health care production. It is also likely that as U.S. incomes grow, people will demand more and more health care relative to other goods, so that with diminishing returns, the incremental health benefits will be limited. E XAM PLE 6.2 MALTHUS AND THE FOOD CRISIS The law of diminishing marginal returns was central to the thinking of political economist Thomas Malthus (1766–1834).6 Malthus believed that the world’s limited amount of land would not be able to supply enough food as the population grew. He predicted that as both the marginal and average productivity of labor fell and there were more mouths to feed, mass hunger and starvation would result. Fortunately, 6Thomas Malthus, Essay on the Principle of Population, 1798. Malthus was wrong (although he was right about the diminishing marginal returns to labor). Over the past century, technological improvements have dramatically altered food production in most countries (including developing countries, such as India). As a result, the average product of labor and total food output have increased. These improvements include new high-yielding, disease-resistant strains of seeds, better fertilizers, and better harvesting equipment. As the food production index in Table 6.2 shows, overall food production throughout the world has outpaced population growth continually since 1960.7 This increase in world agricultural productivity is also illustrated in Figure 6.4, which shows average cereal yields from 1970 through 2005, along with a world price index for food.8 Note that cereal yields have increased steadily over the period. Because growth in agricultural productivity led to increases in food supplies that ) 350 300 250 200 150 100 50 CHAPTER 6 • Production 213 TABLE 6.2 INDEX OF WORLD FOOD PRODUCTION PER CAPITA YEAR 1948-52 1961 1965 1970 1975 1980 1985 1990 1995 2000 2005 2009 Cereal Yield Food Price Index INDEX 100 115 119 124 125 127 134 135 135 144 151 155 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1. ) 1970 1975 1980 1985 1990 1995 2000 2005 2010 FIGURE 6.4 CEREAL YIELDS AND THE WORLD PRICE OF FOOD Cereal yields have increased. The average world price of food increased temporarily in the early 1970s but has declined since. 7World per capita food production data are from the United Nations Food and Agriculture Organization (FAO). See also http://faostat.fao.org. 8Data are from the United Nations Food and Agriculture Organization and the World Bank. See also http://faostat.fao.org. 214 PART 2 • Producers, Consumers, and Competitive Markets outstripped the growth in demand, prices, apart from a temporary increase in the early 1970s, have been declining. Hunger remains a severe problem in some areas, such as the Sahel region of Africa, in part because of the low productivity of labor there. Although other countries produce an agricultural surplus, mass hunger still occurs because of the difficulty of redistributing food from more to less productive regions of the world and because of the low incomes of those less productive regions. • labor productivity Average product of labor for an entire industry or for the economy as a whole. • stock of capital Total amount of capital available for use in production. • technological change Development of new technologies allowing factors of production to be used more effectively. Labor Productivity Although this is a textbook in microeconomics, many of the concepts developed here provide a foundation |
for macroeconomic analysis. Macroeconomists are particularly concerned with labor productivity—the average product of labor for an entire industry or for the economy as a whole. In this subsection we discuss labor productivity in the United States and a number of foreign countries. This topic is interesting in its own right, but will also help to illustrate one of the links between micro- and macroeconomics. Because the average product measures output per unit of labor input, it is relatively easy to measure (total labor input and total output are the only pieces of information you need). Labor productivity can provide useful comparisons across industries and for one industry over a long period. But labor productivity is especially important because it determines the real standard of living that a country can achieve for its citizens. PRODUCTIVITY AND THE STANDARD OF LIVING There is a simple link between labor productivity and the standard of living. In any particular year, the aggregate value of goods and services produced by an economy is equal to the payments made to all factors of production, including wages, rental payments to capital, and profit to firms. Consumers ultimately receive these factor payments in the form of wages, salaries, dividends, or interest payments. As a result, consumers in the aggregate can increase their rate of consumption in the long run only by increasing the total amount they produce. Understanding the causes of productivity growth is an important area of research in economics. We do know that one of the most important sources of growth in labor productivity is growth in the stock of capital—i.e., the total amount of capital available for use in production. Because an increase in capital means more and better machinery, each worker can produce more output for each hour worked. Another important source of growth in labor productivity is technological change—i.e., the development of new technologies that allow labor (and other factors of production) to be used more effectively and to produce new and higher-quality goods. As Example 6.3 shows, levels of labor productivity have differed considerably across countries, as have rates of growth of productivity. Given the central role that productivity has in affecting our standards of living, understanding these differences is important. EXAM PLE 6.3 LABOR PRODUCTIVITY AND THE STANDARD OF LIVING CHAPTER 6 • Production 215 Will the standard of living in the United States, Europe, and Japan continue to improve, or will these economies barely keep future generations from being worse off than they are today? Because the real incomes of consumers in these countries increase only as fast as productivity does, the answer depends on the labor productivity of workers. As Table 6.3 shows, the level of the stock of capital in each country. The greatest capital growth during the postwar period was in Japan, France, and Germany, which were rebuilt substantially after World War II. To some extent, therefore, the lower rate of growth of productivity in the United States, when compared to that of Japan, France, and Germany, is the result of these countries catching up after the war. output per employed person in the United States in 2009 was higher than in other industrial countries. But two patterns over the post–World War II period have been disturbing. First, until the 1990s, productivity in the United States grew on average less rapidly than productivity in most other developed nations. Second, productivity growth during 1974–2009 was much lower in all developed countries than it had been in the past.9 Throughout most of the 1960–1991 period, Japan had the highest rate of productivity growth, followed by Germany and France. U.S. productivity growth was the lowest, even somewhat lower than that of the United Kingdom. This is partly due to differences in rates of investment and growth in Productivity growth is also tied to the natural resource sector of the economy. As oil and other resources began to be depleted, output per worker fell. Environmental regulations (e.g., the need to restore land to its original condition after stripmining for coal) magnified this effect as the public became more concerned with the importance of cleaner air and water. Observe from Table 6.3 that productivity growth in the United States accelerated in the 1990s. Some economists believe that information and communication technology (ICT) has been the key impetus for this growth. However, sluggish growth in more recent years suggests that ICT’s contribution may have already peaked. TABLE 6.3 LABOR PRODUCTIVITY IN DEVELOPED COUNTRIES UNITED STATES JAPAN FRANCE GERMANY UNITED KINGDOM GDP PER HOUR WORKED (IN 2009 US DOLLARS) $56.90 $38.20 $54.70 $53.10 $45.80 Years 1960–1973 1974–1982 1983–1991 1992–2000 2001–2009 Annual Rate of Growth of Labor Productivity (%) 2.29 0.22 1.54 1.94 1.90 7.86 2.29 2.64 1.08 1.50 4.70 1.73 1.50 1.40 0.90 3.98 2.28 2.07 1.64 0.80 2.84 1.53 1.57 2.22 1.30 9Recent growth numbers on GDP, employment, and PPP data are from the OECD. For more information, visit http://www.oecd.org: select Frequently Requested Statistics within the Statistics directory. 216 PART 2 • Producers, Consumers, and Competitive Markets • isoquant Curve showing all possible combinations of inputs that yield the same output. 6.3 Production with Two Variable Inputs We have completed our analysis of the short-run production function in which one input, labor, is variable, and the other, capital, is fixed. Now we turn to the long run, for which both labor and capital are variable. The firm can now produce its output in a variety of ways by combining different amounts of labor and capital. In this section, we will see how a firm can choose among combinations of labor and capital that generate the same output. In the first subsection, we will examine the scale of the production process, analyzing how output changes as input combinations are doubled, tripled, and so on. Isoquants Let’s begin by examining the production technology of a firm that uses two inputs and can vary both of them. Suppose that the inputs are labor and capital and that they are used to produce food. Table 6.4 tabulates the output achievable for various combinations of inputs. Labor inputs are listed across the top row, capital inputs down the column on the left. Each entry in the table is the maximum (technically efficient) output that can be produced each year with each combination of labor and capital used over that year. For example, 4 units of labor per year and 2 units of capital per year yield 85 units of food per year. Reading along each row, we see that output increases as labor inputs are increased, while capital inputs remain fixed. Reading down each column, we see that output also increases as capital inputs are increased, while labor inputs remain fixed. The information in Table 6.4 can also be represented graphically using isoquants. An isoquant is a curve that shows all the possible combinations of inputs that yield the same output. Figure 6.5 shows three isoquants. (Each axis in the figure measures the quantity of inputs.) These isoquants are based on the data in Table 6.4, but are drawn as smooth curves to allow for the use of fractional amounts of inputs. For example, isoquant q1 shows all combinations of labor and capital per year that together yield 55 units of output per year. Two of these points, A and D, correspond to Table 6.4. At A, 1 unit of labor and 3 units of capital yield 55 units of output; at D, the same output is produced from 3 units of labor and 1 unit of capital. Isoquant q2 shows all combinations of inputs that yield 75 units of output and corresponds to the four combinations of labor and capital circled in the table (e.g., at B, where 2 units of labor and 3 units of capital are combined). Isoquant q2 lies above and to the right of q1 because obtaining a higher level of output requires TABLE 6.4 PRODUCTION WITH TWO VARIABLE INPUTS CAPITAL INPUT 1 2 3 4 5 1 20 40 55 65 75 LABOR INPUT 2 40 60 75 85 90 3 55 75 90 100 105 4 65 85 100 110 115 5 75 90 105 115 120 Capital per year 90 q3 75 q2 55 q1 1 2 3 4 5 Labor per year CHAPTER 6 • Production 217 FIGURE 6.5 PRODUCTION WITH TWO VARIABLE INPUTS Production isoquants show the various combinations of inputs necessary for the firm to produce a given output. A set of isoquants, or isoquant map, describes the firm’s production function. Output increases as we move from isoquant q1 (at which 55 units per year are produced at points such as A and D), to isoquant q2 (75 units per year at points such as B), and to isoquant q3 (90 units per year at points such as C and E ). more labor and capital. Finally, isoquant q3 shows labor-capital combinations that yield 90 units of output. Point C, for example, involves 3 units of labor and 3 units of capital, whereas Point E involves 2 units of labor and 5 units of capital. ISOQUANT MAPS When a number of isoquants are combined in a single graph, we call the graph an isoquant map. Figure 6.5 shows three of the many isoquants that make up an isoquant map. An isoquant map is another way of describing a production function, just as an indifference map is a way of describing a utility function. Each isoquant corresponds to a different level of output, and the level of output increases as we move up and to the right in the figure. • isoquant map Graph combining a number of isoquants, used to describe a production function. Input Flexibility Isoquants show the flexibility that firms have when making production decisions: They can usually obtain a particular output by substituting one input for another. It is important for managers to understand the nature of this flexibility. For example, fast-food restaurants have recently faced shortages of young, low-wage employees. Companies have responded by automating—adding selfservice salad bars and introducing more sophisticated cooking equipment. They have also r |
ecruited older people to fill positions. As we will see in Chapters 7 and 8, by taking into account this flexibility in the production process, managers can choose input combinations that minimize cost and maximize profit. Diminishing Marginal Returns Even though both labor and capital are variable in the long run, it is useful for a firm that is choosing the optimal mix of inputs to ask what happens to output as each input is increased, with the other input held fixed. The outcome of this exercise is described in Figure 6.5, which reflects diminishing marginal returns to both labor and capital. We can see why there are diminishing marginal returns to labor by drawing a horizontal line at a particular level of capital—say, 3. Reading the levels of output from each isoquant as labor is increased, we note that each additional unit of labor generates less and less additional output. For example, 218 PART 2 • Producers, Consumers, and Competitive Markets when labor is increased from 1 unit to 2 (from A to B), output increases by 20 (from 55 to 75). However, when labor is increased by an additional unit (from B to C), output increases by only 15 (from 75 to 90). Thus there are diminishing marginal returns to labor both in the long and short run. Because adding one factor while holding the other factor constant eventually leads to lower and lower incremental output, the isoquant must become steeper as more capital is added in place of labor and flatter when labor is added in place of capital. There are also diminishing marginal returns to capital. With labor fixed, the marginal product of capital decreases as capital is increased. For example, when capital is increased from 1 to 2 and labor is held constant at 3, the marginal product of capital is initially 20 (75 – 55) but falls to 15 (90 – 75) when capital is increased from 2 to 3. Substitution Among Inputs With two inputs that can be varied, a manager will want to consider substituting one input for another. The slope of each isoquant indicates how the quantity of one input can be traded off against the quantity of the other, while output is held constant. When the negative sign is removed, we call the slope the marginal rate of technical substitution (MRTS). The marginal rate of technical substitution of labor for capital is the amount by which the input of capital can be reduced when one extra unit of labor is used, so that output remains constant. This is analogous to the marginal rate of substitution (MRS) in consumer theory. Recall from Section 3.1 that the MRS describes how consumers substitute among two goods while holding the level of satisfaction constant. Like the MRS, the MRTS is always measured as a positive quantity: MRTS = -Change in capital input/change in labor input = - K/L(for a fixed level of q) where K and L are small changes in capital and labor along an isoquant. In Figure 6.6 the MRTS is equal to 2 when labor increases from 1 unit to 2 and output is fixed at 75. However, the MRTS falls to 1 when labor is increased from • marginal rate of technical substitution (MRTS) Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant. In §3.1, we explain that the marginal rate of substitution is the maximum amount of one good that the consumer is willing to give up to obtain one unit of another good. FIGURE 6.6 MARGINAL RATE OF TECHNICAL SUBSTITUTION Like indifference curves, isoquants are downward sloping and convex. The slope of the isoquant at any point measures the marginal rate of technical substitution—the ability of the firm to replace capital with labor while maintaining the same level of output. On isoquant q2, the MRTS falls from 2 to 1 to 2/3 to 1/3. Capital per year q3 = 90 q2 = 75 L = 1 q1 = 55 1 2 3 4 5 Labor per year CHAPTER 6 • Production 219 2 units to 3, and then declines to 2/3 and to 1/3. Clearly, as more and more labor replaces capital, labor becomes less productive and capital becomes relatively more productive. Therefore, we need less capital to keep output constant, and the isoquant becomes flatter. DIMINISHING MRTS We assume that there is a diminishing MRTS. In other words, the MRTS falls as we move down along an isoquant. The mathematical implication is that isoquants, like indifference curves, are convex, or bowed inward. This is indeed the case for most production technologies. The diminishing MRTS tells us that the productivity of any one input is limited. As more and more labor is added to the production process in place of capital, the productivity of labor falls. Similarly, when more capital is added in place of labor, the productivity of capital falls. Production needs a balanced mix of both inputs. As our discussion has just suggested, the MRTS is closely related to the marginal products of labor MPL and capital MPK. To see how, imagine adding some labor and reducing the amount of capital sufficient to keep output constant. The additional output resulting from the increased labor input is equal to the additional output per unit of additional labor (the marginal product of labor) times the number of units of additional labor: Additional output from increased use of labor = (MPL)(L) Similarly, the decrease in output resulting from the reduction in capital is the loss of output per unit reduction in capital (the marginal product of capital) times the number of units of capital reduction: Reduction in output from decreased use of capital = (MPK)(K) Because we are keeping output constant by moving along an isoquant, the total change in output must be zero. Thus, (MPL)(L) + (MPK)(K) = 0 Now, by rearranging terms we see that (MPL)/(MPK) = -(K/L) = MRTS (6.2) Equation (6.2) tells us that the marginal rate of technical substitution between two inputs is equal to the ratio of the marginal products of the inputs. This formula will be useful when we look at the firm’s cost-minimizing choice of inputs in Chapter 7. In §3.1, we explain that an indifference curve is convex if the marginal rate of substitution diminishes as we move down along the curve. Production Functions—Two Special Cases Two extreme cases of production functions show the possible range of input substitution in the production process. In the first case, shown in Figure 6.7, inputs to production are perfect substitutes for one another. Here the MRTS is constant at all points on an isoquant. As a result, the same output (say q3) can be produced with mostly capital (at A), with mostly labor (at C), or with a balanced combination of both (at B). For example, musical instruments can be manufactured almost entirely with machine tools or with very few tools and highly skilled labor. Figure 6.8 illustrates the opposite extreme, the fixed-proportions production function, sometimes called a Leontief production function. In this case, In §3.1, we explain that two goods are perfect substitutes if the marginal rate of substitution of one for the other is a constant. • fixed-proportions production function Production function with L-shaped isoquants, so that only one combination of labor and capital can be used to produce each level of output. 220 PART 2 • Producers, Consumers, and Competitive Markets Capital per year A FIGURE 6.7 ISOQUANTS WHEN INPUTS ARE PERFECT SUBSTITUTES When the isoquants are straight lines, the MRTS is constant. Thus the rate at which capital and labor can be substituted for each other is the same no matter what level of inputs is being used. Points A, B, and C represent three different capital-labor combinations that generate the same output q3. B C q1 q2 q3 Labor per year it is impossible to make any substitution among inputs. Each level of output requires a specific combination of labor and capital: Additional output cannot be obtained unless more capital and labor are added in specific proportions. As a result, the isoquants are L-shaped, just as indifference curves are L-shaped when two goods are perfect complements. An example is the reconstruction of concrete sidewalks using jackhammers. It takes one person to use a jackhammer— neither two people and one jackhammer nor one person and two jackhammers will increase production. As another example, suppose that a cereal company offers a new breakfast cereal, Nutty Oat Crunch, whose two inputs, not surprisingly, are oats and nuts. The secret formula for the cereal requires exactly one FIGURE 6.8 FIXED-PROPORTIONS PRODUCTION FUNCTION When the isoquants are L-shaped, only one combination of labor and capital can be used to produce a given output (as at point A on isoquant q1, point B on isoquant q2, and point C on isoquant q3). Adding more labor alone does not increase output, nor does adding more capital alone. Capital per year K1 q3 q2 B C q1 Labor per year A L1 CHAPTER 6 • Production 221 ounce of nuts for every four ounces of oats in every serving. If the company were to purchase additional nuts but not additional oats, the output of cereal would remain unchanged, since the nuts must be combined with the oats in a fixed proportion. Similarly, purchasing additional oats without additional nuts would also be unproductive. In Figure 6.8 points A, B, and C represent technically efficient combinations of inputs. For example, to produce output q1, a quantity of labor L1 and capital K1 can be used, as at A. If capital stays fixed at K1, adding more labor does not change output. Nor does adding capital with labor fixed at L1. Thus, on the vertical and the horizontal segments of the L-shaped isoquants, either the marginal product of capital or the marginal product of labor is zero. Higher output results only when both labor and capital are added, as in the move from input combination A to input combination B. The fixed-proportions production function describes situations in which methods of production are limited. For example, the production of a television show might involve a certain mix of capital (camera and sound equipment, etc |
.) and labor (producer, director, actors, etc.). To make more television shows, all inputs to production must be increased proportionally. In particular, it would be difficult to increase capital inputs at the expense of labor, because actors are necessary inputs to production (except perhaps for animated films). Likewise, it would be difficult to substitute labor for capital, because filmmaking today requires sophisticated film equipment. In §3.1, we explain that two goods are perfect complements when the indifference curves for the goods are shaped as right angles. EXAM PLE 6.4 A PRODUCTION FUNCTION FOR WHEAT Crops can be produced using different methods. Food grown on large farms in the United States is usually produced with a capital-intensive technology, which involves substantial investments in capital, such as buildings and equipment, and relatively little input of labor. However, food can also be produced using very little capital (a hoe) and a lot of labor (several people with the patience and stamina to work the soil). One way to describe the agricultural production process is to show one isoquant (or more) that describes the combination of inputs which generates a given level of output (or several output levels). The description that follows comes from a production function for wheat that was estimated statistically.10 Figure 6.9 shows one isoquant, associated with the production function, corresponding to an output of 13,800 bushels of wheat per year. The manager of the farm can use this isoquant to decide whether it is profitable to hire more labor or use more machinery. Assume the farm is currently operating at A, with a labor input L of 500 hours and a capital input K of 100 machine hours. The manager decides to experiment by using only 90 hours of machine time. To produce the same crop per year, he finds that he needs to replace this machine time by adding 260 hours of labor. The results of this experiment tell the manager about the shape of the wheat production isoquant. When he compares points A (where 10The food production function on which this example is based is given by the equation q = 100(K.8L.2), where q is the rate of output in bushels of wheat per year, K is the quantity of machines in use per year, and L is the number of hours of labor per year. 222 PART 2 • Producers, Consumers, and Competitive Markets Capital (machine hours per year) 120 100 90 80 40 FIGURE 6.9 ISOQUANT DESCRIBING THE PRODUCTION OF WHEAT A wheat output of 13,800 bushels per year can be produced with different combinations of labor and capital. The more capital-intensive production process is shown as point A, the more labor-intensive process as point B. The marginal rate of substitution technical between A and B is 10/260 0.04. A ΔK = 10 B ΔL = 260 Output = 13,800 Bushels per Year 250 500 760 1000 Labor (hours per year) L 500 and K 100) and B (where L 760 and K 90) in Figure 6.9, both of which are on the same isoquant, the manager finds that the marginal rate of technical substitution is equal to 0.04 (−K/L (10)/260 .04). The MRTS reveals the nature of the trade-off involved in adding labor and reducing the use of farm machinery. Because the MRTS is substantially less than 1 in value, the manager knows that when the wage of a laborer is equal to the cost of running a machine, he ought to use more capital. (At his current level of production, he needs 260 units of labor to substitute for 10 units of capital.) In fact, he knows that unless labor is much less expensive than the use of a machine, his production process ought to become more capital-intensive. The decision about how many laborers to hire and machines to use cannot be fully resolved until we discuss the costs of production in the next chapter. However, this example illustrates how knowledge about production isoquants and the marginal rate of technical substitution can help a manager. It also suggests why most farms in the United States and Canada, where labor is relatively expensive, operate in the range of production in which the MRTS is relatively high (with a high capital-to-labor ratio), whereas farms in developing countries, in which labor is cheap, operate with a lower MRTS (and a lower capital-to-labor ratio).11 The exact labor/capital combination to use depends on input prices, a subject that we discuss in Chapter 7. 11With the production function given in footnote 6, it is not difficult (using calculus) to show that the marginal rate of technical substitution is given by MRTS (MPL/MPK) (1/4) (K/L). Thus, the MRTS decreases as the capital-to-labor ratio falls. For an interesting study of agricultural production in Israel, see Richard E. Just, David Zilberman, and Eithan Hochman, “Estimation of Multicrop Production Functions,” American Journal of Agricultural Economics 65 (1983): 770–80. CHAPTER 6 • Production 223 6.4 Returns to Scale Our analysis of input substitution in the production process has shown us what happens when a firm substitutes one input for another while keeping output constant. However, in the long run, with all inputs variable, the firm must also consider the best way to increase output. One way to do so is to change the scale of the operation by increasing all of the inputs to production in proportion. If it takes one farmer working with one harvesting machine on one acre of land to produce 100 bushels of wheat, what will happen to output if we put two farmers to work with two machines on two acres of land? Output will almost certainly increase, but will it double, more than double, or less than double? Returns to scale is the rate at which output increases as inputs are increased proportionately. We will examine three different cases: increasing, constant, and decreasing returns to scale. INCREASING RETURNS TO SCALE If output more than doubles when inputs are doubled, there are increasing returns to scale. This might arise because the larger scale of operation allows managers and workers to specialize in their tasks and to make use of more sophisticated, large-scale factories and equipment. The automobile assembly line is a famous example of increasing returns. The prospect of increasing returns to scale is an important issue from a public- policy perspective. If there are increasing returns, then it is economically advantageous to have one large firm producing (at relatively low cost) rather than to have many small firms (at relatively high cost). Because this large firm can control the price that it sets, it may need to be regulated. For example, increasing returns in the provision of electricity is one reason why we have large, regulated power companies. CONSTANT RETURNS TO SCALE A second possibility with respect to the scale of production is that output may double when inputs are doubled. In this case, we say there are constant returns to scale. With constant returns to scale, the size of the firm’s operation does not affect the productivity of its factors: Because one plant using a particular production process can easily be replicated, two plants produce twice as much output. For example, a large travel agency might provide the same service per client and use the same ratio of capital (office space) and labor (travel agents) as a small agency that services fewer clients. DECREASING RETURNS TO SCALE Finally, output may less than double when all inputs double. This case of decreasing returns to scale applies to some firms with large-scale operations. Eventually, difficulties in organizing and running a large-scale operation may lead to decreased productivity of both labor and capital. Communication between workers and managers can become difficult to monitor as the workplace becomes more impersonal. Thus, the decreasing-returns case is likely to be associated with the problems of coordinating tasks and maintaining a useful line of communication between management and workers. • returns to scale Rate at which output increases as inputs are increased proportionately. • increasing returns to scale Situation in which output more than doubles when all inputs are doubled. • constant returns to scale Situation in which output doubles when all inputs are doubled. • decreasing returns to scale Situation in which output less than doubles when all inputs are doubled. 224 PART 2 • Producers, Consumers, and Competitive Markets Capital (machine hours) 6 4 2 0 A Capital (machine hours) A 30 20 10 5 10 15 Labor (hours) (a) 4 2 0 30 20 10 5 10 (b) Labor (hours) FIGURE 6.10 RETURNS TO SCALE When a firm’s production process exhibits constant returns to scale as shown by a movement along line 0A in part (a), the isoquants are equally spaced as output increases proportionally. However, when there are increasing returns to scale as shown in (b), the isoquants move closer together as inputs are increased along the line. Describing Returns to Scale Returns to scale need not be uniform across all possible levels of output. For example, at lower levels of output, the firm could have increasing returns to scale, but constant and eventually decreasing returns at higher levels of output. The presence or absence of returns to scale is seen graphically in the two parts of Figure 6.10. The line 0A from the origin in each panel describes a production process in which labor and capital are used as inputs to produce various levels of output in the ratio of 5 hours of labor to 2 hours of machine time. In Figure 6.10 (a), the firm’s production function exhibits constant returns to scale. When 5 hours of labor and 2 hours of machine time are used, an output of 10 units is produced. When both inputs double, output doubles from 10 to 20 units; when both inputs triple, output triples, from 10 to 30 units. Put differently, twice as much of both inputs is needed to produce 20 units, and three times as much is needed to produce 30 units. In Figure 6.10 (b), the firm’s production function exhibits increasing returns to scale. Now the isoquants come closer together |
as we move away from the origin along 0A. As a result, less than twice the amount of both inputs is needed to increase production from 10 units to 20; substantially less than three times the inputs are needed to produce 30 units. The reverse would be true if the production function exhibited decreasing returns to scale (not shown here). With decreasing returns, the isoquants are increasingly distant from one another as output levels increase proportionally. Returns to scale vary considerably across firms and industries. Other things being equal, the greater the returns to scale, the larger the firms in an industry are likely to be. Because manufacturing involves large investments in capital equipment, manufacturing industries are more likely to have increasing returns to scale than service-oriented industries. Services are more labor-intensive and can usually be provided as efficiently in small quantities as they can on a large scale. CHAPTER 6 • Production 225 EXAM PLE 6.5 RETURNS TO SCALE IN THE CARPET INDUSTRY The carpet industry in the United States centers on the town of Dalton in northern Georgia. From a relatively small industry with many small firms in the first half of the twentieth century, it grew rapidly and became a major industry with a large number of firms of all sizes. For example, the top five carpet manufacturers, ranked by shipments in millions of dollars in 2005, are shown in Table 6.5.12 Currently, there are three relatively large manufacturers (Shaw, Mohawk, and Beaulieu), along with a number of smaller producers. There are also many retailers, wholesale distributors, buying groups, and national retail chains. The carpet industry has grown rapidly for several reasons. Consumer demand for wool, nylon, and polypropylene carpets in commercial and residential uses has skyrocketed. In addition, innovations such as the introduction of larger, faster, and more efficient carpet-tufting machines have reduced costs and greatly increased carpet production. Along with the increase in production, innovation and competition have worked together to reduce real carpet prices. To what extent, if any, can the growth of the carpet industry be explained by the presence of returns to scale? There have certainly been substantial improvements in the processing of key production inputs (such as stain-resistant yarn) and in the distribution of carpets to retailers and consumers. But what about the production of carpets? Carpet production is capital intensive—manufacturing plants require heavy investments in high-speed tufting machines that turn various types of yarn into carpet, as well as machines that put the backings onto the carpets, cut the carpets into appropriate sizes, and package, label, and distribute them. Overall, physical capital (including plant and equipment) accounts for about 77 percent of a typical carpet manufacturer’s costs, while labor accounts for the remaining 23 percent. Over time, the major carpet manufacturers have increased the scale of their operations by putting larger and more efficient tufting machines into larger plants. At the same time, the use of labor in these plants has also increased significantly. The result? Proportional increases in inputs have resulted in a more than proportional increase in output for these larger plants. For example, a doubling of capital and labor inputs might lead to a 110-percent increase in output. This pattern has not, however, been uniform across the industry. Most smaller carpet manufacturers have found that small changes in scale have little or no effect on output; i.e., small proportional increases in inputs have only increased output proportionally. TABLE 6.5 THE U.S. CARPET INDUSTRY CARPET SALES, 2005 (MILLIONS OF DOLLARS PER YEAR) 1. Shaw 2. Mohawk 3. Beaulieu 4. Interface 5. Royalty 4346 3779 1115 421 298 12Floor Focus, May 2005. 226 PART 2 • Producers, Consumers, and Competitive Markets We can therefore characterize the carpet industry as one in which there are constant returns to scale for relatively small plants but increasing returns to scale for larger plants. These increasing returns, however, are limited, and we can expect that if plant size were increased further, there would eventually be decreasing returns to scale. SUMMARY 1. A production function describes the maximum output that a firm can produce for each specified combination of inputs. 2. In the short run, one or more inputs to the production process are fixed. In the long run, all inputs are potentially variable. 3. Production with one variable input, labor, can be usefully described in terms of the average product of labor (which measures output per unit of labor input) and the marginal product of labor (which measures the additional output as labor is increased by 1 unit). 4. According to the law of diminishing marginal returns, when one or more inputs are fixed, a variable input (usually labor) is likely to have a marginal product that eventually diminishes as the level of input increases. 5. An isoquant is a curve that shows all combinations of inputs that yield a given level of output. A firm’s production function can be represented by a series of isoquants associated with different levels of output. 6. Isoquants always slope downward because the marginal product of all inputs is positive. The shape of each isoquant can be described by the marginal rate of technical substitution at each point on the isoquant. The marginal rate of technical substitution of labor for capital (MRTS) is the amount by which the input of capital can be reduced when one extra unit of labor is used so that output remains constant. 7. The standard of living that a country can attain for its citizens is closely related to its level of labor productivity. Decreases in the rate of productivity growth in developed countries are due in part to the lack of growth of capital investment. 8. The possibilities for substitution among inputs in the production process range from a production function in which inputs are perfect substitutes to one in which the proportions of inputs to be used are fixed (a fixedproportions production function). 9. In long-run analysis, we tend to focus on the firm’s choice of its scale or size of operation. Constant returns to scale means that doubling all inputs leads to doubling output. Increasing returns to scale occurs when output more than doubles when inputs are doubled; decreasing returns to scale applies when output less than doubles. QUESTIONS FOR REVIEW 1. What is a production function? How does a long-run production function differ from a short-run production function? 2. Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired? 3. Why does production eventually experience diminish- ing marginal returns to labor in the short run? 4. You are an employer seeking to fill a vacant position on an assembly line. Are you more concerned with the average product of labor or the marginal product of labor for the last person hired? If you observe that your average product is just beginning to decline, should you hire any more workers? What does this situation imply about the marginal product of your last worker hired? 5. What is the difference between a production function and an isoquant? 6. Faced with constantly changing conditions, why would a firm ever keep any factors fixed? What criteria determine whether a factor is fixed or variable? 7. Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the nature of the production function? What does each of these shapes tell you about the MRTS? 8. Can an isoquant ever slope upward? Explain. 9. Explain the term “marginal rate of technical substitu- tion.” What does a MRTS 4 mean? 10. Explain why the marginal rate of technical substitution is likely to diminish as more and more labor is substituted for capital. 11. Is it possible to have diminishing returns to a single factor of production and constant returns to scale at the same time? Discuss. 12. Can a firm have a production function that exhibits increasing returns to scale, constant returns to scale, and decreasing returns to scale as output increases? Discuss. 13. Suppose that output q is a function of a single input, labor (L). Describe the returns to scale associated with each of the following production functions: 1a2 q = L/2 1b2 q = L2 + L 1c2 q = log1L2. EXERCISES 1. The menu at Joe’s coffee shop consists of a variety of coffee drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one worker, but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. Why might you expect the marginal product of additional workers to diminish eventually? 2. Suppose a chair manufacturer is producing in the short run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers: NUMBER OF WORKERS NUMBER OF CHAIRS 1 2 3 4 5 6 7 10 18 24 28 30 28 25 a. Calculate the marginal and average product of labor for this production function. b. Does this production function exhibit diminishing returns to labor? Explain. c. Explain intuitively what might cause the marginal product of labor to become negative. 3. Fill in the gaps in the table below. QUANTITY OF VARIABLE INPUT TOTAL OUTPUT MARGINAL PRODUCT OF VARIABLE INPUT AVERAGE PRODUCT OF VARIABLE INPUT 0 225 1140 — 300 225 0 1 2 3 4 5 6 — 300 225 4. A political campaign manager must decide whether to emphasize television advertisements or letters to potential voters in a reelection campaign. Describe the CHAPTER 6 • Production 227 production function for campaign votes. How might information about this function (such as the shap |
e of the isoquants) help the campaign manager to plan strategy? 5. For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case? a. A firm can hire only full-time employees to produce its output, or it can hire some combination of fulltime and part-time employees. For each full-time worker let go, the firm must hire an increasing number of temporary employees to maintain the same level of output. b. A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant. c. A firm requires exactly two full-time workers to operate each piece of machinery in the factory. 6. A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss. 7. The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital? 8. Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor held constant? a. q 3L 2K b. q (2L 2K)1/2 c. q 3LK2 d. q L1/2K1/2 e. q 4L1/2 4K 9. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5 where q is the number of computers produced per day, K is hours of machine time, and L is hours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4 a. If both companies use the same amounts of capital and labor, which will generate more output? b. Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. In which company is the marginal product of labor greater? Explain. 228 PART 2 • Producers, Consumers, and Competitive Markets 10. In Example 6.4, wheat is produced according to the production function q = 100(K0.8L0.2) a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. b. Does this production function exhibit increasing, decreasing, or constant returns to scale? 11. Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is L c H0.8N0.2. a. Beginning with a health input of $400 per year (H 4) and a nutrition input of $4900 per year (N 49), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. b. Does this production function exhibit increasing, decreasing, or constant returns to scale? c. Suppose that in a country suffering from famine, N is fixed at 2 and that c 20. Plot the production function for life expectancy as a function of health expenditures, with L on the vertical axis and H on the horizontal axis. d. Now suppose another nation provides food aid to the country suffering from famine so that N increases to 4. Plot the new production function. e. Now suppose that N 4 and H 2. You run a charity that can provide either food aid or health aid to this country. Which would provide a greater benefit: increasing H by 1 or N by 1? C H A P T E R 7 The Cost of Production In the last chapter, we examined the firm’s production technology— the relationship that shows how factor inputs can be transformed into outputs. Now we will see how the production technology, together with the prices of factor inputs, determines the firm’s cost of production. Given a firm’s production technology, managers must decide how to produce. As we saw, inputs can be combined in different ways to yield the same amount of output. For example, one can produce a certain output with a lot of labor and very little capital, with very little labor and a lot of capital, or with some other combination of the two. In this chapter we see how the optimal—i.e., cost-minimizing—combination of inputs is chosen. We will also see how a firm’s costs depend on its rate of output and show how these costs are likely to change over time. We begin by explaining how cost is defined and measured, distinguishing between the concept of cost used by economists, who are concerned about the firm’s future performance, and by accountants, who focus on the firm’s financial statements. We then examine how the characteristics of the firm’s production technology affect costs, both in the short run, when the firm can do little to change its capital stock, and in the long run, when the firm can change all its factor inputs. We then show how the concept of returns to scale can be generalized to allow for both changes in the mix of inputs and the production of many different outputs. We also show how cost sometimes falls over time as managers and workers learn from experience and make production processes more efficient. Finally, we show how empirical information can be used to estimate cost functions and predict future costs. 7.1 Measuring Cost: Which Costs Matter.1 Measuring Cost: Which Costs Matter? 7.2 Cost in the Short Run 7.3 Cost in the Long Run 7.4 Long-Run versus 229 237 243 Short-Run Cost Curves 253 7.5 Production with Two Outputs—Economies of Scope *7.6 Dynamic Changes in Costs—The Learning Curve 258 261 *7.7 Estimating and Predicting Cost 265 Appendix: Production and Cost Theory—A Mathematical 273 Treatment .1 Choosing the Location for a New Law School Building 7.2 Sunk, Fixed, and Variable Costs: Computers, Software, and Pizzas 232 235 7.3 The Short-Run Cost of Aluminum Smelting 240 7.4 The Effect of Effluent Fees on Input Choices 247 7.5 Reducing the Use of Energy 251 7.6 Economies of Scope in the Trucking Industry 260 Before we can analyze how firms minimize costs, we must clarify what we mean by cost in the first place and how we should measure it. What items, for example, should be included as part of a firm’s cost? Cost obviously includes the wages that a firm pays its workers and the rent that it pays for office space. But what if the firm already owns an 7.7 The Learning Curve in Practice 7.8 Cost Functions for Electric Power 264 268 229 230 PART 2 • Producers, Consumers, and Competitive Markets • accounting cost Actual expenses plus depreciation charges for capital equipment. • economic cost Cost to a firm of utilizing economic resources in production. • opportunity cost Cost associated with opportunities forgone when a firm’s resources are not put to their best alternative use. office building and doesn’t have to pay rent? How should we treat money that the firm spent two or three years ago (and can’t recover) for equipment or for research and development? We’ll answer questions such as these in the context of the economic decisions that managers make. Economic Cost versus Accounting Cost Economists think of cost differently from financial accountants, who are usually concerned with keeping track of assets and liabilities and reporting past performance for external use, as in annual reports. Financial accountants tend to take a retrospective view of the firm’s finances and operations. As a result accounting cost—the cost that financial accountants measure—can include items that an economist would not include and may not include items that economists usually do include. For example, accounting cost includes actual expenses plus depreciation expenses for capital equipment, which are determined on the basis of the allowable tax treatment by the Internal Revenue Service. Economists—and we hope managers—take a forward-looking view. They are concerned with the allocation of scarce resources. Therefore, they care about what cost is likely to be in the future and about ways in which the firm might be able to rearrange its resources to lower its costs and improve its profitability. As we will see, economists are therefore concerned with economic cost, which is the cost of utilizing resources in production. What kinds of resources are part of economic cost? The word economic tells us to distinguish between the costs the firm can control and those it cannot. It also tells us to consider all costs relevant to production. Clearly capital, labor, and raw materials are resources whose costs should be included. But the firm might use other resources with costs that are less obvious, but equally important. Here the concept of opportunity cost plays an important role. Opportunity Cost Opportunity cost is the cost associated with opportunities that are forgone by not putting the firm’s resources to their best alternative use. This is easiest to understand through an example. Consider a firm that owns a building and therefore pays no rent for office space. Does this mean the cost of office space is zero? The firm’s managers and accountant might say yes, but an economist would disagree. The economist would note that the firm could have earned rent on the office space by leasing it to another company. Leasing the office space would mean putting this resource to an alternative use, a use that would have provided the firm with rental income. This forgone rent is the opportunity cost of utilizing the office space. And because the office space is a resource that the firm is utilizing, this opportunity cost is also an economic cost of doing business. What about the wages and salaries paid to the firm’s workers? This is clearly an economic cost of doing business, but if you think about it, you will see that it is also an opportunity cost. The reason is that the money paid to the workers could have been put to some alternative use instead. Perhaps the firm could have used some or all of that money to buy more labor-saving machines, or even to produce a different product altogether. Thus w |
e see that economic cost and opportunity cost actually boil down to the same thing. As long as we account for and measure all of the firm’s resources properly, we will find that: Economic cost Opportunity cost CHAPTER 7 • The Cost of Production 231 While economic cost and opportunity cost both describe the same thing, the concept of opportunity cost is particularly useful in situations where alternatives that are forgone do not reflect monetary outlays. Let’s take a more detailed look at opportunity cost to see how it can make economic cost differ from accounting cost in the treatment of wages, and then in the cost of production inputs. Consider an owner that manages her own retail toy store and does not pay herself a salary. (We’ll put aside the rent that she pays for the office space just to simplify the discussion.) Had our toy store owner chosen to work elsewhere she would have been able to find a job that paid $60,000 per year for essentially the same effort. In this case the opportunity cost of the time she spends working in her toy store business is $60,000. Now suppose that last year she acquired an inventory of toys for which she paid $1 million. She hopes to be able to sell those toys during the holiday season for a substantial markup over her acquisition cost. However, early in the fall she receives an offer from another toy retailer to acquire her inventory for $1.5 million. Should she sell her inventory or not? The answer depends in part on her business prospects, but it also depends on the opportunity cost of acquiring a toy inventory. Assuming that it would cost $1.5 million to acquire the new inventory all over again, the opportunity cost of keeping it is $1.5 million, not the $1.0 million she originally paid. You might ask why the opportunity cost isn’t just $500,000, since that is the difference between the market value of the inventory and the cost of its acquisition. The key is that when the owner is deciding what to do with the inventory, she is deciding what is best for her business in the future. To do so, she needs to account for the fact that if she keeps the inventory for her own use, she would be sacrificing the $1.5 million that she could have received by selling the inventory to another firm.1 Note that an accountant may not see things this way. The accountant might tell the toy store owner that the cost of utilizing the inventory is just the $1 million that she paid for it. But we hope that you understand why this would be misleading. The actual economic cost of keeping and utilizing that inventory is the $1.5 million that the owner could have obtained by instead selling it to another retailer. Accountants and economists will also sometimes differ in their treatment of depreciation. When estimating the future profitability of a business, economists and managers are concerned with the capital cost of plant and machinery. This cost involves not only the monetary outlay for buying and then running the machinery, but also the cost associated with wear and tear. When evaluating past performance, cost accountants use tax rules that apply to broadly defined types of assets to determine allowable depreciation in their cost and profit calculations. But these depreciation allowances need not reflect the actual wear and tear on the equipment, which is likely to vary asset by asset. Sunk Costs Although an opportunity cost is often hidden, it should be taken into account when making economic decisions. Just the opposite is true of a sunk cost: an expenditure that has been made and cannot be recovered. A sunk cost is usually • sunk cost Expenditure that has been made and cannot be recovered. 1Of course, opportunity cost will change from circumstance to circumstance and from one time period to the next. If the value of our retailer’s inventory suddenly increased to $1.7 million because that inventory included some holiday products that were in great demand, the opportunity cost of keeping and using the inventory would increase to $1.7 million. 232 PART 2 • Producers, Consumers, and Competitive Markets visible, but after it has been incurred it should always be ignored when making future economic decisions. Because a sunk cost cannot be recovered, it should not influence the firm’s decisions. For example, consider the purchase of specialized equipment for a plant. Suppose the equipment can be used to do only what it was originally designed for and cannot be converted for alternative use. The expenditure on this equipment is a sunk cost. Because it has no alternative use, its opportunity cost is zero. Thus it should not be included as part of the firm’s economic costs. The decision to buy this equipment may have been good or bad. It doesn’t matter. It’s water under the bridge and shouldn’t affect current decisions. What if, instead, the equipment could be put to other use or could be sold or rented to another firm? In that case, its use would involve an economic cost—namely, the opportunity cost of using it rather than selling or renting it to another firm. Now consider a prospective sunk cost. Suppose, for example, that the firm has not yet bought the specialized equipment but is merely considering whether to do so. A prospective sunk cost is an investment. Here the firm must decide whether that investment in specialized equipment is economical—i.e., whether it will lead to a flow of revenues large enough to justify its cost. In Chapter 15, we explain in detail how to make investment decisions of this kind. As an example, suppose a firm is considering moving its headquarters to a new city. Last year it paid $500,000 for an option to buy a building in the city. The option gives the firm the right to buy the building at a cost of $5,000,000, so that if it ultimately makes the purchase its total expenditure will be $5,500,000. Now it finds that a comparable building has become available in the same city at a price of $5,250,000. Which building should it buy? The answer is the original building. The $500,000 option is a cost that has been sunk and thus should not affect the firm’s current decision. What’s at issue is spending an additional $5,000,000 or an additional $5,250,000. Because the economic analysis removes the sunk cost of the option from the analysis, the economic cost of the original property is $5,000,000. The newer property, meanwhile, has an economic cost of $5,250,000. Of course, if the new building costs $4,900,000, the firm should buy it and forgo its option. E XAM PLE 7.1 CHOOSING THE LOCATION FOR A NEW LAW SCHOOL BUILDING The Northwestern University Law School has long been located in Chicago, along the shores of Lake Michigan. However, the main campus of the university is located in the suburb of Evanston. In the mid-1970s, the law school began planning the construction of a new building and needed to decide on an appropriate location. Should it be built on the current site, where it would remain near downtown Chicago law firms? Or should it be moved to Evanston, where it would be physically integrated with the rest of the university? The downtown location had many prominent supporters. They argued in part that it was costeffective to locate the new building in the city because the university already owned the land. A large parcel of land would have to be purchased in Evanston if the building were to be built there. Does this argument make economic sense? No. It makes the common mistake of failing to appreciate opportunity cost. From an economic point of view, it is very expensive to locate downtown because the opportunity cost of the valuable CHAPTER 7 • The Cost of Production 233 lakeshore location is high: That property could have been sold for enough money to buy the Evanston land with substantial funds left over. In the end, Northwestern decided to keep the law school in Chicago. This was a costly deci- sion. It may have been appropriate if the Chicago location was particularly valuable to the law school, but it was inappropriate if it was made on the presumption that the downtown land had no cost. • total cost (TC or C) Total economic cost of production, consisting of fixed and variable costs. • fixed cost (FC) Cost that does not vary with the level of output and that can be eliminated only by shutting down. • variable cost (VC) Cost that varies as output varies. Fixed Costs and Variable Costs Some costs vary with output, while others remain unchanged as long as the firm is producing any output at all. This distinction will be important when we examine the firm’s profit-maximizing choice of output in the next chapter. We therefore divide total cost (TC or C)—the total economic cost of production— into two components. • Fixed cost (FC): A cost that does not vary with the level of output and that can be eliminated only by going out of business. • Variable cost (VC): A cost that varies as output varies. Depending on circumstances, fixed costs may include expenditures for plant maintenance, insurance, heat and electricity, and perhaps a minimal number of employees. They remain the same no matter how much output the firm produces. Variable costs, which include expenditures for wages, salaries, and raw materials used for production, increase as output increases. Fixed cost does not vary with the level of output—it must be paid even if there is no output. The only way that a firm can eliminate its fixed costs is by shutting down. SHUTTING DOWN Shutting down doesn’t necessarily mean going out of business. Suppose a clothing company owns several factories, is experiencing declining demand, and wants to reduce output and costs as much as possible at one factory. By reducing the output of that factory to zero, the company could eliminate the costs of raw materials and much of the labor, but it would still incur the fixed costs of paying the factory’s managers, security guards, and ongoing maintenance. The only way to eliminate those fixed costs would be to close the doors, turn off t |
he electricity, and perhaps even sell off or scrap the machinery. The company would still remain in business and could operate its remaining factories. It might even be able to re-open the factory it had closed, although doing so could be costly if it involved buying new machinery or refurbishing the old machinery. FIXED OR VARIABLE? How do we know which costs are fixed and which are variable? The answer depends on the time horizon that we are considering. Over a very short time horizon—say, a few months—most costs are fixed. Over such a short period, a firm is usually obligated to pay for contracted shipments of materials and cannot easily lay off workers, no matter how much or how little the firm produces. On the other hand, over a longer time period—say, two or three years—many costs become variable. Over this time horizon, if the firm wants to reduce its output, it can reduce its workforce, purchase fewer raw materials, and perhaps even sell off some of its machinery. Over a very long time horizon—say, ten 234 PART 2 • Producers, Consumers, and Competitive Markets years—nearly all costs are variable. Workers and managers can be laid off (or employment can be reduced by attrition), and much of the machinery can be sold off or not replaced as it becomes obsolete and is scrapped. Knowing which costs are fixed and which are variable is important for the management of a firm. When a firm plans to increase or decrease its production, it will want to know how that change will affect its costs. Consider, for example, a problem that Delta Air Lines faced. Delta wanted to know how its costs would change if it reduced the number of its scheduled flights by 10 percent. The answer depends on whether we are considering the short run or the long run. Over the short run—say six months—schedules are fixed and it is difficult to lay off or discharge workers. As a result, most of Delta’s short-run costs are fixed and won’t be reduced significantly with the flight reduction. In the long run—say two years or more—the situation is quite different. Delta has sufficient time to sell or lease planes that are not needed and to discharge unneeded workers. In this case, most of Delta’s costs are variable and thus can be reduced significantly if a 10-percent flight reduction is put in place. Fixed versus Sunk Costs People often confuse fixed and sunk costs. As we just explained, fixed costs are costs that are paid by a firm that is operating, regardless of the level of output it produces. Such costs can include, for example, the salaries of the key executives and expenses for their office space and support staff, as well as insurance and the costs of plant maintenance. Fixed costs can be avoided if the firm shuts down a plant or goes out of business—the key executives and their support staff, for example, will no longer be needed. Sunk costs, on the other hand, are costs that have been incurred and cannot be recovered. An example is the cost of R&D to a pharmaceutical company to develop and test a new drug and then, if the drug has been proven to be safe and effective, the cost of marketing it. Whether the drug is a success or a failure, these costs cannot be recovered and thus are sunk. Another example is the cost of a chip-fabrication plant to produce microprocessors for use in computers. Because the plant’s equipment is too specialized to be of use in any other industry, most if not all of this expenditure is sunk, i.e., cannot be recovered. (Some small part of the cost might be recovered if the equipment is sold for scrap.) Suppose, on the other hand, that a firm had agreed to make annual payments into an employee retirement plan as long as the firm was in operation, regardless of its output or its profitability. These payments could cease only if the firm went out of business. In this case, the payments should be viewed as a fixed cost. Why distinguish between fixed and sunk costs? Because fixed costs affect the firm’s decisions looking forward, whereas sunk costs do not. Fixed costs that are high relative to revenue and cannot be reduced might lead a firm to shut down—eliminating those fixed costs and earning zero profit might be better than incurring ongoing losses. Incurring a high sunk cost might later turn out to be a bad decision (for example, the unsuccessful development of a new product), but the expenditure is gone and cannot be recovered by shutting down. Of course a prospective sunk cost is different and, as we mentioned earlier, would certainly affect the firm’s decisions looking forward. (Should the firm, for example, undertake the development of that new product?) AMORTIZING SUNK COSTS In practice, many firms don’t always distinguish between sunk and fixed costs. For example, the semiconductor company that spent $600 million for a chip-fabrication plant (clearly a sunk cost) might CHAPTER 7 • The Cost of Production 235 amortize the expenditure over six years and treat it as a fixed cost of $100 million per year. This is fine as long as the firm’s managers understand that shutting down will not make the $100 million annual cost go away. In fact, amortizing capital expenditures this way—spreading them out over many years and treating them as fixed costs—can be a useful way of evaluating the firm’s long-term profitability. Amortizing large capital expenditures and treating them as ongoing fixed costs can also simplify the economic analysis of a firm’s operation. As we will see, for example, treating capital expenditures this way can make it easier to understand the tradeoff that a firm faces in its use of labor versus capital. For simplicity, we will usually treat sunk costs in this way as we examine the firm’s production decisions. When distinguishing sunk from fixed costs does become essential to the economic analysis, we will let you know. • amortization Policy of treating a one-time expenditure as an annual cost spread out over some number of years. EXAM PLE 7.2 SUNK, FIXED, AND VARIABLE COSTS: COMPUTERS, SOFTWARE, AND PIZZAS As you progress through this book, you will see that a firm’s pricing and production decisions—and its profitability—depend strongly on the structure of its costs. It is therefore important for managers to understand the characteristics of production costs and to be able to identify which costs are fixed, which are variable, and which are sunk. The relative sizes of these different cost components can vary considerably across industries. Good examples include the personal computer industry (where most costs are variable), the computer software industry (where most costs are sunk), and the pizzeria business (where most costs are fixed). Let’s look at each of these in turn. Companies like Dell, Gateway, Hewlett-Packard, and IBM produce millions of personal computers every year. Because computers are very similar, competition is intense, and profitability depends critically on the ability to keep costs down. Most of these costs are variable—they increase in proportion to the number of computers produced each year. Most important is the cost of components: the microprocessor that does much of the actual computation, memory chips, hard disk drives and other storage devices, video and sound cards, etc. Typically, the majority of these components are purchased from outside suppliers in quantities that depend on the number of computers to be produced. Another important variable cost is labor: Workers are needed to assemble computers and then package and ship them. There is little in the way of sunk costs because factories cost little relative to the value of the company’s annual output. Likewise, there is little in the way of fixed costs—perhaps the salaries of the top executives, some security guards, and electricity. Thus, when Dell and Hewlett-Packard think about ways of reducing cost, they focus largely on getting better prices for components or reducing labor requirements—both of which are ways of reducing variable cost. What about the software programs that run on these personal computers? Microsoft produces the Windows operating system as well as a variety of applications such as Word, Excel, and PowerPoint. But many other firms—some large and some small—also produce software programs that run on personal computers. For such firms, production costs are quite different from those facing hardware manufacturers. In software production, most costs are sunk. Typically, a software firm will spend a large amount of money to develop a new application program. These expenditures cannot be recovered. Once the program is completed, the company can try to recoup its investment (and make a profit as well) by selling as many copies of the program as possible. The variable cost of producing copies of the program is very small—largely the cost of copying the program to CDs and then packaging and shipping the product. Likewise, the fixed cost of production is small. Because most costs are sunk, entering the software business can involve considerable risk. Until the development money has been 236 PART 2 • Producers, Consumers, and Competitive Markets spent and the product has been released for sale, an entrepreneur is unlikely to know how many copies can be sold and whether or not he will be able to make money. Finally, let’s turn to your neighborhood pizzeria. For the pizzeria, the largest component of cost is fixed. Sunk costs are fairly low because pizza ovens, chairs, tables, and dishes can be resold if the pizzeria goes out of business. Variable costs are also fairly low—mainly the ingredients for pizza (flour, tomato sauce, cheese, and pepperoni for a typical large pizza might cost $1 or $2) and perhaps wages for a couple of workers to help produce, serve, and deliver pizzas. Most of the cost is fixed—the opportunity cost of the owner’s time (he might typically work a 60- or 70-hour week), rent, and utilities. Because of these high fixed costs, most pizzerias (which might charge $12 for a large pizza cost |
ing about $3 in variable cost to produce) don’t make very high profits. Marginal and Average Cost To complete our discussion of costs, we now turn to the distinction between marginal and average cost. In explaining this distinction, we use a specific numerical example of a cost function (the relationship between cost and output) that typifies the cost situation of many firms. The example is shown in Table 7.1. After we explain the concepts of marginal and average cost, we will consider how the analysis of costs differs between the short run and the long run. • marginal cost (MC) in cost resulting from the production of one extra unit of output. Increase MARGINAL COST (MC) Marginal cost—sometimes called incremental cost—is the increase in cost that results from producing one extra unit of output. Because fixed cost does not change as the firm’s level of output changes, marginal cost is TABLE 7.1 A FIRM’S COSTS RATE OF OUTPUT (UNITS PER YEAR) FIXED COST (DOLLARS PER YEAR) VARIABLE COST (DOLLARS PER YEAR) TOTAL COST (DOLLARS PER YEAR) MARGINAL COST (DOLLARS PER UNIT) AVERAGE FIXED COST (DOLLARS PER UNIT) AVERAGE VARIABLE COST (DOLLARS PER UNIT) AVERAGE TOTAL COST (DOLLARS PER UNIT) (FC) (1) (VC) (2) (TC) (3) (MC) (4) (AFC) (5) (AVC) (6) (ATC) (7 10 11 50 50 50 50 50 50 50 50 50 50 50 50 0 50 78 98 112 130 150 175 204 242 300 385 50 100 128 148 162 180 200 225 254 292 350 435 — 50 28 20 14 18 20 25 29 38 58 85 — 50 25 16.7 12.5 10 8.3 7.1 6.3 5.6 5 4.5 — 50 39 32.7 28 26 25 25 25.5 26.9 30 35 — 100 64 49.3 40.5 36 33.3 32.1 31.8 32.4 35 39.5 CHAPTER 7 • The Cost of Production 237 equal to the increase in variable cost or the increase in total cost that results from an extra unit of output. We can therefore write marginal cost as MC = VC/q = TC/q Marginal cost tells us how much it will cost to expand output by one unit. In Table 7.1, marginal cost is calculated from either the variable cost (column 2) or the total cost (column 3). For example, the marginal cost of increasing output from 2 to 3 units is $20 because the variable cost of the firm increases from $78 to $98. (The total cost of production also increases by $20, from $128 to $148. Total cost differs from variable cost only by the fixed cost, which by definition does not change as output changes.) AVERAGE TOTAL COST (ATC) Average total cost, used interchangeably with AC and average economic cost, is the firm’s total cost divided by its level of output, TC/q. Thus the average total cost of producing at a rate of five units is $36—that is, $180/5. Basically, average total cost tells us the per-unit cost of production. ATC has two components. Average fixed cost (AFC) is the fixed cost (column 1 of Table 7.1) divided by the level of output, FC/q. For example, the average fixed cost of producing 4 units of output is $12.50 ($50/4). Because fixed cost is constant, average fixed cost declines as the rate of output increases. Average variable cost (AVC) is variable cost divided by the level of output, VC/q. The average variable cost of producing 5 units of output is $26—that is, $130/5. We have now discussed all of the different types of costs that are relevant to production decisions in both competitive and non-competitive markets. Now we turn to how costs differ in the short run versus the long run. This is particularly important for fixed costs. Costs that are fixed in the very short run, e.g., the wages of employees under fixed-term contracts—may not be fixed over a longer time horizon. Similarly, the fixed capital costs of plant and equipment become variable if the time horizon is sufficiently long to allow the firm to purchase new equipment and build a new plant. Fixed costs, however, need not disappear, even in the long run. Suppose, for example, that a firm has been contributing to an employee retirement program. Its obligations, which are fixed in part, may remain even in the long run; they might only disappear if the firm were to declare bankruptcy. 7.2 Cost in the Short Run In this section we focus our attention on short-run costs. We turn to long-run costs in Section 7.3. The Determinants of Short-Run Cost The data in Table 7.1 show how variable and total costs increase with output in the short run. The rate at which these costs increase depends on the nature of the production process and, in particular, on the extent to which production involves diminishing marginal returns to variable factors. Recall from Chapter 6 that diminishing marginal returns to labor occur when the marginal product of labor is decreasing. If labor is the only input, what happens as we increase the firm’s output? To produce more output, the firm must hire more labor. Then, if the marginal product of labor decreases as the amount of labor hired is increased (owing to diminishing returns), successively greater expenditures must be made • average total cost (ATC) Firm’s total cost divided by its level of output. • average fixed cost (AFC) Fixed cost divided by the level of output. • average variable cost (AVC) Variable cost divided by the level of output. In §6.2, we explain that diminishing marginal returns occurs when additional inputs result in decreasing additions to output. 238 PART 2 • Producers, Consumers, and Competitive Markets to produce output at the higher rate. As a result, variable and total costs increase as the rate of output is increased. On the other hand, if the marginal product of labor decreases only slightly as the amount of labor is increased, costs will not rise so quickly when the rate of output is increased.2 Let’s look at the relationship between production and cost in more detail by concentrating on the costs of a firm that can hire as much labor as it wishes at a fixed wage w. Recall that marginal cost MC is the change in variable cost for a 1-unit change in output (i.e., VC/q). But the change in variable cost is the perunit cost of the extra labor w times the amount of extra labor needed to produce the extra output L. Because VCwL, it follows that MC = VC/q = wL/q The marginal product of labor is discussed in §6.2. Recall from Chapter 6 that the marginal product of labor MPL is the change in output resulting from a 1-unit change in labor input, or q/L. Therefore, the extra labor needed to obtain an extra unit of output is L/q 1/MPL. As a result, MC = w/MPL (7.1) Equation (7.1) states that when there is only one variable input, the marginal cost is equal to the price of the input divided by its marginal product. Suppose, for example, that the marginal product of labor is 3 and the wage rate is $30 per hour. In that case, 1 hour of labor will increase output by 3 units, so that 1 unit of output will require 1/3 additional hour of labor and will cost $10. The marginal cost of producing that unit of output is $10, which is equal to the wage, $30, divided by the marginal product of labor, 3. A low marginal product of labor means that a large amount of additional labor is needed to produce more output—a fact that leads, in turn, to a high marginal cost. Conversely, a high marginal product means that the labor requirement is low, as is the marginal cost. More generally, whenever the marginal product of labor decreases, the marginal cost of production increases, and vice versa.3 DIMINISHING MARGINAL RETURNS AND MARGINAL COST Diminishing marginal returns means that the marginal product of labor declines as the quantity of labor employed increases. As a result, when there are diminishing marginal returns, marginal cost will increase as output increases. This can be seen by looking at the numbers for marginal cost in Table 7.1. For output levels from 0 through 4, marginal cost is declining; for output levels from 4 through 11, however, marginal cost is increasing—a reflection of the presence of diminishing marginal returns. The Shapes of the Cost Curves Figure 7.1 illustrates how various cost measures change as output changes. The top part of the figure shows total cost and its two components, variable cost and fixed cost; the bottom part shows marginal cost and average costs. These cost curves, which are based on the information in Table 7.1, provide different kinds of information. 2We are implicitly assuming that because labor is hired in competitive markets, the payment per unit of labor used is the same regardless of the firm’s output. 3With two or more variable inputs, the relationship is more complex. The basic principle, however, still holds: The greater the productivity of factors, the less the variable cost that the firm must incur to produce any given level of output. CHAPTER 7 • The Cost of Production 239 FIGURE 7.1 COST CURVES FOR A FIRM In (a) total cost TC is the vertical sum of fixed cost FC and variable cost VC. In (b) average total cost ATC is the sum of average variable cost AVC and average fixed cost AFC. Marginal cost MC crosses the average variable cost and average total cost curves at their minimum points. Cost (dollars per year) 400 300 Cost (dollars per unit) 175 100 0 100 75 50 25 0 TC VC FC a) 11 10 Output (units per year) MC ATC AVC AFC b) 11 10 Output (units per year) Observe in Figure 7.1 (a) that fixed cost FC does not vary with output—it is shown as a horizontal line at $50. Variable cost VC is zero when output is zero and then increases continuously as output increases. The total cost curve TC is determined by vertically adding the fixed cost curve to the variable cost curve. Because fixed cost is constant, the vertical distance between the two curves is always $50. Figure 7.1 (b) shows the corresponding set of marginal and average variable cost curves.4 Because total fixed cost is $50, the average fixed cost curve AFC falls continuously from $50 when output is 1, toward zero for large output. The shapes of the remaining curves are determined by the relationship between the marginal and average cost curves. Whenever marginal cost lies below average cost, the average cost curve falls. Whenever marginal cost lies above average cost |
, the average cost curve rises. When average cost is at a minimum, marginal cost equals average cost. THE AVERAGE-MARGINAL RELATIONSHIP Marginal and average costs are another example of the average-marginal relationship described in Chapter 6 4The curves do not exactly match the numbers in Table 7.1. Because marginal cost represents the change in cost associated with a change in output, we have plotted the MC curve for the first unit of output by setting output equal to 1 2, for the second unit by setting output equal to 11 2, and so on. 240 PART 2 • Producers, Consumers, and Competitive Markets (with respect to marginal and average product). At an output of 5 in Table 7.1, for example, the marginal cost of $18 is below the average variable cost of $26; thus the average is lowered in response to increases in output. But when marginal cost is $29, which is greater than average variable cost ($25.5), the average increases as output increases. Finally, when marginal cost ($25) and average variable cost ($25) are nearly the same, average variable cost increases only slightly. The ATC curve shows the average total cost of production. Because average total cost is the sum of average variable cost and average fixed cost and the AFC curve declines everywhere, the vertical distance between the ATC and AVC curves decreases as output increases. The AVC cost curve reaches its minimum point at a lower output than the ATC curve. This follows because MC = AVC at its minimum point and MC = ATC at its minimum point. Because ATC is always greater than AVC and the marginal cost curve MC is rising, the minimum point of the ATC curve must lie above and to the right of the minimum point of the AVC curve. Another way to see the relationship between the total cost curves and the average and marginal cost curves is to consider the line drawn from origin to point A in Figure 7.1 (a). In that figure, the slope of the line measures average variable cost (a total cost of $175 divided by an output of 7, or a cost per unit of $25). Because the slope of the VC curve is the marginal cost (it measures the change in variable cost as output increases by 1 unit), the tangent to the VC curve at A is the marginal cost of production when output is 7. At A, this marginal cost of $25 is equal to the average variable cost of $25 because average variable cost is minimized at this output. TOTAL COST AS A FLOW Note that the firm’s output is measured as a flow: The firm produces a certain number of units per year. Thus its total cost is a flow—for example, some number of dollars per year. (Average and marginal costs, however, are measured in dollars per unit.) For simplicity, we will often drop the time reference, and refer to total cost in dollars and output in units. But you should remember that a firm’s production of output and expenditure of cost occur over some time period. In addition, we will often use cost (C) to refer to total cost. Likewise, unless noted otherwise, we will use average cost (AC) to refer to average total cost. Marginal and average cost are very important concepts. As we will see in Chapter 8, they enter critically into the firm’s choice of output level. Knowledge of short-run costs is particularly important for firms that operate in an environment in which demand conditions fluctuate considerably. If the firm is currently producing at a level of output at which marginal cost is sharply increasing, and if demand may increase in the future, management might want to expand production capacity to avoid higher costs. EXAMPLE 7.3 THE SHORT-RUN COST OF ALUMINUM SMELTING Aluminum is a lightweight, versatile metal used in a wide variety of applications, including airplanes, automobiles, packaging, and building materials. The production of aluminum begins with the mining of bauxite in such countries as Australia, Brazil, Guinea, Jamaica, and Suriname. Bauxite is an ore that contains a relatively high concentration of alumina (aluminum oxide), which is separated from the bauxite through a chemical refining process. The CHAPTER 7 • The Cost of Production 241 alumina is then converted to aluminum through a smelting process in which an electric current is used to separate the oxygen atoms from the aluminum oxide molecules. It is this smelting process—which is the most costly step in producing aluminum—that we focus on here. All of the major aluminum producers, including UC RUSAL, Alcoa, Alcan, Chalco, and Hydro Aluminum, operate smelting plants. A typical smelting plant will have two production lines, each of which produces approximately 300 to 400 tons of aluminum per day. We will examine the short-run cost of production. Thus we consider the cost of operating an existing plant because there is insufficient time in the short run to build additional plants. (It takes about four years to plan, build, and fully equip an aluminum smelting plant.) Although the cost of a smelting plant is substantial (over $1 billion), we will assume that the plant cannot be sold; the expenditure is therefore sunk and can be ignored. Furthermore, because fixed costs, which are largely for administrative expenses, are relatively small, we will ignore them also. Thus we can focus entirely on short-run variable costs. Table 7.2 shows the average (per-ton) production costs for a typical aluminum smelter.5 The cost numbers apply to a plant that runs two shifts per day to produce 600 tons of aluminum per day. If prices were sufficiently high, the firm could choose to operate the plant on a three-shifts-per-day basis by asking workers to work overtime. However, wage and maintenance costs would likely increase about 50 percent for this third shift because of the need to pay higher overtime wages. We have divided the cost components in Table 7.2 into two groups. The first group includes those costs that would remain the same at any output level; the second includes costs that would increase if output exceeded 600 tons per day. TABLE 7.2 PRODUCTION COSTS FOR ALUMINUM SMELTING ($/TON) (BASED ON AN OUTPUT OF 600 TONS/DAY) PER-TON COSTS THAT ARE CONSTANT FOR ALL OUTPUT LEVELS OUTPUT " 600 TONS/DAY OUTPUT + 600 TONS/DAY Electricity Alumina Other raw materials Plant power and fuel Subtotal PER-TON COSTS THAT INCREASE WHEN OUTPUT EXCEEDS 600 TONS/DAY Labor Maintenance Freight Subtotal Total per-ton production costs $316 369 125 10 $820 $150 120 50 $320 $1140 $316 369 125 10 $820 $225 180 75 $480 $1300 5This example is based on Kenneth S. Corts, “The Aluminum Industry in 1994,” Harvard Business School Case N9-799-129, April 1999. 242 PART 2 • Producers, Consumers, and Competitive Markets Note that the largest cost components for an aluminum smelter are electricity and the cost of alumina; together, they represent about 60 percent of total production costs. Because electricity, alumina, and other raw materials are used in direct proportion to the amount of aluminum produced, they represent perton production costs that are constant with respect to the level of output. The costs of labor, maintenance, and freight are also proportional to the level of output, but only when the plant operates two shifts per day. To increase output above 600 tons per day, a third shift would be necessary and would result in a 50-percent increase in the per-ton costs of labor, maintenance, and freight. The short-run marginal cost and average variable cost curves for the smelting plant are shown in Figure 7.2. For an output q up to 600 tons per day, total variable cost is $1140q, so marginal cost and average variable cost are constant at $1140 per ton. If we increase production beyond 600 tons per day by means of a third shift, the marginal cost of labor, maintenance, and freight increases from $320 per ton to $480 per ton, which causes marginal cost as a whole to increase from $1140 per ton to $1300 per ton. What happens to average variable cost when output is greater than 600 tons per day? When q> 600, total variable cost is given by: TVC = (1140)(600) + 1300(q - 600) = 1300q - 96,000 Therefore average variable cost is AVC = 1300 - 96,000 q As Figure 7.2 shows, when output reaches 900 tons per day, an absolute capacity constraint is reached, at which point the marginal and average costs of production become infinite. FIGURE 7.2 THE SHORT-RUN VARIABLE COSTS OF ALUMINUM SMELTING The short-run average variable cost of smelting is constant for output levels using up to two labor shifts. When a third shift is added, marginal cost and average variable cost increase until maximum capacity is reached. Cost (dollars per ton) 1300 1200 1140 1100 MC AVC 300 600 900 Output (tons per day) CHAPTER 7 • The Cost of Production 243 7.3 Cost in the Long Run In the long run, a firm has much more flexibility. It can expand its capacity by expanding existing factories or building new ones; it can expand or contract its labor force, and in some cases, it can change the design of its products or introduce new products. In this section, we show how a firm can choose its combination of inputs to minimize its cost of producing a given output. We will also examine the relationship between long-run cost and the level of output. We begin by taking a careful look at the cost of using capital equipment. We then show how this cost, along with the cost of labor, enters into the production decision. The User Cost of Capital Firms often rent or lease equipment, buildings, and other capital used in the production process. On other occasions, the capital is purchased. In our analysis, however, it will be useful to treat capital as though it were rented even if it was purchased. An illustration will help to explain how and why we do this. Let’s suppose that Delta Airlines is thinking about purchasing a new Boeing 777 airplane for $150 million. Even though Delta would pay a large sum for the airplane now, for economic purposes the purchase price can be allocated or amortized across the life of the airplane. This will allow Delta to compare its |
revenues and costs on an annual flow basis. We will assume that the life of the airplane is 30 years; the amortized cost is therefore $5 million per year. The $5 million can be viewed as the annual economic depreciation for the airplane. So far, we have ignored the fact that had the firm not purchased the airplane, it could have earned interest on its $150 million. This forgone interest is an opportunity cost that must be accounted for. Therefore, the user cost of capital— the annual cost of owning and using the airplane instead of selling it or never buying it in the first place—is given by the sum of the economic depreciation and the interest (i.e., the financial return) that could have been earned had the money been invested elsewhere.6 Formally, User Cost of Capital = Economic Depreciation + (Interest Rate) (Value of Capital) In our example, economic depreciation on the airplane is $5 million per year. Suppose Delta could have earned a return of 10 percent had it invested its money elsewhere. In that case, the user cost of capital is $5 million + (.10) ($150 million − depreciation). As the plane depreciates over time, its value declines, as does the opportunity cost of the financial capital that is invested in it. For example, at the time of purchase, looking forward for the first year, the user cost of capital is $5 million + (.10)($150 million) = $20 million. In the tenth year of ownership, the airplane, which will have depreciated by $50 million, will be worth $100 million. At that point, the user cost of capital will be $5 million + (.10)($100 million) = $15 million per year. We can also express the user cost of capital as a rate per dollar of capital: r = Depreciation rate + Interest rate 6More precisely, the financial return should reflect an investment with similar risk. The interest rate, therefore, should include a risk premium. We discuss this point in Chapter 15. Note also that the user cost of capital is not adjusted for taxes; when taxes are taken into account, revenues and costs should be measured on an after-tax basis. • user cost of capital Annual cost of owning and using a capital asset, equal to economic depreciation plus forgone interest. 244 PART 2 • Producers, Consumers, and Competitive Markets For our airplane example, the depreciation rate is 1>30 = 3.33 percent per year. If Delta could have earned a rate of return of 10 percent per year, its user cost of capital would be r = 3.33 + 10 = 13.33 percent per year. As we’ve already pointed out, in the long run the firm can change all of its inputs. We will now show how the firm chooses the combination of inputs that minimizes the cost of producing a certain output, given information about wages and the user cost of capital. We will then examine the relationship between long-run cost and the level of output. The Cost-Minimizing Input Choice We now turn to a fundamental problem that all firms face: how to select inputs to produce a given output at minimum cost. For simplicity, we will work with two variable inputs: labor (measured in hours of work per year) and capital (measured in hours of use of machinery per year). The amount of labor and capital that the firm uses will depend, of course, on the prices of these inputs. We will assume that because there are competitive markets for both inputs, their prices are unaffected by what the firm does. (In Chapter 14 we will examine labor markets that are not competitive.) In this case, the price of labor is simply the wage rate, w. But what about the price of capital? THE PRICE OF CAPITAL In the long run, the firm can adjust the amount of capital it uses. Even if the capital includes specialized machinery that has no alternative use, expenditures on this machinery are not yet sunk and must be taken into account; the firm is deciding prospectively how much capital to obtain. Unlike labor expenditures, however, large initial expenditures on capital are necessary. In order to compare the firm’s expenditure on capital with its ongoing cost of labor, we want to express this capital expenditure as a flow—e.g., in dollars per year. To do this, we must amortize the expenditure by spreading it over the lifetime of the capital, and we must also account for the forgone interest that the firm could have earned by investing the money elsewhere. As we have just seen, this is exactly what we do when we calculate the user cost of capital. As above, the price of capital is its user cost, given by r Depreciation rate Interest rate. THE RENTAL RATE OF CAPITAL As we noted, capital is often rented rather than purchased. An example is office space in a large office building. In this case, the price of capital is its rental rate—i.e., the cost per year for renting a unit of capital. Does this mean that we must distinguish between capital that is rented and capital that is purchased when we determine the price of capital? No. If the capital market is competitive (as we have assumed it is), the rental rate should be equal to the user cost, r. Why? Because in a competitive market, firms that own capital (e.g., the owner of the large office building) expect to earn a competitive return when they rent it—namely, the rate of return that they could have earned by investing their money elsewhere, plus an amount to compensate for the depreciation of the capital. This competitive return is the user cost of capital. Many textbooks simply assume that all capital is rented at a rental rate r. As we have just seen, this assumption is reasonable. However, you should now understand why it is reasonable: Capital that is purchased can be treated as though it were rented at a rental rate equal to the user cost of capital. For the remainder of this chapter, we will therefore assume that a firm rents all of its capital at a rental rate, or “price,” r, just as it hires labor at a wage rate, or “price,” w. We will also assume that firms treat any sunk cost of capital as a fixed cost that is spread out over time. We need not, therefore, concern ourselves • rental rate Cost per year of renting one unit of capital. with sunk costs. Rather, we can now focus on how a firm takes these prices into account when determining how much capital and labor to utilize.7 CHAPTER 7 • The Cost of Production 245 The Isocost Line We begin by looking at the cost of hiring factor inputs, which can be represented by a firm’s isocost lines. An isocost line shows all possible combinations of labor and capital that can be purchased for a given total cost. To see what an isocost line looks like, recall that the total cost C of producing any particular output is given by the sum of the firm’s labor cost wL and its capital cost rK: • isocost line Graph showing all possible combinations of labor and capital that can be purchased for a given total cost. C = wL + rK (7.2) For each different level of total cost, equation (7.2) describes a different isocost line. In Figure 7.3, for example, the isocost line C0 describes all possible combinations of labor and capital that cost a total of C0 to hire. If we rewrite the total cost equation as an equation for a straight line, we get K = C/r - (w/r)L It follows that the isocost line has a slope of K/L −(w/r), which is the ratio of the wage rate to the rental cost of capital. Note that this slope is similar to the slope of the budget line that the consumer faces (because it is determined solely by the prices of the goods in question, whether inputs or outputs). It tells us that if the firm gave up a unit of labor (and recovered w dollars in cost) to buy w/r units of capital at a cost of r dollars per unit, its total cost of production would remain the same. For example, if the wage rate were $10 and the rental cost of capital $5, the firm could replace one unit of labor with two units of capital with no change in total cost. Choosing Inputs Suppose we wish to produce at an output level q1. How can we do so at minimum cost? Look at the firm’s production isoquant, labeled q1, in Figure 7.3. The problem is to choose the point on this isoquant that minimizes total cost. Figure 7.3 illustrates the solution to this problem. Suppose the firm were to spend C0 on inputs. Unfortunately, no combination of inputs can be purchased for expenditure C0 that will allow the firm to achieve output q1. However, output q1 can be achieved with the expenditure of C2, either by using K2 units of capital and L2 units of labor, or by using K3 units of capital and L3 units of labor. But C2 is not the minimum cost. The same output q1 can be produced more cheaply, at a cost of C1, by using K1 units of capital and L1 units of labor. In fact, isocost line C1 is the lowest isocost line that allows output q1 to be produced. The point of tangency of the isoquant q1 and the isocost line C1 at point A gives us the cost-minimizing choice of inputs, L1 and K1, which can be read directly from the diagram. At this point, the slopes of the isoquant and the isocost line are just equal. When the expenditure on all inputs increases, the slope of the isocost line does not change because the prices of the inputs have not changed. The intercept, however, increases. Suppose that the price of one of the inputs, such as labor, were to increase. In that case, the slope of the isocost line −(w/r) would increase in 7It is possible, of course, that input prices might increase with demand because of overtime or a relative shortage of capital equipment. We discuss the possibility of a relationship between the price of factor inputs and the quantities demanded by a firm in Chapter 14. 246 PART 2 • Producers, Consumers, and Competitive Markets FIGURE 7.3 PRODUCING A GIVEN OUTPUT AT MINIMUM COST Isocost curves describe the combination of inputs to production that cost the same amount to the firm. Isocost curve C1 is tangent to isoquant q1 at A and shows that output q1 can be produced at minimum cost with labor input L1 and capital input K1. Other input combinations—L2, K2 and L3, K3—yiel |
d the same output but at higher cost. Capital per year K2 K1 K3 A q1 C0 C1 C2 L 2 L 1 L 3 Labor per year magnitude and the isocost line would become steeper. Figure 7.4 shows this. Initially, the isocost line is C1, and the firm minimizes its costs of producing output q1 at A by using L1 units of labor and K1 units of capital. When the price of labor increases, the isocost line becomes steeper. The isocost line C2 reflects the higher price of labor. Facing this higher price of labor, the firm minimizes its cost of producing output q1 by producing at B, using L2 units of labor and K2 units Capital per year K2 K1 FIGURE 7.4 INPUT SUBSTITUTION WHEN AN INPUT PRICE CHANGES Facing an isocost curve C1, the firm produces output q1 at point A using L1 units of labor and K1 units of capital. When the price of labor increases, the isocost curves become steeper. Output q1 is now produced at point B on isocost curve C2 by using L2 units of labor and K2 units of capital. B A q1 C 1 C 2 L 2 L 1 Labor per year CHAPTER 7 • The Cost of Production 247 In §6.3, we explain that the MRTS is the amount by which the input of capital can be reduced when one extra unit of labor is used, so that output remains constant. of capital. The firm has responded to the higher price of labor by substituting capital for labor in the production process. How does the isocost line relate to the firm’s production process? Recall that in our analysis of production technology, we showed that the marginal rate of technical substitution of labor for capital (MRTS) is the negative of the slope of the isoquant and is equal to the ratio of the marginal products of labor and capital: MRTS = - K/L = MPL/MPK (7.3) Above, we noted that the isocost line has a slope of K/L = -w/r It follows that when a firm minimizes the cost of producing a particular output, the following condition holds: MPL/MPK = w/r We can rewrite this condition slightly as follows: MPL/w = MPK/r (7.4) MPL/w is the additional output that results from spending an additional dollar for labor. Suppose that the wage rate is $10 and that adding a worker to the production process will increase output by 20 units. The additional output per dollar spent on an additional worker will be 20/10 = 2 units of output per dollar. Similarly, MPK/r is the additional output that results from spending an additional dollar for capital. Therefore, equation (7.4) tells us that a cost-minimizing firm should choose its quantities of inputs so that the last dollar’s worth of any input added to the production process yields the same amount of extra output. Why must this condition hold for cost minimization? Suppose that in addition to the $10 wage rate, the rental rate on capital is $2. Suppose also that adding a unit of capital will increase output by 20 units. In that case, the additional output per dollar of capital input would be 20/$2 = 10 units of output per dollar. Because a dollar spent for capital is five times more productive than a dollar spent for labor, the firm will want to use more capital and less labor. If the firm reduces labor and increases capital, its marginal product of labor will rise and its marginal product of capital will fall. Eventually, the point will be reached at which the production of an additional unit of output costs the same regardless of which additional input is used. At that point, the firm is minimizing its cost. EXAM PLE 7.4 THE EFFECT OF EFFLUENT FEES ON INPUT CHOICES Steel plants are often built on or near rivers. Rivers offer readily available, inexpensive transportation for both the iron ore that goes into the production process and the finished steel itself. Unfortunately, rivers also provide cheap disposal methods for by-products of the production process, called effluent. For example, a steel plant processes iron ore for use in blast furnaces by grinding taconite deposits into a fine consistency. During this process, the ore is extracted by a magnetic field as a flow of water and fine ore passes through the plant. One by-product of this process—fine taconite particles—can be dumped in the river at relatively little cost to the firm. Alternative 248 PART 2 • Producers, Consumers, and Competitive Markets D F Capital (machinehours per month) 5000 4000 3500 3000 2000 1000 B A Output of 2000 Tons of Steel per Month E C 5000 10,000 12,000 18,000 20,000 Wastewater (gallons per month) FIGURE 7.5 THE COST-MINIMIZING RESPONSE TO AN EFFLUENT FEE When the firm is not charged for dumping its wastewater in a river, it chooses to produce a given output using 10,000 gallons of wastewater and 2000 machine-hours of capital at A. However, an effluent fee raises the cost of wastewater, shifts the isocost curve from FC to DE, and causes the firm to produce at B—a process that results in much less effluent. removal methods or private treatment plants are relatively expensive. Because taconite particles are a nondegradable waste that can harm vegetation and fish, the Environmental Protection Agency (EPA) has imposed an effluent fee—a per-unit fee that the steel firm must pay for the effluent that goes into the river. How should the manager of a steel plant deal with the imposition of this fee to minimize production costs? Suppose that without regulation the plant is producing 2000 tons of steel per month, using 2000 machine-hours of capital and 10,000 gallons of water (which contains taconite particles when returned to the river). The manager estimates that a machine-hour costs $40 and that dumping each gallon of wastewater in the river costs $10. The total cost of production is therefore $180,000: $80,000 for capital and $100,000 for wastewater. How should the manager respond to an EPA-imposed effluent fee of $10 per gallon of wastewater dumped? The manager knows that there is some flexibility in the production process. If the firm puts into place more expensive effluent treatment equipment, it can achieve the same output with less wastewater. Figure 7.5 shows the cost-minimizing response. The vertical axis measures the firm’s input of capital in machine-hours per month—the horizontal axis measures the quantity of wastewater in gallons per month. First, consider the level at which the firm produces when there is no effluent fee. Point A represents the input of capital and the level of wastewater that allows the firm to produce its quota of steel at minimum cost. Because the firm is minimizing cost, A lies on the isocost line FC, which is tangent to the isoquant. The slope of the isocost line is equal to -$10/$40 = -0.25 because a unit of capital costs four times more than a unit of wastewater. CHAPTER 7 • The Cost of Production 249 When the effluent fee is imposed, the cost of wastewater increases from $10 per gallon to $20: For every gallon of wastewater (which costs $10), the firm has to pay the government an additional $10. The effluent fee therefore increases the cost of wastewater relative to capital. To produce the same output at the lowest possible cost, the manager must choose the isocost line with a slope of −$20/$40 = −0.5 that is tangent to the isoquant. In Figure 7.5, DE is the appropriate isocost line, and B gives the appropriate combination of capital and wastewater. The move from A to B shows that with an effluent fee the use of an alternative production technology that emphasizes the greater use of capital (3500 machine-hours) and less production of wastewater (5000 gallons) is cheaper than the original process, which did not emphasize recycling. Note that the total cost of production has increased to $240,000: $140,000 for capital, $50,000 for wastewater, and $50,000 for the effluent fee. We can learn two lessons from this decision. First, the more easily factors can be substituted in the production process—that is, the more easily the firm can deal with its taconite particles without using the river for waste treatment—the more effective the fee will be in reducing effluent. Second, the greater the degree of substitution, the less the firm will have to pay. In our example, the fee would have been $100,000 had the firm not changed its inputs. By moving production from A to B, however, the steel company pays only a $50,000 fee. Cost Minimization with Varying Output Levels In the previous section we saw how a cost-minimizing firm selects a combination of inputs to produce a given level of output. Now we extend this analysis to see how the firm’s costs depend on its output level. To do this, we determine the firm’s cost-minimizing input quantities for each output level and then calculate the resulting cost. The cost-minimization exercise yields the result illustrated by Figure 7.6. We have assumed that the firm can hire labor L at w = $10/hour and rent a unit of capital K for r = $20/hour. Given these input costs, we have drawn three of the firm’s isocost lines. Each isocost line is given by the following equation: C = ($10/hour)(L) + ($20/hour)(K) In Figure 7.6 (a), the lowest (unlabeled) line represents a cost of $1000, the middle line $2000, and the highest line $3000. You can see that each of the points A, B, and C in Figure 7.6 (a) is a point of tangency between an isocost curve and an isoquant. Point B, for example, shows us that the lowest-cost way to produce 200 units of output is to use 100 units of labor and 50 units of capital; this combination lies on the $2000 isocost line. Similarly, the lowest-cost way to produce 100 units of output (the lowest unlabeled isoquant) is $1000 (at point A, L = 50, K = 25); the least-cost means of getting 300 units of output is $3000 (at point C, L = 150, K = 75). The curve passing through the points of tangency between the firm’s isocost lines and its isoquants is its expansion path. The expansion path describes the combinations of labor and capital that the firm will choose to minimize costs at each output level. As long as the use of both labor and capital increases with output, the curve will be upward sloping. In this particular c |
ase we can easily calculate the slope of the line. As output increases from 100 to 200 units, capital increases from 25 to 50 units, while labor increases from 50 to 100 units. For each level of output, the firm uses half as much capital as labor. Therefore, the expansion path is a straight line with a slope equal to K/L = (50 - 25)/(100 - 50) = 1 2 • expansion path Curve passing through points of tangency between a firm’s isocost lines and its isoquants. 250 PART 2 • Producers, Consumers, and Competitive Markets Capital per year 150 $3000 Isocost Line 100 75 50 25 3000 2000 1000 Cost (dollars per year) $2000 Isocost Line Expansion Path C B A 300 Unit Isoquant 200 Unit Isoquant 50 100 150 200 300 Labor per year (a) E 200 (b) D 100 F Long-Run Total Cost 300 Output (units per year) FIGURE 7.6 A FIRM’S EXPANSION PATH AND LONG-RUN TOTAL COST CURVE In (a), the expansion path (from the origin through points A, B, and C) illustrates the lowestcost combinations of labor and capital that can be used to produce each level of output in the long run—i.e., when both inputs to production can be varied. In (b), the corresponding long-run total cost curve (from the origin through points D, E, and F) measures the least cost of producing each level of output. The Expansion Path and Long-Run Costs The firm’s expansion path contains the same information as its long-run total cost curve, C(q). This can be seen in Figure 7.6 (b). To move from the expansion path to the cost curve, we follow three steps: 1. Choose an output level represented by an isoquant in Figure 7.6 (a). Then find the point of tangency of that isoquant with an isocost line. CHAPTER 7 • The Cost of Production 251 2. From the chosen isocost line, determine the minimum cost of producing the output level that has been selected. 3. Graph the output-cost combination in Figure 7.6 (b). Suppose we begin with an output of 100 units. The point of tangency of the 100-unit isoquant with an isocost line is given by point A in Figure 7.6 (a). Because A lies on the $1000 isocost line, we know that the minimum cost of producing an output of 100 units in the long run is $1000. We graph this combination of 100 units of output and $1000 cost as point D in Figure 7.6 (b). Point D thus represents the $1000 cost of producing 100 units of output. Similarly, point E represents the $2000 cost of producing 200 units which corresponds to point B on the expansion path. Finally, point F represents the $3000 cost of 300 units corresponding to point C. Repeating these steps for every level of output gives the long-run total cost curve in Figure 7.6 (b)—i.e., the minimum long-run cost of producing each level of output. In this particular example, the long-run total cost curve is a straight line. Why? Because there are constant returns to scale in production: As inputs increase proportionately, so do outputs. As we will see in the next section, the shape of the expansion path provides information about how costs change with the scale of the firm’s operation. EXAM PLE 7.5 REDUCING THE USE OF ENERGY Policy makers around the world have been concerned with finding ways to reduce the use of energy. In part, this reflects environmental concerns—most energy consumption uses fossil fuels and thus contributes to the emission of greenhouse gases and global warming. But energy, whether in the form of oil, natural gas, coal or nuclear, is also expensive, so if companies can find ways to reduce their energy use, they can lower their costs. There are essentially two ways that companies can reduce the amount of energy they use. The first is to substitute other factors of production for energy. For example, some machines might be more costly but also use less energy, so if energy prices rise, firms could respond by buying and using those energy-efficient machines, effectively substituting capital for energy. This is exactly what has happened as energy prices rose in recent years: firms bought and installed expensive but more energy-efficient heating and cooling systems, industrial processing equipment, trucks, cars, and other vehicles. The second way to reduce energy use is through technological change. As time passes, research and development lead to innovations that make it possible to produce the same output using fewer inputs—less labor, less capital, and less energy. Thus even if the relative prices of energy and capital stay the same, firms will use less energy (and less capital) to produce the same output. Advances in robotics during the past two decades are an example of this; cars and trucks are now produced with less capital and energy (as well as less labor). These two ways of reducing energy use are illustrated in Figures 7.7(a) and (b), which show how capital and energy are combined to produce output.8 The isoquants in each figure represent the various combinations of capital and energy that can be used to generate the same level of output. The figures illustrate how reductions in energy use can be achieved in two ways. First, firms can substitute more capital for energy, perhaps in response to a government subsidy for investment in energysaving equipment and/or an increase in the cost of electricity. This is shown as a movement along isoquant q1 from point A to point B in Figure 7.7(a), with capital increasing from K1 to K2 and energy decreasing from E2 to E1 in response to a shift in the isocost curve from C0 to C1. Second, technological 8This example was inspired by Kenneth Gillingham, Richard G. Newell, and Karen Palmer, “Energy Efficiency Economics and Policy,” Annual Review of Resource Economics, 2009, Vol. 1: 597–619. 252 PART 2 • Producers, Consumers, and Competitive Markets Capital C1 FIGURE 7.7a ENERGY EFFICIENCY THROUGH CAPITAL SUBSTITUTION FOR LABOR Greater energy efficiency can be achieved if capital is substituted for energy. This is shown as a movement along isoquant q1 from point A to point B, with capital increasing from K1 to K2 and energy decreasing from E2 to E1 in response to a shift in the isocost curve from C0 to C1. K2 K1 FIGURE 7.7b ENERGY EFFICIENCY THROUGH TECHNOLOGICAL CHANGE Technological change implies that the same output can be produced with smaller amounts of inputs. Here the isoquant labeled q1 shows combinations of energy and capital that will yield output q1; the tangency with the isocost line at point C occurs with energy and capital combinations E2 and K2. Because of technological change the isoquant shifts inward, so the same output q1 can now be produced with less energy and capital, in this case at point D, with energy and capital combination E1 and K1. Capital K2 K1 B E1 A E2 Energy (a) q1 C0 C D E1 E2 Energy (b) q1 New q1 CHAPTER 7 • The Cost of Production 253 change can shift the isoquant q1 that represents a particular output level inward, as in Figure 7.7(b). Be careful when you read this graph. Both isoquants generate the same level of output, but the technological change has made it possible to achieve the same output with less capital (a move from K2 to K1) and with less energy (a move from E2 to E1). The result is that isoquant q1 has moved inward from one that is tangent to an isocost curve at point C to one that is tangent at point D because we can now achieve the same output (q1) with less capital and less energy. 7.4 Long-Run versus Short-Run Cost Curves We saw earlier (see Figure 7.1— page 239) that short-run average cost curves are U-shaped. We will see that long-run average cost curves can also be U-shaped, but different economic factors explain the shapes of these curves. In this section, we discuss long-run average and marginal cost curves and highlight the differences between these curves and their short-run counterparts. The Inflexibility of Short-Run Production Recall that we defined the long run as occurring when all inputs to the firm are variable. In the long run, the firm’s planning horizon is long enough to allow for a change in plant size. This added flexibility allows the firm to produce at a lower average cost than in the short run. To see why, we might compare the situation in which capital and labor are both flexible to the case in which capital is fixed in the short run. Figure 7.8 shows the firm’s production isoquants. The firm’s long-run expansion path is the straight line from the origin that corresponds to the expansion Capital per year E C A K2 K1 FIGURE 7.8 THE INFLEXIBILITY OF SHORT-RUN PRODUCTION When a firm operates in the short run, its cost of production may not be minimized because of inflexibility in the use of capital inputs. Output is initially at level q1. In the short run, output q2 can be produced only by increasing labor from L1 to L3 because capital is fixed at K1. In the long run, the same output can be produced more cheaply by increasing labor from L1 to L2 and capital from K1 to K2. Long-Run Expansion Path Short-Run Expansion Path P q2 q1 L1 L2 B L3 D F Labor per year 254 PART 2 • Producers, Consumers, and Competitive Markets path in Figure 7.6. Now, suppose capital is fixed at a level K1 in the short run. To produce output q1, the firm would minimize costs by choosing labor equal to L1, corresponding to the point of tangency with the isocost line AB. The inflexibility appears when the firm decides to increase its output to q2 without increasing its use of capital. If capital were not fixed, it would produce this output with capital K2 and labor L2. Its cost of production would be reflected by isocost line CD. However, the fact that capital is fixed forces the firm to increase its output by using capital K1 and labor L3 at point P. Point P lies on the isocost line EF, which represents a higher cost than isocost line CD. Why is the cost of production higher when capital is fixed? Because the firm is unable to substitute relatively inexpensive capital for more costly labor when it expands production. This inflexibility is reflected in the short-run expansion path, which begins as a line from the origin an |
d then becomes a horizontal line when the capital input reaches K1. Long-Run Average Cost In the long run, the ability to change the amount of capital allows the firm to reduce costs. To see how costs vary as the firm moves along its expansion path in the long run, we can look at the long-run average and marginal cost curves.9 The most important determinant of the shape of the long-run average and marginal cost curves is the relationship between the scale of the firm’s operation and the inputs that are required to minimize its costs. Suppose, for example, that the firm’s production process exhibits constant returns to scale at all input levels. In this case, a doubling of inputs leads to a doubling of output. Because input prices remain unchanged as output increases, the average cost of production must be the same for all levels of output. Suppose instead that the firm’s production process is subject to increasing returns to scale: A doubling of inputs leads to more than a doubling of output. In that case, the average cost of production falls with output because a doubling of costs is associated with a more than twofold increase in output. By the same logic, when there are decreasing returns to scale, the average cost of production must be increasing with output. We saw that the long-run total cost curve associated with the expansion path in Figure 7.6 (a) was a straight line from the origin. In this constant-returns-to-scale case, the long-run average cost of production is constant: It is unchanged as output increases. For an output of 100, long-run average cost is $1000/100 = $10 per unit. For an output of 200, long-run average cost is $2000/200 = $10 per unit; for an output of 300, average cost is also $10 per unit. Because a constant average cost means a constant marginal cost, the long-run average and marginal cost curves are given by a horizontal line at a $10/unit cost. Recall that in the last chapter we examined a firm’s production technology that exhibits first increasing returns to scale, then constant returns to scale, and eventually decreasing returns to scale. Figure 7.9 shows a typical long-run average cost curve (LAC) consistent with this description of the production process. Like the short-run average cost curve (SAC), the long-run average cost curve is U-shaped, but the source of the U-shape is increasing and decreasing returns to scale, rather than diminishing returns to a factor of production. The long-run marginal cost curve (LMC) can be determined from the longrun average cost curve; it measures the change in long-run total costs as output 9In the short run, the shapes of the average and marginal cost curves were determined primarily by diminishing returns. As we showed in Chapter 6, diminishing returns to each factor is consistent with constant (or even increasing) returns to scale. • long-run average cost curve (LAC) Curve relating average cost of production to output when all inputs, including capital, are variable. • short-run average cost curve (SAC) Curve relating average cost of production to output when level of capital is fixed. • long-run marginal cost curve (LMC) Curve showing the change in long-run total cost as output is increased incrementally by 1 unit. Cost (dollars per unit of output) CHAPTER 7 • The Cost of Production 255 FIGURE 7.9 LONG-RUN AVERAGE AND MARGINAL COST When a firm is producing at an output at which the long-run average cost LAC is falling, the long-run marginal cost LMC is less than LAC. Conversely, when LAC is increasing, LMC is greater than LAC. The two curves intersect at A, where the LAC curve achieves its minimum. A LMC LAC Output is increased incrementally. LMC lies below the long-run average cost curve when LAC is falling and above it when LAC is rising.10 The two curves intersect at A, where the long-run average cost curve achieves its minimum. In the special case in which LAC is constant, LAC and LMC are equal. Economies and Diseconomies of Scale As output increases, the firm’s average cost of producing that output is likely to decline, at least to a point. This can happen for the following reasons: 1. If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive. 2. Scale can provide flexibility. By varying the combination of inputs utilized to produce the firm’s output, managers can organize the production process more effectively. 3. The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and can therefore negotiate better prices. The mix of inputs might change with the scale of the firm’s operation if managers take advantage of lower-cost inputs. At some point, however, it is likely that the average cost of production will begin to increase with output. There are three reasons for this shift: 1. At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs effectively. 2. Managing a larger firm may become more complex and inefficient as the number of tasks increases. 3. The advantages of buying in bulk may have disappeared once certain quantities are reached. At some point, available supplies of key inputs may be limited, pushing their costs up. To analyze the relationship between the scale of the firm’s operation and the firm’s costs, we need to recognize that when input proportions do change, the firm’s expansion path is no longer a straight line, and the concept of returns to 10Recall that AC TC/q. It follows that AC/q [q(TC/q) − TC]/q2 (MC − AC)/q. Clearly, when AC is increasing, AC/q is positive and MC > AC. Correspondingly, when AC is decreasing, AC/q is negative and MC < AC. 256 PART 2 • Producers, Consumers, and Competitive Markets • economies of scale Situation in which output can be doubled for less than a doubling of cost. • diseconomies of scale Situation in which a doubling of output requires more than a doubling of cost. In §6.4, we explain that increasing returns to scale occurs when output more than doubles as inputs are doubled proportionately. scale no longer applies. Rather, we say that a firm enjoys economies of scale when it can double its output for less than twice the cost. Correspondingly, there are diseconomies of scale when a doubling of output requires more than twice the cost. The term economies of scale includes increasing returns to scale as a special case, but it is more general because it reflects input proportions that change as the firm changes its level of production. In this more general setting, a U-shaped long-run average cost curve characterizes the firm facing economies of scale for relatively low output levels and diseconomies of scale for higher levels. To see the difference between returns to scale (in which inputs are used in constant proportions as output is increased) and economies of scale (in which input proportions are variable), consider a dairy farm. Milk production is a function of land, equipment, cows, and feed. A dairy farm with 50 cows will use an input mix weighted toward labor and not equipment (i.e., cows are milked by hand). If all inputs were doubled, a farm with 100 cows could double its milk production. The same will be true for the farm with 200 cows, and so forth. In this case, there are constant returns to scale. Large dairy farms, however, have the option of using milking machines. If a large farm continues milking cows by hand, regardless of the size of the farm, constant returns would continue to apply. However, when the farm moves from 50 to 100 cows, it switches its technology toward the use of machines, and, in the process, is able to reduce its average cost of milk production from 20 cents per gallon to 15 cents per gallon. In this case, there are economies of scale. This example illustrates the fact that a firm’s production process can exhibit constant returns to scale, but still have economies of scale as well. Of course, firms can enjoy both increasing returns to scale and economies of scale. It is helpful to compare the two: Increasing Returns to Scale: Output more than doubles when the quantities of all inputs are doubled. Economies of Scale: A doubling of output requires less than a doubling of cost. Economies of scale are often measured in terms of a cost-output elasticity, EC. EC is the percentage change in the cost of production resulting from a 1-percent increase in output: EC = (C/C)/(q/q) (7.5) To see how EC relates to our traditional measures of cost, rewrite equation (7.5) as follows: EC = (C/q)/(C/q) = MC/AC (7.6) Clearly, EC is equal to 1 when marginal and average costs are equal. In that case, costs increase proportionately with output, and there are neither economies nor diseconomies of scale (constant returns to scale would apply if input proportions were fixed). When there are economies of scale (when costs increase less than proportionately with output), marginal cost is less than average cost (both are declining) and EC is less than 1. Finally, when there are diseconomies of scale, marginal cost is greater than average cost and EC is greater than 1. CHAPTER 7 • The Cost of Production 257 The Relationship between Short-Run and Long-Run Cost Figure 7.10 shows the relationship between short-run and long-run cost. Assume that a firm is uncertain about the future demand for its product and is considering three alternative plant sizes. The short-run average cost curves for the three plants are given by SAC1, SAC2, and SAC3. The decision is important because, once built, the firm may not be able to change the plant size for some time. Figure 7.10 illustrates the case in which there are three possible plant sizes. If the firm expects to produce q0 units of output, then it should build the smallest plant. Its average cost of production would be $8. (If it then decided to produce an output of q1, its short run average cost would still be $8.) However, if it expects to produce q2, the middle-size plant |
is best. Similarly, with an output of q3, the largest of the three plants would be the most efficient choice. What is the firm’s long-run average cost curve? In the long run, the firm can change the size of its plant. In doing so, it will always choose the plant that minimizes the average cost of production. The long-run average cost curve is given by the crosshatched portions of the short-run average cost curves because these show the minimum cost of production for any output level. The long-run average cost curve is the envelope of the short-run average cost curves—it envelops or surrounds the short-run curves. Now suppose that there are many choices of plant size, each having a different short-run average cost curve. Again, the long-run average cost curve is the envelope of the short-run curves. In Figure 7.10 it is the curve LAC. Whatever the firm wants to produce, it can choose the plant size (and the mix of capital and labor) that allows it to produce that output at the minimum average cost. The long-run average cost curve exhibits economies of scale initially but exhibits diseconomies at higher output levels. To clarify the relationship between short-run and long-run cost curves, consider a firm that wants to produce output q1. If it builds a small plant, the short-run average cost curve SAC1 is relevant. The average cost of production (at B on SAC1) is $8. A small plant is a better choice than a medium-sized plant with an average cost of production of $10 (A on curve SAC2). Point B would therefore become one point on the long-run cost function when only three plant sizes are possible. If plants of Cost (dollars per unit of output) $10 $8 LMC SMC1 A B SAC1 SAC2 SMC3 SAC3 LAC SMC2 q0 q1 q2 q3 Output FIGURE 7.10 LONG-RUN COST WITH ECONOMIES AND DISECONOMIES OF SCALE The long-run average cost curve LAC is the envelope of the short-run average cost curves SAC1, SAC2, and SAC3. With economies and diseconomies of scale, the minimum points of the short-run average cost curves do not lie on the long-run average cost curve. 258 PART 2 • Producers, Consumers, and Competitive Markets other sizes could be built, and if at least one size allowed the firm to produce q1 at less than $8 per unit, then B would no longer be on the long-run cost curve. In Figure 7.10, the envelope that would arise if plants of any size could be built is U-shaped. Note, once again, that the LAC curve never lies above any of the short-run average cost curves. Also note that because there are economies and diseconomies of scale in the long run, the points of minimum average cost of the smallest and largest plants do not lie on the long-run average cost curve. For example, a small plant operating at minimum average cost is not efficient because a larger plant can take advantage of increasing returns to scale to produce at a lower average cost. Finally, note that the long-run marginal cost curve LMC is not the envelope of the short-run marginal cost curves. Short-run marginal costs apply to a particular plant; long-run marginal costs apply to all possible plant sizes. Each point on the long-run marginal cost curve is the short-run marginal cost associated with the most cost-efficient plant. Consistent with this relationship, SMC1 intersects LMC in Figure 7.10 at the output level q0 at which SAC1 is tangent to LAC. 7.5 Production with Two Outputs— Economies of Scope Many firms produce more than one product. Sometimes a firm’s products are closely linked to one another: A chicken farm, for instance, produces poultry and eggs, an automobile company produces automobiles and trucks, and a university produces teaching and research. At other times, firms produce physically unrelated products. In both cases, however, a firm is likely to enjoy production or cost advantages when it produces two or more products. These advantages could result from the joint use of inputs or production facilities, joint marketing programs, or possibly the cost savings of a common administration. In some cases, the production of one product yields an automatic and unavoidable byproduct that is valuable to the firm. For example, sheet metal manufacturers produce scrap metal and shavings that they can sell. Product Transformation Curves To study the economic advantages of joint production, let’s consider an automobile company that produces two products, cars and tractors. Both products use capital (factories and machinery) and labor as inputs. Cars and tractors are not typically produced at the same plant, but they do share management resources, and both rely on similar machinery and skilled labor. The managers of the company must choose how much of each product to produce. Figure 7.11 shows two product transformation curves, each showing the various combinations of cars and tractors that can be produced with a given input of labor and machinery. Curve O1 describes all combinations of the two outputs that can be produced with a relatively low level of inputs, and curve O2 describes the output combinations associated with twice the inputs. Why does the product transformation curve have a negative slope? Because in order to get more of one output, the firm must give up some of the other output. For example, a firm that emphasizes car production will devote less of its resources to producing tractors. In Figure 7.11, curve O2 lies twice as far from the origin as curve O1, signifying that this firm’s production process exhibits constant returns to scale in the production of both commodities. • product transformation curve Curve showing the various combinations of two different outputs (products) that can be produced with a given set of inputs. Number of tractors O2 O1 CHAPTER 7 • The Cost of Production 259 FIGURE 7.11 PRODUCT TRANSFORMATION CURVE The product transformation curve describes the different combinations of two outputs that can be produced with a fixed amount of production inputs. The product transformation curves O1 and O2 are bowed out (or concave) because there are economies of scope in production. 0 Number of cars If curve O1 were a straight line, joint production would entail no gains (or losses). One smaller company specializing in cars and another in tractors would generate the same output as a single company producing both. However, the product transformation curve is bowed outward (or concave) because joint production usually has advantages that enable a single company to produce more cars and tractors with the same resources than would two companies producing each product separately. These production advantages involve the joint sharing of inputs. A single management, for example, is often able to schedule and organize production and to handle accounting and financial activities more effectively than separate managements. Economies and Diseconomies of Scope In general, economies of scope are present when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single product (with equivalent production inputs allocated between them). If a firm’s joint output is less than that which could be achieved by separate firms, then its production process involves diseconomies of scope. This possibility could occur if the production of one product somehow conflicted with the production of the second. There is no direct relationship between economies of scale and economies of scope. A two-output firm can enjoy economies of scope even if its production process involves diseconomies of scale. Suppose, for example, that manufacturing flutes and piccolos jointly is cheaper than producing both separately. Yet the production process involves highly skilled labor and is most effective if undertaken on a small scale. Likewise, a joint-product firm can have economies of scale for each individual product yet not enjoy economies of scope. Imagine, for example, a large conglomerate that owns several firms that produce efficiently on a large scale but that do not take advantage of economies of scope because they are administered separately. The Degree of Economies of Scope The extent to which there are economies of scope can also be determined by studying a firm’s costs. If a combination of inputs used by one firm generates more output than two independent firms would produce, then it costs less • economies of scope Situation in which joint output of a single firm is greater than output that could be achieved by two different firms when each produces a single product. • diseconomies of scope Situation in which joint output of a single firm is less than could be achieved by separate firms when each produces a single product. 260 PART 2 • Producers, Consumers, and Competitive Markets • degree of economies of scope (SC) Percentage of cost savings resulting when two or more products are produced jointly rather than individually. for a single firm to produce both products than it would cost the independent firms. To measure the degree to which there are economies of scope, we should ask what percentage of the cost of production is saved when two (or more) products are produced jointly rather than individually. Equation (7.7) gives the degree of economies of scope (SC) that measures this savings in cost: SC = C(q1) + C(q2) - C(q1, q2) C(q1, q2) (7.7) C(q1) represents the cost of producing only output q1, C(q2) represents the cost of producing only output q2, and C(q1, q2) the joint cost of producing both outputs. When the physical units of output can be added, as in the car–tractor example, + q2). With economies of scope, the joint cost is less the expression becomes C(q1 than the sum of the individual costs. Thus, SC is greater than 0. With diseconomies of scope, SC is negative. In general, the larger the value of SC, the greater the economies of scope. E XAM PLE 7.6 ECONOMIES OF SCOPE IN THE TRUCKING INDUSTRY Suppose that you are managing a trucking firm that hauls loads of different sizes between cities.11 In the tru |
cking business, several related but distinct products can be offered, depending on the size of the load and the length of the haul. First, any load, small or large, can be taken directly from one location to another without intermediate stops. Second, a load can be combined with other loads (which may go between different locations) and eventually be shipped indirectly from its origin to the appropriate destination. Each type of load, partial or full, may involve different lengths of haul. This range of possibilities raises questions about both economies of scale and economies of scope. The scale question asks whether large-scale, direct hauls are cheaper and more profitable than individual hauls by small truckers. The scope question asks whether a large trucking firm enjoys cost advantages in operating both direct quick hauls and indirect, slower (but less expensive) hauls. Central planning and organization of routes could provide for economies of scope. The key to the presence of economies of scale is the fact that the organization of routes and the types of hauls we have described can be accomplished more efficiently when many hauls are involved. In such cases, a firm is more likely to be able to schedule hauls in which most truckloads are full rather than half-full. Studies of the trucking industry show that economies of scope are present. For example, one analysis of 105 trucking firms looked at four distinct outputs: (1) short hauls with partial loads, (2) intermediate hauls with partial loads, (3) long hauls with partial loads, and (4) hauls with total loads. The results indicate that the degree of economies of scope SC was 1.576 for a reasonably large firm. However, the degree of economies of scope falls to 0.104 when the firm becomes very large. Because large firms carry sufficiently large truckloads, there is usually no advantage to stopping at an intermediate terminal to fill a partial load. A direct trip from the origin to the destination is sufficient. Apparently, however, because other disadvantages are associated with the management of very large firms, the economies of scope 11This example is based on Judy S. Wang Chiang and Ann F. Friedlaender, “Truck Technology and Efficient Market Structure,” Review of Economics and Statistics 67 (1985): 250–58. CHAPTER 7 • The Cost of Production 261 get smaller as the firm gets bigger. In any event, the ability to combine partial loads at an intermediate location lowers the firm’s costs and increases its profitability. The study suggests, therefore, that to compete in the trucking industry, a firm must be large enough to be able to combine loads at intermediate stopping points. *7.6 Dynamic Changes in Costs— The Learning Curve Our discussion thus far has suggested one reason why a large firm may have a lower long-run average cost than a small firm: increasing returns to scale in production. It is tempting to conclude that firms that enjoy lower average cost over time are growing firms with increasing returns to scale. But this need not be true. In some firms, long-run average cost may decline over time because workers and managers absorb new technological information as they become more experienced at their jobs. As management and labor gain experience with production, the firm’s marginal and average costs of producing a given level of output fall for four reasons: 1. Workers often take longer to accomplish a given task the first few times they do it. As they become more adept, their speed increases. 2. Managers learn to schedule the production process more effectively, from the flow of materials to the organization of the manufacturing itself. 3. Engineers who are initially cautious in their product designs may gain enough experience to be able to allow for tolerances in design that save costs without increasing defects. Better and more specialized tools and plant organization may also lower cost. 4. Suppliers may learn how to process required materials more effectively and pass on some of this advantage in the form of lower costs. As a consequence, a firm “learns” over time as cumulative output increases. Managers can use this learning process to help plan production and forecast future costs. Figure 7.11 illustrates this process in the form of a learning curve—a curve that describes the relationship between a firm’s cumulative output and the amount of inputs needed to produce each unit of output. Graphing the Learning Curve Figure 7.12 shows a learning curve for the production of machine tools. The horizontal axis measures the cumulative number of lots of machine tools (groups of approximately 40) that the firm has produced. The vertical axis shows the number of hours of labor needed to produce each lot. Labor input per unit of output directly affects the production cost because the fewer the hours of labor needed, the lower the marginal and average cost of production. The learning curve in Figure 7.12 is based on the relationship L = A + BN -b (7.8) • learning curve Graph relating amount of inputs needed by a firm to produce each unit of output to its cumulative output. 262 PART 2 • Producers, Consumers, and Competitive Markets FIGURE 7.12 THE LEARNING CURVE A firm’s production cost may fall over time as managers and workers become more experienced and more effective at using the available plant and equipment. The learning curve shows the extent to which hours of labor needed per unit of output fall as the cumulative output increases. Hours of labor per machine lot 8 6 4 2 0 10 20 30 40 50 Cumulative number of machine lots produced where N is the cumulative units of output produced and L the labor input per unit of output. A, B, and b are constants, with A and B positive, and b between 0 and 1. When N is equal to 1, L is equal to A B, so that A B measures the labor input required to produce the first unit of output. When b equals 0, labor input per unit of output remains the same as the cumulative level of output increases; there is no learning. When b is positive and N gets larger and larger, L becomes arbitrarily close to A. A, therefore, represents the minimum labor input per unit of output after all learning has taken place. The larger b is, the more important the learning effect. With b equal to 0.5, for example, the labor input per unit of output falls proportionately to the square root of the cumulative output. This degree of learning can substantially reduce production costs as a firm becomes more experienced. In this machine tool example, the value of b is 0.31. For this particular learning curve, every doubling in cumulative output causes the input requirement (less the minimum attainable input requirement) to fall by about 20 percent.12 As Figure 7.12 shows, the learning curve drops sharply as the cumulative number of lots increases to about 20. Beyond an output of 20 lots, the cost savings are relatively small. Learning versus Economies of Scale Once the firm has produced 20 or more machine lots, the entire effect of the learning curve would be complete, and we could use the usual analysis of cost. If, however, the production process were relatively new, relatively high cost at low levels of output (and relatively low cost at higher levels) would indicate learning effects, not economies of scale. With learning, the cost of production for a mature firm is relatively low regardless of the scale of the firm’s operation. If a firm that produces machine tools in lots knows that it enjoys economies of scale, it should produce its machines in very large lots to take advantage of the lower cost associated with size. If there is a learning curve, 12Because (L − A) BN−.31, we can check that 0.8(L − A) is approximately equal to B(2N)−.31. CHAPTER 7 • The Cost of Production 263 Cost (dollars per unit of output) FIGURE 7.13 ECONOMIES OF SCALE VERSUS LEARNING A firm’s average cost of production can decline over time because of growth of sales when increasing returns are present (a move from A to B on curve AC1), or it can decline because there is a learning curve (a move from A on curve AC1 to C on curve AC2). Learning C A Economies of Scale B AC 1 AC 2 Output the firm can lower its cost by scheduling the production of many lots regardless of individual lot size. Figure 7.13 shows this phenomenon. AC1 represents the long-run average cost of production of a firm that enjoys economies of scale in production. Thus the increase in the rate of output from A to B along AC1 leads to lower cost due to economies of scale. However, the move from A on AC1 to C on AC2 leads to lower cost due to learning, which shifts the average cost curve downward. The learning curve is crucial for a firm that wants to predict the cost of producing a new product. Suppose, for example, that a firm producing machine tools knows that its labor requirement per machine for the first 10 machines is 1.0, the minimum labor requirement A is equal to zero, and b is approximately equal to 0.32. Table 7.3 calculates the total labor requirement for producing 80 machines. Because there is a learning curve, the per-unit labor requirement falls with increased production. As a result, the total labor requirement for producing TABLE 7.3 PREDICTING THE LABOR REQUIREMENTS OF PRODUCING A GIVEN OUTPUT CUMULATIVE OUTPUT (N) PER-UNIT LABOR REQUIREMENT FOR EACH 10 UNITS OF OUTPUT (L)* TOTAL LABOR REQUIREMENT 10 20 30 40 50 60 70 80 1.00 .80 .70 .64 .60 .56 .53 .51 10.0 18.0 (10.0 8.0) 25.0 (18.0 7.0) 31.4 (25.0 6.4) 37.4 (31.4 6.0) 43.0 (37.4 5.6) 48.3 (43.0 5.3) 53.4 (48.3 5.1) *The numbers in this column were calculated from the equation log(L) −0.322 log(N/10), where L is the unit labor input and N is cumulative output. 264 PART 2 • Producers, Consumers, and Competitive Markets more and more output increases in smaller and smaller increments. Therefore, a firm looking only at the high initial labor requirement will obtain an overly pessimistic view of the business. Suppose the firm plans to be in busine |
ss for a long time, producing 10 units per year. Suppose the total labor requirement for the first year’s production is 10. In the first year of production, the firm’s cost will be high as it learns the business. But once the learning effect has taken place, production costs will fall. After 8 years, the labor required to produce 10 units will be only 5.1, and per-unit cost will be roughly half what it was in the first year of production. Thus, the learning curve can be important for a firm deciding whether it is profitable to enter an industry. E XAM PLE 7.7 THE LEARNING CURVE IN PRACTICE Suppose that you are the manager of a firm that has just entered the chemical processing industry. You face the following problem: Should you produce a relatively small quantity of industrial chemicals and sell them at a high price, or should you increase your output and reduce your price? The second alternative is appealing if you expect to move down a learning curve: the increased volume will lower your average production costs over time and increase your profit. Before proceeding, you should determine whether there is indeed a learning curve; if so, producing and selling a higher volume will lower your average production costs over time and increase profitability. You also need to distinguish learning from economies of scale. With economies of scale, average cost is lower when output at any point in time is higher, whereas with learning average cost declines as the cumulative output of the firm increases. By producing relatively small volumes over and over, you move down the learning curve, but you don’t get much in the way of scale economies. The opposite is the case if you produce large volumes at one point in time, but you don’t have the opportunity to repeat that experience over time. To decide what to do, you can examine the available statistical evidence that distinguishes the components of the learning curve (learning new processes by labor, engineering improvements, etc.) from increasing returns to scale. For example, a study of 37 chemical products reveals that cost reductions in the chemical processing industry are directly tied to the growth of cumulative industry output, to investment in improved capital equipment, and, to a lesser extent, to economies of scale.13 In fact, for the entire sample of chemical products, average costs of production fall at 5.5 percent per year. The study reveals that for each doubling of plant scale, the average cost of production falls by 11 percent. For each doubling of cumulative output, however, the average cost of production falls by 27 percent. The evidence shows clearly that learning effects are more important than economies of scale in the chemical processing industry.14 13The study was conducted by Marvin Lieberman, “The Learning Curve and Pricing in the Chemical Processing Industries,” RAND Journal of Economics 15 (1984): 213–28. 14The author used the average cost AC of the chemical products, the cumulative industry output X, and the average scale of a production plant Z. He then estimated the relationship log (AC) −0.387 log (X) −0.173 log (Z). The −0.387 coefficient on cumulative output tells us that for every 1-percent increase in cumulative output, average cost decreases 0.387 percent. The −0.173 coefficient on plant size tells us that for every 1-percent increase in plant size, average cost decreases 0.173 percent. By interpreting the two coefficients in light of the output and plant-size variables, we can allocate about 15 percent of the cost reduction to increases in the average scale of plants and 85 percent to increases in cumulative industry output. Suppose plant scale doubled while cumulative output increased by a factor of 5 during the study. In that case, costs would fall by 11 percent from the increased scale and by 62 percent from the increase in cumulative output. CHAPTER 7 • The Cost of Production 265 Relative production hours per aircraft 100 80 60 40 20 0 0 Average for First 100 Aircraft Average for First 500 Aircraft 100 200 300 400 500 Number of aircraft produced FIGURE 7.14 LEARNING CURVE FOR AIRBUS INDUSTRIE The learning curve relates the labor requirement per aircraft to the cumulative number of aircraft produced. As the production process becomes better organized and workers gain familiarity with their jobs, labor requirements fall dramatically. The learning curve has also been shown to be important in the semiconductor industry. A study of seven generations of dynamic random-access memory (DRAM) semiconductors from 1974 to 1992 found that the learning rates averaged about 20 percent; thus a 10-percent increase in cumulative production would lead to a 2-percent decrease in cost.15 The study also compared learning by firms in Japan to firms in the United States and found that there was no distinguishable difference in the speed of learning. Another example is the aircraft industry, where studies have found learning rates that are as high as 40 percent. This is illustrated in Figure 7.14, which shows the labor requirements for producing aircraft by Airbus Industrie. Observe that the first 10 or 20 airplanes require far more labor to produce than the hundredth or two hundredth airplane. Also note how the learning curve flattens out after a certain point; in this case nearly all learning is complete after 200 airplanes have been built. Learning-curve effects can be important in determining the shape of long-run cost curves and can thus help guide management decisions. Managers can use learning-curve information to decide whether a production operation is profitable and, if so, how to plan how large the plant operation and the volume of cumulative output need be to generate a positive cash flow. *7.7 Estimating and Predicting Cost A business that is expanding or contracting its operation must predict how costs will change as output changes. Estimates of future costs can be obtained from a cost function, which relates the cost of production to the level of output and other variables that the firm can control. • cost function Function relating cost of production to level of output and other variables that the firm can control. 15The study was conducted by D. A. Irwin and P. J. Klenow, “Learning-by-Doing Spillovers in the Semiconductor Industry,” Journal of Political Economy 102 (December 1994): 1200–27. 266 PART 2 • Producers, Consumers, and Competitive Markets FIGURE 7.15 VARIABLE COST CURVE FOR THE AUTOMOBILE INDUSTRY An empirical estimate of the variable cost curve can be obtained by using data for individual firms in an industry. The variable cost curve for automobile production is obtained by determining statistically the curve that best fits the points that relate the output of each firm to the firm’s variable cost of production. Variable cost General Motors • Toyota • Honda Nissan •• Volvo • • Ford • Chrysler Quantity of cars Least-squares regression is explained in the appendix to this book. Suppose we wanted to characterize the short-run cost of production in the automobile industry. We could obtain data on the number of automobiles Q produced by each car company and relate this information to the company’s variable cost of production VC. The use of variable cost, rather than total cost, avoids the problem of trying to allocate the fixed cost of a multiproduct firm’s production process to the particular product being studied.16 Figure 7.15 shows a typical pattern of cost and output data. Each point on the graph relates the output of an auto company to that company’s variable cost of production. To predict cost accurately, we must determine the underlying relationship between variable cost and output. Then, if a company expands its production, we can calculate what the associated cost is likely to be. The curve in the figure is drawn with this in mind—it provides a reasonably close fit to the cost data. (Typically, least-squares regression analysis would be used to fit the curve to the data.) But what shape is the most appropriate, and how do we represent that shape algebraically? Here is one cost function that we might choose: VC = bq (7.9) Although easy to use, this linear relationship between cost and output is applicable only if marginal cost is constant.17 For every unit increase in output, variable cost increases by b; marginal cost is thus constant and equal to b. If we wish to allow for a U-shaped average cost curve and a marginal cost that is not constant, we must use a more complex cost function. One possibility 16If an additional piece of equipment is needed as output increases, then the annual rental cost of the equipment should be counted as a variable cost. If, however, the same machine can be used at all output levels, its cost is fixed and should not be included. 17In statistical cost analyses, other variables might be added to the cost function to account for differences in input costs, production processes, production mix, etc., among firms. CHAPTER 7 • The Cost of Production 267 is the quadratic cost function, which relates variable cost to output and output squared: VC = bq + gq 2 (7.10) This function implies a straight-line marginal cost curve of the form MC = b + 2g q.18 Marginal cost increases with output if g is positive and decreases with output if g is negative. If the marginal cost curve is not linear, we might use a cubic cost function: VC = bq + gq 2 + dq 3 (7.11) Figure 7.16 shows this cubic cost function. It implies U-shaped marginal as well as average cost curves. Cost functions can be difficult to measure for several reasons. First, output data often represent an aggregate of different types of products. The automobiles produced by General Motors, for example, involve different models of cars. Second, cost data are often obtained directly from accounting information that fails to reflect opportunity costs. Third, allocating maintenance and other plant costs to a particular product is difficult when the firm is a |
conglomerate that produces more than one product line. Cost Functions and the Measurement of Scale Economies Recall that the cost-output elasticity EC is less than one when there are economies of scale and greater than one when there are diseconomies of scale. The scale economies index (SCI) provides an index of whether or not there are scale economies. SCI is defined as follows: SCI = 1 - EC (7.12) = 1, SCI = 0 and there are no economies or diseconomies of scale. When EC When EC is greater than one, SCI is negative and there are diseconomies of scale. Finally, when EC is less than 1, SCI is positive and there are economies of scale. Cost (dollars per unit of output) MC = ß + 2γ q + 3δq2 AVC = ß + γ q + δq2 Output (per time period) 18Short-run marginal cost is given by VC/q = b + g(q 2). But (q2)/q = 2q. (Check this by using calculus or by numerical example.) Therefore, MC = b + 2gq. FIGURE 7.16 CUBIC COST FUNCTION A cubic cost function implies that the average and the marginal cost curves are U-shaped. 268 PART 2 • Producers, Consumers, and Competitive Markets EXAMPLE 7.8 COST FUNCTIONS FOR ELECTRIC POWER In 1955, consumers bought 369 billion kilowatt-hours (kwh) of electricity; in 1970 they bought 1083 billion. Because there were fewer electric utilities in 1970, the output per firm had increased substantially. Was this increase due to economies of scale or to other factors? If it was the result of economies of scale, it would be economically inefficient for regulators to “break up” electric utility monopolies. An interesting study of scale economies was based on the years 1955 and 1970 for investor-owned utilities with more than $1 million in revenues.19 The cost of electric power was estimated by using a cost function that is somewhat more sophisticated than the quadratic and cubic functions discussed earlier.20 Table 7.4 shows the resulting estimates of the scale economies index. The results are based on a classification of all utilities into five size categories, with the median output (measured in kilowatt-hours) in each category listed. The positive values of SCI tell us that all sizes of firms had some economies of scale in 1955. However, the magnitude of the economies of scale diminishes as firm size increases. The average cost curve associated with the 1955 study is drawn in Figure 7.17 and labeled 1955. The point of minimum average cost occurs at point A, at an output of approximately 20 billion kilowatts. Because there were no firms of this size in 1955, no firm had exhausted the opportunity for returns to scale in production. Note, however, that the average cost curve is relatively flat from an output of 9 billion kilowatts and higher, a range in which 7 of 124 firms produced. When the same cost functions were estimated with 1970 data, the cost curve labeled 1970 in Figure 7.17 was the result. The graph shows clearly that the average costs of production fell from 1955 to 1970. (The data are in real 1970 dollars.) But the flat part of the curve now begins at about 15 billion kwh. By 1970, 24 of 80 firms were producing in this range. Thus, many more firms were operating in the flat portion of the average cost curve in which economies of scale are not an important phenomenon. More important, most of the firms were producing in a portion of the 1970 cost curve that was flatter than their point of operation on the 1955 curve. (Five firms were at points of diseconomies of scale: Consolidated Edison [SCI = -0.003], TABLE 7.4 SCALE ECONOMIES IN THE ELECTRIC POWER INDUSTRY Output (million kwh) Value of SCI, 1955 43 .41 338 .26 1109 .16 2226 .10 5819 .04 19This example is based on Laurits Christensen and William H. Greene, “Economies of Scale in U.S. Electric Power Generation,” Journal of Political Economy 84 (1976): 655–76. 20The translog cost function used in this study provides a more general functional relationship than any of those we have discussed. CHAPTER 7 • The Cost of Production 269 Detroit Edison [SCI = -0.004], Duke Power [SCI = -0.012], Commonwealth Edison [SCI = -0.014], and Southern [SCI = -0.028].) Thus, unexploited scale economies were much smaller in 1970 than in 1955. This cost function analysis makes it clear that the decline in the cost of producing electric power cannot be explained by the ability of larger firms to take advantage of economies of scale. Rather, improvements in technology unrelated to the scale of the firms’ operation and the decline in the real cost of energy inputs, such as coal and oil, are important reasons for the lower costs. The tendency toward lower average cost reflecting a movement to the right along an average cost curve is minimal compared with the effect of technological improvement. Average cost (dollars per 1000 kwh) 6.5 6.0 5.5 5.0 A 1955 1970 6 12 18 24 30 36 Output (billion kwh) FIGURE 7.17 AVERAGE COST OF PRODUCTION IN THE ELECTRIC POWER INDUSTRY The average cost of electric power in 1955 achieved a minimum at approximately 20 billion kilowatt-hours. By 1970 the average cost of production had fallen sharply and achieved a minimum at an output of more than 33 billion kilowatt-hours. SUMMARY 1. Managers, investors, and economists must take into account the opportunity cost associated with the use of a firm’s resources: the cost associated with the opportunities forgone when the firm uses its resources in its next best alternative. 2. Economic cost is the cost to a firm of utilizing economic resources in production. While economic cost and opportunity cost are identical concepts, opportunity cost is particularly useful in situations when alternatives that are forgone do not reflect monetary outlays. 3. A sunk cost is an expenditure that has been made and cannot be recovered. After it has been incurred, it should be ignored when making future economic decisions. Because an expenditure that is sunk has no alternative use, its opportunity cost is zero. 4. In the short run, one or more of a firm’s inputs are fixed. Total cost can be divided into fixed cost and variable cost. A firm’s marginal cost is the additional variable cost associated with each additional unit of output. The average variable cost is the total variable cost divided by the number of units of output. 5. In the short run, when not all inputs are variable, the presence of diminishing returns determines the shape of the cost curves. In particular, there is an inverse 270 PART 2 • Producers, Consumers, and Competitive Markets relationship between the marginal product of a single variable input and the marginal cost of production. The average variable cost and average total cost curves are U-shaped. The short-run marginal cost curve increases beyond a certain point, and cuts both average cost curves from below at their minimum points. 6. In the long run, all inputs to the production process are variable. As a result, the choice of inputs depends both on the relative costs of the factors of production and on the extent to which the firm can substitute among inputs in its production process. The cost-minimizing input choice is made by finding the point of tangency between the isoquant representing the level of desired output and an isocost line. 7. The firm’s expansion path shows how its cost-minimizing input choices vary as the scale or output of its operation increases. As a result, the expansion path provides useful information relevant for long-run planning decisions. 8. The long-run average cost curve is the envelope of the firm’s short-run average cost curves, and it reflects the presence or absence of returns to scale. When there are increasing returns to scale initially and then decreasing returns to scale, the long-run average cost curve is U-shaped, and the envelope does not include all points of minimum short-run average cost. 9. A firm enjoys economies of scale when it can double its output at less than twice the cost. Correspondingly, there are diseconomies of scale when a doubling of output requires more than twice the cost. Scale economies and diseconomies apply even when input proportions are variable; returns to scale apply only when input proportions are fixed. 10. Economies of scope arise when the firm can produce any combination of the two outputs more cheaply than could two independent firms that each produced a single output. The degree of economies of scope is measured by the percentage reduction in cost when one firm produces two products relative to the cost of producing them individually. 11. A firm’s average cost of production can fall over time if the firm “learns” how to produce more effectively. The learning curve shows how much the input needed to produce a given output falls as the cumulative output of the firm increases. 12. Cost functions relate the cost of production to the firm’s level of output. The functions can be measured in both the short run and the long run by using either data for firms in an industry at a given time or data for an industry over time. A number of functional relationships, including linear, quadratic, and cubic, can be used to represent cost functions. QUESTIONS FOR REVIEW 1. A firm pays its accountant an annual retainer of $10,000. Is this an economic cost? 2. The owner of a small retail store does her own accounting work. How would you measure the opportunity cost of her work? 3. Please explain whether the following statements are true or false. a. If the owner of a business pays himself no salary, then the accounting cost is zero, but the economic cost is positive. b. A firm that has positive accounting profit does not necessarily have positive economic profit. c. If a firm hires a currently unemployed worker, the opportunity cost of utilizing the worker’s services is zero. 4. Suppose that labor is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor? 5. Suppose a chair manufacturer finds that t |
he marginal rate of technical substitution of capital for labor in her production process is substantially greater than the ratio of the rental rate on machinery to the wage rate for assembly-line labor. How should she alter her use of capital and labor to minimize the cost of production? 6. Why are isocost lines straight lines? 7. Assume that the marginal cost of production is increasing. Can you determine whether the average variable cost is increasing or decreasing? Explain. 8. Assume that the marginal cost of production is greater than the average variable cost. Can you determine whether the average variable cost is increasing or decreasing? Explain. 9. If the firm’s average cost curves are U-shaped, why does its average variable cost curve achieve its minimum at a lower level of output than the average total cost curve? 10. If a firm enjoys economies of scale up to a certain output level, and cost then increases proportionately with output, what can you say about the shape of the longrun average cost curve? 11. How does a change in the price of one input change the firm’s long-run expansion path? 12. Distinguish between economies of scale and economies of scope. Why can one be present without the other? 13. Is the firm’s expansion path always a straight line? 14. What is the difference between economies of scale and returns to scale? EXERCISES 1. Joe quits his computer programming job, where he was earning a salary of $50,000 per year, to start his own computer software business in a building that he owns and was previously renting out for $24,000 per year. In his first year of business he has the following expenses: salary paid to himself, $40,000; rent, $0; other expenses, $25,000. Find the accounting cost and the economic cost associated with Joe’s computer software business. 2. a. Fill in the blanks in the table below. b. Draw a graph that shows marginal cost, average variable cost, and average total cost, with cost on the vertical axis and quantity on the horizontal axis. 3. A firm has a fixed production cost of $5000 and a constant marginal cost of production of $500 per unit produced. a. What is the firm’s total cost function? Average cost? b. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain. 4. Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. a. How does this tax affect the firm’s fixed, marginal, and average costs? b. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm’s fixed, marginal, and average costs? 5. A recent issue of Business Week reported the following: During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That’s because closing and reopening plants is expensive, partly because the auto makers’ current CHAPTER 7 • The Cost of Production 271 union contracts obligate them to pay many workers even if they’re not working. When the article discusses selling cars “at a loss,” is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly. 6. Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path. 7. The cost of flying a passenger plane from point A to point B is $50,000. The airline flies this route four times per day at 7 AM, 10 AM, 1 PM, and 4 PM. The first and last flights are filled to capacity with 240 people. The second and third flights are only half full. Find the average cost per passenger for each flight. Suppose the airline hires you as a marketing consultant and wants to know which type of customer it should try to attract—the off-peak customer (the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer? 8. You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q = 5 KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r $10,000 per week, and each team costs w $5000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw UNITS OF OUTPUT FIXED COST VARIABLE COST TOTAL COST MARGINAL COST AVERAGE FIXED COST AVERAGE VARIABLE COST AVERAGE TOTAL COST 10 100 125 145 157 177 202 236 270 326 398 490 272 PART 2 • Producers, Consumers, and Competitive Markets materials. Your plant has a fixed installation of 5 assembly machines as part of its design. a. What is the cost function for your plant—namely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output? b. How many teams are required to produce 250 engines? What is the average cost per engine? c. You are asked to make recommendations for the design of a new production facility. What capital/ labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q? 9. The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the total cost and q is the total quantity of output, both measured in thousands. a. What is the company’s fixed cost? b. If the company produced 100,000 units of goods, what would be its average variable cost? c. What would be its marginal cost of production? d. What would be its average fixed cost? e. Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its variable cost falls to $45,000 per 1000 units. The cost of interest (i) also enters into the equation. Each 1-point increase in the interest rate raises costs by $3000. Write the new cost equation. *10. A chair manufacturer hires its assembly-line labor for $30 an hour and calculates that the rental cost of its machinery is $15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation? Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and for the optimal combination of labor and capital. *11. Suppose that a firm’s production function is q = 10L 2. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a. The firm is currently producing 100 units of output and has determined that the cost-minimizing 2 K 1 1 quantities of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquants and isocost lines. b. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this graphically and find the firm’s new total cost. c. Graphically identify the cost-minimizing level of capital and labor in the long run if the firm wants to produce 140 units. d. If the marginal rate of technical substitution is K/L, find the optimal level of capital and labor required to produce the 140 units of output. *12. A computer company’s cost function, which relates its average cost of production AC to its cumulative output in thousands of computers Q and its plant size in terms of thousands of computers produced per year q (within the production range of 10,000 to 50,000 computers), is given by AC = 10 - 0.1Q + 0.3q a. Is there a learning-curve effect? b. Are there economies or diseconomies of scale? c. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain. *13. Suppose the long-run total cost function for an industry is given by the cubic equation TC = a + bq + cq2 + dq3. Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values of a, b, c, and d. *14. A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units H and software programs S is given by TC = aH + bS - cHS where a, b, and c are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? With economies or diseconomies of scope? Appendix to Chapter 7 Production and Cost Theory— A Mathematical Treatment This appendix presents a mathematical treatment of the basics of production and cost theory. As in the appendix to Chapter 4, we use the method of Lagrange multipliers to solve the firm’s cost-minimizing problem. Cost Minimization The theory of the firm relies on the assumption that firms choose inputs to the production process that minimize the cost of producing output. If there are two inputs, capital K and labor L, the production function F(K, L) describes the maximum output that can be produced for every possible combination of inputs. We assume that each factor in the production process has positive but decreasing marginal products. Therefore, writing the marginal product of capital and labor as MPK(K, L) and MPL(K, L), respectively, it follows that MPK(K,L) = MPL(K,L) = 0F(K, L) 0K 0F(K, L) 0L 7 0, 7 0, 02F(K, L) 0K2 02F(K, L) 0L2 6 0 6 0 A competitive firm takes the prices of both labor w and capital r as given. Then the cost-minimization problem can be written as Minimize C = wL + rK subject to the constraint that a fixed output q0 be produced: F(K, L) = q0 (A7.1) (A7.2) C represents the cost of producing the fixed level |
of output q0. To determine the firm’s demand for capital and labor inputs, we choose the values of K and L that minimize (A7.1) subject to (A7.2). We can solve this constrained optimization problem in three steps using the method discussed in the appendix to Chapter 4: • Step 1: Set up the Lagrangian, which is the sum of two components: the cost of production (to be minimized) and the Lagrange multiplier l times the output constraint faced by the firm: = wL + rK - l[F(K, L) - q0] (A7.3) • Step 2: Differentiate the Lagrangian with respect to K, L, and l. Then equate the resulting derivatives to zero to obtain the necessary conditions for a minimum.1 1These conditions are necessary for a solution involving positive amounts of both inputs. 273 274 PART 2 • Producers, Consumers, and Competitive Markets 0/0K = r - lMPK(K, L) = 0 0/0L = w - lMPL(K, L) = 0 0/0l = q0 - F(K, L) = 0 (A7.4) • Step 3: In general, these equations can be solved to obtain the optimizing values of L, K, and l. It is particularly instructive to combine the first two conditions in (A7.4) to obtain MPK(K, L)/r = MPL(K, L)/w (A7.5) Equation (A7.5) tells us that if the firm is minimizing costs, it will choose its factor inputs to equate the ratio of the marginal product of each factor divided by its price. This is exactly the same condition that we derived as Equation 7.4 (page 247) in the text. Finally, we can rewrite the first two conditions of (A7.4) to evaluate the Lagrange multiplier: r - lMPK(K, L) = 0 1 l = w - lMPL(K, L) = 0 1 l = r MPK(K, L) w MPL(K, L) (A7.6) Suppose output increases by one unit. Because the marginal product of capital measures the extra output associated with an additional input of capital, 1/MPK(K, L) measures the extra capital needed to produce one unit of output. Therefore, r/MPK(K, L) measures the additional input cost of producing an additional unit of output by increasing capital. Likewise, w/MPL(K, L) measures the additional cost of producing a unit of output using additional labor as an input. In both cases, the Lagrange multiplier is equal to the marginal cost of production because it tells us how much the cost increases if the amount produced is increased by one unit. Marginal Rate of Technical Substitution Recall that an isoquant is a curve that represents the set of all input combinations that give the firm the same level of output—say, q0. Thus, the condition that F(K, L) q0 represents a production isoquant. As input combinations are changed along an isoquant, the change in output, given by the total derivative of F(K, L), equals zero (i.e., dq 0). Thus MPK(K, L)dK + MPL(K, L)dL = dq = 0 (A7.7) It follows by rearrangement that -dK/dL = MRTSLK = MPL(K, L)/MPK(K, L) (A7.8) where MRTSLK is the firm’s marginal rate of technical substitution between labor and capital. Now, rewrite the condition given by (A7.5) to get MPL(K, L)/MPK(K, L) = w/r (A7.9) CHAPTER 7 • The Cost of Production 275 Because the left side of (A7.8) represents the negative of the slope of the isoquant, it follows that at the point of tangency of the isoquant and the isocost line, the firm’s marginal rate of technical substitution (which trades off inputs while keeping output constant) is equal to the ratio of the input prices (which represents the slope of the firm’s isocost line). We can look at this result another way by rewriting (A7.9): MPL/w = MPK/r (A7.10) Equation (A7.10) is the same as (A7.5) and tells us that the marginal products of all production inputs must be equal when these marginal products are adjusted by the unit cost of each input. Duality in Production and Cost Theory As in consumer theory, the firm’s input decision has a dual nature. The optimum choice of K and L can be analyzed not only as the problem of choosing the lowest isocost line tangent to the production isoquant, but also as the problem of choosing the highest production isoquant tangent to a given isocost line. Suppose we wish to spend C0 on production. The dual problem asks what combination of K and L will let us produce the most output at a cost of C0. We can see the equivalence of the two approaches by solving the following problem: Maximize F(K, L) subject to wL + rL = C0 (A7.11) We can solve this problem using the Lagrangian method: • Step 1: We set up the Lagrangian = F(K, L) - o(wL + rK - C0) (A7.12) where μ is the Lagrange multiplier. • Step 2: We differentiate the Lagrangian with respect to K, L, and o and set the resulting equation equal to zero to find the necessary conditions for a maximum: 0 0K 0 0L 0 0l = MPK(K, L) - or = 0 = MPL(K, L) - ow = 0 (A7.13) = wL - rK + C0 = 0 • Step 3: Normally, we can use the equations of (A7.13) to solve for K and L. In particular, we combine the first two equations to see that o = MPK(K, L) r o = MPL(K, L) w 1 MPK(K, L) r = MPL(K, L) w (A7.14) 276 PART 2 • Producers, Consumers, and Competitive Markets a • Cobb-Douglas production function Production function of the form q AK , where q is the rate of output, K is the quantity of capital, and L is the quantity of labor, and where A, a, and b are positive constants. b L This is the same result as (A7.5)—that is, the necessary condition for cost minimization. The Cobb-Douglas Cost and Production Functions Given a specific production function F(K, L), conditions (A7.13) and (A7.14) can be used to derive the cost function C(q). To understand this principle, let’s work through the example of a Cobb-Douglas production function. This production function is F(K,L) = AK b a L where A, a, and b are positive constants. We assume that a 6 1 and b 6 1, so that the firm has decreasing marginal products of labor and capital.2 If a + b = 1, the firm has constant returns to scale, because doubling K and L doubles F. If a + b 7 1, the firm has increasing returns to scale, and if a + b 6 1, it has decreasing returns to scale. As an application, consider the carpet industry described in Example 6.4 (page 221). The production of both small and large firms can be described by CobbDouglas production functions. For small firms, a = .77 and b = .23. Because a + b = 1, there are constant returns to scale. For larger firms, however, a = .83 and b = .22. Thus a + b = 1.05, and there are increasing returns to scale. The Cobb-Douglas production function is frequently encountered in economics and can be used to model many kinds of production. We have already seen how it can accommodate differences in returns to scale. It can also account for changes in technology or productivity through changes in the value of A: The larger the value of A, more can be produced for a given level of K and L. To find the amounts of capital and labor that the firm should utilize to mini- mize the cost of producing an output q0, we first write the Lagrangian = wL + rK - l(AK b - q0) a L (A7.15) Differentiating with respect to L, K, and l, and setting those derivatives equal to 0, we obtain 0/0L = w - l(bAK 0/0K = r - l(aAK b - q0 a 0/0l = AK L b - 1) = 0 a L a - 1L b ) = 0 = 0 From equation (A7.16) we have l = w/AbK b - 1 a L Substituting this formula into equation (A7.17) gives us (A7.16) (A7.17) (A7.18) (A7.19) or rbAK b - 1 = waAK a L b a - 1L (A7.20) L = br aw K (A7.21) 2For example, the marginal product of labor is given by MPL MPL falls as L increases. = 0[F(K,L)]/0L = bAK b - 1. Thus, a L (A7.21) is the expansion path. Now use Equation (A7.21) to substitute for L in equation (A7.18): CHAPTER 7 • The Cost of Production 277 aa AK br aw b Kb - q0 = 0 We can rewrite the new equation as: or a + b = a K aw br b bq0 A K = a b a + b aw br b 1 a + b a q0 A b (A7.22) (A7.23) (A7.24) (A7.24) is the factor demand for capital. We have now determined the cost-minimizing quantity of capital: Thus, if we wish to produce q0 units of output at least cost, (A7.24) tells us how much capital we should employ as part of our production plan. To determine the cost-minimizing quantity of labor, we simply substitute equation (A7.24) into equation (A7.21): L = br aw K = br aw £ a aw br q0 A b (A7.25) L = a a a + b br aw b a q0 A b 1 a + b (A7.25) is the constrained factor demand for labor. Note that if the wage rate w rises relative to the price of capital r, the firm will use more capital and less labor. Suppose that, because of technological change, A increases (so the firm can produce more output with the same inputs); in that case, both K and L will fall. We have shown how cost-minimization subject to an output constraint can be used to determine the firm’s optimal mix of capital and labor. Now we will determine the firm’s cost function. The total cost of producing any output q can be obtained by substituting equations (A7.24) for K and (A7.25) for L into the equation C wL rK. After some algebraic manipulation we find that C = w b/(a + b)r a/(a + b)£ a b/(a + ba/(a + b) § a b q A 1/(a + b) (A7.26) This cost function tells us (1) how the total cost of production increases as the level of output q increases, and (2) how cost changes as input prices change. When a + b equals 1, equation (A7.26) simplifies to C = w b r a [(a/b) b + (a/b) -a ](1/A)q (A7.27) 278 PART 2 • Producers, Consumers, and Competitive Markets In this case, therefore, cost will increase proportionately with output. As a result, the production process exhibits constant returns to scale. Likewise, if a + b is greater than 1, there are increasing returns to scale; if a + b is less than 1, there are decreasing returns to scale. The firm’s cost function contains many desirable features. To appreciate this fact, consider the special constant returns to scale cost function (A7.27). Suppose that we wish to produce q0 in output but are faced with a doubling of the wage. How should we expect our costs to change? New costs are given by = 12w2b r a £ a C1 b b + a a b -a a b b § a 1 A b q0 b = 2 w b - q0 (+++1++)+++1++* C0 § a 1 A b = 2 C0 Recall that at the beginning of this section, we assumed that a < 1 and ß < 1. 6 2C0. Even though wages doubled, the cost of producing q0 less T |
herefore, C1 than doubled. This is the expected result. If a firm suddenly had to pay more for labor, it would substitute away from labor and employ more of the relatively cheaper capital, thereby keeping the increase in total cost in check. Now consider the dual problem of maximizing the output that can be produced with the expenditure of C0 dollars. We leave it to you to work through this problem for the Cobb-Douglas production function. You should be able to show that equations (A7.24) and (A7.25) describe the cost-minimizing input choices. To get you started, note that the Lagrangian for this dual problem is a = AK L b - o(wL + rK - C0). EXERCISES 1. Of the following production functions, which exhibit increasing, constant, or decreasing returns to scale? a. F(K, L) K2L b. F(K, L) 10K 5L c. F(K, L) (KL).5 2. The production function for a product is given by q 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output? 3. Suppose a production function is given by F(K, L) KL2; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output? 4. Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function q = 10K.8(L - 40).2 where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $10 worth of raw materials is used in the production of each parka. a. By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates on machines (r). Use these results to derive the total cost function: that is, costs as a function of q, r, w, and the constant $10 per unit materials cost. b. This process requires skilled workers, who earn $32 per hour. The rental rate on the machines used in the process is $64 per hour. At these factor prices, what are total costs as a function of q? Does this technology exhibit decreasing, constant, or increasing returns to scale? c. Polly’s Parkas plans to produce 2000 parkas per week. At the factor prices given above, how many workers should the firm hire (at 40 hours per week) and how many machines should it rent (at 40 machine-hours per week)? What are the marginal and average costs at this level of production? C H A P T E R 8 Profit Maximization and Competitive Supply A cost curve describes the minimum cost at which a firm can pro- duce various amounts of output. Once we know its cost curve, we can turn to a fundamental problem faced by every firm: How much should be produced? In this chapter, we will see how a firm chooses the level of output that maximizes its profit. We will also see how the output choices of individual firms lead to a supply curve for an entire industry. Because our discussion of production and cost in Chapters 6 and 7 applies to firms in all kinds of markets, we will begin by explaining the profit-maximizing output decision in a general setting. However, we will then turn to the focus of this chapter—perfectly competitive markets, in which all firms produce an identical product and each is so small in relation to the industry that its production decisions have no effect on market price. New firms can easily enter the industry if they perceive a potential for profit, and existing firms can exit if they start losing money. We begin by explaining exactly what is meant by a competitive market. We then explain why it makes sense to assume that firms (in any market) have the objective of maximizing profit. We provide a rule for choosing the profit-maximizing output for firms in all markets, competitive or otherwise. Following this we show how a competitive firm chooses its output in the short and long run. We next examine how the firm’s output choice changes as the cost of production or the prices of inputs change. In this way, we show how to derive the firm’s supply curve. We then aggregate the supply curves of individual firms to obtain the industry supply curve. In the short run, firms in an industry choose which level of output to produce in order to maximize profit. In the long run, they not only make output choices, but also decide whether to be in a market at all. We will see that while the prospect of high profits encourages firms to enter an industry, losses encourage them to leave. 8.1 Perfectly Competitive Markets In Chapter 2, we used supply–demand analysis to explain how changing market conditions affect the market price of such products as wheat and gasoline. We saw that the equilibrium price and quantity of each .1 Perfectly Competitive Markets 8.2 Profit Maximization 8.3 Marginal Revenue, Marginal Cost, and Profit Maximization 8.4 Choosing Output in the Short Run 8.5 The Competitive Firm’s Short-Run Supply Curve 8.6 The Short-Run Market Supply Curve 8.7 Choosing Output in the Long Run 8.8 The Industry’s Long-Run Supply Curve 279 282 284 287 292 295 300 306 .1 Condominiums versus Cooperatives in New York City 283 8.2 The Short-Run Output Decision of an Aluminum Smelting Plant 290 8.3 Some Cost Considerations for Managers 291 8.4 The Short-Run Production of Petroleum Products 294 8.5 The Short-Run World Supply of Copper 8.6 Constant-, Increasing-, and Decreasing-Cost Industries: Coffee, Oil, and Automobiles 8.7 The Supply of Taxicabs in New York 8.8 The Long-Run Supply of Housing 297 310 312 313 279 280 PART 2 • Producers, Consumers, and Competitive Markets product was determined by the intersection of the market demand and market supply curves. Underlying this analysis is the model of a perfectly competitive market. The model of perfect competition is very useful for studying a variety of markets, including agriculture, fuels and other commodities, housing, services, and financial markets. Because this model is so important, we will spend some time laying out the basic assumptions that underlie it. The model of perfect competition rests on three basic assumptions: (1) price taking, (2) product homogeneity, and (3) free entry and exit. You have encountered these assumptions earlier in the book; here we summarize and elaborate on them. PRICE TAKING Because many firms compete in the market, each firm faces a significant number of direct competitors for its products. Because each individual firm sells a sufficiently small proportion of total market output, its decisions have no impact on market price. Thus, each firm takes the market price as given. In short, firms in perfectly competitive markets are price takers. Suppose, for example, that you are the owner of a small electric lightbulb distribution business. You buy your lightbulbs from the manufacturer and resell them at wholesale to small businesses and retail outlets. Unfortunately, you are only one of many competing distributors. As a result, you find that there is little room to negotiate with your customers. If you do not offer a competitive price—one that is determined in the marketplace—your customers will take their business elsewhere. In addition, you know that the number of lightbulbs that you sell will have little or no effect on the wholesale price of bulbs. You are a price taker. The assumption of price taking applies to consumers as well as firms. In a perfectly competitive market, each consumer buys such a small proportion of total industry output that he or she has no impact on the market price, and therefore takes the price as given. Another way of stating the price-taking assumption is that there are many independent firms and independent consumers in the market, all of whom believe—correctly—that their decisions will not affect prices. PRODUCT HOMOGENEITY Price-taking behavior typically occurs in markets where firms produce identical, or nearly identical, products. When the products of all of the firms in a market are perfectly substitutable with one another—that is, when they are homogeneous—no firm can raise the price of its product above the price of other firms without losing most or all of its business. Most agricultural products are homogeneous: Because product quality is relatively similar among farms in a given region, for example, buyers of corn do not ask which individual farm grew the product. Oil, gasoline, and raw materials such as copper, iron, lumber, cotton, and sheet steel are also fairly homogeneous. Economists refer to such homogeneous products as commodities. In contrast, when products are heterogeneous, each firm has the opportunity to raise its price above that of its competitors without losing all of its sales. Premium ice creams such as Häagen-Dazs, for example, can be sold at higher prices because Häagen-Dazs has different ingredients and is perceived by many consumers to be a higher-quality product. The assumption of product homogeneity is important because it ensures that there is a single market price, consistent with supply–demand analysis. FREE ENTRY AND EXIT This third assumption, free entry (or exit), means that there are no special costs that make it difficult for a new firm either to enter • price taker Firm that has no influence over market price and thus takes the price as given. • free entry (or exit) Condition under which there are no special costs that make it difficult for a firm to enter (or exit) an industry. CHAPTER 8 • Profit Maximization and Competitive Supply 281 an industry and produce, or to exit if it cannot make a profit. As a result, buyers can easily switch from one supplier to another, and suppliers can easily enter or exit a market. The special costs that could restrict entry are costs which an entrant to a market would have to bear, but which a firm that is already producing would not. The pharmaceutical industry, for example, is not perfectly competitive because Merck, Pfizer, and other firms hold patents that give them unique ri |
ghts to produce drugs. Any new entrant would either have to invest in research and development to obtain its own competing drugs or pay substantial license fees to one or more firms already in the market. R&D expenditures or license fees could limit a firm’s ability to enter the market. Likewise, the aircraft industry is not perfectly competitive because entry requires an immense investment in plant and equipment that has little or no resale value. The assumption of free entry and exit is important for competition to be effective. It means that consumers can easily switch to a rival firm if a current supplier raises its price. For businesses, it means that a firm can freely enter an industry if it sees a profit opportunity and exit if it is losing money. Thus a firm can hire labor and purchase capital and raw materials as needed, and it can release or move these factors of production if it wants to shut down or relocate. If these three assumptions of perfect competition hold, market demand and supply curves can be used to analyze the behavior of market prices. In most markets, of course, these assumptions are unlikely to hold exactly. This does not mean, however, that the model of perfect competition is not useful. Some markets do indeed come close to satisfying our assumptions. But even when one or more of these three assumptions fails to hold, so that a market is not perfectly competitive, much can be learned by making comparisons with the perfectly competitive ideal. When Is a Market Highly Competitive? Apart from agriculture, few real-world markets are perfectly competitive in the sense that each firm faces a perfectly horizontal demand curve for a homogeneous product in an industry that it can freely enter or exit. Nevertheless, many markets are highly competitive in the sense that firms face highly elastic demand curves and relatively easy entry and exit. A simple rule of thumb to describe whether a market is close to being perfectly competitive would be appealing. Unfortunately, we have no such rule, and it is important to understand why. Consider the most obvious candidate: an industry with many firms (say, at least 10 to 20). Because firms can implicitly or explicitly collude in setting prices, the presence of many firms is not sufficient for an industry to approximate perfect competition. Conversely, the presence of only a few firms in a market does not rule out competitive behavior. Suppose that only three firms are in the market but that market demand for the product is very elastic. In this case, the demand curve facing each firm is likely to be nearly horizontal and the firms will behave as if they were operating in a perfectly competitive market. Even if market demand is not very elastic, these three firms might compete very aggressively (as we will see in Chapter 13). The important point to remember is that although firms may behave competitively in many situations, there is no simple indicator to tell us when a market is highly competitive. Often it is necessary to analyze both the firms themselves and their strategic interactions, as we do in Chapters 12 and 13. In §2.4, we explain that demand is price elastic when the percentage decline in quantity demanded is greater than the percentage increase in price. 282 PART 2 • Producers, Consumers, and Competitive Markets 8.2 Profit Maximization We now turn to the analysis of profit maximization. In this section, we ask whether firms do indeed seek to maximize profit. Then in Section 8.3, we will describe a rule that any firm—whether in a competitive market or not—can use to find its profit-maximizing output level. Finally, we will consider the special case of a firm in a competitive market. We distinguish the demand curve facing a competitive firm from the market demand curve, and use this information to describe the competitive firm’s profit-maximization rule. Do Firms Maximize Profit? The assumption of profit maximization is frequently used in microeconomics because it predicts business behavior reasonably accurately and avoids unnecessary analytical complications. But the question of whether firms actually do seek to maximize profit has been controversial. For smaller firms managed by their owners, profit is likely to dominate almost all decisions. In larger firms, however, managers who make day-to-day decisions usually have little contact with the owners (i.e., the stockholders). As a result, owners cannot monitor the managers’ behavior on a regular basis. Managers then have some leeway in how they run the firm and can deviate from profit-maximizing behavior. Managers may be more concerned with such goals as revenue maximization, revenue growth, or the payment of dividends to satisfy shareholders. They might also be overly concerned with the firm’s short-run profit (perhaps to earn a promotion or a large bonus) at the expense of its longer-run profit, even though long-run profit maximization better serves the interests of the stockholders.1 Because technical and marketing information is costly to obtain, managers may sometimes operate using rules of thumb that require less-than-ideal information. On some occasions they may engage in acquisition and/or growth strategies that are substantially more risky than the owners of the firm might wish. The recent rise in the number of corporate bankruptcies, especially those in the financial sector, along with the rapid increase in CEO salaries, has raised questions about the motivations of managers of large corporations. These are important questions, which we will address in Chapter 17, when we discuss the incentives of managers and owners in detail. For now, it is important to realize that a manager’s freedom to pursue goals other than long-run profit maximization is limited. If they do pursue such goals, shareholders or boards of directors can replace them, or the firm can be taken over by new management. In any case, firms that do not come close to maximizing profit are not likely to survive. Firms that do survive in competitive industries make long-run profit maximization one of their highest priorities. Thus our working assumption of profit maximization is reasonable. Firms that have been in business for a long time are likely to care a lot about profit, whatever else their managers may appear to be doing. For example, a firm that subsidizes public television may seem public-spirited and altruistic. Yet this beneficence is likely to be in the long-run financial interest of the firm because it generates goodwill. 1To be more exact, maximizing the market value of the firm is a more appropriate goal than profit maximization because market value includes the stream of profits that the firm earns over time. It is the stream of current and future profits that is of direct interest to the stockholders. CHAPTER 8 • Profit Maximization and Competitive Supply 283 Alternative Forms of Organization Now that we’ve underscored the fact that profit maximization is a fundamental assumption in most economic analyses of firm behavior, let’s pause to consider an important qualifier to this assumption: Some forms of organizations have objectives that are quite different from profit maximization. An important such organization is the cooperative—an association of businesses or people jointly owned and operated by members for mutual benefit. For example, several farms might decide to enter into a cooperative agreement by which they pool their resources in order to distribute and market milk to consumers. Because each participating member of the milk cooperative is an autonomous economic unit, each farm will act to maximize its own profits (rather than the profits of the cooperative as a whole), taking the common marketing and distribution agreement as given. Such cooperative agreements are common in agricultural markets. In many towns or cities, one can join a food cooperative, the objective of which is to provide its members with food and other groceries at the lowest possible cost. Usually, a food cooperative looks like a store or small supermarket. Shopping is either restricted to members or else unrestricted with members receiving discounts. Prices are set so that the cooperative avoids losing money, but any profits are incidental and are returned to the members (usually in proportion to their purchases). Housing cooperatives, or co-ops, are another example of this form of organization. A co-op might be an apartment building for which the title to the land and the building is owned by a corporation. The member residents of the co-op own shares in the corporation, accompanied by a right to occupy a unit—an arrangement much like a long-term lease. The members of the co-op can participate in the management of their building in a variety of ways: organizing social events, handling finances, or even deciding who their neighbors will be. As with other types of cooperatives, the objective is not to maximize profits, but rather to provide members with high-quality housing at the lowest possible cost. A related type of organization, especially relevant for housing, is the condominium. A condominium (or “condo”) is a housing unit (an apartment, connected town house, or other form of real estate) that is individually owned, while use of and access to common facilities such as hallways, heating system, elevators, and exterior areas are controlled jointly by an association of condo owners. Those owners also share in the payment for the maintenance and operation of those common facilities. Compared to a cooperative, the condominium has the important advantage of simplifying governance, as we discuss below in Example 8.1. • cooperative Association of businesses or people jointly owned and operated by members for mutual benefit. • condominium A housing unit that is individually owned but provides access to common facilities that are paid for and controlled jointly by an association of owners. EXAM PLE 8.1 CONDOMINIUMS VERSUS COOPE |
RATIVES IN NEW YORK CITY While owners of condominiums must join with fellow condo owners to manage common spaces (e.g., entry areas), they can make their own decisions as to how to manage their individual units so as to achieve the greatest value possible. In contrast, co-ops share joint liability on any outstanding mortgage on the co-op building and are subject to more complex governance rules. Although much of the governance is usually delegated to a board that represents all co-op members, members must often spend substantial time in the governance of the association. In addition, condo members can sell their units whenever and to whomever they choose, whereas co-op members must get permission from the co-op board before a sale can be made. 284 PART 2 • Producers, Consumers, and Competitive Markets Nationwide, condos are far more common than co-ops, outnumbering them by a factor of nearly 10 to 1. In this regard, New York City is very different from the rest of the nation—co-ops are more popular, and outnumber condos by a factor of about 4 to 1. What accounts for the relative popularity of housing cooperatives in New York City? Part of the answer is historical. Housing cooperatives are a much older form of organization in the U.S., dating back to the mid-nineteenth century, whereas the development of condominiums began only in the 1960s, at which point a large number of buildings in New York were already co-ops. In addition, while condominiums were becoming increasingly popular in other parts of the country, building regulations in New York made the co-op the required governance structure. But that’s history. The building restrictions in New York have long disappeared, and yet the conversion of apartments from co-ops to condos has been relatively slow. Why? A recent study provides some interesting answers.2 The authors find that the typical condominium apartment is worth about 15.5 percent more than an equivalent apartment held in the form of a co-op. Clearly, holding an apartment in the form of a co-op is not the best way to maximize the apartment’s value. On the other hand, co-op owners can be more selective in choosing their neighbors when sales are made—something that New Yorkers seem to care a great deal about. It appears that in New York, many owners have been willing to forgo substantial amounts of money in order to achieve non-monetary benefits. • profit Difference between total revenue and total cost. • marginal revenue Change in revenue resulting from a oneunit increase in output. 8.3 Marginal Revenue, Marginal Cost, and Profit Maximization We now return to our working assumption of profit maximization and examine the implications of this objective for the operation of a firm. We will begin by looking at the profit-maximizing output decision for any firm, whether it operates in a perfectly competitive market or is one that can influence price. Because profit is the difference between (total) revenue and (total) cost, finding the firm’s profit-maximizing output level means analyzing its revenue. Suppose that the firm’s output is q, and that it obtains revenue R. This revenue is equal to the price of the product P times the number of units sold: R = Pq. The cost of production C also depends on the level of output. The firm’s profit, p, is the difference between revenue and cost: p(q) = R(q) - C(q) (Here we show explicitly that p, R, and C depend on output. Usually we will omit this reminder.) To maximize profit, the firm selects the output for which the difference between revenue and cost is the greatest. This principle is illustrated in Figure 8.1. Revenue R(q) is a curved line, which reflects the fact that the firm can sell a greater level of output only by lowering its price. The slope of this revenue curve is marginal revenue: the change in revenue resulting from a oneunit increase in output. Also shown is the total cost curve C(q). The slope of this curve, which measures the additional cost of producing one additional unit of output, is the firm’s marginal cost. Note that total cost C(q) is positive when output is zero because there is a fixed cost in the short run. 2Michael H. Schill, Ioan Voicu, and Jonathan Miller, “The Condominium v. Cooperative Puzzle: An Empirical Analysis of Housing in New York City,” Journal of Legal Studies, Vol. 36 (2007); 275–324. CHAPTER 8 • Profit Maximization and Competitive Supply 285 Cost, revenue, profit (dollars per year) C(q) R(q) A B FIGURE 8.1 PROFIT MAXIMIZATION IN THE SHORT RUN A firm chooses output q*, so that profit, the difference AB between revenue R and cost C, is maximized. At that output, marginal revenue (the slope of the revenue curve) is equal to marginal cost (the slope of the cost curve). 0 q0 q* q1 π(q) Output (units per year) For the firm illustrated in Figure 8.1, profit is negative at low levels of output because revenue is insufficient to cover fixed and variable costs. As output increases, revenue rises more rapidly than cost, so that profit eventually becomes positive. Profit continues to increase until output reaches the level q*. At this point, marginal revenue and marginal cost are equal, and the vertical distance between revenue and cost, AB, is greatest. q* is the profit-maximizing output level. Note that at output levels above q*, cost rises more rapidly than revenue— i.e., marginal revenue is less than marginal cost. Thus, profit declines from its maximum when output increases above q*. The rule that profit is maximized when marginal revenue is equal to marginal cost holds for all firms, whether competitive or not. This important rule can also be derived algebraically. Profit, p = R - C, is maximized at the point at which an additional increment to output leaves profit unchanged (i.e., p/q = 0): p/q = R/q - C/q = 0 R/q is marginal revenue MR and C/q is marginal cost MC. Thus we conclude that profit is maximized when MR - MC = 0, so that MR(q) = MC(q) Demand and Marginal Revenue for a Competitive Firm Because each firm in a competitive industry sells only a small fraction of the entire industry output, how much output the firm decides to sell will have no effect on the market price of the product. The market price is determined by the industry demand and supply curves. Therefore, the competitive firm is a price taker. Recall that price taking is one of the fundamental assumptions of perfect competition. The price-taking firm knows that its production decision will have no effect on the price of the product. For example, when a farmer is deciding how many acres of wheat to plant in a given year, he can take the market price of wheat—say, $4 per bushel—as given. That price will not be affected by his acreage decision. 286 PART 2 • Producers, Consumers, and Competitive Markets In §4.1, we explain how the demand curve relates the quantity of a good that a consumer will buy to the price of that good. Often we will want to distinguish between market demand curves and the demand curves faced by individual firms. In this chapter we will denote market output and demand by capital letters (Q and D) and the firm’s output and demand by lowercase letters (q and d). Because it is a price taker, the demand curve d facing an individual competitive firm is given by a horizontal line. In Figure 8.2(a), the farmer’s demand curve corresponds to a price of $4 per bushel of wheat. The horizontal axis measures the amount of wheat that the farmer can sell, and the vertical axis measures the price. Compare the demand curve facing the firm (in this case, the farmer) in Figure 8.2(a) with the market demand curve D in Figure 8.2(b). The market demand curve shows how much wheat all consumers will buy at each possible price. It is downward sloping because consumers buy more wheat at a lower price. The demand curve facing the firm, however, is horizontal because the firm’s sales will have no effect on price. Suppose the firm increased its sales from 100 to 200 bushels of wheat. This would have almost no effect on the market because industry output is 2,000 million bushels. Price is determined by the interaction of all firms and consumers in the market, not by the output decision of a single firm. By the same token, when an individual firm faces a horizontal demand curve, it can sell an additional unit of output without lowering price. As a result, when it sells an additional unit, the firm’s total revenue increases by an amount equal to the price: one bushel of wheat sold for $4 yields additional revenue of $4. Thus, marginal revenue is constant at $4. At the same time, average revenue received by Price (dollars per bushel) Firm Price (dollars per bushel) Industry $4 d $4 100 (a) 200 q Output (bushels) 2,000 (b) D Q Output (millions of bushels) FIGURE 8.2 DEMAND CURVE FACED BY A COMPETITIVE FIRM A competitive firm supplies only a small portion of the total output of all the firms in an industry. Therefore, the firm takes the market price of the product as given, choosing its output on the assumption that the price will be unaffected by the output choice. In (a) the demand curve facing the firm is perfectly elastic, even though the market demand curve in (b) is downward sloping. CHAPTER 8 • Profit Maximization and Competitive Supply 287 the firm is also $4 because every bushel of wheat produced will be sold at $4. Therefore: The demand curve d facing an individual firm in a competitive market is both its average revenue curve and its marginal revenue curve. Along this demand curve, marginal revenue, average revenue, and price are all equal. Profit Maximization by a Competitive Firm Because the demand curve facing a competitive firm is horizontal, so that MR = P, the general rule for profit maximization that applies to any firm can be simplified. A perfectly competitive firm should choose its output so that marginal cost equals price: MC(q) = MR = P Note that because competitive firms take price as fixed, this is a rule for setting output, not price. The choice |
of the profit-maximizing output by a competitive firm is so important that we will devote most of the rest of this chapter to analyzing it. We begin with the short-run output decision and then move to the long run. 8.4 Choosing Output in the Short Run How much output should a firm produce over the short run, when its plant size is fixed? In this section we show how a firm can use information about revenue and cost to make a profit-maximizing output decision. Short-Run Profit Maximization by a Competitive Firm In the short run, a firm operates with a fixed amount of capital and must choose the levels of its variable inputs (labor and materials) to maximize profit. Figure 8.3 shows the firm’s short-run decision. The average and marginal revenue curves are drawn as a horizontal line at a price equal to $40. In this figure, we have drawn the average total cost curve ATC, the average variable cost curve AVC, and the marginal cost curve MC so that we can see the firm’s profit more easily. Profit is maximized at point A, where output is q* 8 and the price is $40, because marginal revenue is equal to marginal cost at this point. To see that q* 8 is indeed the profit-maximizing output, note that at a lower output, say q1 7, marginal revenue is greater than marginal cost; profit could thus be increased by increasing output. The shaded area between q1 7 and q* shows the lost profit associated with producing at q1. At a higher output, say q2, marginal cost is greater than marginal revenue; thus, reducing output saves a cost that exceeds the reduction in revenue. The shaded area between q* and q2 9 shows the lost profit associated with producing at q2. When output is q* 8, profit is given by the area of rectangle ABCD. The MR and MC curves cross at an output of q0 as well as q*. At q0, however, profit is clearly not maximized. An increase in output beyond q0 increases profit because marginal cost is well below marginal revenue. We can thus Marginal, average, and total cost are discussed in §7.1. 288 PART 2 • Producers, Consumers, and Competitive Markets Price (dollars per unit) D C 60 50 40 30 20 10 0 MC Lost profit for q1 < q* Lost profit for q2 > q* AR = MR = P ATC AVC A B 1 q0 2 3 4 5 6 7 q1 8 q* 9 q2 10 11 Output FIGURE 8.3 A COMPETITIVE FIRM MAKING A POSITIVE PROFIT In the short run, the competitive firm maximizes its profit by choosing an output q* at which its marginal cost MC is equal to the price P (or marginal revenue MR) of its product. The profit of the firm is measured by the rectangle ABCD. Any change in output, whether lower at q1 or higher at q2, will lead to lower profit. state the condition for profit maximization as follows: Marginal revenue equals marginal cost at a point at which the marginal cost curve is rising. This conclusion is very important because it applies to the output decisions of firms in markets that may or may not be perfectly competitive. We can restate it as follows: Output Rule: If a firm is producing any output, it should produce at the level at which marginal revenue equals marginal cost. Figure 8.3 also shows the competitive firm’s short-run profit. The distance AB is the difference between price and average cost at the output level q*, which is the average profit per unit of output. Segment BC measures the total number of units produced. Rectangle ABCD, therefore, is the firm’s profit. A firm need not always earn a profit in the short run, as Figure 8.4 shows. The major difference from Figure 8.3 is a higher fixed cost of production. This higher fixed cost raises average total cost but does not change the average variable cost and marginal cost curves. At the profit-maximizing output q*, Price (dollars per unit of output) C D F CHAPTER 8 • Profit Maximization and Competitive Supply 289 MC ATC P = MR AVC B A E q* Output FIGURE 8.4 A COMPETITIVE FIRM INCURRING LOSSES A competitive firm should shut down if price is below AVC. The firm may produce in the short run if price is greater than average variable cost. the price P is less than average cost. Line segment AB, therefore, measures the average loss from production. Likewise, the rectangle ABCD now measures the firm’s total loss. When Should the Firm Shut Down? Suppose a firm is losing money. Should it shut down and leave the industry? The answer depends in part on the firm’s expectations about its future business conditions. If it believes that conditions will improve and the business will be profitable in the future, it might make sense to operate at a loss in the short run. But let’s assume for the moment that the firm expects the price of its product to remain the same for the foreseeable future. What, then, should it do? Note that the firm is losing money when its price is less than average total cost at the profit-maximizing output q*. In that case, if there is little chance that conditions will improve, it should shut down and leave the industry. This decision is appropriate even if price is greater than average variable cost, as shown in Figure 8.4. If the firm continues to produce, the firm minimizes its losses at output q*, but it will still have losses rather than profits because price is less than average total cost. Note also that in Figure 8.4, because of the presence of fixed costs, average total cost exceeds average variable cost, and average total cost also exceeds price, so that the firm is indeed losing money. Recall that 290 PART 2 • Producers, Consumers, and Competitive Markets fixed costs do not change with the level of output, but they can be eliminated if the firm shuts down. (Examples of fixed costs include the salaries of plant managers and security personnel, and the electricity to keep the lights and heat running.) Will shutting down always be the sensible strategy? Not necessarily. The firm might operate at a loss in the short run because it expects to become profitable again in the future, when the price of its product increases or the cost of production falls. Operating at a loss might be painful, but it will keep open the prospect of better times in the future. Moreover, by staying in business, the firm retains the flexibility to change the amount of capital that it uses and thereby reduce its average total cost. This alternative seems particularly appealing if the price of the product is greater than the average variable cost of production, since operating at q* will allow the firm to cover a portion of its fixed costs. Our example of a pizzeria in Chapter 7 (Example 7.2) provides a useful illustration. Recall that pizzerias have high fixed costs (the rent that must be paid, the pizza ovens, and so on) and low variable costs (the ingredients and perhaps some employee wages). Suppose the price that the pizzeria is charging its customers is below the average total cost of production.Then the pizzeria is losing money by continuing to sell pizzas and it should shut down if it expects business conditions to remain unchanged in the future. But, should the owner sell the store and go out of business? Not necessarily; that decision depends on the owner’s expectation as to how the pizza business will fare in the future. Perhaps adding jalapeno peppers, raising the price, and advertising the new spicy pizzas will do the trick. Remember from §7.1 that a fixed cost is an ongoing cost that does not change with the level of output but is eliminated if the firm shuts down. E XAM PLE 8.2 THE SHORT-RUN OUTPUT DECISION OF AN ALUMINUM SMELTING PLANT How should the manager of an aluminum smelting plant determine the plant’s profit-maximizing output? Recall from Example 7.3 (page 240) that the smelting plant’s short-run marginal cost of production depends on whether it is running two or three shifts per day. As shown in Figure 8.5, marginal cost is $1140 per ton for output levels up to 600 tons per day and $1300 per ton for output levels between 600 and 900 tons per day. Suppose that the price of aluminum is initially P1 $1250 per ton. In that case, the profit-maximizing output is 600 tons; the firm can make a profit above its variable cost of $110 per ton by employing workers for two shifts a day. Running a third shift would involve overtime, and the price of the aluminum is insufficient to make the added production profitable. Suppose, however, that the price of aluminum were to increase to P2 $1360 per ton. This price is greater than the $1300 marginal cost of the third shift, making it profitable to increase output to 900 tons per day. Finally, suppose the price drops to only $1100 per ton. In this case, the firm should stop producing, but it should probably stay in business. By taking this step, it could resume producing in the future should the price increase. CHAPTER 8 • Profit Maximization and Competitive Supply 291 Cost (dollars per ton) MC 1400 1300 1200 1140 1100 P2 P1 0 300 600 900 Output (tons per day) FIGURE 8.5 THE SHORT-RUN OUTPUT OF AN ALUMINUM SMELTING PLANT In the short run, the plant should produce 600 tons per day if price is above $1140 per ton but less than $1300 per ton. If price is greater than $1300 per ton, it should run an overtime shift and produce 900 tons per day. If price drops below $1140 per ton, the firm should stop producing, but it should probably stay in business because the price may rise in the future. EXAM PLE 8.3 SOME COST CONSIDERATIONS FOR MANAGERS The application of the rule that marginal revenue should equal marginal cost depends on a manager’s ability to estimate marginal cost.3 To obtain useful measures of cost, managers should keep three guidelines in mind. First, except under limited circumstances, average variable cost should not be used as a substitute for marginal cost. When marginal and average variable cost are nearly constant, there is little difference between them. However, if both marginal and average cost are increasing sharply, the use of average variable cost can be misleading in deciding how much to produce. Suppose for example, that a company has the follo |
wing cost information: Current output 100 units per day, 80 of which are produced during the regular shift and 20 of which are produced during overtime Materials cost $8 per unit for all output Labor cost $30 per unit for the regular shift; $50 per unit for the overtime shift 3This example draws on the discussion of costs and managerial decision making in Thomas Nagle and Reed Holden, The Strategy and Tactics of Pricing, 5th ed. (Upper Saddle River, NJ: Prentice Hall, 2010), ch. 2. 292 PART 2 • Producers, Consumers, and Competitive Markets Let’s calculate average variable cost and marginal cost for the first 80 units of output and then see how both cost measures change when we include the additional 20 units produced with overtime labor. For the first 80 units, average variable cost is simply the labor cost ($2400 $30 per unit 80 units) plus the materials cost ($640 $8 per unit 80 units) divided by the 80 units—($2400 $640)/80 $38 per unit. Because average variable cost is the same for each unit of output, marginal cost is also equal to $38 per unit. When output increases to 100 units per day, both average variable cost and marginal cost change. The variable cost has now increased; it includes the additional materials cost of $160 (20 units $8 per unit) and the additional labor cost of $1000 (20 units $50 per unit). Average variable cost is therefore the total labor cost plus the materials cost ($2400 $1000 $640 $160) divided by the 100 units of output, or $42 per unit. What about marginal cost? While the materials cost per unit has remained unchanged at $8 per unit, the marginal cost of labor has now increased to $50 per unit, so that the marginal cost of each unit of overtime output is $58 per day. Because marginal cost is higher than average variable cost, a manager who relies on average variable cost will produce too much. Second, a single item on a firm’s accounting ledger may have two components, only one of which involves marginal cost. Suppose that a manager is trying to cut back production. She reduces the number of hours that some employees work and lays off others. But the salary of an employee who is laid off may not be an accurate measure of the marginal cost of production when cuts are made. Union contracts, for example, often require the firm to pay laid-off employees part of their salaries. In this case, the marginal cost of increasing production is not the same as the savings in marginal cost when production is decreased. The savings is the labor cost after the required layoff salary has been subtracted. Third, all opportunity costs should be included in determining marginal cost. Suppose a department store wants to sell children’s furniture. Instead of building a new selling area, the manager decides to use part of the third floor, which had been used for appliances, for the furniture. The marginal cost of this space is the $90 per square foot per day in profit that would have been earned had the store continued to sell appliances there. This opportunity cost measure may be much greater than what the store actually paid for that part of the building. These three guidelines can help a manager to measure marginal cost correctly. Failure to do so can cause production to be too high or too low and thereby reduce profit. 8.5 The Competitive Firm’s Short-Run Supply Curve A supply curve for a firm tells us how much output it will produce at every possible price. We have seen that competitive firms will increase output to the point at which price is equal to marginal cost, but will shut down if price is below average variable cost. Therefore, the firm’s supply curve is the portion of the marginal cost curve for which marginal cost is greater than average variable cost. Figure 8.6 illustrates the short-run supply curve. Note that for any P greater than minimum AVC, the profit-maximizing output can be read directly from the graph. At a price P1, for example, the quantity supplied will be q1; and at P2, it will be q2. For P less than (or equal to) minimum AVC, the profit-maximizing output is equal to zero. In Figure 8.6 the entire short-run supply curve consists of the crosshatched portion of the vertical axis plus the marginal cost curve above the point of minimum average variable cost. Short-run supply curves for competitive firms slope upward for the same reason that marginal cost increases—the presence of diminishing marginal returns to one or more factors of production. As a result, an increase in the market price will induce those firms already in the market to increase the quantities they produce. Price (dollars per unit) P2 P1 P = AVC CHAPTER 8 • Profit Maximization and Competitive Supply 293 MC AC AVC FIGURE 8.6 THE SHORT-RUN SUPPLY CURVE FOR A COMPETITIVE FIRM In the short run, the firm chooses its output so that marginal cost MC is equal to price as long as the firm covers its average variable cost. The short-run supply curve is given by the crosshatched portion of the marginal cost curve. 0 q 1 q 2 Output The higher price not only makes the additional production profitable, but also increases the firm’s total profit because it applies to all units that the firm produces. The Firm’s Response to an Input Price Change When the price of its product changes, the firm changes its output level to ensure that marginal cost of production remains equal to price. Often, however, the product price changes at the same time that the prices of inputs change. In this section we show how the firm’s output decision changes in response to a change in the price of one of its inputs. Figure 8.7 shows a firm’s marginal cost curve that is initially given by MC1 when the firm faces a price of $5 for its product. The firm maximizes profit by producing In §6.2, we explain that diminishing marginal returns occurs when each additional increase in an input results in a smaller and smaller increase in output. Price, cost (dollars per unit) $5 MC2 MC1 FIGURE 8.7 THE RESPONSE OF A FIRM TO A CHANGE IN INPUT PRICE When the marginal cost of production for a firm increases (from MC1 to MC2), the level of output that maximizes profit falls (from q1 to q2). q2 q1 Output 294 PART 2 • Producers, Consumers, and Competitive Markets an output of q1. Now suppose the price of one input increases. Because it now costs more to produce each unit of output, this increase causes the marginal cost curve to shift upward from MC1 to MC2. The new profit-maximizing output is q2, at which P MC2. Thus, the higher input price causes the firm to reduce its output. If the firm had continued to produce q1, it would have incurred a loss on the last unit of production. In fact, all production beyond q2 would reduce profit. E XAM PLE 8.4 THE SHORT-RUN PRODUCTION OF PETROLEUM PRODUCTS ity of the refinery and the cost of production. How much should you produce each day?4 Information about the refinery’s marginal cost of production is essential for this decision. Figure 8.8 shows the short-run (SMC). marginal cost curve SMC Suppose you are managing an oil refinery that converts crude oil into a particular mix of products, including gasoline, jet fuel, and residual fuel oil for home heating. Although plenty of crude oil is available, the amount that you refine depends on the capac- Cost (dollars per barrel) 77 76 75 74 73 8000 9000 10,000 11,000 Output (barrels per day) FIGURE 8.8 THE SHORT-RUN PRODUCTION OF PETROLEUM PRODUCTS As the refinery shifts from one processing unit to another, the marginal cost of producing petroleum products from crude oil increases sharply at several levels of output. As a result, the output level can be insensitive to some changes in price but very sensitive to others. 4This example is based on James M. Griffin, “The Process Analysis Alternative to Statistical Cost Functions: An Application to Petroleum Refining,” American Economic Review 62 (1972): 46–56. The numbers have been updated and applied to a particular refinery. CHAPTER 8 • Profit Maximization and Competitive Supply 295 Marginal cost increases with output, but in a series of uneven segments rather than as a smooth curve. The increase occurs in segments because the refinery uses different processing units to turn crude oil into finished products. When a particular processing unit reaches capacity, output can be increased only by substituting a more expensive process. For example, gasoline can be produced from light crude oils rather inexpensively in a processing unit called a “thermal cracker.” When this unit becomes full, additional gasoline can still be produced (from heavy as well as light crude oil), but only at a higher cost. In the case illustrated by Figure 8.8, the first capacity constraint comes into effect when production reaches about 9700 barrels a day. A second capacity constraint becomes important when production increases beyond 10,700 barrels a day. Deciding how much output to produce now becomes relatively easy. Suppose that refined products can be sold for $73 per barrel. Because the marginal cost of production is close to $74 for the first unit of output, no crude oil should be run through the refinery when the price is $73. If, however, price is between $74 and $75, the refinery should produce 9700 barrels a day (filling the thermal cracker). Finally, if the price is above $75, the more expensive refining unit should be used and production expanded toward 10,700 barrels a day. Because the cost function rises in steps, you know that your production decisions need not change much in response to small changes in price. You will typically use sufficient crude oil to fill the appropriate processing unit until price increases (or decreases) substantially. In that case, you need simply calculate whether the increased price warrants using an additional, more expensive processing unit. The shaded area in the figure gives the total savings to the firm (or equivalently, the reduction in lost profit) associated with the reduction in output from q1 to q2. 8.6 Th |
e Short-Run Market Supply Curve The short-run market supply curve shows the amount of output that the industry will produce in the short run for every possible price. The industry’s output is the sum of the quantities supplied by all of its individual firms. Therefore, the market supply curve can be obtained by adding the supply curves of each of these firms. Figure 8.9 shows how this is done when there are only three firms, all of which have different short-run production costs. Each firm’s marginal cost curve is drawn only for the portion that lies above its average variable cost curve. (We have shown only three firms to keep the graph simple, but the same analysis applies when there are many firms.) At any price below P1, the industry will produce no output because P1 is the minimum average variable cost of the lowest-cost firm. Between P1 and P2, only firm 3 will produce. The industry supply curve, therefore, will be identical to that portion of firm 3’s marginal cost curve MC3. At price P2, the industry supply will be the sum of the quantity supplied by all three firms. Firm 1 supplies 2 units, firm 2 supplies 5 units, and firm 3 supplies 8 units. Industry supply is thus 15 units. At price P3, firm 1 supplies 4 units, firm 2 supplies 7 units, and firm 3 supplies 10 units; the industry supplies 21 units. Note that the industry supply curve is upward sloping but has a kink at price P2, the lowest price at which all three firms produce. With many firms in the market, however, the kink becomes unimportant. Thus we usually draw industry supply as a smooth, upward-sloping curve. 296 PART 2 • Producers, Consumers, and Competitive Markets MC1 MC2 MC3 S Dollars per unit P3 P2 P1 2 4 5 7 8 10 15 21 Quantity FIGURE 8.9 INDUSTRY SUPPLY IN THE SHORT RUN The short-run industry supply curve is the summation of the supply curves of the individual firms. Because the third firm has a lower average variable cost curve than the first two firms, the market supply curve S begins at price P1 and follows the marginal cost curve of the third firm MC3 until price equals P2, when there is a kink. For P2 and all prices above it, the industry quantity supplied is the sum of the quantities supplied by each of the three firms. Elasticity of Market Supply Unfortunately, finding the industry supply curve is not always as simple as adding up a set of individual supply curves. As price rises, all firms in the industry expand their output. This additional output increases the demand for inputs to production and may lead to higher input prices. As we saw in Figure 8.7, increasing input prices shifts a firm’s marginal cost curve upward. For example, an increased demand for beef could also increase demand for corn and soybeans (which are used to feed cattle) and thereby cause the prices of these crops to rise. In turn, higher input prices will cause firms’ marginal cost curves to shift upward. This increase lowers each firm’s output choice (for any given market price) and causes the industry supply curve to be less responsive to changes in output price than it would otherwise be. The price elasticity of market supply measures the sensitivity of industry output to market price. The elasticity of supply Es is the percentage change in quantity supplied Q in response to a 1-percent change in price P: Es = (Q/Q)/(P/P) Because marginal cost curves are upward sloping, the short-run elasticity of supply is always positive. When marginal cost increases rapidly in response to increases in output, the elasticity of supply is low. In the short run, firms are capacity-constrained and find it costly to increase output. But when marginal In §2.4, we define the elasticity of supply as the percentage change in quantity supplied resulting from a 1-percent increase in price. CHAPTER 8 • Profit Maximization and Competitive Supply 297 cost increases slowly in response to increases in output, supply is relatively elastic; in this case, a small price increase induces firms to produce much more. At one extreme is the case of perfectly inelastic supply, which arises when the industry’s plant and equipment are so fully utilized that greater output can be achieved only if new plants are built (as they will be in the long run). At the other extreme is the case of perfectly elastic supply, which arises when marginal cost is constant. EXAM PLE 8.5 THE SHORT-RUN WORLD SUPPLY OF COPPER In the short run, the shape of the market supply curve for a mineral such as copper depends on how the cost of mining varies within and among the world’s major producers. Costs of mining, smelting, and refining copper differ because of differences in labor and transportation costs and because of differences in the copper content of the ore. Table 8.1 summarizes some of the relevant cost and production data for the nine largest copper- producing nations.5 Remember that in the short run, because the costs of building mines, smelters, and refineries are taken as sunk, the marginal cost numbers in Table 8.1 reflect the costs of operating (but not building) these facilities. These data can be used to plot the short-run world supply curve for copper. It is a short-run curve because it takes the existing mines and refineries as fixed. Figure 8.10 shows how the curve is constructed for the nine countries listed in the table. (The curve is incomplete because there are a few smaller and higher-cost producers that we have not included.) Note that the curve in Figure 8.10 is an approximation. The marginal cost number for each country is an average for all copper producers in that country, and we are assuming that marginal cost and average cost are approximately the same. In the United States, for example, some producers have a marginal cost greater than $1.70 and some less. The lowest-cost copper is mined in Russia, where the marginal cost of refined copper is roughly $1.30 per pound. The line segment labeled MCR represents the marginal cost curve for Russia. The curve is horizontal until the total capacity for mining and refining copper in Russia is reached. (That point TABLE 8.1 THE WORLD COPPER INDUSTRY (2010) COUNTRY ANNUAL PRODUCTION (THOUSAND METRIC TONS) MARGINAL COST (DOLLARS PER POUND) Australia Canada Chile Indonesia Peru Poland Russia US Zambia 900 480 5,520 840 1285 430 750 1120 770 2.30 2.60 1.60 1.80 1.70 2.40 1.30 1.70 1.50 Data from U.S. Geological Survey, Mineral Commodity Summaries, January 2011 (http:// minerals.usgs.gov/minerals/pubs/commodity/copper/mcs-2011-coppe.pdf) 5Our thanks to James Burrows of Charles River Associates, Inc., who was kind enough to provide data on marginal production cost. Updated data and related information are available on the Web at: http://minerals.usgs.gov/minerals. 298 PART 2 • Producers, Consumers, and Competitive Markets MCCa MCPo MCA MCCh MCPe MCUS MCI 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0. MCZ MCR 0 0 1500 3000 4500 6000 7500 9000 10,500 12,000 Production (thousand metric tons) FIGURE 8.10 THE SHORT-RUN WORLD SUPPLY OF COPPER The supply curve for world copper is obtained by summing the marginal cost curves for each of the major copper-producing countries. The supply curve slopes upward because the marginal cost of production ranges from a low of $1.30 in Russia to a high of $2.60 in Canada. is reached at a production level of 750 thousand metric tons per year.) Line segment MCZ represents the marginal cost curve for Zambia, segment MCCh the marginal cost curve for Chile, and so on. The world supply curve is obtained by summing each nation’s supply curve horizontally. As can be seen from the figure, the elasticity of supply depends on the price of copper. At relatively low prices, such as $1.30 and $1.80 per pound, the curve is quite elastic because small price increases lead to large increases in the quantity of copper supplied. At higher prices— say, above $2.40 per pound—the curve becomes more inelastic because, at those prices, most producers would be operating close to or at capacity. For a review of consumer surplus, see §4.4, where it is defined as the difference between what a consumer is willing to pay for a good and what the consumer actually pays when buying it. • producer surplus Sum over all units produced by a firm of differences between the market price of a good and the marginal cost of production. Producer Surplus in the Short Run In Chapter 4, we measured consumer surplus as the difference between the maximum that a person would pay for an item and its market price. An analogous concept applies to firms. If marginal cost is rising, the price of the product is greater than marginal cost for every unit produced except the last one. As a result, firms earn a surplus on all but the last unit of output. The producer surplus of a firm is the sum over all units produced of the differences between the market price of the good and the marginal cost of production. Just as consumer surplus measures the area below an individual’s demand curve and above the market price of the product, producer surplus measures the area above a producer’s supply curve and below the market price. CHAPTER 8 • Profit Maximization and Competitive Supply 299 Price (dollars per unit of output) Producer Surplus MC A D 0 B C AVC P FIGURE 8.11 PRODUCER SURPLUS FOR A FIRM The producer surplus for a firm is measured by the yellow area below the market price and above the marginal cost curve, between outputs 0 and q*, the profit-maximizing output. Alternatively, it is equal to rectangle ABCD because the sum of all marginal costs up to q* is equal to the variable costs of producing q*. q* Output Figure 8.11 illustrates short-run producer surplus for a firm. The profit-maximizing output is q*, where P MC. The surplus that the producer obtains from selling each unit is the difference between the price and the marginal cost of producing the unit. The producer surplus is then the sum of these “unit surpluses” over all units that the firm produces. It is given by t |
he yellow area under the firm’s horizontal demand curve and above its marginal cost curve, from zero output to the profit-maximizing output q*. When we add the marginal cost of producing each level of output from 0 to q*, we find that the sum is the total variable cost of producing q*. Marginal cost reflects increments to cost associated with increases in output; because fixed cost does not vary with output, the sum of all marginal costs must equal the sum of the firm’s variable costs.6 Thus producer surplus can alternatively be defined as the difference between the firm’s revenue and its total variable cost. In Figure 8.11, producer surplus is also given by the rectangle ABCD, which equals revenue (0ABq*) minus variable cost (0DCq*). PRODUCER SURPLUS VERSUS PROFIT Producer surplus is closely related to profit but is not equal to it. In the short run, producer surplus is equal to revenue minus variable cost, which is variable profit. Total profit, on the other hand, is equal to revenue minus all costs, both variable and fixed: Producer surplus = PS = R - VC Profit = p = R - VC - FC It follows that in the short run, when fixed cost is positive, producer surplus is greater than profit. The extent to which firms enjoy producer surplus depends on their costs of production. Higher-cost firms have less producer surplus and lower-cost firms have more. By adding up the producer surpluses of all firms, we can determine the producer 6The area under the marginal cost curve from 0 to q* is TC(q*) − TC(0) TC − FC VC. 300 PART 2 • Producers, Consumers, and Competitive Markets Price (dollars per unit of output) P* FIGURE 8.12 PRODUCER SURPLUS FOR A MARKET The producer surplus for a market is the area below the market price and above the market supply curve, between 0 and output Q*. Producer Surplus S D 0 Q* Output surplus for a market. This can be seen in Figure 8.12. The market supply curve begins at the vertical axis at a point representing the average variable cost of the lowest-cost firm in the market. Producer surplus is the area that lies below the market price of the product and above the supply curve between the output levels 0 and Q*. 8.7 Choosing Output in the Long Run In the short run, one or more of the firm’s inputs are fixed. Depending on the time available, this may limit the flexibility of the firm to adapt its production process to new technological developments, or to increase or decrease its scale of operation as economic conditions change. In contrast, in the long run, a firm can alter all its inputs, including plant size. It can decide to shut down (i.e., to exit the industry) or to begin producing a product for the first time (i.e., to enter an industry). Because we are concerned here with competitive markets, we allow for free entry and free exit. In other words, we are assuming that firms may enter or exit without legal restriction or any special costs associated with entry. (Recall from Section 8.1 that this is one of the key assumptions underlying perfect competition.) After analyzing the long-run output decision of a profit-maximizing firm in a competitive market, we discuss the nature of competitive equilibrium in the long run. We also discuss the relationship between entry and exit, and economic and accounting profits. Long-Run Profit Maximization Figure 8.13 shows how a competitive firm makes its long-run, profit-maximizing output decision. As in the short run, the firm faces a horizontal demand curve. (In Figure 8.13 the firm takes the market price of $40 as given.) Its short-run average (total) cost curve SAC and short-run marginal cost curve SMC are low enough for the firm to make a positive profit, given by rectangle ABCD, by producing an output of q1, where SMC P MR. The long-run average cost curve LAC reflects the presence of economies of scale up to output level q2 and diseconomies of scale at higher output levels. The long-run marginal cost curve LMC cuts the long-run average cost from below at q2, the point of minimum long-run average cost. In §7.4, we explain that economies of scale arise when a firm can double its output for less than twice the cost. CHAPTER 8 • Profit Maximization and Competitive Supply 301 Dollars per unit of output D $40 C G $30 LMC LAC P = MR SAC SMC A B E F FIGURE 8.13 OUTPUT CHOICE IN THE LONG RUN The firm maximizes its profit by choosing the output at which price equals long-run marginal cost LMC. In the diagram, the firm increases its profit from ABCD to EFGD by increasing its output in the long run. q1 q2 q3 Output If the firm believes that the market price will remain at $40, it will want to increase the size of its plant to produce at output q3, at which its long-run marginal cost equals the $40 price. When this expansion is complete, the profit margin will increase from AB to EF, and total profit will increase from ABCD to EFGD. Output q3 is profit-maximizing because at any lower output (say, q2), the marginal revenue from additional production is greater than the marginal cost. Expansion is, therefore, desirable. But at any output greater than q3, marginal cost is greater than marginal revenue. Additional production would therefore reduce profit. In summary, the long-run output of a profit-maximizing competitive firm is the point at which long-run marginal cost equals the price. Note that the higher the market price, the higher the profit that the firm can earn. Correspondingly, as the price of the product falls from $40 to $30, the profit also falls. At a price of $30, the firm’s profit-maximizing output is q2, the point of long-run minimum average cost. In this case, because P ATC, the firm earns zero economic profit. Long-Run Competitive Equilibrium For an equilibrium to arise in the long run, certain economic conditions must prevail. Firms in the market must have no desire to withdraw at the same time that no firms outside the market wish to enter. But what is the exact relationship between profitability, entry, and long-run competitive equilibrium? We can see the answer by relating economic profit to the incentive to enter and exit a market. ACCOUNTING PROFIT AND ECONOMIC PROFIT As we saw in Chapter 7, it is important to distinguish between accounting profit and economic profit. Accounting profit is measured by the difference between the firm’s revenues and its cash flows for labor, raw materials, and interest plus depreciation expenses. Economic profit takes into account opportunity costs. One such opportunity cost is the return to the firm’s owners if their capital were used elsewhere. Suppose, 302 PART 2 • Producers, Consumers, and Competitive Markets • zero economic profit A firm is earning a normal return on its investment—i.e., it is doing as well as it could by investing its money elsewhere. for example, that the firm uses labor and capital inputs; its capital equipment has been purchased. Accounting profit will equal revenues R minus labor cost wL, which is positive. Economic profit p, however, equals revenues R minus labor cost wL minus the capital cost, rK: p = R - wL - rK As we explained in Chapter 7, the correct measure of capital cost is the user cost of capital, which is the annual return that the firm could earn by investing its money elsewhere instead of purchasing capital, plus the annual depreciation on the capital. ZERO ECONOMIC PROFIT When a firm goes into a business, it does so in the expectation that it will earn a return on its investment. A zero economic profit means that the firm is earning a normal—i.e., competitive—return on that investment. This normal return, which is part of the user cost of capital, is the firm’s opportunity cost of using its money to buy capital rather than investing it elsewhere. Thus, a firm earning zero economic profit is doing as well by investing its money in capital as it could by investing elsewhere—it is earning a competitive return on its money. Such a firm, therefore, is performing adequately and should stay in business. (A firm earning a negative economic profit, however, should consider going out of business if it does not expect to improve its financial picture.) As we will see, in competitive markets economic profit becomes zero in the long run. Zero economic profit signifies not that firms are performing poorly, but rather that the industry is competitive. ENTRY AND EXIT Figure 8.13 shows how a $40 price induces a firm to increase output and realize a positive profit. Because profit is calculated after subtracting the opportunity cost of capital, a positive profit means an unusually high return on a financial investment, which can be earned by entering a profitable industry. This high return causes investors to direct resources away from other industries and into this one—there will be entry into the market. Eventually the increased production associated with new entry causes the market supply curve to shift to the right. As a result, market output increases and the market price of the product falls.7 Figure 8.14 illustrates this. In part (b) of the figure, the supply curve has shifted from S1 to S2, causing the price to fall from P1 ($40) to P2 ($30). In part (a), which applies to a single firm, the long-run average cost curve is tangent to the horizontal price line at output q2. A similar story would apply to exit. Suppose that each firm’s minimum longrun average cost remains $30 but the market price falls to $20. Recall our discussion earlier in the chapter; absent expectations of a price change, the firm will leave the industry when it cannot cover all of its costs, i.e., when price is less than average variable cost. But the story does not end here. The exit of some firms from the market will decrease production, which will cause the market supply curve to shift to the left. Market output will decrease and the price of the product will rise until an equilibrium is reached at a break-even price of $30. To summarize: In a market with entry and exit, a firm enters when it can earn a p |
ositive longrun profit and exits when it faces the prospect of a long-run loss. 7We discuss why the long-run supply curve might be upward sloping in the next section. CHAPTER 8 • Profit Maximization and Competitive Supply 303 Industry S1 Dollars per unit of output $40 $30 Firm LMC Dollars per unit of output LAC P1 P2 P1 P2 S2 D Output q2 (a) Output Q1 Q2 (b) FIGURE 8.14 LONG-RUN COMPETITIVE EQUILIBRIUM Initially the long-run equilibrium price of a product is $40 per unit, shown in (b) as the intersection of demand curve D and supply curve S1. In (a) we see that firms earn positive profits because long-run average cost reaches a minimum of $30 (at q2). Positive profit encourages entry of new firms and causes a shift to the right in the supply curve to S2, as shown in (b). The long-run equilibrium occurs at a price of $30, as shown in (a), where each firm earns zero profit and there is no incentive to enter or exit the industry. • long-run competitive equilibrium All firms in an industry are maximizing profit, no firm has an incentive to enter or exit, and price is such that quantity supplied equals quantity demanded. When a firm earns zero economic profit, it has no incentive to exit the industry. Likewise, other firms have no special incentive to enter. A long-run competitive equilibrium occurs when three conditions hold: 1. All firms in the industry are maximizing profit. 2. No firm has an incentive either to enter or exit the industry because all firms are earning zero economic profit. 3. The price of the product is such that the quantity supplied by the industry is equal to the quantity demanded by consumers. The dynamic process that leads to long-run equilibrium may seem puzzling. Firms enter the market because they hope to earn a profit, and likewise they exit because of economic losses. In long-run equilibrium, however, firms earn zero economic profit. Why does a firm enter a market knowing that it will eventually earn zero profit? The answer is that zero economic profit represents a competitive return for the firm’s investment of financial capital. With zero economic profit, the firm has no incentive to go elsewhere because it cannot do better financially by doing so. If the firm happens to enter a market sufficiently early to enjoy an economic profit in the short run, so much the better. Similarly, if a firm exits an unprofitable market quickly, it can save its investors money. Thus the concept of long-run equilibrium tells us the direction that a firm’s behavior is likely to take. 304 PART 2 • Producers, Consumers, and Competitive Markets The idea of an eventual zero-profit, long-run equilibrium should not discourage a manager—it should be seen in a positive light, because it reflects the opportunity to earn a competitive return. FIRMS HAVING IDENTICAL COSTS To see why all the conditions for long-run equilibrium must hold, assume that all firms have identical costs. Now consider what happens if too many firms enter the industry in response to an opportunity for profit. The industry supply curve in Figure 8.14(b) will shift further to the right, and price will fall below $30—say, to $25. At that price, however, firms will lose money. As a result, some firms will exit the industry. Firms will continue to exit until the market supply curve shifts back to S2. Only when there is no incentive to exit or enter can a market be in long-run equilibrium. FIRMS HAVING DIFFERENT COSTS Now suppose that all firms in the industry do not have identical cost curves. Perhaps one firm has a patent that lets it produce at a lower average cost than all the others. In that case, it is consistent with long-run equilibrium for that firm to earn a greater accounting profit and to enjoy a higher producer surplus than other firms. As long as other investors and firms cannot acquire the patent that lowers costs, they have no incentive to enter the industry. Conversely, as long as the process is particular to this product and this industry, the fortunate firm has no incentive to exit the industry. The distinction between accounting profit and economic profit is important here. If the patent is profitable, other firms in the industry will pay to use it (or attempt to buy the entire firm to acquire it). The increased value of the patent thus represents an opportunity cost to the firm that holds it. It could sell the rights to the patent rather than use it. If all firms are equally efficient otherwise, the economic profit of the firm falls to zero. However, if the firm with the patent is more efficient than other firms, then it will be earning a positive profit. But if the patent holder is otherwise less efficient, it should sell off the patent and exit the industry. THE OPPORTUNITY COST OF LAND There are other instances in which firms earning positive accounting profit may be earning zero economic profit. Suppose, for example, that a clothing store happens to be located near a large shopping center. The additional flow of customers can substantially increase the store’s accounting profit because the cost of the land is based on its historical cost. However, as far as economic profit is concerned, the cost of the land should reflect its opportunity cost, which in this case is the current market value of the land. When the opportunity cost of land is included, the profitability of the clothing store is no higher than that of its competitors. Thus the condition that economic profit be zero is essential for the market to be in long-run equilibrium. By definition, positive economic profit represents an opportunity for investors and an incentive to enter an industry. Positive accounting profit, however, may signal that firms already in the industry possess valuable assets, skills, or ideas, which will not necessarily encourage entry. Economic Rent We have seen that some firms earn higher accounting profit than others because they have access to factors of production that are in limited supply; these might include land and natural resources, entrepreneurial skill, or other creative talent. In these situations, what makes economic profit zero in the long run is the willingness of other firms to use the factors of production that are in limited supply. The positive accounting profits are therefore translated into economic CHAPTER 8 • Profit Maximization and Competitive Supply 305 • economic rent Amount that firms are willing to pay for an input less the minimum amount necessary to obtain it. rent that is earned by the scarce factors. Economic rent is what firms are willing to pay for an input less the minimum amount necessary to buy it. In competitive markets, in both the short and the long run, economic rent is often positive even though profit is zero. For example, suppose that two firms in an industry own their land outright; thus the minimum cost of obtaining the land is zero. One firm, however, is located on a river and can ship its products for $10,000 a year less than the other firm, which is inland. In this case, the $10,000 higher profit of the first firm is due to the $10,000 per year economic rent associated with its river location. The rent is created because the land along the river is valuable and other firms would be willing to pay for it. Eventually, the competition for this specialized factor of production will increase the value of that factor to $10,000. Land rent—the difference between $10,000 and the zero cost of obtaining the land—is also $10,000. Note that while the economic rent has increased, the economic profit of the firm on the river has become zero. Economic rent reflects the fact that there is an opportunity cost to owning the land and more generally to owning any factor of production whose supply is restricted. Here the opportunity cost of owning the land is $10,000, which is identified as the economic rent. The presence of economic rent explains why there are some markets in which firms cannot enter in response to profit opportunities. In those markets, the supply of one or more inputs is fixed, one or more firms earn economic rents, and all firms enjoy zero economic profit. Zero economic profit tells a firm that it should remain in a market only if it is at least as efficient in production as other firms. It also tells possible entrants to the market that entry will be profitable only if they can produce more efficiently than firms already in the market. Producer Surplus in the Long Run Suppose that a firm is earning a positive accounting profit but that there is no incentive for other firms to enter or exit the industry. This profit must reflect economic rent. How then does rent relate to producer surplus? To begin with, note that while economic rent applies to factor inputs, producer surplus applies to outputs. Note also that producer surplus measures the difference between the market price that a producer receives and the marginal cost of production. Thus, in the long run, in a competitive market, the producer surplus that a firm earns on the output that it sells consists of the economic rent that it enjoys from all its scarce inputs.8 Let’s say, for example, that a baseball team has a franchise allowing it to operate in a particular city. Suppose also that the only alternative location for the team is a city in which it will generate substantially lower revenues. The team will therefore earn an economic rent associated with its current location. This rent will reflect the difference between what the firm would be willing to pay for its current location and the amount needed to locate in the alternative city. The firm will also be earning a producer surplus associated with the sale of baseball tickets and other franchise items at its current location. This surplus will reflect all economic rents, including those rents associated with the firm’s other factor inputs (the stadium and the players). Figure 8.15 shows that firms earning economic rent earn the same economic profit as firms that do not earn rent. |
Part (a) shows the economic profit of a baseball team located in a moderate-sized city. The average price of a ticket is $7, and costs are such that the team earns zero economic profit. Part (b) shows the profit of a team that has the same cost curves even though it is located in a larger city. 8In a noncompetitive market, producer surplus will reflect economic profit as well as economic rent. 306 PART 2 • Producers, Consumers, and Competitive Markets Ticket price $7 LMC LAC Ticket price $10 $7.20 Economic Rent LMC LAC 1.0 (a) Season ticket sales (millions) 1.3 Season ticket sales (millions) (b) FIGURE 8.15 FIRMS EARN ZERO PROFIT IN LONG-RUN EQUILIBRIUM In long-run equilibrium, all firms earn zero economic profit. In (a), a baseball team in a moderate-sized city sells enough tickets so that price ($7) is equal to marginal and average cost. In (b), the demand is greater, so a $10 price can be charged. The team increases sales to the point at which the average cost of production plus the average economic rent is equal to the ticket price. When the opportunity cost associated with owning the franchise is taken into account, the team earns zero economic profit. Because more people want to see baseball games, the latter team can sell tickets for $10 apiece and thereby earn an accounting profit of $2.80 above its average cost of $7.20 on each ticket. However, the rent associated with the more desirable location represents a cost to the firm—an opportunity cost—because it could sell its franchise to another team. As a result, the economic profit in the larger city is also zero. 8.8 The Industry’s Long-Run Supply Curve In our analysis of short-run supply, we first derived the firm’s supply curve and then showed how the summation of individual firms’ supply curves generated a market supply curve. We cannot, however, analyze long-run supply in the same way: In the long run, firms enter and exit markets as the market price changes. This makes it impossible to sum up supply curves—we do not know which firms’ supplies to add up in order to get market totals. The shape of the long-run supply curve depends on the extent to which increases and decreases in industry output affect the prices that firms must pay for inputs into the production process. In cases in which there are economies of scale in production or cost savings associated with the purchase of large volumes of inputs, input prices will decline as output increases. In cases where diseconomies of scale are present, input prices may increase with output. The third possibility is that input costs may not change with output. In any of these CHAPTER 8 • Profit Maximization and Competitive Supply 307 cases, to determine long-run supply, we assume that all firms have access to the available production technology. Output is increased by using more inputs, not by invention. We also assume that the conditions underlying the market for inputs to production do not change when the industry expands or contracts. For example, an increased demand for labor does not increase a union’s ability to negotiate a better wage contract for its workers. In our analysis of long-run supply, it will be useful to distinguish among three types of industries: constant cost, increasing cost, and decreasing cost. Constant-Cost Industry Figure 8.16 shows the derivation of the long-run supply curve for a constantcost industry. A firm’s output choice is given in (a), while industry output is shown in (b). Assume that the industry is initially in equilibrium at the intersection of market demand curve D1 and short-run market supply curve S1. Point A at the intersection of demand and supply is on the long-run supply curve SL because it tells us that the industry will produce Q1 units of output when the long-run equilibrium price is P1. To obtain other points on the long-run supply curve, suppose the market demand for the product unexpectedly increases (say, because of a reduction in personal income taxes). A typical firm is initially producing at an output of q1, where P1 is equal to long-run marginal cost and long-run average cost. But because the firm is also in short-run equilibrium, price also equals short-run marginal cost. • constant-cost industry Industry whose long-run supply curve is horizontal. Dollars per unit of output P2 P1 Firm MC AC Dollars per unit of output P2 P1 Industry S1 C S2 A B SL D1 D2 q2 q1 (a) Output Q1 Q2 (b) Output FIGURE 8.16 LONG-RUN SUPPLY IN A CONSTANT-COST INDUSTRY In (b), the long-run supply curve in a constant-cost industry is a horizontal line SL. When demand increases, initially causing a price rise (represented by a move from point A to point C), the firm initially increases its output from q1 to q2, as shown in (a). But the entry of new firms causes a shift to the right in industry supply. Because input prices are unaffected by the increased output of the industry, entry occurs until the original price is obtained (at point B in (b)). 308 PART 2 • Producers, Consumers, and Competitive Markets Suppose that the tax cut shifts the market demand curve from D1 to D2. Demand curve D2 intersects supply curve S1 at C. As a result, price increases from P1 to P2. Part (a) of Figure 8.16 shows how this price increase affects a typical firm in the industry. When the price increases to P2, the firm follows its short-run marginal cost curve and increases output to q2. This output choice maximizes profit because it satisfies the condition that price equal short-run marginal cost. If every firm responds this way, each will be earning a positive profit in shortrun equilibrium. This profit will be attractive to investors and will cause existing firms to expand operations and new firms to enter the market. As a result, in Figure 8.16 (b) the short-run supply curve shifts to the right from S1 to S2. This shift causes the market to move to a new long-run equilibrium at the intersection of D2 and S2. For this intersection to be a long-run equilibrium, output must expand enough so that firms are earning zero profit and the incentive to enter or exit the industry disappears. In a constant-cost industry, the additional inputs necessary to produce higher output can be purchased without an increase in per-unit price. This might happen, for example, if unskilled labor is a major input in production, and the market wage of unskilled labor is unaffected by the increase in the demand for labor. Because the prices of inputs have not changed, firms’ cost curves are also unchanged; the new equilibrium must be at a point such as B in Figure 8.16 (b), at which price is equal to P1, the original price before the unexpected increase in demand occurred. The long-run supply curve for a constant-cost industry is, therefore, a horizontal line at a price that is equal to the long-run minimum average cost of production. At any higher price, there would be positive profit, increased entry, increased short-run supply, and thus downward pressure on price. Remember that in a constant-cost industry, input prices do not change when conditions change in the output market. Constant-cost industries can have horizontal long-run average cost curves. Increasing-Cost Industry In an increasing-cost industry the prices of some or all inputs to production increase as the industry expands and the demand for the inputs grows. Diseconomies of scale in the production of one or more inputs may be the explanation. Suppose, for example, that the industry uses skilled labor, which becomes in short supply as the demand for it increases. Or, if a firm requires mineral resources that are available only on certain types of land, the cost of land as an input increases with output. Figure 8.17 shows the derivation of longrun supply, which is similar to the previous constant-cost derivation. The industry is initially in equilibrium at A in part (b). When the demand curve unexpectedly shifts from D1 to D2, the price of the product increases in the short run to P2, and industry output increases from Q1 to Q2. A typical firm, as shown in part (a), increases its output from q1 to q2 in response to the higher price by moving along its short-run marginal cost curve. The higher profit earned by this and other firms induces new firms to enter the industry. As new firms enter and output expands, increased demand for inputs causes some or all input prices to increase. The short-run market supply curve shifts to the right as before, though not as much, and the new equilibrium at B results in a price P3 that is higher than the initial price P1. Because the higher input prices raise the firms’ short-run and long-run cost curves, the higher market price is needed to ensure that firms earn zero profit in long-run equilibrium. Figure 8.17 (a) illustrates this. The average cost curve shifts up from AC1 to AC2, while the marginal cost curve shifts to the left, from MC1 to MC2. The new long-run equilibrium price P3 is equal to the new minimum average • increasing-cost industry long-run supply curve is upward sloping. Industry whose Dollars per unit of output P2 P3 P1 CHAPTER 8 • Profit Maximization and Competitive Supply 309 Firm MC2 MC1 Dollars per unit of output Industry AC2 AC1 P2 P3 P1 S1 S2 SL B A D1 D2 q2 q1 (a) Q1 Q2 Q3 (b) FIGURE 8.17 LONG-RUN SUPPLY IN AN INCREASING-COST INDUSTRY In (b), the long-run supply curve in an increasing-cost industry is an upward-sloping curve SL. When demand increases, initially causing a price rise, the firms increase their output from q1 to q2 in (a). In that case, the entry of new firms causes a shift to the right in supply from S1 to S2. Because input prices increase as a result, the new long-run equilibrium occurs at a higher price than the initial equilibrium. cost. As in the constant-cost case, the higher short-run profit caused by the initial increase in demand disappears in the long run as firms increase output and input costs rise. The new equilibrium at B in Figure 8.17 (b) is, therefore, on the long-run supp |
ly curve for the industry. In an increasing-cost industry, the long-run industry supply curve is upward sloping. The industry produces more output, but only at the higher price needed to compensate for the increase in input costs. The term “increasing cost” refers to the upward shift in the firms’ long-run average cost curves, not to the positive slope of the cost curve itself. Decreasing-Cost Industry The industry supply curve can also be downward sloping. In this case, the unexpected increase in demand causes industry output to expand as before. But as the industry grows larger, it can take advantage of its size to obtain some of its inputs more cheaply. For example, a larger industry may allow for an improved transportation system or for a better, less expensive financial network. In this case, firms’ average cost curves shift downward (even if they do not enjoy economies of scale), and the market price of the product falls. The lower market price and lower average cost of production induce a new longrun equilibrium with more firms, more output, and a lower price. Therefore, in a decreasing-cost industry, the long-run supply curve for the industry is downward sloping. • decreasing-cost industry long-run supply curve is downward sloping. Industry whose 310 PART 2 • Producers, Consumers, and Competitive Markets E XAM PLE 8.6 CONSTANT-, INCREASING-, AND DECREASING-COST INDUSTRIES: COFFEE, OIL, AND AUTOMOBILES As you have progressed through this book, you have been introduced to industries that have constant, increasing, and decreasing long-run costs. Let’s look back at some of these industries, beginning with one that has constant long-run costs. In Example 2.7, we saw that the supply of coffee is extremely elastic in the long run (see Figure 2.18c). The reason is that land for growing coffee is widely available and the costs of planting and caring for trees remains constant as the volume of coffee produced grows. Thus, coffee is a constant-cost industry. Now consider the case of an increasing-cost industry. We explained in Example 2.9 that the oil industry is an increasing cost industry with an upwardsloping long-run supply curve (see Figure 2.23b). Why are costs increasing? Because there is a limited availability of easily accessible, large-volume oil fields. Consequently, as oil companies increase output, they are forced to obtain oil from increasingly expensive fields. Finally, a decreasing-cost industry. We discussed the demand for automobiles in Examples 3.1 and 3.3, but what about supply? In the automobile industry, certain cost advantages arise because inputs can be acquired more cheaply as the volume of production increases. Indeed, the major automobile manufacturers—such as General Motors, Toyota, Ford, and Honda—acquire batteries, engines, brake systems, and other key inputs from firms that specialize in producing those inputs efficiently. As a result, the average cost of automobile production decreases as the volume of production increases. The Effects of a Tax In Chapter 7, we saw that a tax on one of a firm’s inputs (in the form of an effluent fee) creates an incentive for the firm to change the way it uses inputs in its production process. Now we consider ways in which a firm responds to a tax on its output. To simplify the analysis, assume that the firm uses a fixed-proportions production technology. If it’s a polluter, the output tax might encourage the firm to reduce its output, and therefore its effluent, or it might be imposed merely to raise revenue. First, suppose the output tax is imposed only on this firm and thus does not affect the market price of the product. We will see that the tax on output encourages the firm to reduce its output. Figure 8.18 shows the relevant short-run cost curves for a firm enjoying positive economic profit by producing an output of q1 and selling its product at the market price P1. Because the tax is assessed for every unit of output, it raises the firm’s marginal cost curve from MC1 to MC2 MC1 t, where t is the tax per unit of the firm’s output. The tax also raises the average variable cost curve by the amount t. The output tax can have two possible effects. If the firm can still earn a positive or zero economic profit after the imposition of the tax, it will maximize its profit by choosing an output level at which marginal cost plus the tax is equal to the price of the product. Its output falls from q1 to q2, and the implicit effect of the tax is to shift its supply curve upward (by the amount of the tax). If the firm can no longer earn an economic profit after the tax has been imposed, it will choose to exit the market. Now suppose that every firm in the industry is taxed and so has increasing marginal costs. Because each firm reduces its output at the current market price, the total output supplied by the industry will also fall, causing the price of the product to increase. Figure 8.19 illustrates this. An upward shift in the supply curve, from S1 t, causes the market price of the product to increase (by less than S1 to S2 the amount of the tax) from P1 to P2. This increase in price diminishes some of the effects that we described previously. Firms will reduce their output less than they would without a price increase. Dollars per unit of output P1 CHAPTER 8 • Profit Maximization and Competitive Supply 311 MC2 = MC1 + t MC1 t AVC1 + t AVC1 q2 q1 Output FIGURE 8.18 EFFECT OF AN OUTPUT TAX ON A COMPETITIVE FIRM’S OUTPUT An output tax raises the firm’s marginal cost curve by the amount of the tax. The firm will reduce its output to the point at which the marginal cost plus the tax is equal to the price of the product. Finally, output taxes may also encourage some firms (those whose costs are somewhat higher than others) to exit the industry. In the process, the tax raises the long-run average cost curve for each firm. Long-Run Elasticity of Supply The long-run elasticity of industry supply is defined in the same way as the short-run elasticity: It is the percentage change in output (Q/Q) that results from a percentage change in price (P/P). In a constant-cost industry, the long-run supply curve is horizontal, and the long-run supply elasticity is infinitely large. (A small increase in price will induce an extremely large increase in output.) In an increasing-cost industry, however, the long-run Dollars per unit of output P2 P1 S2 = S1 + t S1 t D FIGURE 8.19 EFFECT OF AN OUTPUT TAX ON INDUSTRY OUTPUT An output tax placed on all firms in a competitive market shifts the supply curve for the industry upward by the amount of the tax. This shift raises the market price of the product and lowers the total output of the industry. Q2 Q1 Output 312 PART 2 • Producers, Consumers, and Competitive Markets supply elasticity will be positive but finite. Because industries can adjust and expand in the long run, we would generally expect long-run elasticities of supply to be larger than short-run elasticities.9 The magnitude of the elasticity will depend on the extent to which input costs increase as the market expands. For example, an industry that depends on inputs that are widely available will have a more elastic long-run supply than will an industry that uses inputs in short supply. E XAM PLE 8.7 THE SUPPLY OF TAXICABS IN NEW YORK The price of a taxi ride depends, of course, on the distance. Most cities regulate the fares that a taxicab can charge, and typically the price of a ride begins with a fixed fee to enter the cab, and then a charge per mile driven. In 2011 there were 13,150 taxicabs operating in New York City. One would expect that if fares went down, fewer drivers would want to operate cabs and the quantity supplied would fall. Likewise, one would expect that if fares went up, more drivers would want to operate cabs and the quantity would increase. Let’s see if that’s right. Driving a cab is not an easy job. Most drivers work a 12-hour shift six days per week. What annual income can the driver expect to earn? Assuming the driver works 50 weeks per year, the total hours worked will be 11221621502 = 3600 hours per year. But part of that time is spent waiting at a cab stand or cruising for passengers; only about 2/3 of the time will there actually be a paying passenger inside, i.e., about 2400 hours per year. Driving about 10 miles per hour (remember, this is New York), the cabbie will drive about 24,000 “paid” miles per year. Some rides are longer than others, but the average taxi ride in New York is about 5 miles, and (in 2011) the average cost was about $12.60 on the meter, or about $15 with tip. Based on 5-mile average trips, the driver will therefore make about 124,0002>152 = 4,800 trips and earn a gross income of 1$152 14,8002 = $72,000 per year. From this, the driver must pay for gas, insurance, and maintenance and depreciation on the cab, which can add up to $10,000 per year. But that is not the only cost. As in most cities, driving a taxi in New York requires a medallion. The medallions, which were issued by the city, are owned by taxicab companies. The companies lease the medallions to drivers at a rate that is also regulated by the city: $110 per 12-hour shift. Driving 6 shifts per week and 50 weeks per year, the cab driver must therefore pay an additional 162 1502 11102 = $33,000 per year to lease the medallion. This leaves the driver with a net income of only $72,000 - $10,000 - $33,000 = $29,000 per year. Suppose New York City reduced the fare schedule, so that a 5-mile trip only brought the driver $10 instead of $15. Then the driver’s annual gross revenue would drop from $72,000 to $48,000. After covering the costs of leasing the medallion as well as gas, etc., the driver would be left with only $5,000 of net annual income. Under those circumstances, hardly anyone would want to drive a cab. And now suppose that New York instead raised taxi fares so that a 5-mile trip brought in $20 instead of $15. Now the driver’s annual gross revenue will be $96 |
,000, and his net income after expenses would be $53,000. That’s not bad for a job that requires little education and no special skills, so many more people will want to drive cabs. Thus we would expect the supply curve for taxis to be very elastic—small reductions in the price (the fare earned on an average five-mile ride) will cause a sharp reduction in quantity, and small increases in price will cause a sharp increase in quantity (the number of operating taxicabs). This is illustrated by the supply curve labeled S in Figure 8.20. Something is missing, however. While reducing fares will indeed cause a reduction in the quantity supplied, raising the price will not cause an increase in the quantity supplied. Why not? Because the number of medallions is fixed at 13,150, roughly the same number that were in circulation in 1937. By refusing to issue more medallions, New York effectively limits 9In some cases the opposite is true. Consider the elasticity of supply of scrap metal from a durable good like copper. Recall from Chapter 2 that because there is an existing stock of scrap, the long-run elasticity of supply will be smaller than the short-run elasticity. CHAPTER 8 • Profit Maximization and Competitive Supply 313 S′ S P $20 $15 $10 FIGURE 8.20 THE SUPPLY CURVE FOR NEW YORK TAXICABS If there were no restriction on the number of medallions, the supply curve would be highly elastic. Cab drivers work hard and don’t earn much, so a drop in the price P (of a 5-mile ride) would lead many of them to find another job. Likewise, an increase in price would bring many new drivers into the market. But the number of medallions—and therefore the number of taxicabs—is limited to 13,150, so the supply curve becomes vertical at this quantity. the supply of taxis to be no greater than 13,150. Thus the supply curve becomes vertical at the quantity 13,150 (and is labeled S’ in the figure). Many cities require taxis to have medallions and restrict the number of medallions. You’ll find out why in Chapter 9, when you read Example 9.5. 13,150 Q EX AM PLE 8.8 THE LONG-RUN SUPPLY OF HOUSING Owner-occupied and rental housing provide interesting examples of the range of possible supply elasticities. People buy or rent housing to obtain the services that a house provides—a place to eat and sleep, comfort, and so on. If the price of housing services were to rise in one area of the country, the quantity of services provided could increase substantially. not increase substantially as the quantity of housing supplied increases. Likewise, costs associated with construction are not likely to increase because there is a national market for lumber and other materials. Therefore, the long-run elasticity of the housing supply is likely to be very large, approximating that of a constant-cost industry. In fact, many studies find the long- To begin, consider the supply of owner-occupied housing in suburban or rural areas where land is not scarce. In this case, the price of land does run supply curve to be nearly horizontal.10 The market for rental housing is different, however. The construction of rental housing is often 10For a review of the relevant literature, see Dixie M. Blackley, “The Long-Run Elasticity of New Housing Supply in the United States: Empirical Evidence for 1950 to 1994,” Journal of Real Estate Finance and Economics 18 (1999): 25–42. 314 PART 2 • Producers, Consumers, and Competitive Markets restricted by local zoning laws. Many communities outlaw it entirely, while others limit it to certain areas. Because urban land on which most rental housing is located is restricted and valuable, the long-run elasticity of supply of rental housing is much lower than the elasticity of supply of owner-occupied housing. As the price of rental-housing services rises, new high-rise rental units are built and older units are renovated—a practice that increases the quantity of rental services. With urban land becoming more valuable as housing density increases, and with the cost of construction soaring with the height of buildings, increased demand causes the input costs of rental housing to rise. In this increasing-cost case, the elasticity of supply can be much less than 1; in one study, the authors found it to be 0.36.11 SUMMARY 1. Managers can operate in accordance with a complex set of objectives and under various constraints. However, we can assume that firms act as if they are maximizing long-run profit. 2. Many markets may approximate perfect competition in that one or more firms act as if they face a nearly horizontal demand curve. In general, the number of firms in an industry is not always a good indicator of the extent to which that industry is competitive. 3. Because a firm in a competitive market accounts for a small share of total industry output, it makes its output choice under the assumption that its production decision will have no effect on the price of the product. In this case, the demand curve and the marginal revenue curve are identical. 4. In the short run, a competitive firm maximizes its profit by choosing an output at which price is equal to (short-run) marginal cost. Price must, however, be greater than or equal to the firm’s minimum average variable cost of production. 5. The short-run market supply curve is the horizontal summation of the supply curves of the firms in an industry. It can be characterized by the elasticity of supply: the percentage change in quantity supplied in response to a percentage change in price. 6. The producer surplus for a firm is the difference between its revenue and the minimum cost that would QUESTIONS FOR REVIEW be necessary to produce the profit-maximizing output. In both the short run and the long run, producer surplus is the area under the horizontal price line and above the marginal cost of production. 7. Economic rent is the payment for a scarce factor of production less the minimum amount necessary to hire that factor. In the long run in a competitive market, producer surplus is equal to the economic rent generated by all scarce factors of production. 8. In the long run, profit-maximizing competitive firms choose the output at which price is equal to long-run marginal cost. 9. A long-run competitive equilibrium occurs under these conditions: (a) when firms maximize profit; (b) when all firms earn zero economic profit, so that there is no incentive to enter or exit the industry; and (c) when the quantity of the product demanded is equal to the quantity supplied. 10. The long-run supply curve for a firm is horizontal when the industry is a constant-cost industry in which the increased demand for inputs to production (associated with an increased demand for the product) has no effect on the market price of the inputs. But the longrun supply curve for a firm is upward sloping in an increasing-cost industry, where the increased demand for inputs causes the market price of some or all inputs to rise. 1. Why would a firm that incurs losses choose to produce 5. Why do firms enter an industry when they know that rather than shut down? 2. Explain why the industry supply curve is not the long- run industry marginal cost curve. 3. In long-run equilibrium, all firms in the industry earn zero economic profit. Why is this true? 4. What is the difference between economic profit and producer surplus? in the long run economic profit will be zero? 6. At the beginning of the twentieth century, there were many small American automobile manufacturers. At the end of the century, there were only three large ones. Suppose that this situation is not the result of lax federal enforcement of antimonopoly laws. How do you explain the decrease in the number of manufacturers? 11John M. Quigley and Stephen S. Raphael, “Regulation and the High Cost of Housing in California,” American Economic Review, Vol. 95(2), 2005: 323–328. CHAPTER 8 • Profit Maximization and Competitive Supply 315 (Hint: What is the inherent cost structure of the automobile industry?) 7. Because industry X is characterized by perfect competition, every firm in the industry is earning zero economic profit. If the product price falls, no firm can survive. Do you agree or disagree? Discuss. 8. An increase in the demand for movies also increases the salaries of actors and actresses. Is the long-run supply curve for films likely to be horizontal or upward sloping? Explain. 9. True or false: A firm should always produce at an output at which long-run average cost is minimized. Explain. 10. Can there be constant returns to scale in an industry with an upward-sloping supply curve? Explain. 11. What assumptions are necessary for a market to be perfectly competitive? In light of what you have learned in this chapter, why is each of these assumptions important? 12. Suppose a competitive industry faces an increase in demand (i.e., the demand curve shifts upward). What are the steps by which a competitive market ensures increased output? Will your answer change if the government imposes a price ceiling? 13. The government passes a law that allows a substantial subsidy for every acre of land used to grow tobacco. How does this program affect the long-run supply curve for tobacco? 14. A certain brand of vacuum cleaners can be purchased from several local stores as well as from several catalogues or websites. a. If all sellers charge the same price for the vacuum cleaner, will they all earn zero economic profit in the long run? b. If all sellers charge the same price and one local seller owns the building in which he does business, paying no rent, is this seller earning a positive economic profit? c. Does the seller who pays no rent have an incentive to lower the price that he charges for the vacuum cleaner? EXERCISES 1. The data in the table below give information about the price (in dollars) for which a firm can sell a unit of output and the total cost of production. a. Fill in the blanks in the table. b. Show what happens to the firm’s output choice and pro |
fit if the price of the product falls from $60 to $50. R P MC MR R MR P q P P 60 C P 60 P 60 P 60 P 50 P 50 P 50 0 60 1 60 2 60 3 60 4 60 5 60 6 60 7 60 8 60 9 60 10 60 11 60 100 150 178 198 212 230 250 272 310 355 410 475 2. Using the data in the table, show what happens to the firm’s output choice and profit if the fixed cost of production increases from $100 to $150 and then to $200. Assume that the price of the output remains at $60 per unit. What general conclusion can you reach about the effects of fixed costs on the firm’s output choice? 3. Use the same information as in Exercise 1. a. Derive the firm’s short-run supply curve. (Hint: You may want to plot the appropriate cost curves.) b. If 100 identical firms are in the market, what is the industry supply curve? 4. Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by C 200 2q2, where q is the level of output and C is total cost. (The marginal cost of production is 4q; the fixed cost is $200.) a. If the price of watches is $100, how many watches should you produce to maximize profit? b. What will the profit level be? c. At what minimum price will the firm produce a positive output? 5. Suppose that a competitive firm’s marginal cost of producing output q is given by MC(q) 3 2q. Assume that the market price of the firm’s product is $9. a. What level of output will the firm produce? b. What is the firm’s producer surplus? c. Suppose that the average variable cost of the firm is given by AVC(q) 3 q. Suppose that the firm’s fixed costs are known to be $3. Will the firm be earning a positive, negative, or zero profit in the short run? 6. A firm produces a product in a competitive industry and has a total cost function C 50 4q 2q2 and a marginal cost function MC 4 4q. At the given market price of $20, the firm is producing 5 units of 316 PART 2 • Producers, Consumers, and Competitive Markets output. Is the firm maximizing its profit? What quantity of output should the firm produce in the long run? 7. Suppose the same firm’s cost function is C(q) 4q2 16. a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost. (Hint: Marginal cost is given by MC 8q.) b. Show the average cost, marginal cost, and average variable cost curves on a graph. c. Find the output that minimizes average cost. d. At what range of prices will the firm produce a pos- itive output? e. At what range of prices will the firm earn a nega- tive profit? f. At what range of prices will the firm earn a positive profit? *8. A competitive firm has the following short-run cost function: C(q) q3 − 8q2 30q 5. a. Find MC, AC, and AVC and sketch them on a graph. b. At what range of prices will the firm supply zero output? c. Identify the firm’s supply curve on your graph. d. At what price would the firm supply exactly 6 units of output? *9. a. Suppose that a firm’s production function is q 9x1/2 in the short run, where there are fixed costs of $1000, and x is the variable input whose cost is $4000 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). b. Write down the equation for the supply curve. c. If price is $1000, how many units will the firm produce? What is the level of profit? Illustrate your answer on a cost-curve graph. * 10. Suppose you are given the following information about a particular industry: Q D = 6500 - 100P Market demand Q S = 1200P Market supply C(q) = 722 + MC(q) = 2q 200 q 2 200 Firm total cost function Firm marginal cost function Assume that all firms are identical and that the market is characterized by perfect competition. a. Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm. b. Would you expect to see entry into or exit from the industry in the long run? Explain. What effect will entry or exit have on market equilibrium? c. What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain. d. What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain. *11. Suppose that a competitive firm has a total cost function C(q) 450 15q 2q2 and a marginal cost function MC(q) 15 4q. If the market price is P $115 per unit, find the level of output produced by the firm. Find the level of profit and the level of producer surplus. *12. A number of stores offer film developing as a service to their customers. Suppose that each store offering this service has a cost function C(q) 50 0.5q 0.08q2 and a marginal cost MC 0.5 0.16q. a. If the going rate for developing a roll of film is $8.50, is the industry in long-run equilibrium? If not, find the price associated with long-run equilibrium. b. Suppose now that a new technology is developed which will reduce the cost of film developing by 25 percent. Assuming that the industry is in longrun equilibrium, how much would any one store be willing to pay to purchase this new technology? *13. Consider a city that has a number of hot dog stands operating throughout the downtown area. Suppose that each vendor has a marginal cost of $1.50 per hot dog sold and no fixed cost. Suppose the maximum number of hot dogs that any one vendor can sell is 100 per day. a. If the price of a hot dog is $2, how many hot dogs does each vendor want to sell? b. If the industry is perfectly competitive, will the price remain at $2 for a hot dog? If not, what will the price be? c. If each vendor sells exactly 100 hot dogs a day and the demand for hot dogs from vendors in the city is Q 4400 − 1200P, how many vendors are there? d. Suppose the city decides to regulate hot dog vendors by issuing permits. If the city issues only 20 permits and if each vendor continues to sell 100 hot dogs a day, what price will a hot dog sell for? e. Suppose the city decides to sell the permits. What is the highest price that a vendor would pay for a permit? *14. A sales tax of $1 per unit of output is placed on a particular firm whose product sells for $5 in a competitive industry with many firms. a. How will this tax affect the cost curves for the firm? b. What will happen to the firm’s price, output, and profit? c. Will there be entry or exit in the industry? *15. A sales tax of 10 percent is placed on half the firms (the polluters) in a competitive industry. The revenue is paid to the remaining firms (the nonpolluters) as a 10 percent subsidy on the value of output sold. a. Assuming that all firms have identical constant long-run average costs before the sales tax-subsidy policy, what do you expect to happen (in both the short run and the long run), to the price of the product, the output of firms, and industry output? (Hint: How does price relate to industry input?) b. Can such a policy always be achieved with a balanced budget in which tax revenues are equal to subsidy payments? Why or why not? Explain. C H A P T E R 9 The Analysis of Competitive Markets In Chapter 2, we saw how supply and demand curves can help us describe and understand the behavior of competitive markets. In Chapters 3 to 8, we saw how these curves are derived and what determines their shapes. Building on this foundation, we return to supply–demand analysis and show how it can be applied to a wide variety of economic problems—problems that might concern a consumer faced with a purchasing decision, a firm faced with a long-range planning problem, or a government agency that has to design a policy and evaluate its likely impact. We begin by showing how consumer and producer surplus can be used to study the welfare effects of a government policy—in other words, who gains and who loses from the policy, and by how much. We also use consumer and producer surplus to demonstrate the efficiency of a competitive market—why the equilibrium price and quantity in a competitive market maximizes the aggregate economic welfare of producers and consumers. Then we apply supply–demand analysis to a variety of problems. Because very few markets in the United States have been untouched by government interventions of one kind or another, most of the problems that we will study deal with the effects of such interventions. Our objective is not simply to solve these problems, but to show you how to use the tools of economic analysis to deal with them and others like them on your own. We hope that by working through the examples we provide, you will see how to calculate the response of markets to changing economic conditions or government policies and to evaluate the resulting gains and losses to consumers and producers. 9.1 Evaluating the Gains and Losses from Government Policies— Consumer and Producer Surplus We saw at the end of Chapter 2 that a government-imposed price ceiling causes the quantity of a good demanded to rise (at the lower price, consumers want to buy more) and the quantity supplied to fall (producers are not willing to supply as much at the lower price). The result .1 Evaluating the Gains and Losses from Government Policies—Consumer and Producer Surplus 317 9.2 The Efficiency of a Competitive Market 323 9.3 Minimum Prices 328 9.4 Price Supports and Production Quotas 332 9.5 Import Quotas and Tariffs 340 9.6 The Impact of a Tax or Subsidy 345 .1 Price Controls and Natural Gas Shortages 322 9.2 The Market for Human Kidneys 325 9.3 Airline Regulation 330 9.4 Supporting the Price of Wheat 335 9.5 Why Can’t I Find a Taxi? 338 9.6 The Sugar Quota 342 9.7 A Tax on Gasoline 349 317 318 PART 2 • Producers, Consumers, and Competitive Markets In §2.7, we explain that under price controls, the price of a product can be no higher than a maximum allowable ceiling price. For a review of consumer surplus, see §4.4, where it is defined as the difference between what a consumer is willing to pay for a good and what the consumer actually pays when buying |
it. is a shortage—i.e., excess demand. Of course, those consumers who can still buy the good will be better off because they will now pay less. (Presumably, this was the objective of the policy in the first place.) But if we also take into account those who cannot obtain the good, how much better off are consumers as a whole? Might they be worse off? And if we lump consumers and producers together, will their total welfare be greater or lower, and by how much? To answer questions such as these, we need a way to measure the gains and losses from government interventions and the changes in market price and quantity that such interventions cause. Our method is to calculate the changes in consumer and producer surplus that result from an intervention. In Chapter 4, we saw that consumer surplus measures the aggregate net benefit that consumers obtain from a competitive market. In Chapter 8, we saw how producer surplus measures the aggregate net benefit to producers. Here we will see how consumer and producer surplus can be applied in practice. Review of Consumer and Producer Surplus In an unregulated, competitive market, consumers and producers buy and sell at the prevailing market price. But remember, for some consumers the value of the good exceeds this market price; they would pay more for the good if they had to. Consumer surplus is the total benefit or value that consumers receive beyond what they pay for the good. For example, suppose the market price is $5 per unit, as in Figure 9.1. Some consumers probably value this good very highly and would pay much more than $5 for it. Consumer A, for example, would pay up to $10 for the good. However, because the market price is only $5, he enjoys a net benefit of $5—the $10 value he places on the good, less the $5 he must pay to obtain it. Consumer B values the good somewhat less highly. She would be willing to pay $7, and Price $10 7 5 FIGURE 9.1 CONSUMER AND PRODUCER SURPLUS Consumer A would pay $10 for a good whose market price is $5 and therefore enjoys a benefit of $5. Consumer B enjoys a benefit of $2, and Consumer C, who values the good at exactly the market price, enjoys no benefit. Consumer surplus, which measures the total benefit to all consumers, is the yellow-shaded area between the demand curve and the market price. Producer surplus measures the total profits of producers, plus rents to factor inputs. It is the green-shaded area between the supply curve and the market price. Together, consumer and producer surplus measure the welfare benefit of a competitive market. Consumer Surplus S Producer Surplus Consumer A Consumer B Consumer C Q0 D Quantity CHAPTER 9 • The Analysis of Competitive Markets 319 thus enjoys a $2 net benefit. Finally, Consumer C values the good at exactly the market price, $5. He is indifferent between buying or not buying the good, and if the market price were one cent higher, he would forgo the purchase. Consumer C, therefore, obtains no net benefit.1 For consumers in the aggregate, consumer surplus is the area between the demand curve and the market price (i.e., the yellow-shaded area in Figure 9.1). Because consumer surplus measures the total net benefit to consumers, we can measure the gain or loss to consumers from a government intervention by measuring the resulting change in consumer surplus. Producer surplus is the analogous measure for producers. Some producers are producing units at a cost just equal to the market price. Other units, however, could be produced for less than the market price and would still be produced and sold even if the market price were lower. Producers, therefore, enjoy a benefit—a surplus—from selling those units. For each unit, this surplus is the difference between the market price the producer receives and the marginal cost of producing this unit. For the market as a whole, producer surplus is the area above the supply curve up to the market price; this is the benefit that lower-cost producers enjoy by selling at the market price. In Figure 9.1, it is the green triangle. And because producer surplus measures the total net benefit to producers, we can measure the gain or loss to producers from a government intervention by measuring the resulting change in producer surplus. Application of Consumer and Producer Surplus With consumer and producer surplus, we can evaluate the welfare effects of a government intervention in the market. We can determine who gains and who loses from the intervention, and by how much. To see how this is done, let’s return to the example of price controls that we first encountered toward the end of Chapter 2. The government makes it illegal for producers to charge more than a ceiling price set below the market-clearing level. Recall that by decreasing production and increasing the quantity demanded, such a price ceiling creates a shortage (excess demand). Figure 9.2 replicates Figure 2.24 (page 58), except that it also shows the changes in consumer and producer surplus that result from the government price-control policy. Let’s go through these changes step by step. 1. Change in Consumer Surplus: Some consumers are worse off as a result of the policy, and others are better off. The ones who are worse off are those who have been rationed out of the market because of the reduction in production and sales from Q0 to Q1. Other consumers, however, can still purchase the good (perhaps because they are in the right place at the right time or are willing to wait in line). These consumers are better off because they can buy the good at a lower price (Pmax rather than P0). How much better off or worse off is each group? The consumers who can still buy the good enjoy an increase in consumer surplus, which is given by the blue-shaded rectangle A. This rectangle measures the reduction of price in each unit times the number of units consumers are able to buy at the lower price. On the other hand, those consumers who can no longer buy the good lose surplus; their loss is given by the green-shaded 1Of course, some consumers value the good at less than $5. These consumers make up the part of the demand curve to the right of the equilibrium quantity Q0 and will not purchase the good. For a review of producer surplus, see §8.6, where it is defined as the sum over all units produced of the difference between the market price of the good and the marginal cost of its production. • welfare effects Gains and losses to consumers and producers. 320 PART 2 • Producers, Consumers, and Competitive Markets FIGURE 9.2 CHANGE IN CONSUMER AND PRODUCER SURPLUS FROM PRICE CONTROLS The price of a good has been regulated to be no higher than Pmax, which is below the marketclearing price P0. The gain to consumers is the difference between rectangle A and triangle B. The loss to producers is the sum of rectangle A and triangle C. Triangles B and C together measure the deadweight loss from price controls. Price P0 Pmax Deadweight Loss B C A Shortage S D Q1 Q0 Q2 Quantity triangle B. This triangle measures the value to consumers, less what they would have had to pay, that is lost because of the reduction in output from Q0 to Q1. The net change in consumer surplus is therefore A − B. In Figure 9.2, because rectangle A is larger than triangle B, we know that the net change in consumer surplus is positive. It is important to stress that we have assumed that those consumers who are able to buy the good are the ones who value it most highly. If that were not the case—e.g., if the output Q1 were rationed randomly— the amount of lost consumer surplus would be larger than triangle B. In many cases, there is no reason to expect that those consumers who value the good most highly will be the ones who are able to buy it. As a result, the loss of consumer surplus might greatly exceed triangle B, making price controls highly inefficient.2 In addition, we have ignored the opportunity costs that arise with rationing. For example, those people who want the good might have to wait in line to obtain it. In that case, the opportunity cost of their time should be included as part of lost consumer surplus. 2. Change in Producer Surplus: With price controls, some producers (those with relatively lower costs) will stay in the market but will receive a lower price for their output, while other producers will leave the market. Both groups will lose producer surplus. Those who remain in the market and produce quantity Q1 are now receiving a lower price. They have lost the producer surplus given by rectangle A. However, total production has also dropped. The purple-shaded triangle C measures the additional loss of producer surplus for those producers who have left the market and those 2For a nice analysis of this aspect of price controls, see David Colander, Sieuwerd Gaastra, and Casey Rothschild, “The Welfare Costs of Market Restriction,” Southern Economic Journal, Vol. 77(1), 2011: 213–223. CHAPTER 9 • The Analysis of Competitive Markets 321 • deadweight loss Net loss of total (consumer plus producer) surplus. who have stayed in the market but are producing less. Therefore, the total change in producer surplus is −A − C. Producers clearly lose as a result of price controls. 3. Deadweight Loss: Is the loss to producers from price controls offset by the gain to consumers? No. As Figure 9.2 shows, price controls result in a net loss of total surplus, which we call a deadweight loss. Recall that the change in consumer surplus is A − B and that the change in producer surplus is −A − C. The total change in surplus is therefore (A − B) (−A − C) −B − C. We thus have a deadweight loss, which is given by the two triangles B and C in Figure 9.2. This deadweight loss is an inefficiency caused by price controls; the loss in producer surplus exceeds the gain in consumer surplus. If politicians value consumer surplus more than producer surplus, this deadweight loss from price controls may not carry much political weight. However, if the demand curve is v |
ery inelastic, price controls can result in a net loss of consumer surplus, as Figure 9.3 shows. In that figure, triangle B, which measures the loss to consumers who have been rationed out of the market, is larger than rectangle A, which measures the gain to consumers able to buy the good. Here, because consumers value the good highly, those who are rationed out suffer a large loss. The demand for gasoline is very inelastic in the short run (but much more elastic in the long run). During the summer of 1979, gasoline shortages resulted from oil price controls that prevented domestic gasoline prices from increasing to rising world levels. Consumers spent hours waiting in line to buy gasoline. This was a good example of price controls making consumers—the group whom the policy was presumably intended to protect—worse off. Price D B P0 Pmax A C S FIGURE 9.3 EFFECT OF PRICE CONTROLS WHEN DEMAND IS INELASTIC If demand is sufficiently inelastic, triangle B can be larger than rectangle A. In this case, consumers suffer a net loss from price controls. Q1 Q2 Quantity 322 PART 2 • Producers, Consumers, and Competitive Markets EXAMPLE 9.1 PRICE CONTROLS AND NATURAL GAS SHORTAGES In Example 2.10 (page 59), we discussed the price controls that were imposed on natural gas markets during the 1970s, and we analyzed what would happen if the government were once again to regulate the wholesale price of natural gas. Specifically, we saw that, in 2007, the free-market wholesale price of natural gas was about $6.40 per thousand cubic feet (mcf), and we calculated the quantities that would be supplied and demanded if the price were regulated to be no higher than $3.00 per mcf. Now, equipped with the concepts of consumer surplus, producer surplus, and deadweight loss, we can calculate the welfare impact of this ceiling price. Recall from Example 2.10 that we found that the supply and demand curves for natural gas could be approximated as follows: Supply: QS = 15.90 + 0.72PG + 0.05PO Demand: QD = 0.02 - 1.8PG + 0.69PO where QS and QD are the quantities supplied and demanded, each measured in trillion cubic feet (Tcf), PG is the price of natural gas in dollars per thousand cubic feet ($/mcf), and PO is the price of oil in dollars per barrel ($/b). As you can verify by setting QS equal to QD and using a price of oil of $50 per barrel, the equilibrium free market price and quantity are $6.40 per mcf and 23 Tcf, respectively. Under the hypothetical regulations, however, the maximum allowable price was $3.00 per mcf, which implies a supply of 20.6 Tcf and a demand of 29.1 Tcf. Figure 9.4 shows these supply and demand curves and compares the free market and regulated prices. Rectangle A and triangles B and C measure the changes in consumer and producer surplus resulting from price controls. By calculating the areas of the rectangle and triangles, we can determine the gains and losses from controls. To do the calculations, first note that 1 Tcf is equal to 1 billion mcf. (We must put the quantities and prices in common units.) Also, by substituting the quantity 20.6 Tcf into the equation for the demand curve, we can determine that the vertical line at 20.6 Tcf intersects the demand curve at a price of $7.73 per mcf. Then we can calculate the areas as follows: A = (20.6 billion mcf ) * ($3.40/mcf) = $70.04 billion B = (1/2) * (2.4 billion mcf) * ($1.33/mcf ) = $1.60 billion C = (1/2) * (2.4 billion mcf ) * ($3.40/mcf ) = $4.08 billion (The area of a triangle is one-half the product of its altitude and its base.) The annual change in consumer surplus that would result from these hypothetical price controls would therefore be A - B = 70.04 - 1.60 = $68.44 billion. The change in producer surplus would be -A - C = -70.04 - 4.08 = -$74.12 billion. And finally, the annual deadweight loss CHAPTER 9 • The Analysis of Competitive Markets 323 would be -B - C = -1.60 - 4.08 = -$5.68 billion. Note that most of this deadweight loss is from triangle C, i.e., the loss to those consumers who are unable to obtain natural gas as a result of the price controls 20 18 16 14 12 10 8 6 4 2 0 P= $19.20 Demand Supply $7.73 PO = $6.40 Pmax = $3.00 0 A 10 B C QS = 20.6 QD = 29.1 20 30 40 Quantity (Tcf) Q* = 23 FIGURE 9.4 EFFECTS OF NATURAL GAS PRICE CONTROLS The market-clearing price of natural gas was $6.40 per mcf, and the (hypothetical) maximum allowable price is $3.00. A shortage of 29.1 - 20.6 = 8.5 Tcf results. The gain to consumers is rectangle A minus triangle B, and the loss to producers is rectangle A plus triangle C. The deadweight loss is the sum of triangles B plus C. 9.2 The Efficiency of a Competitive Market To evaluate a market outcome, we often ask whether it achieves economic efficiency—the maximization of aggregate consumer and producer surplus. We just saw how price controls create a deadweight loss. The policy therefore imposes an efficiency cost on the economy: Taken together, producer and consumer surplus are reduced by the amount of the deadweight loss. (Of course, this does not mean that such a policy is bad; it may achieve other objectives that policymakers and the public deem important.) MARKET FAILURE One might think that if the only objective is to achieve economic efficiency, a competitive market is better left alone. This is sometimes, • economic efficiency Maximization of aggregate consumer and producer surplus. 324 PART 2 • Producers, Consumers, and Competitive Markets • market failure Situation in which an unregulated competitive market is inefficient because prices fail to provide proper signals to consumers and producers. but not always, the case. In some situations, a market failure occurs: Because prices fail to provide the proper signals to consumers and producers, the unregulated competitive market is inefficient—i.e., does not maximize aggregate consumer and producer surplus. There are two important instances in which market failure can occur: • externality Action taken by either a producer or a consumer which affects other producers or consumers but is not accounted for by the market price. 1. Externalities: Sometimes the actions of either consumers or producers result in costs or benefits that do not show up as part of the market price. Such costs or benefits are called externalities because they are “external” to the market. One example is the cost to society of environmental pollution by a producer of industrial chemicals. Without government intervention, such a producer will have no incentive to consider the social cost of pollution. We examine externalities and the proper government response to them in Chapter 18. 2. Lack of Information: Market failure can also occur when consumers lack information about the quality or nature of a product and so cannot make utility-maximizing purchasing decisions. Government intervention (e.g., requiring “truth in labeling”) may then be desirable. The role of information is discussed in detail in Chapter 17. In the absence of externalities or a lack of information, an unregulated competitive market does lead to the economically efficient output level. To see this, let’s consider what happens if price is constrained to be something other than the equilibrium market-clearing price. We have already examined the effects of a price ceiling (a price held below the market-clearing price). As you can see in Figure 9.2 (page 320), production falls (from Q0 to Q1), and there is a corresponding loss of total surplus (the deadweight-loss triangles B and C). Too little is produced, and consumers and producers in the aggregate are worse off. Now suppose instead that the government required the price to be above the market-clearing price—say, P2 instead of P0. As Figure 9.5 shows, although producers would like to produce more at this higher price (Q2 instead of Q0), consumers will now buy less (Q3 instead of Q0). If we assume that producers produce only what can be sold, the market output level will be Q3, and again, there is a net loss of total surplus. In Figure 9.5, rectangle A now represents a FIGURE 9.5 WELFARE LOSS WHEN PRICE IS HELD ABOVE MARKET-CLEARING LEVEL When price is regulated to be no lower than P2, only Q3 will be demanded. If Q3 is produced, the deadweight loss is given by triangles B and C. At price P2, producers would like to produce more than Q3. If they do, the deadweight loss will be even larger. Price P2 P0 Quantity CHAPTER 9 • The Analysis of Competitive Markets 325 transfer from consumers to producers (who now receive a higher price), but triangles B and C again represent a deadweight loss. Because of the higher price, some consumers are no longer buying the good (a loss of consumer surplus given by triangle B), and some producers are no longer producing it (a loss of producer surplus given by triangle C). In fact, the deadweight loss triangles B and C in Figure 9.5 give an optimistic assessment of the efficiency cost of policies that force price above market-clearing levels. Some producers, enticed by the high price P2, might increase their capacity and output levels, which would result in unsold output. (This happened in the airline industry when, prior to 1980, fares were regulated above market-clearing levels by the Civil Aeronautics Board.) Or to satisfy producers, the government might buy up unsold output to maintain production at Q2 or close to it. (This is what happens in U.S. agriculture.) In both cases, the total welfare loss will exceed the areas of triangles B and C. We will examine minimum prices, price supports, and related policies in some detail in the next few sections. Besides showing how supply–demand analysis can be used to understand and assess these policies, we will see how deviations from the competitive market equilibrium lead to efficiency costs. EXAM PLE 9.2 THE MARKET FOR HUMAN KIDNEYS Should people have the right to sell parts of their bodies? Congress believes the answer is no. In 1984, it passed the National Organ Transplantation Act, which prohibi |
ts the sale of organs for transplantation. Organs may only be donated. Although the law prohibits their sale, it does not make organs valueless. Instead, it prevents those who supply organs (living persons or the families of the deceased) from reaping their economic value. It also creates a shortage of organs. Each year, about 16,000 kidneys, 44,000 corneas, and 2300 hearts are transplanted in the United States. But there is considerable excess demand for these organs, so that many potential recipients must do without them, some of whom die as a result. For example, as of July 2011, there were about 111,500 patients on the national Organ Procurement and Transplantation Network (OPTN) waiting list. However, only 28,662 transplant surgeries were performed in the United States in 2010. Although the number of transplant surgeries has nearly doubled since 1990, the number of patients waiting for organs has increased to nearly five times its level in 1990.3 To understand the effects of this law, let’s consider the supply and demand for kidneys. First the supply curve. Even at a price of zero (the effective price under the law), donors supply about 16,000 kidneys per 3Source: Organ Procurement and Transplantation Network, http://www.optn.transplant.hrsa.gov. 326 PART 2 • Producers, Consumers, and Competitive Markets In §2.6, we explain how to fit linear demand and supply curves from information about the equilibrium price and quantity and the price elasticities of demand and supply. year. But many other people who need kidney transplants cannot obtain them because of a lack of donors. It has been estimated that 8000 more kidneys would be supplied if the price were $20,000. We can fit a linear supply curve to this data—i.e., a supply curve of the form Q = a + bP. When P = 0, Q = 16,000, so a = 16,000. If P = $20,000, Q = 24,000, so b = (24,000 - 16,000)/20,000 = 0.4. Thus the supply curve is Supply: QS = 16,000 + 0.4P Note that at a price of $20,000, the elasticity of supply is 0.33. It is expected that at a price of $20,000, the number of kidneys demanded would be 24,000 per year. Like supply, demand is relatively price inelastic; a reasonable estimate for the price elasticity of demand at the $20,000 price is −0.33. This implies the following linear demand curve: Demand: QD = 32,000 - 0.4P These supply and demand curves are plotted in Figure 9.6, which shows the market-clearing price and quantity of $20,000 and 24,000, respectively. $40,000 $30,000 e c i r P $20,000 $10,000 $0 0 S S′ B C D A 8,000 16,000 Quantity D 24,000 32,000 FIGURE 9.6 THE MARKET FOR KIDNEYS AND THE EFFECT OF THE NATIONAL ORGAN TRANSPLANTATION ACT The market-clearing price is $20,000; at this price, about 24,000 kidneys per year would be supplied. The law effectively makes the price zero. About 16,000 kidneys per year are still donated; this constrained supply is shown as S'. The loss to suppliers is given by rectangle A and triangle C. If consumers received kidneys at no cost, their gain would be given by rectangle A less triangle B. In practice, kidneys are often rationed on the basis of willingness to pay, and many recipients pay most or all of the $40,000 price that clears the market when supply is constrained. Rectangles A and D measure the total value of kidneys when supply is constrained. CHAPTER 9 • The Analysis of Competitive Markets 327 Because the sale of kidneys is prohibited, supply is limited to 16,000 (the number of kidneys that people donate). This constrained supply is shown as the vertical line S´. How does this affect the welfare of kidney suppliers and recipients? First consider suppliers. Those who provide kidneys fail to receive the $20,000 that each kidney is worth—a loss of surplus represented by rectangle A and equal to (16,000)($20,000) $320 million. Moreover, some people who would supply kidneys if they were paid do not. These people lose an amount of surplus represented by triangle C, which is equal to (1/2)(8000) ($20,000) $80 million. Therefore, the total loss to suppliers is $400 million. What about recipients? Presumably the law intended to treat the kidney as a gift to the recipient. In this case, those recipients who obtain kidneys gain rectangle A ($320 million) because they (or their insurance companies) do not have to pay the $20,000 price. Those who cannot obtain kidneys lose surplus of an amount given by triangle B and equal to $80 million. This implies a net increase in the surplus of recipients of $320 million − $80 million $240 million. It also implies a deadweight loss equal to the areas of triangles B and C (i.e., $160 million). These estimates of the welfare effects of the policy may need adjustment for two reasons. First, kidneys will not necessarily be allocated to those who value them most highly. If the limited supply of kidneys is partly allocated to people with valuations below $40,000, the true deadweight loss will be higher than our estimate. Second, with excess demand, there is no way to ensure that recipients will receive their kidneys as gifts. In practice, kidneys are often rationed on the basis of willingness to pay, and many recipients end up paying all or most of the $40,000 price that is needed to clear the market when supply is constrained to 16,000. A good part of the value of the kidneys—rectangles A and D in the figure—is then captured by hospitals and middlemen. As a result, the law reduces the surplus of recipients as well as of suppliers.4 There are, of course, arguments in favor of prohibiting the sale of organs.5 One argument stems from the problem of imperfect information; if people receive payment for organs, they may hide adverse information about their health histories. This argument is probably most applicable to the sale of blood, where there is a possibility of transmitting hepatitis, AIDS, or other viruses. But even in such cases, screening (at a cost that would be included in the market price) may be more efficient than prohibiting sales. This issue has been central to the debate in the United States over blood policy. A second argument holds that it is simply unfair to allocate a basic necessity of life on the basis of ability to pay. This argument transcends economics. 4For further analyses of these efficiency costs, see Dwane L. Barney and R. Larry Reynolds, “An Economic Analysis of Transplant Organs,” Atlantic Economic Journal 17 (September 1989): 12–20; David L. Kaserman and A. H. Barnett, “An Economic Analysis of Transplant Organs: A Comment and Extension,” Atlantic Economic Journal 19 (June 1991): 57–64; and A. Frank Adams III, A. H. Barnett, and David L. Kaserman, “Markets for Organs: The Question of Supply,” Contemporary Economic Policy 17 (April 1999); 147–55. Kidney exchange is also complicated by the need to match blood type; for a recent analysis, see Alvin E. Roth, Tayfun Sönmez, and M. Utku Ünver, “Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences,” American Economic Review 97 (June 2007). 5For discussions of the strengths and weaknesses of these arguments, see Susan Rose-Ackerman, “Inalienability and the Theory of Property Rights,” Columbia Law Review 85 (June 1985): 931–69, and Roger D. Blair and David L. Kaserman, “The Economics and Ethics of Alternative Cadaveric Organ Procurement Policies,” Yale Journal on Regulation 8 (Summer 1991): 403–52. 328 PART 2 • Producers, Consumers, and Competitive Markets However, two points should be kept in mind. First, when the price of a good that has a significant opportunity cost is forced to zero, there is bound to be reduced supply and excess demand. Second, it is not clear why live organs should be treated differently from close substitutes; artificial limbs, joints, and heart valves, for example, are sold even though real kidneys are not. Many complex ethical and economic issues are involved in the sale of organs. These issues are important, and this example is not intended to sweep them away. Economics, the dismal science, simply shows us that human organs have economic value that cannot be ignored, and that prohibiting their sale imposes a cost on society that must be weighed against the benefits. 9.3 Minimum Prices As we have seen, government policy sometimes seeks to raise prices above market-clearing levels, rather than lower them. Examples include the former regulation of the airlines by the Civil Aeronautics Board, the minimum wage law, and a variety of agricultural policies. (Most import quotas and tariffs also have this intent, as we will see in Section 9.5.) One way to raise prices above market-clearing levels is by direct regulation—simply make it illegal to charge a price lower than a specific minimum level. Look again at Figure 9.5 (page 324). If producers correctly anticipate that they can sell only the lower quantity Q3, the net welfare loss will be given by triangles B and C. But as we explained, producers might not limit their output to Q3. What happens if producers think they can sell all they want at the higher price and produce accordingly? That situation is illustrated in Figure 9.7, where Pmin denotes a minimum price set by the government. The quantity supplied is now Q2 and the quantity demanded is Q3, the difference representing excess, unsold supply. Now let’s determine the resulting changes in consumer and producer surplus. Those consumers who still purchase the good must now pay a higher price and so suffer a loss of surplus, which is given by rectangle A in Figure 9.7. Some FIGURE 9.7 PRICE MINIMUM Price is regulated to be no lower than Pmin. Producers would like to supply Q2, but consumers will buy only Q3. If producers indeed produce Q2, the amount Q2 − Q3 will go unsold and the change in producer surplus will be A − C − D. In this case, producers as a group may be worse off. S Price Pmin P0 A B C D Q3 Q0 Q2 D Quantity CHAPTER 9 • The Analysis of Competitive Markets 329 consumers have also dropped out of the market because of the highe |
r price, with a corresponding loss of surplus given by triangle B. The total change in consumer surplus is therefore CS = -A - B Consumers clearly are worse off as a result of this policy. What about producers? They receive a higher price for the units they sell, which results in an increase of surplus, given by rectangle A. (Rectangle A represents a transfer of money from consumers to producers.) But the drop in sales from Q0 to Q3 results in a loss of surplus, which is given by triangle C. Finally, consider the cost to producers of expanding production from Q0 to Q2. Because they sell only Q3, there is no revenue to cover the cost of producing Q2 − Q3. How can we measure this cost? Remember that the supply curve is the aggregate marginal cost curve for the industry. The supply curve therefore gives us the additional cost of producing each incremental unit. Thus the area under the supply curve from Q3 to Q2 is the cost of producing the quantity Q2 − Q3. This cost is represented by the shaded trapezoid D. So unless producers respond to unsold output by cutting production, the total change in producer surplus is PS = A - C - D Given that trapezoid D can be large, a minimum price can even result in a net loss of surplus to producers alone! As a result, this form of government intervention can reduce producers’ profits because of the cost of excess production. Another example of a government-imposed price minimum is a minimum wage law. The effect of this policy is illustrated in Figure 9.8, which shows the supply and demand for labor. The wage is set at wmin, a level higher than the market-clearing wage w0. As a result, those workers who can find jobs obtain a higher wage. However, some people who want to work will be unable to. The policy results in unemployment, which in the figure is L2 − L1. We will examine the minimum wage in more detail in Chapter 14. w wmin w0 A B C L1 L 0 L2 Unemployment S D L FIGURE 9.8 THE MINIMUM WAGE Although the market-clearing wage is w0, firms are not allowed to pay less than wmin. This results in unemployment of an amount L2 − L1 and a deadweight loss given by triangles B and C. 330 PART 2 • Producers, Consumers, and Competitive Markets E XAM PLE 9.3 AIRLINE REGULATION Before 1980, the airline industry in the United States looked very different than it does today. Fares and routes were tightly regulated by the Civil Aeronautics Board (CAB). The CAB set most fares well above what would have prevailed in a free market. It also restricted entry, so that many routes were served by only one or two airlines. By the late 1970s, however, the CAB liberalized fare regulation and allowed airlines to serve any routes they wished. By 1981, the industry had been completely deregulated, and the CAB itself was dissolved in 1982. Since that time, many new airlines have begun service, others have gone out of business, and price competition has become much more intense. Many airline executives feared that deregulation would lead to chaos in the industry, with competitive pressure causing sharply reduced profits and even bankruptcies. After all, the original rationale for CAB regulation was to provide “stability” in an industry that was considered vital to the U.S. economy. And one might think that as long as price was held above its market-clearing level, profits would be higher than they would be in a free market. Deregulation did lead to major changes in the industry. Some airlines merged or went out of business as new ones entered. Although prices fell considerably (to the benefit of consumers), profits overall did not fall much because the CAB’s minimum prices had caused inefficiencies and artificially high costs. The effect of minimum prices is illustrated in Figure 9.9, where P0 and Q0 are the marketclearing price and quantity, Pmin is the minimum price, and Q1 is the amount demanded at this higher price. The problem was that at price Pmin, airlines wanted to supply a quantity Q2, much larger than Q1. Although they did not expand output to Q2, they did expand it well beyond Q1—to Q3 in the figure—hoping to Price Pmin P0 A B C D FIGURE 9.9 EFFECT OF AIRLINE REGULATION BY THE CIVIL AERONAUTICS BOARD At price Pmin, airlines would like to supply Q2, well above the quantity Q1 that consumers will buy. Here they supply Q3. Trapezoid D is the cost of unsold output. Airline profits may have been lower as a result of regulation because triangle C and trapezoid D can together exceed rectangle A. In addition, consumers lose A B. S D Q1 Q3 Q0 Q2 Quantity CHAPTER 9 • The Analysis of Competitive Markets 331 sell this quantity at the expense of competitors. As a result, load factors (the percentage of seats filled) were relatively low, and so were profits. (Trapezoid D measures the cost of unsold output.) Table 9.1 gives some key numbers that illustrate the evolution of the airline industry.6 The number of carriers increased dramatically after deregulation, as did passenger load factors (the percentage of seats with passengers). The passenger-mile rate (the revenue per passenger-mile flown) fell sharply in real (inflation-adjusted) terms from 1980 to 1990, and then continued to drop through 2010. This decline was the result of increased competition and reductions in fares, and made air travel affordable to many more consumers. And what about costs? The real cost index indicates that even after adjusting for inflation, costs increased by about 45 percent between 1975 and 1980, and then fell considerably over the next 20 years. Changes in cost, however, are driven to a great extent by changes in the cost of fuel, which is driven in turn by changes in the price of oil. (For most airlines, fuel accounts for close to 30 percent of total operating costs.) As Table 9.1 shows, the real cost of fuel has fluctuated dramatically, and this had nothing to do with deregulation. Because airlines have no control over oil prices, it is more informative to examine a “corrected” real cost index which removes the effects of changing fuel costs. Real fuel costs increased considerably from 1975 to 1980, which accounts for much of the increase in the real cost index. Real fuel costs nearly tripled from 2000 to 2010 (because of sharp increases in the price of oil); had fuel costs remained level, the real cost index would have declined (from 85 to 76) rather than increasing sharply (from 89 to 148). What, then, did airline deregulation do for consumers and producers? As new airlines entered the industry and fares went down, consumers benefited. This fact is borne out by the increase in consumer surplus given by rectangle A and triangle B in Figure 9.9. (The actual benefit to consumers was somewhat smaller because quality declined as planes became more crowded and delays and cancellations multiplied.) As for the airlines, they had to learn to live in a more competitive—and therefore more turbulent—environment, and some firms did not survive. But overall, airlines became so much more efficient that producer surplus may have increased. The total welfare gain from deregulation was positive and quite large.7 TABLE 9.1 AIRLINE INDUSTRY DATA Number of U.S. Carriers Passenger Load Factor (%) Passenger-Mile Rate (constant 1995 dollars) Real Cost Index (1995 100) Real Fuel Cost Index (1995 100) Real Cost Index w/o Fuel Cost Increases (1995 100) 1975 36 54.0 0.218 101 249 71 1980 63 58.0 0.210 145 300 87 1990 70 62.4 0.149 119 163 104 2000 94 72.1 0.118 89 125 85 2010 63 82.1 0.094 148 342 76 6Department of Commerce, Air Transport Association. 7Studies of the effects of deregulation include John M. Trapani and C. Vincent Olson, “An Analysis of the Impact of Open Entry on Price and the Quality of Service in the Airline Industry,” Review of Economics and Statistics 64 (February 1982): 118–38; David R. Graham, Daniel P. Kaplan, and David S. Sibley, “Efficiency and Competition in the Airline Industry,” Bell Journal of Economics (Spring 1983): 118–38; S. Morrison and Clifford Whinston, The Economic Effects of Airline Deregulation (Washington: Brookings Institution, 1986); and Nancy L. Rose, “Profitability and Product Quality: Economic Determinants of Airline Safety Performance,” Journal of Political Economy 98 (October 1990): 944–64. 332 PART 2 • Producers, Consumers, and Competitive Markets • price support Price set by government above freemarket level and maintained by governmental purchases of excess supply. 9.4 Price Supports and Production Quotas Besides imposing a minimum price, the government can increase the price of a good in other ways. Much of American agricultural policy is based on a system of price supports, whereby the government sets the market price of a good above the free-market level and buys up whatever output is needed to maintain that price. The government can also increase prices by restricting production, either directly or through incentives to producers. In this section, we show how these policies work and examine their impact on consumers, producers, and the federal budget. Price Supports In the United States, price supports aim to increase the prices of dairy products, tobacco, corn, peanuts, and so on, so that the producers of those goods can receive higher incomes. Under a price support program, the government sets a support price Ps and then buys up whatever output is needed to keep the market price at this level. Figure 9.10 illustrates this. Let’s examine the resulting gains and losses to consumers, producers, and the government. CONSUMERS At price Ps, the quantity that consumers demand falls to Q1, but the quantity supplied increases to Q2. To maintain this price and avoid having inventories pile up in producer warehouses, the government must buy the quantity Qg Q2 − Q1. In effect, because the government adds its demand Qg to the demand of consumers, producers can sell all they want at price Ps. Because those consumers who purchase the good must pay the higher price Ps instead of Po, they suffer a loss of consume |
r surplus given by rectangle A. Because of the higher price, other consumers no longer buy the good or buy less of it, and their loss of surplus is given by triangle B. So, as with the minimum price that we examined above, consumers lose, in this case by an amount CS = -A - B PRODUCERS On the other hand, producers gain (which is why such a policy is implemented). Producers are now selling a larger quantity Q2 instead of Q0, and at a higher price Ps. Observe from Figure 9.10 that producer surplus increases by the amount PS = A + B + D THE GOVERNMENT But there is also a cost to the government (which must be paid for by taxes, and so is ultimately a cost to consumers). That cost is (Q2 − Q1)Ps, which is what the government must pay for the output it purchases. In Figure 9.10, this amount is represented by the large speckled rectangle. This cost may be reduced if the government can “dump” some of its purchases—i.e., sell them abroad at a low price. Doing so, however, hurts the ability of domestic producers to sell in foreign markets, and it is domestic producers that the government is trying to please in the first place. What is the total welfare cost of this policy? To find out, we add the change in consumer surplus to the change in producer surplus and then subtract the cost to the government. Thus the total change in welfare is CS + PS - Cost to Govt. = D - (Q2 - Q1)Ps CHAPTER 9 • The Analysis of Competitive Markets 333 S Price PS P0 Qg A D B D + Qg D Q1 Q0 Q2 Quantity FIGURE 9.10 PRICE SUPPORTS To maintain a price Ps above the market-clearing price P0, the government buys a quantity Qg. The gain to producers is A B D. The loss to consumers is A B. The cost to the government is the speckled rectangle, the area of which is Ps(Q2 Q1). In terms of Figure 9.10, society as a whole is worse off by an amount given by the large speckled rectangle, less triangle D. As we will see in Example 9.4, this welfare loss can be very large. But the most unfortunate part of this policy is the fact that there is a much more efficient way to help farmers. If the objective is to give farmers an additional income equal to A B D, it is far less costly to society to give them this money directly rather than via price supports. Because price supports are costing consumers A B anyway, by paying farmers directly, society saves the large speckled rectangle, less triangle D. So why doesn’t the government simply give farmers money? Perhaps because price supports are a less obvious giveaway and, therefore, politically more attractive.8 Production Quotas Besides entering the market and buying up output—thereby increasing total demand—the government can also cause the price of a good to rise by reducing supply. It can do this by decree—that is, by simply setting quotas on how much each firm can produce. With appropriate quotas, the price can then be forced up to any arbitrary level. As we will see in Example 9.5, this is how many city governments maintain high taxi fares. They limit total supply by requiring each taxicab to have a medallion, and then limit the total number of medallions. Another example is the control of liquor licenses by state governments. By requiring any bar or restaurant that serves alcohol to have a liquor license and then limiting the number of licenses, entry by new restaurateurs is limited, which allows those who have licenses to earn higher prices and profit margins. 8In practice, price supports for many agricultural commodities are effected through loans. The loan rate is in effect a price floor. If during the loan period market prices are not sufficiently high, farmers can forfeit their grain to the government (specifically to the Commodity Credit Corporation) as full payment for the loan. Farmers have the incentive to do this unless the market price rises above the support price. 334 PART 2 • Producers, Consumers, and Competitive Markets The welfare effects of production quotas are shown in Figure 9.11. The government restricts the quantity supplied to Q1, rather than the marketclearing level Q0. Thus the supply curve becomes the vertical line S' at Q1. Consumer surplus is reduced by rectangle A (those consumers who buy the good pay a higher price) plus triangle B (at this higher price, some consumers no longer purchase the good). Producers gain rectangle A (by selling at a higher price) but lose triangle C (because they now produce and sell Q1 rather than Q0). Once again, there is a deadweight loss, given by triangles B and C. INCENTIVE PROGRAMS In U.S. agricultural policy, output is reduced by incentives rather than by outright quotas. Acreage limitation programs give farmers financial incentives to leave some of their acreage idle. Figure 9.11 also shows the welfare effects of reducing supply in this way. Note that because farmers agree to limit planted acreage, the supply curve again becomes completely inelastic at the quantity Q1, and the market price is increased from P0 to Ps. As with direct production quotas, the change in consumer surplus is CS = -A - B Farmers now receive a higher price for the production Q1, which corresponds to a gain in surplus of rectangle A. But because production is reduced from Q0 to Q1, there is a loss of producer surplus corresponding to triangle C. Finally, farmers receive money from the government as an incentive to reduce production. Thus the total change in producer surplus is now PS = A - C + Payments for not producing FIGURE 9.11 SUPPLY RESTRICTIONS To maintain a price Ps above the market-clearing price P0, the government can restrict supply to Q1, either by imposing production quotas (as with taxicab medallions) or by giving producers a financial incentive to reduce output (as with acreage limitations in agriculture). For an incentive to work, it must be at least as large as B C D, which would be the additional profit earned by planting, given the higher price Ps. The cost to the government is therefore at least B C D. Price S′ Ps P0 A D B C S Q1 Q0 D Quantity CHAPTER 9 • The Analysis of Competitive Markets 335 The cost to the government is a payment sufficient to give farmers an incentive to reduce output to Q1. That incentive must be at least as large as B C D because that area represents the additional profit that could be made by planting, given the higher price Ps. (Remember that the higher price Ps gives farmers an incentive to produce more even though the government is trying to get them to produce less.) Thus the cost to the government is at least B C D, and the total change in producer surplus is PS = This is the same change in producer surplus as with price supports maintained by government purchases of output. (Refer to Figure 9.10.) Farmers, then, should be indifferent between the two policies because they end up gaining the same amount of money from each. Likewise, consumers lose the same amount of money. Which policy costs the government more? The answer depends on whether the sum of triangles B C D in Figure 9.11 is larger or smaller than (Q2 − Q1)Ps (the large speckled rectangle) in Figure 9.10. Usually it will be smaller, so that an acreage-limitation program costs the government (and society) less than price supports maintained by government purchases. Still, even an acreage-limitation program is more costly to society than simply handing the farmers money. The total change in welfare (CS + PS - Cost to Govt.) under the acreage-limitation program is Welfare = -B - C Society would clearly be better off in efficiency terms if the government simply gave the farmers A B D, leaving price and output alone. Farmers would then gain A B D and the government would lose A B D, for a total welfare change of zero, instead of a loss of B C. However, economic efficiency is not always the objective of government policy. EXAM PLE 9.4 SUPPORTING THE PRICE OF WHEAT In Examples 2.5 (page 37) and 4.3 (page 128), we began to examine the market for wheat in the United States. Using linear demand and supply curves, we found that the market-clearing price of wheat was about $3.46 in 1981. The price fell to about $2.78 by 2002 because of a drop in export demand. In fact, government programs kept the actual price of wheat higher and provided direct subsidies to farmers. How did these programs work, how much did they end up costing consumers, and how much did they add to the federal deficit? 336 PART 2 • Producers, Consumers, and Competitive Markets First, let’s examine the market in 1981. In that year, although there were no effective limitations on the production of wheat, the price was increased to $3.70 by government purchases. How much would the government have had to buy to get the price from $3.46 to $3.70? To answer this question, first write the equations for supply and for total private (domestic plus export) demand: 1981 Supply: Qs 1981 Demand: QD = 1800 + 240P = 3550 - 266P By equating supply and demand, you can check that the market-clearing price is $3.46, and that the quantity produced is 2630 million bushels. Figure 9.12 illustrates this. To increase the price to $3.70, the government must buy a quantity of wheat Qg. Total demand (private plus government) will then be 1981 Total demand: QDT = 3550 - 266P + Qg Now equate supply with this total demand: 1800 + 240P = 3550 - 266P + Qg or Qg = 506P - 1750 Price (dollars per bushel) Ps = $3.70 P0 = $3.46 A Qg C B S D + Qg D 1800 2566 2630 2688 Quantity FIGURE 9.12 THE WHEAT MARKET IN 1981 By buying 122 million bushels of wheat, the government increased the market-clearing price from $3.46 per bushel to $3.70. CHAPTER 9 • The Analysis of Competitive Markets 337 This equation can be used to determine the required quantity of government wheat purchases Qg as a function of the desired support price P. To achieve a price of $3.70, the government must buy Qg = (506)(3.70) - 1750 = 122 million bushels Note in Figure 9.12 that these 122 million bushels are the difference between the quantity supplied at the $3.70 price (2688 mill |
ion bushels) and the quantity of private demand (2566 million bushels). The figure also shows the gains and losses to consumers and producers. Recall that consumers lose rectangle A and triangle B. You can verify that rectangle A is (3.70 − 3.46) (2566) $616 million, and triangle B is (1/2)(3.70 − 3.46)(2630 − 2566) $8 million, so that the total cost to consumers is $624 million. The cost to the government is the $3.70 it pays for the wheat times the 122 million bushels it buys, or $451.4 million. The total cost of the program is then $624 million $451.4 million $1075 million. Compare this with the gain to producers, which is rectangle A plus triangles B and C. You can verify that this gain is $638 million. Price supports for wheat were expensive in 1981. To increase the surplus of farmers by $638 million, consumers and taxpayers had to pay $1076 million. In fact, taxpayers paid even more than that. Wheat producers were also given subsidies of about 30 cents per bushel, which adds up to another $806 million. In 1996, the U.S. Congress passed a new farm bill, nicknamed the “Freedom to Farm” law. It was designed to reduce the role of government and to make agriculture more market oriented. The law eliminated production quotas (for wheat, corn, rice, and other products) and gradually reduced government purchases and subsidies through 2003. However, the law did not completely deregulate U.S. agriculture. For example, price support programs for peanuts and sugar remained in place. Furthermore, pre-1996 price supports and production quotas would be reinstated unless Congress renewed the law in 2003. (Congress did not renew it—more on this below.) Even under the 1996 law, agricultural subsidies remained substantial. In Example 2.5, we saw that the market-clearing price of wheat in 2007 had increased to about $6.00 per bushel. The supply and demand curves in 2007 were as follows: Demand: QD Supply: QS = 2900 - 125P = 1460 + 115P You can check to see that the market-clearing quantity is 2150 million bushels. Congress did not renew the 1996 Freedom to Farm Act. Instead, in 2002, Congress and the Bush administration essentially reversed the effects of the 1996 bill through passage of the Farm Security and Rural Investment Act, which reinstates subsidies for most crops, in particular grain and cotton.9 9See Mike Allen, “Bush Signs Bill Providing Big Farm Subsidy Increases,” The Washington Post, May 14, 2002; see David E. Sanger, “Reversing Course, Bush Signs Bill Raising Farm Subsidies,” The New York Times, May 14, 2002. 338 PART 2 • Producers, Consumers, and Competitive Markets Although the bill does not explicitly restore price supports, it calls for the government to issue “fixed direct payments” to producers based on a fixed payment rate and the base acreage for a particular crop. Using U.S. wheat acreage and production levels in 2001, we can calculate that this bill cost taxpayers nearly $1.1 billion in annual payments to wheat producers alone.10 The 2002 farm bill was projected to cost taxpayers $190 billion over 10 years. Congress revisited agricultural subsidies in 2007. For most crops, previous subsidy rates were either maintained or increased, thus making the burden on U.S. taxpayers even higher. In fact, the Food, Conservation, and Energy Act of 2008 raised subsidy rates on most crops through 2012, at a projected cost of $284 billion over five years. Recently, however, the pendulum has swung back toward eliminating subsidies, and new cuts were approved as part of the deal to resolve the 2011 budget crisis. E XAM PLE 9.5 WHY CAN’T I FIND A TAXI? Ever try to catch a cab in New York? Good luck! If it’s raining or it’s a peak commuting time, you can wait an hour before successfully hailing a cab. Why? Why aren’t there more taxis in New York? The reason is simple. The city of New York limits the number of taxis by requiring each taxi to have a medallion (essentially a permit), and then limiting the number of medallions. In 2011 there were 13,150 medallions in New York—roughly the same number as in 1937, a time when it was much easier to find a taxi. But since 1937 the city has grown and the demand for taxi rides has increased greatly, so that now the limit of 13,150 medallions is a constraint that can make life difficult for New Yorkers. But that just raises another question. Why would a city do something that makes life difficult for its citizens? Why not just issue more medallions? Again, the reason is simple. Doing so would incur the wrath of the current owners of medallions— mostly large taxi companies that lease the medal- lions and taxis to drivers, and have considerable political and lobbying power. Medallions can be bought and sold by the companies that own them. In 1937, there were plenty of medallions to go around, so they had little value. By 1947, the value of a medallion had increased to $2,500, by 1980 to $55,000, and by 2011 to $880,000. That’s right—because New York City won’t issue more medallions, the value of a taxi medallion is approaching $1 million! But of course that value would drop sharply if the city starting issuing more medallions. So the New York taxi companies that collectively own the 13,150 available medallions have done everything possible to prevent the city from issuing any more—and have succeeded in their efforts. The situation is illustrated in Figure 9.13. The demand curve D and supply curve S are based on elasticities taken from statistical studies of taxicab markets in New York and other cities.11 If the 10Estimated 2001 Wheat direct payments (payment rate)*(payment yield)*(base acres)* 0.85 ($0.52)*(40.2)*(59,617,000)*0.85 $1.06 billion. 11Elasticities are taken from Bruce Schaller, “Elasticities for Taxicab Fares and Service Availability,” Transportation 26 (1999): 283–297. Information about New York’s taxi regulations and medallion prices can be found at New York City’s Taxi and Limousine Commission’s website: http://www.nyc. gov/tlc, and at http://www.schallerconsult.com/taxi/. CHAPTER 9 • The Analysis of Competitive Markets 339 P′ = $880,000 D S′ S P = $350,000 Q* = 13,150 Q = 19,725 5000 10,000 15,000 20,000 25,000 30,000 35,000 Number of taxi medallions 1000 900 800 700 600 500 400 300 200 100 ) FIGURE 9.13 TAXI MEDALLIONS IN NEW YORK CITY The demand curve D shows the quantity of medallions demanded by taxi companies as a function of the price of a medallion. The supply curve S shows the number of medallions that would be sold by current owners as a function of price. New York limits the quantity to 13,150, so the supply curve becomes vertical and intersects demand at $880,000, the market price of a medallion in 2011. city were to issue another 7,000 medallions for a total of about 20,000, demand and supply would equilibrate at a price of about $350,000 per medallion – still a lot, but just enough to lease cabs, run a taxi business, and still make a profit. But supply is constrained at 13,150, at which point the supply curve (labeled S’) becomes vertical, and intersects the demand curve at a price of $880,000. Keep in mind that New York’s medallion policy hurts taxi drivers as well as citizens who depend on taxis. Most of the medallions are owned by large taxi companies—not by drivers, who must lease them from the companies (a small portion are reserved for owner-operators). To become a taxi driver, one must take a road test and be certified. In 2011, there were 44,000 certified drivers in New York, but only 13,150 of them can drive a cab at any one time, leaving many unemployed. Is New York City unique in its treatment of taxis? Not at all. In Boston there were only 1,825 medallions available in 2010, and medallions were bought and sold at a price of $410,000. And just try to find a taxi in Milan, Rome, or almost any other Italian city. The Italian government severely constrains the numbers of medallions, which are owned not by large taxi companies as in New York, but by individual families, who have the political clout to preserve the value of their precious medallions. 340 PART 2 • Producers, Consumers, and Competitive Markets • import quota Limit on the quantity of a good that can be imported. • tariff Tax on an imported good. 9.5 Import Quotas and Tariffs Many countries use import quotas and tariffs to keep the domestic price of a product above world levels and thereby enable the domestic industry to enjoy higher profits than it would under free trade. As we will see, the cost to taxpayers from this protection can be high, with the loss to consumers exceeding the gain to domestic producers. Without a quota or tariff, a country will import a good when its world price is below the price that would prevail domestically were there no imports. Figure 9.14 illustrates this principle. S and D are the domestic supply and demand curves. If there were no imports, the domestic price and quantity would be P0 and Q0, which equate supply and demand. But because the world price Pw is below P0, domestic consumers have an incentive to purchase from abroad and will do so if imports are not restricted. How much will be imported? The domestic price will fall to the world price Pw; at this lower price, domestic production will fall to Qs, and domestic consumption will rise to Qd. Imports are then the difference between domestic consumption and domestic production, Qd − Qs. Now suppose the government, bowing to pressure from the domestic industry, eliminates imports by imposing a quota of zero—that is, forbidding any importation of the good. What are the gains and losses from such a policy? With no imports allowed, the domestic price will rise to P0. Consumers who still purchase the good (in quantity Q0) will pay more and will lose an amount of surplus given by trapezoid A and triangle B. In addition, given this higher price, some consumers will no longer buy the good, so there is an additional loss of consumer surplus, given by triangle C. The total change in consumer surplus is there |
fore CS = -A - B - C Price P0 Pw FIGURE 9.14 IMPORT TARIFF OR QUOTA THAT ELIMINATES IMPORTS In a free market, the domestic price equals the world price Pw. A total Qd is consumed, of which Qs is supplied domestically and the rest imported. When imports are eliminated, the price is increased to P0. The gain to producers is trapezoid A. The loss to consumers is A B C, so the deadweight loss is B C. A B C S D Qs Q0 Qd Quantity Imports CHAPTER 9 • The Analysis of Competitive Markets 341 What about producers? Output is now higher (Q0 instead of Qs) and is sold at a higher price (P0 instead of Pw). Producer surplus therefore increases by the amount of trapezoid A: PS = A The change in total surplus, CS + PS, is therefore −B − C. Again, there is a deadweight loss—consumers lose more than producers gain. Imports could also be reduced to zero by imposing a sufficiently large tariff. The tariff would have to be equal to or greater than the difference between P0 and Pw. With a tariff of this size, there will be no imports and, therefore, no government revenue from tariff collections, so the effect on consumers and producers would be the same as with a quota. More often, government policy is designed to reduce but not eliminate imports. Again, this can be done with either a tariff or a quota, as Figure 9.15 shows. Under free trade, the domestic price will equal the world price Pw, and imports will be Qd − Qs. Now suppose that a tariff of T dollars per unit is imposed on imports. Then the domestic price will rise to P* (the world price plus the tariff); domestic production will rise and domestic consumption will fall. In Figure 9.15, this tariff leads to a change of consumer surplus given by CS = -A - B - C - D The change in producer surplus is again PS = A Finally, the government will collect revenue in the amount of the tariff times the quantity of imports, which is rectangle D. The total change in welfare, CS plus PS plus the revenue to the government, is therefore −B − C. Triangles B and C again represent the deadweight loss from restricting Price P* Pw S T A Quota D B C Qs Q's Q'd Qd Quantity D FIGURE 9.15 IMPORT TARIFF OR QUOTA (GENERAL CASE) When imports are reduced, the domestic price is increased from Pw to P*. This can be achieved by a quota, or by a tariff T P* − Pw. Trapezoid A is again the gain to domestic producers. The loss to consumers is A B C D. If a tariff is used, the government gains D, the revenue from the tariff, so the net domestic loss is B C. If a quota is used instead, rectangle D becomes part of the profits of foreign producers, and the net domestic loss is B C D. 342 PART 2 • Producers, Consumers, and Competitive Markets imports. (B represents the loss from domestic overproduction and C the loss from too little consumption.) Suppose the government uses a quota instead of a tariff to restrict imports: Foreign producers can only ship a specific quantity (Q'd − Q's in Figure 9.15) to the United States and can then charge the higher price P* for their U.S. sales. The changes in U.S. consumer and producer surplus will be the same as with the tariff, but instead of the U.S. government collecting the revenue given by rectangle D, this money will go to the foreign producers in the form of higher profits. The United States as a whole will be even worse off than it was under the tariff, losing D as well as the deadweight loss B and C.12 This situation is exactly what transpired with automobile imports from Japan in the 1980s. Under pressure from domestic automobile producers, the Reagan administration negotiated “voluntary” import restraints, under which the Japanese agreed to restrict shipments of cars to the United States. The Japanese could therefore sell those cars that were shipped at a price higher than the world level and capture a higher profit margin on each one. The United States would have been better off by simply imposing a tariff on these imports. EXAMPLE 9.6 THE SUGAR QUOTA In recent years, the world price of sugar has been between 10 and 28 cents per pound, while the U.S. price has been 30 to 40 cents per pound. Why? By restricting imports, the U.S. government protects the $4 billion domestic sugar industry, which would virtually be put out of business if it had to compete with low-cost foreign producers. This policy has been good for U.S. sugar producers. It has even been good for some foreign sugar producers—in particular, those whose successful lobbying efforts have given them big shares of the quota. But like most policies of this sort, it has been bad for consumers. To see just how bad, let’s look at the sugar market in 2010. Here are the relevant data for that year: U.S. production: 15.9 billion pounds U.S. consumption: 22.8 billion pounds U.S. price: World price: 36 cents per pound 24 cents per pound 12Alternatively, an import quota can be maintained by rationing imports to U.S. importing firms or trading companies. These middlemen would have the rights to import a fixed amount of the good each year. These rights are valuable because the middleman can buy the product on the world market at price Pw and then sell it at price P*. The aggregate value of these rights is, therefore, given by rectangle D. If the government sells the rights for this amount of money, it can capture the same revenue it would receive with a tariff. But if these rights are given away, as sometimes happens, the money becomes a windfall to middlemen. CHAPTER 9 • The Analysis of Competitive Markets 343 In §2.6, we explain how to fit linear supply and demand functions to data of this kind. At these prices and quantities, the price elasticity of U.S. supply is 1.5, and the price elasticity of U.S. demand is −0.3.13 We will fit linear supply and demand curves to these data, and then use them to calculate the effects of the quotas. You can verify that the f ollowing U.S. supply curve is consistent with a production level of 15.9 billion pounds, a price of 36 cents per pound, and a supply elasticity of 1.5: U.S. supply: QS = -7.95 + 0.66P where quantity is measured in billions of pounds and price in cents per pound. Similarly, the −0.3 demand elasticity, together with the data for U.S. consumption and U.S. price, give the following linear demand curve: U.S. demand: QD = 29.73 - 0.19P These supply and demand curves are plotted in Figure 9.16. Using the U.S. supply and demand curves given above, you can check that at the 24-cent world price, U.S. production would have been only about 7.9 billion pounds and U.S. consumption about 25.2 billion pounds, of which 25.2 − 7.9 17.3 billion pounds would have been imported. But fortunately for U.S. producers, imports were limited to only 6.9 billion pounds. What did limit on imports do to the U.S. price? To find out, use the U.S. supply and demand equations, and set the quantity demanded minus the quantity supplied to 6.9: QS - QD = (29.73 - 0.19P ) - ( -7.95 + 0.66P ) = 6.9 You can check that the solution to this equation is P 36.2 cents. Thus the limit on imports pushed the U.S. price up to about 36 cents, as shown in the figure. What did this policy cost U.S. consumers? The lost consumer surplus is given by the sum of trapezoid A, triangles B and C, and rectangle D. You should go through the calculations to verify that trapezoid A is equal to $1431 million, triangle B to $477 million, triangle C to $137 million, and rectangle D to $836 million. The total cost to consumers in 2010 was about $2.9 billion. How much did producers gain from this policy? Their increase in surplus is given by trapezoid A (i.e., about $1.4 billion). The $836 million of rectangle D was a gain for those foreign producers who succeeded in obtaining large allotments of the quota because they received a higher 13Prices and quantities are from the USDA’s Economic Research Service. Find more information at http://www.ers.usda.gov/Briefing/Sugar/Data.htm. The elasticity estimates are based on Morris E. Morkre and David G. Tarr, Effects of Restrictions on United States Imports: Five Case Studies and Theory, U.S. Federal Trade Commission Staff Report, June 1981; and F. M. Scherer, “The United States Sugar Program,” Kennedy School of Government Case Study, Harvard University, 1992. For a general discussion of sugar quotas and other aspects of U.S. agricultural policy, see D. Gale Johnson, Agricultural Policy and Trade (New York: New York University Press, 1985); and Gail L. Cramer and Clarence W. Jensen, Agricultural Economics and Agribusiness (New York: Wiley, 1985). 344 PART 2 • Producers, Consumers, and Competitive Markets A D B C PUS 36 24 Pw ) 50 45 40 35 30 25 20 15 10 5 0 0 5 10 7.9 Qs 15 20 Q s 15.9 25 22.8 Q d 30 25.2 Qd 35 Quantity (billions of pounds) FIGURE 9.16 SUGAR QUOTA IN 2010 At the world price of 24 cents per pound, about 25.2 billion pounds of sugar would have been consumed in the United States in 2010, of which all but 7.9 billion pounds would have been imported. Restricting imports to 6.9 billion pounds caused the U.S. price to go up by 12 cents. The cost to consumers, A B C D, was about $2.9 billion. The gain to domestic producers was trapezoid A, about $1.4 billion. Rectangle D, $836 million, was a gain to those foreign producers who obtained quota allotments. Triangles B and C represent the deadweight loss of about $614 million. price for their sugar. Triangles B and C represent a deadweight loss of about $614 million. The world price of sugar has been volatile over the past decade. In the mid-2000s, the European Union removed protections on European sugar, causing the region to go from being a net sugar exporter to a net importer. Meanwhile, demand for sugar in rapidly industrializing countries like India, Pakistan and China has skyrocketed. Sugar production in these three countries is often unpredictable: while they are often net exporters, changing governmental policies and volatile weather frequently lead to decreased output, forcing them to import sugar to meet domestic demand. In |
addition, many countries, like Brazil, also use sugar to make ethanol, further decreasing the amount available for food. CHAPTER 9 • The Analysis of Competitive Markets 345 9.6 The Impact of a Tax or Subsidy What would happen to the price of widgets if the government imposed a $1 tax on every widget sold? Many people would answer that the price would increase by a dollar, with consumers now paying a dollar more per widget than they would have paid without the tax. But this answer is wrong. Or consider the following question. The government wants to impose a 50-cent-per-gallon tax on gasoline and is considering two methods of collecting it. Under Method 1, the owner of each gas station would deposit the tax money (50 cents times the number of gallons sold) in a locked box, to be collected by a government agent. Under Method 2, the buyer would pay the tax (50 cents times the number of gallons purchased) directly to the government. Which method costs the buyer more? Many people would say Method 2, but this answer is also wrong. The burden of a tax (or the benefit of a subsidy) falls partly on the consumer and partly on the producer. Furthermore, it does not matter who puts the money in the collection box (or sends the check to the government)—Methods 1 and 2 both cost the consumer the same amount of money. As we will see, the share of a tax borne by consumers depends on the shapes of the supply and demand curves and, in particular, on the relative elasticities of supply and demand. As for our first question, a $1 tax on widgets would indeed cause the price to rise, but usually by less than a dollar and sometimes by much less. To understand why, let’s use supply and demand curves to see how consumers and producers are affected when a tax is imposed on a product, and what happens to price and quantity. THE EFFECTS OF A SPECIFIC TAX For the sake of simplicity, we will consider a specific tax—a tax of a certain amount of money per unit sold. This is in contrast to an ad valorem (i.e., proportional) tax, such as a state sales tax. (The analysis of an ad valorem tax is roughly the same and yields the same qualitative results.) Examples of specific taxes include federal and state taxes on gasoline and cigarettes. Suppose the government imposes a tax of t cents per unit on widgets. Assuming that everyone obeys the law, the government must then receive t cents for every widget sold. This means that the price the buyer pays must exceed the net price the seller receives by t cents. Figure 9.17 illustrates this simple accounting relationship—and its implications. Here, P0 and Q0 represent the market price and quantity before the tax is imposed. Pb is the price that buyers pay, and Ps is the net price that sellers receive after the tax is imposed. Note that Pb − Ps t, so the government is happy. How do we determine what the market quantity will be after the tax is imposed, and how much of the tax is borne by buyers and how much by sellers? First, remember that what buyers care about is the price that they must pay: Pb. The amount that they will buy is given by the demand curve; it is the quantity that we read off of the demand curve given a price Pb. Similarly, sellers care about the net price they receive, Ps. Given Ps, the quantity that they will produce and sell is read off the supply curve. Finally, we know that the quantity sold must equal the quantity bought. The solution, then, is to find the quantity that corresponds to a price of Pb on the demand curve, and a price of Ps on the supply curve, such that the difference Pb − Ps is equal to the tax t. In Figure 9.17, this quantity is shown as Q1. Who bears the burden of the tax? In Figure 9.17, this burden is shared roughly equally by buyers and sellers. The market price (the price buyers pay) rises by half of the tax, and the price that sellers receive falls by roughly half of the tax. • specific tax Tax of a certain amount of money per unit sold. 346 PART 2 • Producers, Consumers, and Competitive Markets S Price Pb P0 Ps A D t B C FIGURE 9.17 INCIDENCE OF A TAX Pb is the price (including the tax) paid by buyers. Ps is the price that sellers receive, less the tax. Here the burden of the tax is split evenly between buyers and sellers. Buyers lose A B, sellers lose D C, and the government earns A D in revenue. The deadweight loss is B C. Q1 Q0 D Quantity As Figure 9.17 shows, market clearing requires four conditions to be satisfied after the tax is in place: 1. The quantity sold and the buyer’s price Pb must lie on the demand curve (because buyers are interested only in the price they must pay). 2. The quantity sold and the seller’s price Ps must lie on the supply curve (because sellers are concerned only with the amount of money they receive net of the tax). 3. The quantity demanded must equal the quantity supplied (Q1 in the figure). 4. The difference between the price the buyer pays and the price the seller receives must equal the tax t. These conditions can be summarized by the following four equations: Q D = Q D(Pb) Q S = Q S(Ps) Q D = Q S = t - Ps Pb (9.1a) (9.1b) (9.1c) (9.1d) If we know the demand curve QD(Pb), the supply curve QS(Ps), and the size of the tax t, we can solve these equations for the buyers’ price Pb, the sellers’ price Ps, and the total quantity demanded and supplied. This task is not as difficult as it may seem, as we will demonstrate in Example 9.7. Figure 9.17 also shows that a tax results in a deadweight loss. Because buyers pay a higher price, there is a change in consumer surplus given by CS = -A - B CHAPTER 9 • The Analysis of Competitive Markets 347 Because sellers now receive a lower price, there is also a change in producer surplus given by PS = -C - D Government tax revenue is tQ1, the sum of rectangles A and D. The total change in welfare, CS plus PS plus the revenue to the government, is therefore −B − C. Triangles B and C represent the deadweight loss from the tax. In Figure 9.17, the burden of the tax is shared almost evenly between buyers and sellers, but this is not always the case. If demand is relatively inelastic and supply is relatively elastic, the burden of the tax will fall mostly on buyers. Figure 9.18(a) shows why: It takes a relatively large increase in price to reduce the quantity demanded by even a small amount, whereas only a small price decrease is needed to reduce the quantity supplied. For example, because cigarettes are addictive, the elasticity of demand is small (about −0.4); thus federal and state cigarette taxes are borne largely by cigarette buyers.14 Price Pb P0 Ps D t S Price Pb P0 Ps S t D Q0 Q1 (a) Quantity Q0 Q1 (b) Quantity FIGURE 9.18 IMPACT OF A TAX DEPENDS ON ELASTICITIES OF SUPPLY AND DEMAND (a) If demand is very inelastic relative to supply, the burden of the tax falls mostly on buyers. (b) If demand is very elastic relative to supply, it falls mostly on sellers. 14See Daniel A. Sumner and Michael K. Wohlgenant, “Effects of an Increase in the Federal Excise Tax on Cigarettes,” American Journal of Agricultural Economics 67 (May 1985): 235–42. 348 PART 2 • Producers, Consumers, and Competitive Markets Figure 9.18(b) shows the opposite case: If demand is relatively elastic and supply is relatively inelastic, the burden of the tax will fall mostly on sellers. So even if we have only estimates of the elasticities of demand and supply at a point or for a small range of prices and quantities, instead of the entire demand and supply curves, we can still roughly determine who will bear the greatest burden of a tax (whether the tax is actually in effect or is only under discussion as a policy option). In general, a tax falls mostly on the buyer if Ed/Es is small, and mostly on the seller if Ed/Es is large. In fact, by using the following “pass-through” formula, we can calculate the percentage of the tax borne by buyers: Pass@through fraction = Es/(Es - Ed) This formula tells us what fraction of the tax is “passed through” to consumers in the form of higher prices. For example, when demand is totally inelastic, so that Ed is zero, the pass-through fraction is 1 and all the tax is borne by consumers. When demand is totally elastic, the pass-through fraction is zero and producers bear all the tax. (The fraction of the tax that producers bear is given by − Ed/(Es − Ed).) The Effects of a Subsidy A subsidy can be analyzed in much the same way as a tax—in fact, you can think of a subsidy as a negative tax. With a subsidy, the sellers’ price exceeds the buyers’ price, and the difference between the two is the amount of the subsidy. As you would expect, the effect of a subsidy on the quantity produced and consumed is just the opposite of the effect of a tax—the quantity will increase. Figure 9.19 illustrates this. At the presubsidy market price P0, the elasticities of supply and demand are roughly equal. As a result, the benefit of the subsidy is shared roughly equally between buyers and sellers. As with a tax, this is not always the case. In general, the benefit of a subsidy accrues mostly to buyers if Ed/Es is small and mostly to sellers if Ed/Es is large. • subsidy Payment reducing the buyer’s price below the seller’s price; i.e., a negative tax. FIGURE 9.19 SUBSIDY A subsidy can be thought of as a negative tax. Like a tax, the benefit of a subsidy is split between buyers and sellers, depending on the relative elasticities of supply and demand. Price Ps P0 Pb s S D Q0 Q1 Quantity CHAPTER 9 • The Analysis of Competitive Markets 349 As with a tax, given the supply curve, the demand curve, and the size of the subsidy s, we can solve for the resulting prices and quantity. The same four conditions needed for the market to clear apply for a subsidy as for a tax, but now the difference between the sellers’ price and the buyers’ price is equal to the subsidy. Again, we can write these conditions algebraically: Q D = Q D(Pb) QS = QS(Ps) Q D = Q S = s - Pb Ps (9.2a) (9.2b) (9.2c) (9.2d) To make sure you understand how to a |
nalyze the impact of a tax or subsidy, you might find it helpful to work through one or two examples, such as Exercises 2 and 14 at the end of this chapter. In §2.5, we explain that demand is often more price elastic in the long run than in the short run because it takes time for people to change their consumption habits and/or because the demand for a good might be linked to the stock of another good that changes slowly. EXAM PLE 9.7 A TAX ON GASOLINE The idea of a large tax on gasoline, both to raise government revenue and to reduce oil consumption and U.S. dependence on oil imports, has been discussed for many years. Let’s see how a $1.00-per-gallon tax would affect the price and consumption of gasoline. We will do this analysis in the setting of market conditions during 2005–2010—when gasoline was selling for about $2 per gallon on average and total consumption was about 100 billion gallons per year (bg/yr).15 We will also use intermediate-run elasticities: elasticities that would apply to a period of about three to six years after a price change. A reasonable number for the intermediate-run elasticity of gasoline demand is −0.5 (see Example 2.6 in Chapter 2—page 43). We can use this figure, together with the $2 and 100 bg/yr price and quantity numbers, to calculate a linear demand curve for gasoline. You can verify that the following demand curve fits these data: Gasoline demand: QD = 150 - 25P Gasoline is refined from crude oil, some of which is produced domestically and some imported. (Some gasoline is also imported directly.) The supply curve for gasoline will therefore depend on the world price of oil, on domestic oil supply, and on the cost of refining. The details are beyond the scope of this example, but a reasonable number for the elasticity of supply is 0.4. You should verify that this elasticity, together with 15Of course, this price varied across regions and grades of gasoline, but we can ignore this here. Quantities of oil and oil products are often measured in barrels; there are 42 gallons in a barrel, so the quantity figure could also be written as 2.4 billion barrels per year. For a review of the procedure for calculating linear curves, see §2.6. Given data for price and quantity, as well as estimates of demand and supply elasticities, we can use a two-step procedure to solve for quantity demanded and supplied. 350 PART 2 • Producers, Consumers, and Competitive Markets the $2 and 100 bg/yr price and quantity, gives the following linear supply curve: Gasoline supply: QS = 60 + 20P You should also verify that these demand and supply curves imply a mar- ket price of $2 and quantity of 100 bg/yr. We can use these linear demand and supply curves to calculate the effect of a $1-per-gallon tax. First, we write the four conditions that must hold, as given by equations (9.2a–d): QD = 150 - 25Pb QS = 60 + 20Ps QD = QS = Ps = 1.00 Pb (Demand) (Supply) (Supply must equal demand) (Government must receive $1.00/gallon) Now combine the first three equations to equate supply and demand: 150 - 25Pb = 60 + 20Ps We can rewrite the last of the four equations as Pb = Ps 1.00 and sub- stitute this for Pb in the above equation: 150 - 25(Ps + 1.00) = 60 + 20Ps Now we can rearrange this equation and solve for Ps: 20Ps + 25Ps = 150 - 25 - 60 45Ps = 65, or Ps = 1.44 Remember that Pb Ps 1.00, so Pb 2.44. Finally, we can determine the total quantity from either the demand or supply curve. Using the demand curve (and the price Pb 2.44), we find that Q 150 − (25) (2.44) 150 − 61, or Q 89 bg/yr. This represents an 11-percent decline in gasoline consumption. Figure 9.20 illustrates these calculations and the effect of the tax. The burden of this tax would be split roughly evenly between consumers and producers. Consumers would pay about 44 cents per gallon more for gasoline, and producers would receive about 56 cents per gallon less. It should not be surprising, then, that both consumers and producers opposed such a tax, and politicians representing both groups fought the proposal every time it came up. But note that the tax would raise significant revenue for the government. The annual revenue would be tQ (1.00)(89) $89 billion per year. The cost to consumers and producers, however, will be more than the $89 billion in tax revenue. Figure 9.20 shows the deadweight loss from this tax as the two shaded triangles. The two rectangles A and D represent the total tax collected by the government, but the total loss of consumer and producer surplus is larger. Before deciding whether a gasoline tax is desirable, it is important to know how large the resulting deadweight loss is likely to be. We can easily CHAPTER 9 • The Analysis of Competitive Markets 351 FIGURE 9.20 IMPACT OF $1 GASOLINE TAX The price of gasoline at the pump increases from $2.00 per gallon to $2.44, and the quantity sold falls from 100 to 89 bg/yr. Annual revenue from the tax is (1.00)(89) $89 billion. The two triangles show the deadweight loss of $5.5 billion per year. Price (dollars per gallon) 3.00 Pb = 2.44 P0 = 2.00 Ps = 1.44 1.00 0.00 0 Lost Consumer Surplus Lost Producer Surplus A D t = 1.00 11 50 89 100 150 Quantity (billion gallons per year) calculate this from Figure 9.20. Combining the two small triangles into one large one, we see that the area is (1/2) * ($1.00/gallon) * (11 billion gallons/year) = $5.5 billion per year This deadweight loss is about 6 percent of the government revenue resulting from the tax, and must be balanced against any additional benefits that the tax might bring. SUMMARY 1. Simple models of supply and demand can be used to analyze a wide variety of government policies, including price controls, minimum prices, price support programs, production quotas or incentive programs to limit output, import tariffs and quotas, and taxes and subsidies. 2. In each case, consumer and producer surplus are used to evaluate the gains and losses to consumers and producers. Applying the methodology to natural gas price controls, airline regulation, price supports for wheat, and the sugar quota shows that these gains and losses can be quite large. 3. When government imposes a tax or subsidy, price usually does not rise or fall by the full amount of the tax or subsidy. Also, the incidence of a tax or subsidy is usually split between producers and consumers. The fraction that each group ends up paying or receiving depends on the relative elasticities of supply and demand. 4. Government intervention generally leads to a deadweight loss; even if consumer surplus and producer surplus are weighted equally, there will be a net loss from government policies that shifts surplus from one group to the other. In some cases, this deadweight loss 352 PART 2 • Producers, Consumers, and Competitive Markets will be small, but in other cases—price supports and import quotas are examples—it is large. This deadweight loss is a form of economic inefficiency that must be taken into account when policies are designed and implemented. 5. Government intervention in a competitive market is not always bad. Government—and the society it represents—might have objectives other than economic efficiency. There are also situations in which government intervention can improve economic efficiency. Examples are externalities and cases of market failure. These situations, and the way government can respond to them, are discussed in Chapters 17 and 18. QUESTIONS FOR REVIEW 1. What is meant by deadweight loss? Why does a price ceiling usually result in a deadweight loss? 2. Suppose the supply curve for a good is completely inelastic. If the government imposed a price ceiling below the market-clearing level, would a deadweight loss result? Explain. 3. How can a price ceiling make consumers better off? Under what conditions might it make them worse off? 4. Suppose the government regulates the price of a good to be no lower than some minimum level. Can such a minimum price make producers as a whole worse off? Explain. 5. How are production limits used in practice to raise the prices of the following goods or services: (a) taxi rides, (b) drinks in a restaurant or bar, (c) wheat or corn? EXERCISES 1. From time to time, Congress has raised the minimum wage. Some people suggested that a government subsidy could help employers finance the higher wage. This exercise examines the economics of a minimum wage and wage subsidies. Suppose the supply of lowskilled labor is given by Ls = 10w where LS is the quantity of low-skilled labor (in millions of persons employed each year), and w is the wage rate (in dollars per hour). The demand for labor is given by LD = 80 - 10w a. What will be the free-market wage rate and employment level? Suppose the government sets a minimum wage of $5 per hour. How many people would then be employed? b. Suppose that instead of a minimum wage, the government pays a subsidy of $1 per hour for each employee. What will the total level of employment be now? What will the equilibrium wage rate be? 6. Suppose the government wants to increase farmers’ incomes. Why do price supports or acreage-limitation programs cost society more than simply giving farmers money? 7. Suppose the government wants to limit imports of a certain good. Is it preferable to use an import quota or a tariff? Why? 8. The burden of a tax is shared by producers and consumers. Under what conditions will consumers pay most of the tax? Under what conditions will producers pay most of it? What determines the share of a subsidy that benefits consumers? 9. Why does a tax create a deadweight loss? What deter- mines the size of this loss? 2. Suppose the market for widgets can be described by the following equations: Demand: P = 10 - Q Supply: P = Q - 4 where P is the price in dollars per unit and Q is the quantity in thousands of units. Then: a. What is the equilibrium price and quantity? b. Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What will |
the new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive? c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of $1 per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government? 3. Japanese rice producers have extremely high production costs, due in part to the high opportunity cost of CHAPTER 9 • The Analysis of Competitive Markets 353 land and to their inability to take advantage of economies of large-scale production. Analyze two policies intended to maintain Japanese rice production: (1) a per-pound subsidy to farmers for each pound of rice produced, or (2) a per-pound tariff on imported rice. Illustrate with supply-and-demand diagrams the equilibrium price and quantity, domestic rice production, government revenue or deficit, and deadweight loss from each policy. Which policy is the Japanese government likely to prefer? Which policy are Japanese farmers likely to prefer? 4. In 1983, the Reagan administration introduced a new agricultural program called the Payment-in-Kind Program. To see how the program worked, let’s consider the wheat market: a. Suppose the demand function is QD 28 − 2P and the supply function is QS 4 4P, where P is the price of wheat in dollars per bushel, and Q is the quantity in billions of bushels. Find the free-market equilibrium price and quantity. b. Now suppose the government wants to lower the supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollars—hence the name of the program. The wheat comes from vast government reserves accumulated from previous price support programs. The amount of wheat paid is equal to the amount that could have been harvested on the land withdrawn from production. Farmers are free to sell this wheat on the market. How much is now produced by farmers? How much is indirectly supplied to the market by the government? What is the new market price? How much do farmers gain? Do consumers gain or lose? c. Had the government not given the wheat back to the farmers, it would have stored or destroyed it. Do taxpayers gain from the program? What potential problems does the program create? cost consumers less than $50 million per year? Under what conditions? Again, use a diagram to illustrate. 6. In Exercise 4 in Chapter 2 (page 62), we examined a vegetable fiber traded in a competitive world market and imported into the United States at a world price of $9 per pound. U.S. domestic supply and demand for various price levels are shown in the following table. PRICE U.S. SUPPLY (MILLION POUNDS) U.S. DEMAND (MILLION POUNDS) 3 6 9 12 15 18 2 4 6 8 10 12 34 28 22 16 10 4 Answer the following questions about the U.S. market: a. Confirm that the demand curve is given by QD 40 − 2P, and that the supply curve is given by QS 2/3P. b. Confirm that if there were no restrictions on trade, the United States would import 16 million pounds. c. If the United States imposes a tariff of $3 per pound, what will be the U.S. price and level of imports? How much revenue will the government earn from the tariff? How large is the deadweight loss? d. If the United States has no tariff but imposes an import quota of 8 million pounds, what will be the U.S. domestic price? What is the cost of this quota for U.S. consumers of the fiber? What is the gain for U.S. producers? 5. About 100 million pounds of jelly beans are consumed in the United States each year, and the price has been about 50 cents per pound. However, jelly bean producers feel that their incomes are too low and have convinced the government that price supports are in order. The government will therefore buy up as many jelly beans as necessary to keep the price at $1 per pound. However, government economists are worried about the impact of this program because they have no estimates of the elasticities of jelly bean demand or supply. a. Could this program cost the government more than $50 million per year? Under what conditions? Could it cost less than $50 million per year? Under what conditions? Illustrate with a diagram. b. Could this program cost consumers (in terms of lost consumer surplus) more than $50 million per year? Under what conditions? Could it 7. The United States currently imports all of its coffee. The annual demand for coffee by U.S. consumers is given by the demand curve Q 250 − 10P, where Q is quantity (in millions of pounds) and P is the market price per pound of coffee. World producers can harvest and ship coffee to U.S. distributors at a constant marginal ( average) cost of $8 per pound. U.S. distributors can in turn distribute coffee for a constant $2 per pound. The U.S. coffee market is competitive. Congress is considering a tariff on coffee imports of $2 per pound. a. If there is no tariff, how much do consumers pay for a pound of coffee? What is the quantity demanded? b. If the tariff is imposed, how much will consumers pay for a pound of coffee? What is the quantity demanded? 354 PART 2 • Producers, Consumers, and Competitive Markets c. Calculate the lost consumer surplus. d. Calculate the tax revenue collected by the govern- ment. e. Does the tariff result in a net gain or a net loss to cents per pound. Suppose imports were expanded to 10 billion pounds. a. What would be the new U.S. domestic price? b. How much would consumers gain and domestic society as a whole? producers lose? 8. A particular metal is traded in a highly competitive world market at a world price of $9 per ounce. Unlimited quantities are available for import into the United States at this price. The supply of this metal from domestic U.S. mines and mills can be represented by the equation QS 2/3P, where QS is U.S. output in million ounces and P is the domestic price. The demand for the metal in the United States is QD 40 − 2P, where QD is the domestic demand in million ounces. In recent years the U.S. industry has been protected by a tariff of $9 per ounce. Under pressure from other foreign governments, the United States plans to reduce this tariff to zero. Threatened by this change, the U.S. industry is seeking a voluntary restraint agreement that would limit imports into the United States to 8 million ounces per year. a. Under the $9 tariff, what was the U.S. domestic price of the metal? b. If the United States eliminates the tariff and the voluntary restraint agreement is approved, what will be the U.S. domestic price of the metal? 9. Among the tax proposals regularly considered by Congress is an additional tax on distilled liquors. The tax would not apply to beer. The price elasticity of supply of liquor is 4.0, and the price elasticity of demand is −0.2. The cross-elasticity of demand for beer with respect to the price of liquor is 0.1. a. If the new tax is imposed, who will bear the greater burden—liquor suppliers or liquor consumers? Why? b. Assuming that beer supply is infinitely elastic, how will the new tax affect the beer market? 10. In Example 9.1 (page 322), we calculated the gains and losses from price controls on natural gas and found that there was a deadweight loss of $5.68 billion. This calculation was based on a price of oil of $50 per barrel. a. If the price of oil were $60 per barrel, what would be the free-market price of gas? How large a deadweight loss would result if the maximum allowable price of natural gas were $3.00 per thousand cubic feet? b. What price of oil would yield a free-market price of natural gas of $3? 11. Example 9.6 (page 342) describes the effects of the sugar quota. In 2011, imports were limited to 6.9 billion pounds, which pushed the domestic price to 36 c. What would be the effect on deadweight loss and foreign producers? 12. The domestic supply and demand curves for hula beans are as follows: Supply: P = 50 + Q Demand: P = 200 - 2Q where P is the price in cents per pound and Q is the quantity in millions of pounds. The U.S. is a small producer in the world hula bean market, where the current price (which will not be affected by anything we do) is 60 cents per pound. Congress is considering a tariff of 40 cents per pound. Find the domestic price of hula beans that will result if the tariff is imposed. Also compute the dollar gain or loss to domestic consumers, domestic producers, and government revenue from the tariff. 13. Currently, the social security payroll tax in the United States is evenly divided between employers and employees. Employers must pay the government a tax of 6.2 percent of the wages they pay, and employees must pay 6.2 percent of the wages they receive. Suppose the tax were changed so that employers paid the full 12.4 percent and employees paid nothing. Would employees be better off? 14. You know that if a tax is imposed on a particular product, the burden of the tax is shared by producers and consumers. You also know that the demand for automobiles is characterized by a stock adjustment process. Suppose a special 20-percent sales tax is suddenly imposed on automobiles. Will the share of the tax paid by consumers rise, fall, or stay the same over time? Explain briefly. Repeat for a 50-centsper-gallon gasoline tax. 15. In 2011, Americans smoked 16 billion packs of cigarettes. They paid an average retail price of $5.00 per pack. a. Given that the elasticity of supply is 0.5 and the elasticity of demand is −0.4, derive linear demand and supply curves for cigarettes. b. Cigarettes are subject to a federal tax, which was about $1.00 per pack in 2011. What does this tax do to the market-clearing price and quantity? c. How much of the federal tax will consumers pay? What part will producers pay? Part Three Market Structure and Competitive Strategy P |
art 3 examines a broad range of markets and explains how the pricing, investment, and output decisions of firms depend on market structure and the behavior of competitors. Chapters 10 and 11 examine market power: the ability to affect price, either by a seller or a buyer. We will see how market power arises, how it differs across firms, how it affects the welfare of consumers and producers, and how it can be limited by government. We will also see how firms can design pricing and advertising strategies to take maximum advantage of their market power. Chapters 12 and 13 deal with markets in which the number of firms is limited. We will examine a variety of such markets, ranging from monopolistic competition, in which many firms sell differentiated products, to a cartel, in which a group of firms coordinates decisions and acts as a monopolist. We are particularly concerned with markets in which there are only a few firms. In these cases, each firm must design its pricing, output, and investment strategies, while keeping in mind how competitors are likely to react. We will develop and apply principles from game theory to analyze such strategies. Chapter 14 shows how markets for factor inputs, such as labor and raw materials, operate. We will examine the firm’s input decisions and show how those decisions depend on the structure of the input market. Chapter 15 then focuses on capital investment decisions. We will see how a firm can value the future profits that it expects an investment to yield and then compare this value with the cost of the investment to determine whether the investment is worthwhile. We will also apply this idea to the decisions of individuals to purchase a car or household appliance, or to invest in education. C H A P T E R S 10 Market Power: Monopoly and Monopsony 357 11 Pricing with Market Power 399 12 Monopolistic Competition and Oligopoly 451 13 Game Theory and Competitive Strategy 487 14 Markets for Factor Inputs 529 15 Investment, Time, and Capital Markets 559 355 This page intentionally left blank C H A P T E R 10 Market Power: Monopoly and Monopsony In a perfectly competitive market, the large number of sellers and buy- ers of a good ensures that no single seller or buyer can affect its price. The market forces of supply and demand determine price. Individual firms take the market price as a given in deciding how much to produce and sell, and consumers take it as a given in deciding how much to buy. Monopoly and monopsony, the subjects of this chapter, are the polar opposites of perfect competition. A monopoly is a market that has only one seller but many buyers. A monopsony is just the opposite: a market with many sellers but only one buyer. Monopoly and monopsony are closely related, which is why we cover them in the same chapter. First we discuss the behavior of a monopolist. Because a monopolist is the sole producer of a product, the demand curve that it faces is the market demand curve. This market demand curve relates the price that the monopolist receives to the quantity it offers for sale. We will see how a monopolist can take advantage of its control over price and how the profit-maximizing price and quantity differ from what would prevail in a competitive market. In general, the monopolist’s quantity will be lower and its price higher than the competitive quantity and price. This imposes a cost on society because fewer consumers buy the product, and those who do pay more for it. This is why antitrust laws exist which forbid firms from monopolizing most markets. When economies of scale make monopoly desirable—for example, with local electric power companies—we will see how the government can increase efficiency by regulating the monopolist’s price. Pure monopoly is rare, but in many markets only a few firms compete with each other. The interactions of firms in such markets can be complicated and often involve aspects of strategic gaming, a topic covered in Chapters 12 and 13. In any case, the firms may be able to affect price and may find it profitable to charge a price higher than marginal cost. These firms have monopoly power. We will discuss the determinants of monopoly power, its measurement, and its implications for pricing. Next we will turn to monopsony. Unlike a competitive buyer, a monopsonist pays a price that depends on the quantity that it purchases. The monopsonist’s problem is to choose the quantity that 10.1 Monopoly 358 10.2 Monopoly Power 368 10.3 Sources of Monopoly Power 375 10.4 The Social Costs of Monopoly Power 377 10.5 Monopsony 382 10.6 Monopsony Power 385 10.7 Limiting Market Power: The Antitrust Laws 389 10.1 Astra-Merck Prices Prilosec 364 10.2 Elasticities of Demand for Soft Drinks 370 10.3 Markup Pricing: Super- markets to Designer Jeans 372 10.4 The Pricing of Videos 374 10.5 Monopsony Power in U.S. Manufacturing 388 10.6 A Phone Call about Prices 392 10.7 Go Directly to Jail. Don’t Pass Go. 393 10.8 The United States and the European Union versus Microsoft 394 357 358 PART 3 • Market Structure and Competitive Strategy • monopoly Market with only one seller. • monopsony Market with only one buyer. • market power Ability of a seller or buyer to affect the price of a good. • marginal revenue Change in revenue resulting from a oneunit increase in output. In §8.3, we explain that marginal revenue is a measure of how much revenue increases when output increases by one unit. maximizes its net benefit from the purchase—the value derived from the good less the money paid for it. By showing how the choice is made, we will demonstrate the close parallel between monopsony and monopoly. Although pure monopsony is also unusual, many markets have only a few buyers who can purchase the good for less than they would pay in a competitive market. These buyers have monopsony power. Typically, this situation occurs in markets for inputs to production. For example, General Motors, the largest U.S. car manufacturer, has monopsony power in the markets for tires, car batteries, and other parts. We will discuss the determinants of monopsony power, its measurement, and its implications for pricing. Monopoly and monopsony power are two forms of market power: the ability—of either a seller or a buyer—to affect the price of a good.1 Because sellers or buyers often have at least some market power (in most real-world markets), we need to understand how market power works and how it affects producers and consumers. 10.1 Monopoly As the sole producer of a product, a monopolist is in a unique position. If the monopolist decides to raise the price of the product, it need not worry about competitors who, by charging lower prices, would capture a larger share of the market at the monopolist’s expense. The monopolist is the market and completely controls the amount of output offered for sale. But this does not mean that the monopolist can charge any price it wants—at least not if its objective is to maximize profit. This textbook is a case in point. Pearson Prentice Hall owns the copyright and is therefore a monopoly producer of this book. So why doesn’t it sell the book for $500 a copy? Because few people would buy it, and Prentice Hall would earn a much lower profit. To maximize profit, the monopolist must first determine its costs and the characteristics of market demand. Knowledge of demand and cost is crucial for a firm’s economic decision making. Given this knowledge, the monopolist must then decide how much to produce and sell. The price per unit that the monopolist receives then follows directly from the market demand curve. Equivalently, the monopolist can determine price, and the quantity it will sell at that price follows from the market demand curve. Average Revenue and Marginal Revenue The monopolist’s average revenue—the price it receives per unit sold—is precisely the market demand curve. To choose its profit-maximizing output level, the monopolist also needs to know its marginal revenue: the change in revenue that results from a unit change in output. To see the relationship among total, average, and marginal revenue, consider a firm facing the following demand curve: P = 6 - Q Table 10.1 shows the behavior of total, average, and marginal revenue for this demand curve. Note that revenue is zero when the price is $6: At that price, nothing is sold. At a price of $5, however, one unit is sold, so total (and 1The courts use the term “monopoly power” to mean significant and sustainable market power, sufficient to warrant particular scrutiny under the antitrust laws. In this book, however, for pedagogic reasons we use “monopoly power” differently, to mean market power on the part of sellers, whether substantial or not. CHAPTER 10 • Market Power: Monopoly and Monopsony 359 TABLE 10.1 TOTAL, MARGINAL, AND AVERAGE REVENUE PRICE (P) QUANTITY (Q) TOTAL REVENUE (R) MARGINAL REVENUE (MR) AVERAGE REVENUE (AR) $0 5 8 9 8 5 — $5 3 1 −1 −3 — $5 4 3 2 1 marginal) revenue is $5. An increase in quantity sold from 1 to 2 increases revenue from $5 to $8; marginal revenue is thus $3. As quantity sold increases from 2 to 3, marginal revenue falls to $1, and when quantity increases from 3 to 4, marginal revenue becomes negative. When marginal revenue is positive, revenue is increasing with quantity, but when marginal revenue is negative, revenue is decreasing. When the demand curve is downward sloping, the price (average revenue) is greater than marginal revenue because all units are sold at the same price. If sales are to increase by 1 unit, the price must fall. In that case, all units sold, not just the additional unit, will earn less revenue. Note, for example, what happens in Table 10.1 when output is increased from 1 to 2 units and price is reduced to $4. Marginal revenue is $3: $4 (the revenue from the sale of the additional unit of output) less $1 (the loss of revenue from selling the first unit for $4 instead of $5). Thus, marginal revenue ($3) is less than price ($4). Figure 10.1 pl |
ots average and marginal revenue for the data in Table 10.1. Our demand curve is a straight line and, in this case, the marginal revenue curve has twice the slope of the demand curve (and the same intercept).2 The Monopolist’s Output Decision What quantity should the monopolist produce? In Chapter 8, we saw that to maximize profit, a firm must set output so that marginal revenue is equal to marginal cost. This is the solution to the monopolist’s problem. In Figure 10.2, the market demand curve D is the monopolist’s average revenue curve. It specifies the price per unit that the monopolist receives as a function of its output level. Also shown are the corresponding marginal revenue curve MR and the average and marginal cost curves, AC and MC. Marginal revenue and marginal cost are equal at quantity Q*. Then from the demand curve, we find the price P* that corresponds to this quantity Q*. How can we be sure that Q* is the profit-maximizing quantity? Suppose the monopolist produces a smaller quantity Q1 and receives the corresponding higher price P1. As Figure 10.2 shows, marginal revenue would then exceed marginal cost. In that case, if the monopolist produced a little more than Q1, 2If the demand curve is written so that price is a function of quantity, P a − bQ, total revenue is given by PQ aQ − bQ2. Marginal revenue (using calculus) is d(PQ)/dQ a − 2bQ. In this example, demand is P 6 − Q and marginal revenue is MR 6 − 2Q. (This holds only for small changes in Q and therefore does not exactly match the data in Table 10.1.) In §7.1, we explain that marginal cost is the change in variable cost associated with a one-unit increase in output. 360 PART 3 • Market Structure and Competitive Strategy FIGURE 10.1 AVERAGE AND MARGINAL REVENUE Average and marginal revenue are shown for the demand curve P 6 − Q. Dollars per unit of output 7 6 5 4 3 2 1 0 Average Revenue (demand) Marginal Revenue 1 2 3 4 5 6 7 Output it would receive extra profit (MR − MC) and thereby increase its total profit. In fact, the monopolist could keep increasing output, adding more to its total profit until output Q*, at which point the incremental profit earned from producing one more unit is zero. So the smaller quantity Q1 is not profit maximizing, even though it allows the monopolist to charge a higher price. If the monopolist produced Q1 instead of Q*, its total profit would be smaller by an amount equal to the shaded area below the MR curve and above the MC curve, between Q1 and Q*. In Figure 10.2, the larger quantity Q2 is likewise not profit maximizing. At this quantity, marginal cost exceeds marginal revenue. Therefore, if the monopolist produced a little less than Q2, it would increase its total profit (by MC − MR). It could increase its profit even more by reducing output all the way to Q*. The increased profit achieved by producing Q* instead of Q2 is given by the area below the MC curve and above the MR curve, between Q* and Q2. We can also see algebraically that Q* maximizes profit. Profit p is the differ- ence between revenue and cost, both of which depend on Q: p(Q) = R(Q) - C(Q) As Q is increased from zero, profit will increase until it reaches a maximum and then begin to decrease. Thus the profit-maximizing Q is such that the incremental profit resulting from a small increase in Q is just zero (i.e., p> Q = 0 ).Then p/Q = R/Q - C/Q = 0 But R> Q is marginal revenue and C> Q is marginal cost. Thus the profit-maximizing condition is that MR - MC = 0, or MR = MC. CHAPTER 10 • Market Power: Monopoly and Monopsony 361 Price P1 P* P2 Lost Profit from Producing Too Little (Q1) and Selling at Too High a Price (P1) MC AC D = AR Lost Profit from Producing Too Much (Q 2) and Selling at Too Low a Price (P2) MR Q1 Q* Q 2 Quantity FIGURE 10.2 PROFIT IS MAXIMIZED WHEN MARGINAL REVENUE EQUALS MARGINAL COST Q* is the output level at which MR MC. If the firm produces a smaller output—say, Q1—it sacrifices some profit because the extra revenue that could be earned from producing and selling the units between Q1 and Q* exceeds the cost of producing them. Similarly, expanding output from Q* to Q2 would reduce profit because the additional cost would exceed the additional revenue. An Example To grasp this result more clearly, let’s look at an example. Suppose the cost of production is C(Q) = 50 + Q2 In other words, there is a fixed cost of $50, and variable cost is Q2. Suppose demand is given by P(Q) = 40 - Q By setting marginal revenue equal to marginal cost, you can verify that profit is maximized when Q = 10, an output level that corresponds to a price of $30.3 3Note that average cost is C(Q)/Q 50/Q Q and marginal cost is C/Q 2Q. Revenue is R(Q) P(Q)Q 40Q − Q2, so marginal revenue is MR R/Q 40 − 2Q. Setting marginal revenue equal to marginal cost gives 40 − 2Q 2Q, or Q 10. 362 PART 3 • Market Structure and Competitive Strategy Cost, revenue, and profit are plotted in Figure 10.3(a). When the firm produces little or no output, profit is negative because of the fixed cost. Profit increases as Q increases, reaching a maximum of $150 at Q* = 10, and then decreases as Q is increased further. At the point of maximum profit, the slopes of the revenue and cost curves are the same. (Note that the tangent lines rr’ and cc’ are parallel.) The slope of the revenue curve is R> Q, or marginal revenue, and the slope of the cost curve is C> Q, or marginal cost. Because profit is maximized when marginal revenue equals marginal cost, the slopes are equal. Figure 10.3(b) shows both the corresponding average and marginal revenue curves and average and marginal cost curves. Marginal revenue and marginal cost intersect at Q* = 10. At this quantity, average cost is $15 per unit and price is $30 per unit. Thus average profit is $30 - $15 = $15 per unit. Because 10 units are sold, profit is (10)($15) = $150, the area of the shaded rectangle. FIGURE 10.3 EXAMPLE OF PROFIT MAXIMIZATION Part (a) shows total revenue R, total cost C, and profit, the difference between the two. Part (b) shows average and marginal revenue and average and marginal cost. Marginal revenue is the slope of the total revenue curve, and marginal cost is the slope of the total cost curve. The profitmaximizing output is Q* 10, the point where marginal revenue equals marginal cost. At this output level, the slope of the profit curve is zero, and the slopes of the total revenue and total cost curves are equal. The profit per unit is $15, the difference between average revenue and average cost. Because 10 units are produced, total profit is $150. $ 400 300 200 150 100 50 $/Q 40 30 20 15 10 r c 5 Profit C R r c Profit 10 (a) 15 20 Quantity MC MR AC AR 5 10 (b) 15 20 Quantity CHAPTER 10 • Market Power: Monopoly and Monopsony 363 A Rule of Thumb for Pricing We know that price and output should be chosen so that marginal revenue equals marginal cost, but how can the manager of a firm find the correct price and output level in practice? Most managers have only limited knowledge of the average and marginal revenue curves that their firms face. Similarly, they might know the firm’s marginal cost only over a limited output range. We therefore want to translate the condition that marginal revenue should equal marginal cost into a rule of thumb that can be more easily applied in practice. To do this, we first write the expression for marginal revenue: MR = R Q = (PQ) Q Note that the extra revenue from an incremental unit of quantity, 1PQ2 > Q, has two components: 1. Producing one extra unit and selling it at price P brings in revenue (1)(P) P. 2. But because the firm faces a downward-sloping demand curve, producing and selling this extra unit also results in a small drop in price P> Q which reduces the revenue from all units sold (i.e., a change in revenue Q[P> Q]). Thus, MR = P + Q P Q = P + Pa Q P b a P Q b We obtained the expression on the right by taking the term Q 1P> Q2 and multiplying and dividing it by P. Recall that the elasticity of demand is defined = 1P>Q2 1Q> P2. Thus 1Q>P2 1P> Q2 is the reciprocal of the elasticas Ed ity of demand, 1/Ed, measured at the profit-maximizing output, and The elasticity of demand is discussed in §§2.4 and 4.3. MR = P + P(1/Ed) Now, because the firm’s objective is to maximize profit, we can set marginal revenue equal to marginal cost: which can be rearranged to give us P + P(1/Ed) = MC P - MC P = - 1 Ed (10.1) This relationship provides a rule of thumb for pricing. The left-hand side, (P - MC)/P, is the markup over marginal cost as a percentage of price. The relationship says that this markup should equal minus the inverse of the elasticity of demand.4 (This figure will be a positive number because the elasticity 4Remember that this markup equation applies at the point of a profit maximum. If both the elasticity of demand and marginal cost vary considerably over the range of outputs under consideration, you may have to know the entire demand and marginal cost curves to determine the optimum output level. On the other hand, you can use this equation to check whether a particular output level and price are optimal. 364 PART 3 • Market Structure and Competitive Strategy of demand is negative.) Equivalently, we can rearrange this equation to express price directly as a markup over marginal cost: P = MC 1 + (1/Ed) (10.2) For example, if the elasticity of demand is −4 and marginal cost is $9 per unit, price should be $9/(1 - 1/4) = $9/.75 = $12 per unit. How does the price set by a monopolist compare with the price under competition? In Chapter 8, we saw that in a perfectly competitive market, price equals marginal cost. A monopolist charges a price that exceeds marginal cost, but by an amount that depends inversely on the elasticity of demand. As the markup equation (10.1) shows, if demand is extremely elastic, Ed is a large negative number, and price will be very close to marginal cost. In that case, a monopolized market will look much like a competitive one. In fact, when demand |
is very elastic, there is little benefit to being a monopolist. Also note that a monopolist will never produce a quantity of output that is on the inelastic portion of the demand curve—i.e., where the elasticity of demand is less than 1 in absolute value. To see why, suppose that the monopolist is producing at a point on the demand curve where the elasticity is −0.5. In that case, the monopolist could make a greater profit by producing less and selling at a higher price. (A 10-percent reduction in output, for example, would allow for a 20-percent increase in price and thus a 10-percent increase in revenue. If marginal cost were greater than zero, the increase in profit would be even more than 10 percent because the lower output would reduce the firm’s costs.) As the monopolist reduces output and raises price, it will move up the demand curve to a point where the elasticity is greater than 1 in absolute value and the markup rule of equation (10.2) will be satisfied. Suppose, however, that marginal cost is zero. In that case, we cannot use equation (10.2) directly to determine the profit-maximizing price. However, we can see from equation (10.1) that in order to maximize profit, the firm will produce at the point where the elasticity of demand is exactly −1. If marginal cost is zero, maximizing profit is equivalent to maximizing revenue, and revenue is maximized when Ed = -1. In §8.1, we explain that a perfectly competitive firm will choose its output so that marginal cost equals price. In §4.3 and Table 4.3, we explain that when price is increased, expenditure—and thus revenue—increases if demand is inelastic, decreases if demand is elastic, and is unchanged if demand has unit elasticity. E XAM PLE 10.1 ASTRA-MERCK PRICES PRILOSEC In 1995, a new drug developed by Astra-Merck became available for the long-term treatment of ulcers. The drug, Prilosec, represented a new generation of antiulcer medication. Other drugs to treat ulcer conditions were already on the market: Tagamet had been introduced in 1977, Zantac in 1983, Pepcid in 1986, and Axid in 1988. These four drugs worked in much the same way to reduce the stomach’s secretion of acid. Prilosec, however, was based on a very different biochemical mechanism and was much more effective than these earlier drugs. By CHAPTER 10 • Market Power: Monopoly and Monopsony 365 1996, it had become the best-selling drug in the world and faced no major competitor.5 In 1995, Astra-Merck was pricing Prilosec at about $3.50 per daily dose. (By contrast, the prices for Tagamet and Zantac were about $1.50 to $2.25 per daily dose.) Is this pricing consistent with the markup formula (10.1)? The marginal cost of producing and packaging Prilosec is only about 30 to 40 cents per daily dose. This low marginal cost implies that the price elasticity of demand, ED, should be in the range of roughly −1.0 to −1.2. Based on statistical studies of pharmaceutical demand, this is indeed a reasonable estimate for the demand elasticity. Thus, setting the price of Prilosec at a markup exceeding 400 percent over marginal cost is consistent with our rule of thumb for pricing. Shifts in Demand In a competitive market, there is a clear relationship between price and the quantity supplied. That relationship is the supply curve, which, as we saw in Chapter 8, represents the marginal cost of production for the industry as a whole. The supply curve tells us how much will be produced at every price. A monopolistic market has no supply curve. In other words, there is no one-to-one relationship between price and the quantity produced. The reason is that the monopolist’s output decision depends not only on marginal cost but also on the shape of the demand curve. As a result, shifts in demand do not trace out the series of prices and quantities that correspond to a competitive supply curve. Instead, shifts in demand can lead to changes in price with no change in output, changes in output with no change in price, or changes in both price and output. This principle is illustrated in Figure 10.4(a) and (b). In both parts of the figure, the demand curve is initially D1, the corresponding marginal revenue curve is MR1, and the monopolist’s initial price and quantity are P1 and Q1. In Figure 10.4(a), the demand curve is shifted down and rotated. The new demand and marginal revenue curves are shown as D2 and MR2. Note that MR2 intersects the marginal cost curve at the same point that MR1 does. As a result, the quantity produced stays the same. Price, however, falls to P2. In Figure 10.4(b), the demand curve is shifted up and rotated. The new marginal revenue curve MR2 intersects the marginal cost curve at a larger quantity, Q2 instead of Q1. But the shift in the demand curve is such that the price charged is exactly the same. Shifts in demand usually cause changes in both price and quantity. But the special cases shown in Figure 10.4 illustrate an important distinction between monopoly and competitive supply. A competitive industry supplies a specific quantity at every price. No such relationship exists for a monopolist, which, depending on how demand shifts, might supply several different quantities at the same price, or the same quantity at different prices. 5Prilosec, developed through a joint venture of the Swedish firm Astra and the U.S. firm Merck, was introduced in 1989, but only for the treatment of gastroesophageal reflux disease, and was approved for short-term ulcer treatment in 1991. It was the approval for long-term ulcer treatment in 1995, however, that created a very large market for the drug. In 1998, Astra bought Merck’s share of the rights to Prilosec. In 1999, Astra acquired the firm Zeneca and is now called AstraZeneca. In 2001, AstraZeneca earned over $4.9 billion in sales of Prilosec, which remained the world’s best-selling prescription drug. As AstraZeneca’s patent on Prilosec neared expiration, the company introduced Nexium, a new (and, according to the company, better) antiulcer drug. In 2006, Nexium was the third-biggest-selling pharmaceutical drug in the world, with sales of about $5.7 billion. 366 PART 3 • Market Structure and Competitive Strategy $/Q P1 P2 MC $/Q P1 = P2 D2 D1 MR2 MC D2 MR2 D1 MR1 MR1 Q1 = Q2 (a) Quantity Q1 Q2 Quantity (b) FIGURE 10.4 SHIFTS IN DEMAND Shifting the demand curve shows that a monopolistic market has no supply curve—i.e., there is no one-to-one relationship between price and quantity produced. In (a), the demand curve D1 shifts to new demand curve D2. But the new marginal revenue curve MR2 intersects marginal cost at the same point as the old marginal revenue curve MR1. The profit-maximizing output therefore remains the same, although price falls from P1 to P2. In (b), the new marginal revenue curve MR2 intersects marginal cost at a higher output level Q2. But because demand is now more elastic, price remains the same. In §9.6, we explain that a specific tax is a tax of a certain amount of money per unit sold, and we show how the tax affects price and quantity. The Effect of a Tax A tax on output can also have a different effect on a monopolist than on a competitive industry. In Chapter 9, we saw that when a specific (i.e., per-unit) tax is imposed on a competitive industry, the market price rises by an amount that is less than the tax, and that the burden of the tax is shared by producers and consumers. Under monopoly, however, price can sometimes rise by more than the amount of the tax. Analyzing the effect of a tax on a monopolist is straightforward. Suppose a specific tax of t dollars per unit is levied, so that the monopolist must remit t dollars to the government for every unit it sells. Therefore, the firm’s marginal (and average) cost is increased by the amount of the tax t. If MC was the firm’s original marginal cost, its optimal production decision is now given by MR = MC + t In §8.2, we explain that a firm maximizes its profit by choosing the output at which marginal revenue is equal to marginal cost. Graphically, we shift the marginal cost curve upward by an amount t, and find the new intersection with marginal revenue. Figure 10.5 shows this. Here Q0 and P0 are the quantity and price before the tax is imposed, and Q1 and P1 are the quantity and price after the tax. $/Q P1 ΔP P0 t CHAPTER 10 • Market Power: Monopoly and Monopsony 367 FIGURE 10.5 EFFECT OF EXCISE TAX ON MONOPOLIST With a tax t per unit, the firm’s effective marginal cost is increased by the amount t to MC t. In this example, the increase in price P is larger than the tax t. MC t D AR MC MR Q1 Q0 Quantity Shifting the marginal cost curve upward results in a smaller quantity and higher price. Sometimes price increases by less than the tax, but not always—in Figure 10.5, price increases by more than the tax. This would be impossible in a competitive market, but it can happen with a monopolist because the relationship between price and marginal cost depends on the elasticity of demand. Suppose, for example, that a monopolist faces a constant elasticity demand curve, with elasticity −2, and has constant marginal cost MC. Equation (10.2) then tells us that price will equal twice marginal cost. With a tax t, marginal cost increases to MC t, so price increases to 2(MC t) 2MC 2t; that is, it rises by twice the amount of the tax. (However, the monopolist’s profit nonetheless falls with the tax.) *The Multiplant Firm We have seen that a firm maximizes profit by setting output at a level where marginal revenue equals marginal cost. For many firms, production takes place in two or more different plants whose operating costs can differ. However, the logic used in choosing output levels is very similar to that for the single-plant firm. Suppose a firm has two plants. What should its total output be, and how much of that output should each plant produce? We can find the answer intuitively in two steps. • Step 1. Whatever the total output, it should be divided between the two plants so that marg |
inal cost is the same in each plant. Otherwise, the firm could reduce its costs and increase its profit by reallocating production. For example, if marginal cost at Plant 1 were higher than at Plant 2, the firm could produce the same output at a lower total cost by producing less at Plant 1 and more at Plant 2. • Step 2. We know that total output must be such that marginal revenue equals marginal cost. Otherwise, the firm could increase its profit by raising or lowering total output. For example, suppose marginal costs were the same at each plant, but marginal revenue exceeded marginal cost. In that case, the firm would do better by producing more at both plants because the revenue earned from the 368 PART 3 • Market Structure and Competitive Strategy additional units would exceed the cost. Because marginal costs must be the same at each plant, and because marginal revenue must equal marginal cost, we see that profit is maximized when marginal revenue equals marginal cost at each plant. We can also derive this result algebraically. Let Q1 and C1 be the output and cost of production for Plant 1, Q2 and C2 be the output and cost of production for + Q2 be total output. Then profit is Plant 2, and QT = Q1 p = PQT - C1(Q1) - C2(Q2) The firm should increase output from each plant until the incremental profit from the last unit produced is zero. Start by setting incremental profit from output at Plant 1 to zero: p Q1 = (PQT) Q1 - C1 Q1 = 0 Here (PQT)/Q1 is the revenue from producing and selling one more unit— i.e., marginal revenue, MR, for all of the firm’s output. The next term, C1/Q1, is marginal cost at Plant 1, MC1. We thus have MR - MC1 0, or MR = MC1 Similarly, we can set incremental profit from output at Plant 2 to zero, MR = MC2 Putting these relations together, we see that the firm should produce so that MR = MC1 = MC2 (10.3) Note the similarity to the way we obtained a competitive industry’s supply curve in §8.5 by horizontally summing the marginal cost curves of the individual firms. Figure 10.6 illustrates this principle for a firm with two plants. MC1 and MC2 are the marginal cost curves for the two plants. (Note that Plant 1 has higher marginal costs than Plant 2.) Also shown is a curve labeled MCT. This is the firm’s total marginal cost and is obtained by horizontally summing MC1 and MC2. Now we can find the profit-maximizing output levels Q1, Q2, and QT. First, find the intersection of MCT with MR; that point determines total output QT. Next, draw a horizontal line from that point on the marginal revenue curve to the vertical axis; point MR* determines the firm’s marginal revenue. The intersections of the marginal revenue line with MC1 and MC2 give the outputs Q1 and Q2 for the two plants, as in equation (10.3). Note that total output QT determines the firm’s marginal revenue (and hence its price P*). Q1 and Q2, however, determine marginal costs at each of the two plants. Because MCT was found by horizontally summing MC1 and MC2, we = QT. Thus these output levels satisfy the condition that know that Q1 MR = MC1 + Q2 = MC2. 10.2 Monopoly Power Pure monopoly is rare. Markets in which several firms compete with one another are much more common. We say more about the forms that this competition can take in Chapters 12 and 13. But we should explain here why each firm in a $/Q P* MR* CHAPTER 10 • Market Power: Monopoly and Monopsony 369 MC1 MC2 MCT FIGURE 10.6 PRODUCTION WITH TWO PLANTS A firm with two plants maximizes profits by choosing output levels Q1 and Q2 so that marginal revenue MR (which depends on total output) equals marginal costs for each plant, MC1 and MC2. D AR Q1 Q2 QT Quantity MR market with several firms is likely to face a downward-sloping demand curve and, as a result, to produce so that price exceeds marginal cost. Suppose, for example, that four firms produce toothbrushes and have the market demand curve Q 50,000 − 20,000P, as shown in Figure 10.7(a). Let’s assume that these four firms are producing an aggregate of 20,000 toothbrushes per day (5000 each per day) and selling them at $1.50 each. Note that market demand is relatively inelastic; you can verify that at this $1.50 price, the elasticity of demand is −1.5. Now suppose that Firm A is deciding whether to lower its price to increase sales. To make this decision, it needs to know how its sales would respond to a change in its price. In other words, it needs some idea of the demand curve it faces, as opposed to the market demand curve. A reasonable possibility is shown in Figure 10.7(b), where the firm’s demand curve DA is much more elastic than the market demand curve. (At the $1.50 price the elasticity is −6.0.) The firm might predict that by raising the price from $1.50 to $1.60, its sales will drop—say, from 5000 units to 3000—as consumers buy more toothbrushes from other firms. (If all firms raised their prices to $1.60, sales for Firm A would fall only to 4500.) For several reasons, sales won’t drop to zero as they would in a perfectly competitive market. First, if Firm A’s toothbrushes are a little different from those of its competitors, some consumers will pay a bit more for them. Second, other firms might also raise their prices. Similarly, Firm A might anticipate that by lowering its price from $1.50 to $1.40, it can sell more toothbrushes—perhaps 7000 instead of 5000. But it will not capture the entire market: Some consumers might still prefer the competitors’ toothbrushes, and competitors might also lower their prices. Thus, Firm A’s demand curve depends both on how much its product differs from its competitors’ products and on how the four firms compete with one another. We will discuss product differentiation and interfirm competition in Chapters 12 and 13. But one important point should be clear: Firm A is likely to face a demand curve which is more elastic than the market demand curve, but which is not infinitely elastic like the demand curve facing a perfectly competitive firm. 370 PART 3 • Market Structure and Competitive Strategy Market Demand 2.00 $/Q 1.50 1.00 10,000 20,000 (a) 2.00 $/Q 1.60 1.50 1.40 1.00 Demand Faced by Firm A MCA DA MRA 7000 QA 5000 (b) 30,000 Quantity 3000 FIGURE 10.7 THE DEMAND FOR TOOTHBRUSHES Part (a) shows the market demand for toothbrushes. Part (b) shows the demand for toothbrushes as seen by Firm A. At a market price of $1.50, elasticity of market demand is −1.5. Firm A, however, sees a much more elastic demand curve DA because of competition from other firms. At a price of $1.50, Firm A’s demand elasticity is −6. Still, Firm A has some monopoly power: Its profit-maximizing price is $1.50, which exceeds marginal cost. E XAM PLE 10.2 ELASTICITIES OF DEMAND FOR SOFT DRINKS Soft drinks provide a good example of the difference between a market elasticity of demand and a firm’s elasticity of demand. In addition, soft drinks are important because their consumption has been linked to childhood obesity; there could be health benefits from taxing them. A recent review of several statistical studies found that the market elasticity of demand for soft drinks is between −0.8 and −1.0.6 That means that if all soft drink producers increased the prices of all of their brands by 1 percent, the quantity of soft drinks demanded would fall by 0.8 to 1.0 percent. The demand for any individual soft drink, however, will be much more elastic, because consumers can readily substitute one drink for another. Although elasticities will differ across different brands, studies have shown that the elasticity of demand for, say, Coca Cola is around −5.7 In other words, if the price of Coke were increased by 1 percent but the prices of all other soft drinks remained unchanged, the quantity of Coke demanded would fall by about 5 percent. Students—and business people—sometimes confuse the market elasticity of demand with the firm (or brand) elasticity of demand. Make sure you understand the difference. 6T. Andreyeva, M.W. Long, and K.D. Brownell, “The Impact of Food Prices on Consumption: A Systematic Review of Research on the Price Elasticity of Demand for Food,” American Journal of Public Health, 2010, Vol. 100, 216–222. 7See Example 12.1. CHAPTER 10 • Market Power: Monopoly and Monopsony 371 Production, Price, and Monopoly Power As we will see in Chapters 12 and 13, determining the elasticity of demand for a firm’s product is usually more difficult than determining the market elasticity of demand. Nonetheless, firms will often use market research and statistical studies to estimate elasticities of demand for their products, because knowledge of these elasticities can be essential for profit-maximizing production and pricing decisions. Let’s return to the demand for toothbrushes in Figure 10.7. Let’s assume that Firm A in that figure has a good knowledge of its demand curve. In that case, how much should Firm A produce? The same principle applies: The profit-maximizing quantity equates marginal revenue and marginal cost. In Figure 10.7(b), that quantity is 5000 units. The corresponding price is $1.50, which exceeds marginal cost. Thus, although Firm A is not a pure monopolist, it does have monopoly power—it can profitably charge a price greater than marginal cost. Of course, its monopoly power is less than it would be if it had driven away the competition and monopolized the market, but it might still be substantial. This raises two questions. 1. How can we measure monopoly power in order to compare one firm with another? (So far we have been talking about monopoly power only in qualitative terms.) 2. What are the sources of monopoly power, and why do some firms have more monopoly power than others? We address both these questions below, although a more complete answer to the second question will be provided in Chapters 12 and 13. Measuring Monopoly Power Remember the important distinction between a perfectly competitive firm and a firm with monopoly power: For the competitive firm, price equals marginal cost; f |
or the firm with monopoly power, price exceeds marginal cost. Therefore, a natural way to measure monopoly power is to examine the extent to which the profitmaximizing price exceeds marginal cost. In particular, we can use the markup ratio of price minus marginal cost to price that we introduced earlier as part of a rule of thumb for pricing. This measure of monopoly power, introduced by economist Abba Lerner in 1934, is called the Lerner Index of Monopoly Power. It is the difference between price and marginal cost, divided by price. Mathematically: L = (P - MC)/P The Lerner index always has a value between zero and one. For a perfectly competitive firm, P MC, so that L 0. The larger is L, the greater is the degree of monopoly power. This index of monopoly power can also be expressed in terms of the elasticity of demand facing the firm. Using equation (10.1), we know that L = (P - MC)/P = - 1/Ed (10.4) Remember, however, that Ed is now the elasticity of the firm’s demand curve, not the market demand curve. In the toothbrush example discussed previously, the • Lerner Index of Monopoly Power Measure of monopoly power calculated as excess of price over marginal cost as a fraction of price. 372 PART 3 • Market Structure and Competitive Strategy elasticity of demand for Firm A is −6.0, and the degree of monopoly power is 1/6 0.167.8 Note that considerable monopoly power does not necessarily imply high profits. Profit depends on average cost relative to price. Firm A might have more monopoly power than Firm B but earn a lower profit because of higher average costs. The Rule of Thumb for Pricing In the previous section, we used equation (10.2) to compute price as a simple markup over marginal cost: P = MC 1 + (1/Ed) This relationship provides a rule of thumb for any firm with monopoly power. We must remember, however, that Ed is the elasticity of demand for the firm, not the elasticity of market demand. It is harder to determine the elasticity of demand for the firm than for the market because the firm must consider how its competitors will react to price changes. Essentially, the manager must estimate the percentage change in the firm’s unit sales that is likely to result from a 1-percent change in the firm’s price. This estimate might be based on a formal model or on the manager’s intuition and experience. Given an estimate of the firm’s elasticity of demand, the manager can calculate the proper markup. If the firm’s elasticity of demand is large, this markup will be small (and we can say that the firm has very little monopoly power). If the firm’s elasticity of demand is small, this markup will be large (and the firm will have considerable monopoly power). Figures 10.8(a) and 10.8(b) illustrate these two extremes. E XAM PLE 10.3 MARKUP PRICING: SUPERMARKETS TO DESIGNER JEANS Three examples should help clarify the use of markup pricing. Consider a supermarket chain. Although the elasticity of market demand for food is small (about −1), several supermarkets usually serve most areas. Thus no single supermarket can raise its prices very much without losing customers to other stores. As a result, the elasticity of demand for any one supermarket is often as large as - 10. Substituting this number for Ed in equation (10.2), we find P = MC> (1 0.1)MC>(0.9)(1.11) MC. In other words, the manager of a typical supermarket should set prices about 11 percent above marginal 8There are three problems with applying the Lerner index to the analysis of public policy toward firms. First, because marginal cost is difficult to measure, average variable cost is often used in Lerner index calculations. Second, if the firm prices below its optimal price (possibly to avoid legal scrutiny), its potential monopoly power will not be noted by the index. Third, the index ignores dynamic aspects of pricing such as effects of the learning curve and shifts in demand. See Robert S. Pindyck, “The Measurement of Monopoly Power in Dynamic Markets,” Journal of Law and Economics 28 (April 1985): 193–222. CHAPTER 10 • Market Power: Monopoly and Monopsony 373 cost. For a reasonably wide range of output levels (over which the size of the store and the number of its employees will remain fixed), marginal cost includes the cost of purchasing the food at wholesale, plus the costs of storing the food, arranging it on the shelves, etc. For most supermarkets, the markup is indeed about 10 or 11 percent. Small convenience stores, which are often open 7 days a week and even 24 hours a day, typically charge higher prices than supermarkets. Why? Because a convenience store faces a less elastic demand curve. Its customers are generally less price sensitive. They might need a quart of milk or a loaf of bread late at night or may find it inconvenient to drive to the supermarket. Because the elasticity of demand for a convenience store is about −5, the markup equation implies that its prices should be about 25 percent above marginal cost, as indeed they typically are. The Lerner index, (P − MC)/P, tells us that the convenience store has more monopoly power, but does it make larger profits? No. Because its volume is far smaller and its average fixed costs are larger, it usually earns a much smaller profit than a large supermarket despite its higher markup. Finally, consider a producer of designer jeans. Many companies produce jeans, but some consumers will pay much more for jeans with a designer label. Just how much more they will pay—or more exactly, how much sales will drop in response to higher prices—is a question that the producer must carefully consider because it is critical in determining the price at which the clothing will be sold (at wholesale to retail stores, which then mark up the price further). With designer jeans, demand elasticities in the range of −2 to −3 are typical for the major labels. This means that price should be 50 to 100 percent higher than marginal cost. Marginal cost is typically $20 to $25 per pair, and depending on the brand, the wholesale price is in the $30 to $50 range. In contrast, “mass-market” jeans will typically wholesale for $18 to $25 per pair. Why? Because without the designer label, they are far more price elastic. $/Q P* $/Q P* – MC MC P* MC AR P* – MC MR Q* (a) Quantity Q* AR Quantity MR (b) FIGURE 10.8 ELASTICITY OF DEMAND AND PRICE MARKUP The markup (P − MC)/P is equal to minus the inverse of the elasticity of demand facing the firm. If the firm’s demand is elastic, as in (a), the markup is small and the firm has little monopoly power. The opposite is true if demand is relatively inelastic, as in (b). 374 PART 3 • Market Structure and Competitive Strategy E XAM PLE 10.4 THE PRICING OF VIDEOS During the mid-1980s, the number of households owning videocassette recorders (VCRs) grew rapidly, as did the markets for rentals and sales of prerecorded cassettes. Although at that time many more videocassettes were rented through small retail outlets than sold outright, the market for sales was large and growing. Producers, however, found it difficult to decide what price to charge for cassettes. As a result, in 1985 popular movies were selling for vastly different prices, as you can see from the data in Table 10.2. Note that while The Empire Strikes Back was selling for nearly $80, Star Trek, a film that appealed to the same audience and was about as popular, sold for only about $25. These price differences reflected uncertainty and a wide divergence of views on pricing by producers. The issue was whether lower prices would induce consumers to buy videocassettes rather than rent them. Because producers do not share in the retailers’ revenues from rentals, they should charge a low price for cassettes only if that will induce enough consumers to buy them. Because the market was young, producers had no good estimates of the elasticity of demand, so they based prices on hunches or trial and error.9 As the market matured, however, sales data and market research studies put pricing decisions on firmer ground. Those studies strongly indicated that demand was price elastic and that the profit-maximizing price was in the range of $15 to $30. By the 1990s, most producers had lowered prices across the board. When DVDs were first introduced in 1997, the prices of top-selling DVDs were much more uniform. Since that time, prices of popular DVDs have remained fairly uniform and continued to fall. As Table 10.2 shows, by 2007, prices were typically in the range of $20. As a result, video sales steadily increased up until 2004, as shown in Figure 10.9. With the introduction of high- definition (HD) DVDs in 2006, sales of conventional DVDs began to be displaced by the new format. Note in Figure 10.9 that total dollar sales of DVDs (conventional and HD) reached a peak in 2007 and then began falling at a rapid rate. What happened? Full-length movies became increasingly available on television through the “Video On Demand” services of cable and satellite TV providers. Many movies were available for free, and for some, viewers had to pay a fee ranging from $4 to $6. “On Demand” movies, along with streaming video on the Internet, became an increasingly attractive substitute, and displaced DVD sales. TABLE 10.2 RETAIL PRICES OF VIDEOS IN 1985 AND 2011 1985 2011 TITLE RETAIL PRICE ($) TITLE RETAIL PRICE ($) Purple Rain Raiders of the Lost Ark Jane Fonda Workout The Empire Strikes Back An Officer and a Gentleman Star Trek: The Motion Picture Star Wars VHS $29.98 $24.95 $59.95 $79.98 $24.95 $24.95 $39.98 Tangled Harry Potter and the Deathly Hallows, Part 1 Megamind Despicable Me Red The King’s Speech Secretariat Data from Nash Information Services, LLC (http://www.thenumbers.com). DVD $20.60 $20.58 $18.74 $14.99 $27.14 $14.99 $20.60 9“Video Producers Debate the Value of Price Cuts,” New York Times, February 19, 1985. For a study of videocassette pricing, see Carl E. Enomoto and Soumendra N. Ghosh, “Pricing in the Home-Video Market” (working paper, New Mexic |
o State University, 1992). CHAPTER 10 • Market Power: Monopoly and Monopsony 375 18 16 14 12 10 8 6 4 2 0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 VHS DVD HD-DVD FIGURE 10.9 VIDEO SALES Between 1990 and 1998, lower prices induced consumers to buy many more videos. By 2001, sales of DVDs overtook sales of VHS videocassettes. High-definition DVDs were introduced in 2006, and are expected to eventually displace sales of conventional DVDs. All DVDs, however, are now being displaced by streaming video. 10.3 Sources of Monopoly Power Why do some firms have considerable monopoly power while other firms have little or none? Remember that monopoly power is the ability to set price above marginal cost and that the amount by which price exceeds marginal cost depends inversely on the elasticity of demand facing the firm. As equation (10.4) shows, the less elastic its demand curve, the more monopoly power a firm has. The ultimate determinant of monopoly power is therefore the firm’s elasticity of demand. Thus we should rephrase our question: Why do some firms (e.g., a supermarket chain) face demand curves that are more elastic than those faced by others (e.g., a producer of designer clothing)? Three factors determine a firm’s elasticity of demand. 1. The elasticity of market demand. Because the firm’s own demand will be at least as elastic as market demand, the elasticity of market demand limits the potential for monopoly power. 2. The number of firms in the market. If there are many firms, it is unlikely that any one firm will be able to affect price significantly. 3. The interaction among firms. Even if only two or three firms are in the market, each firm will be unable to profitably raise price very much if the rivalry among them is aggressive, with each firm trying to capture as much of the market as it can. Let’s examine each of these three determinants of monopoly power. 376 PART 3 • Market Structure and Competitive Strategy The Elasticity of Market Demand If there is only one firm—a pure monopolist—its demand curve is the market demand curve. In this case, the firm’s degree of monopoly power depends completely on the elasticity of market demand. More often, however, several firms compete with one another; then the elasticity of market demand sets a lower limit on the magnitude of the elasticity of demand for each firm. Recall our example of the toothbrush producers illustrated in Figure 10.7 (page 370). The market demand for toothbrushes might not be very elastic, but each firm’s demand will be more elastic. (In Figure 10.7, the elasticity of market demand is −1.5, and the elasticity of demand for each firm is −6.) A particular firm’s elasticity depends on how the firms compete with one another. But no matter how they compete, the elasticity of demand for each firm could never become smaller in magnitude than −1.5. Because the demand for oil is fairly inelastic (at least in the short run), OPEC could raise oil prices far above marginal production cost during the 1970s and early 1980s. Because the demands for such commodities as coffee, cocoa, tin, and copper are much more elastic, attempts by producers to cartelize these markets and raise prices have largely failed. In each case, the elasticity of market demand limits the potential monopoly power of individual producers. The Number of Firms The second determinant of a firm’s demand curve—and thus of its monopoly power—is the number of firms in its market. Other things being equal, the monopoly power of each firm will fall as the number of firms increases: As more and more firms compete, each firm will find it harder to raise prices and avoid losing sales to other firms. What matters, of course, is not just the total number of firms, but the number of “major players”—firms with significant market share. For example, if only two large firms account for 90 percent of sales in a market, with another 20 firms accounting for the remaining 10 percent, the two large firms might have considerable monopoly power. When only a few firms account for most of the sales in a market, we say that the market is highly concentrated.10 It is sometimes said (not always jokingly) that the greatest fear of American business is competition. That may or may not be true. But we would certainly expect that when only a few firms are in a market, their managers will prefer that no new firms enter. An increase in the number of firms can only reduce the monopoly power of each incumbent firm. An important aspect of competitive strategy (discussed in detail in Chapter 13) is finding ways to create barriers to entry—conditions that deter entry by new competitors. Sometimes there are natural barriers to entry. For example, one firm may have a patent on the technology needed to produce a particular product. This makes it impossible for other firms to enter the market, at least until the patent expires. Other legally created rights work in the same way—a copyright can limit the sale of a book, music, or a computer software program to a single company, and the need for a government license can prevent new firms from entering the markets for telephone service, television broadcasting, or interstate trucking. Finally, economies of scale may make it too costly for more than a few firms to supply the 10A statistic called the concentration ratio, which measures the percentage of sales accounted for by, say, the four largest firms, is often used to describe the concentration of a market. Concentration is one, but not the only, determinant of market power. • barrier to entry Condition that impedes entry by new competitors. CHAPTER 10 • Market Power: Monopoly and Monopsony 377 entire market. In some cases, economies of scale may be so large that it is most efficient for a single firm—a natural monopoly—to supply the entire market. We will discuss scale economies and natural monopoly in more detail shortly. The Interaction Among Firms The ways in which competing firms interact is also an important—and sometimes the most important—determinant of monopoly power. Suppose there are four firms in a market. They might compete aggressively, undercutting one another’s prices to capture more market share. This could drive prices down to nearly competitive levels. Each firm will fear that if it raises its price it will be undercut and lose market share. As a result, it will have little monopoly power. On the other hand, the firms might not compete much. They might even collude (in violation of the antitrust laws), agreeing to limit output and raise prices. Because raising prices in concert rather than individually is more likely to be profitable, collusion can generate substantial monopoly power. We will discuss the interaction among firms in detail in Chapters 12 and 13. Now we simply want to point out that, other things being equal, monopoly power is smaller when firms compete aggressively and is larger when they cooperate. Remember that a firm’s monopoly power often changes over time, as its operating conditions (market demand and cost), its behavior, and the behavior of its competitors change. Monopoly power must therefore be thought of in a dynamic context. For example, the market demand curve might be very inelastic in the short run but much more elastic in the long run. (Because this is the case with oil, the OPEC cartel enjoyed considerable short-run but much less long-run monopoly power.) Furthermore, real or potential monopoly power in the short run can make an industry more competitive in the long run: Large short-run profits can induce new firms to enter an industry, thereby reducing monopoly power over the longer term. 10.4 The Social Costs of Monopoly Power In a competitive market, price equals marginal cost. Monopoly power, on the other hand, implies that price exceeds marginal cost. Because monopoly power results in higher prices and lower quantities produced, we would expect it to make consumers worse off and the firm better off. But suppose we value the welfare of consumers the same as that of producers. In the aggregate, does monopoly power make consumers and producers better or worse off? We can answer this question by comparing the consumer and producer surplus that results when a competitive industry produces a good with the surplus that results when a monopolist supplies the entire market.11 (We assume that the competitive market and the monopolist have the same cost curves.) Figure 10.10 shows the average and marginal revenue curves and marginal cost curve for the monopolist. To maximize profit, the firm produces at the point where marginal revenue equals marginal cost, so that the price and quantity are Pm and Qm. In a competitive market, price must equal marginal cost, so the competitive price and quantity, Pc and Qc are found at the intersection of the average revenue (demand) curve and the marginal cost curve. Now let’s examine how surplus 11If there were two or more firms, each with some monopoly power, the analysis would be more complex. However, the basic results would be the same. In §7.4, we explain that a firm enjoys economies of scale when it can double its output with less than a doubling of cost. In §9.1, we explain that consumer surplus is the total benefit or value that consumers receive beyond what they pay for a good; producer surplus is the analogous measure for producers. 378 PART 3 • Market Structure and Competitive Strategy $/Q Pm Pc FIGURE 10.10 DEADWEIGHT LOSS FROM MONOPOLY POWER The shaded rectangle and triangles show changes in consumer and producer surplus when moving from competitive price and quantity, Pc and Qc, to a monopolist’s price and quantity, Pm and Qm. Because of the higher price, consumers lose A B and producer gains A − C. The deadweight loss is B C. Lost Consumer Surplus Deadweight Loss MC A B C AR MR Qm Qc Quantity changes if we move from the competitive price and quantity, Pc and Qc, to the monopoly price and quantity, Pm and Qm. Under monopol |
y, the price is higher and consumers buy less. Because of the higher price, those consumers who buy the good lose surplus of an amount given by rectangle A. Those consumers who do not buy the good at price Pm but who would buy at price Pc also lose surplus—namely, an amount given by triangle B. The total loss of consumer surplus is therefore A B. The producer, however, gains rectangle A by selling at the higher price but loses triangle C, the additional profit it would have earned by selling Qc − Qm at price Pc. The total gain in producer surplus is therefore A − C. Subtracting the loss of consumer surplus from the gain in producer surplus, we see a net loss of surplus given by B C. This is the deadweight loss from monopoly power. Even if the monopolist’s profits were taxed away and redistributed to the consumers of its products, there would be an inefficiency because output would be lower than under conditions of competition. The deadweight loss is the social cost of this inefficiency. Rent Seeking In practice, the social cost of monopoly power is likely to exceed the deadweight loss in triangles B and C of Figure 10.10. The reason is that the firm may engage in rent seeking: spending large amounts of money in socially unproductive efforts to acquire, maintain, or exercise its monopoly power. Rent seeking might involve lobbying activities (and perhaps campaign contributions) to obtain government regulations that make entry by potential competitors more difficult. Rent-seeking activity could also involve advertising and legal efforts to avoid antitrust scrutiny. It might also mean installing but not utilizing extra production capacity to convince potential competitors that they cannot sell enough to make entry worthwhile. We would expect the economic incentive to incur rent-seeking costs to bear a direct relation to the gains from monopoly power (i.e., rectangle A minus triangle C.) Therefore, the larger the • rent seeking Spending money in socially unproductive efforts to acquire, maintain, or exercise monopoly. CHAPTER 10 • Market Power: Monopoly and Monopsony 379 transfer from consumers to the firm (rectangle A), the larger the social cost of monopoly.12 Here’s an example. In 1996, the Archer Daniels Midland Company (ADM) successfully lobbied the Clinton administration for regulations requiring that the ethanol (ethyl alcohol) used in motor vehicle fuel be produced from corn. (The government had already planned to add ethanol to gasoline in order to reduce the country’s dependence on imported oil.) Ethanol is chemically the same whether it is produced from corn, potatoes, grain, or anything else. Then why require that it be produced only from corn? Because ADM had a near monopoly on corn-based ethanol production, so the regulation would increase its gains from monopoly power. Price Regulation Because of its social cost, antitrust laws prevent firms from accumulating excessive amounts of monopoly power. We will say more about such laws at the end of the chapter. Here, we examine another means by which government can limit monopoly power—price regulation. We saw in Chapter 9 that in a competitive market, price regulation always results in a deadweight loss. This need not be the case, however, when a firm has monopoly power. On the contrary, price regulation can eliminate the deadweight loss that results from monopoly power. Figure 10.11 illustrates price regulation. Pm and Qm are the price and quantity that result without regulation—i.e., at the point where marginal revenue equals marginal cost. Now suppose the price is regulated to be no higher than P1. To find the firm’s profit-maximizing output, we must determine how its average and marginal revenue curves are affected by the regulation. Because the firm can charge no more than P1 for output levels up to Q1, its new average revenue curve is a horizontal line at P1. For output levels greater than Q1, the new average revenue curve is identical to the old average revenue curve: At these output levels, the firm will charge less than P1 and so will be unaffected by the regulation. The firm’s new marginal revenue curve corresponds to its new average revenue curve and is shown by the purple line in Figure 10.11. For output levels up to Q1, marginal revenue equals average revenue. (Recall that, as with a competitive firm, if average revenue is constant, average revenue and marginal revenue are equal.) For output levels greater than Q1, the new marginal revenue curve is identical to the original curve. Thus the complete marginal revenue curve now has three pieces: (1) the horizontal line at P1 for quantities up to Q1; (2) a vertical line at the quantity Q1 connecting the original average and marginal revenue curves; and (3) the original marginal revenue curve for quantities greater than Q1. To maximize its profit, the firm should produce the quantity Q1 because that is the point at which its marginal revenue curve intersects its marginal cost curve. You can verify that at price P1 and quantity Q1, the deadweight loss from monopoly power is reduced. As the price is lowered further, the quantity produced continues to increase and the deadweight loss to decline. At price Pc where average revenue and marginal cost intersect, the quantity produced has increased to the competitive level; the deadweight loss from monopoly power has been eliminated. Reducing the 12The concept of rent seeking was first developed by Gordon Tullock. For more detailed discussions, see Gordon Tullock, Rent Seeking (Brookfield, VT: Edward Elgar, 1993), or Robert D. Tollison and Roger D. Congleton, The Economic Analysis of Rent Seeking (Brookfield, VT: Edward Elgar, 1995). 380 PART 3 • Market Structure and Competitive Strategy $/Q Pm P1 P2 Pc P3 P4 MR MC Marginal revenue curve when price is regulated to be no higher than P1 AC AR Qm Q1 Q3 Qc ′ Q3 Quantity FIGURE 10.11 PRICE REGULATION If left alone, a monopolist produces Qm and charges Pm. When the government imposes a price ceiling of P1 the firm’s average and marginal revenue are constant and equal to P1 for output levels up to Q1. For larger output levels, the original average and marginal revenue curves apply. The new marginal revenue curve is, therefore, the dark purple line, which intersects the marginal cost curve at Q1. When price is lowered to Pc, at the point where marginal cost intersects average revenue, output increases to its maximum Qc. This is the output that would be produced by a competitive industry. Lowering price further, to P3, reduces output to Q3 and causes a shortage, Q3 = - Q3. price even more—say, to P3—results in a reduction in quantity. This reduction is equivalent to imposing a price ceiling on a competitive industry. A shortage = - Q3), in addition to the deadweight loss from regulation. As the develops, (Q3 price is lowered further, the quantity produced continues to fall and the shortage grows. Finally, if the price is lowered below P4, the minimum average cost, the firm loses money and goes out of business. Natural Monopoly Price regulation is most often used for natural monopolies, such as local utility companies. A natural monopoly is a firm that can produce the entire output of the market at a cost that is lower than what it would be if there were several firms. If a firm is a natural monopoly, it is more efficient to let it serve the entire market rather than have several firms compete. A natural monopoly usually arises when there are strong economies of scale, as illustrated in Figure 10.12. If the firm represented by the figure was broken up into two competing firms, each supplying half the market, the average cost for each would be higher than the cost incurred by the original monopoly. • natural monopoly Firm that can produce the entire output of the market at a cost lower than what it would be if there were several firms. $/Q Pm Pr Pc CHAPTER 10 • Market Power: Monopoly and Monopsony 381 FIGURE 10.12 REGULATING THE PRICE OF A NATURAL MONOPOLY A firm is a natural monopoly because it has economies of scale (declining average and marginal costs) over its entire output range. If price were regulated to be Pc the firm would lose money and go out of business. Setting the price at Pr yields the largest possible output consistent with the firm’s remaining in business; excess profit is zero. AC MC AR MR Qm Qr Qc Quantity Note in Figure 10.12 that because average cost is declining everywhere, marginal cost is always below average cost. If the firm were unregulated, it would produce Qm and sell at the price Pm. Ideally, the regulatory agency would like to push the firm’s price down to the competitive level Pc. At that level, however, price would not cover average cost and the firm would go out of business. The best alternative is therefore to set the price at Pr, where average cost and average revenue intersect. In that case, the firm earns no monopoly profit, while output remains as large as possible without driving the firm out of business. Regulation in Practice Recall that the competitive price (Pc in Figure 10.11) is found at the point at which the firm’s marginal cost and average revenue (demand) curves intersect. Likewise for a natural monopoly: The minimum feasible price (Pr in Figure 10.12) is found at the point at which average cost and demand intersect. Unfortunately, it is often difficult to determine these prices accurately in practice because the firm’s demand and cost curves may shift as market conditions evolve. As a result, the regulation of a monopoly is sometimes based on the rate of return that it earns on its capital. The regulatory agency determines an allowed price, so that this rate of return is in some sense “competitive” or “fair.” This practice is called rate-of-return regulation: The maximum price allowed is based on the (expected) rate of return that the firm will earn.13 Unfortunately, difficult problems arise when implementing rate-of-return regulation. First, although it is a key el |
ement in determining the firm’s rate of return, a firm’s capital stock is difficult to value. Second, while a “fair” rate of 13Regulatory agencies often use a formula like the following to determine price: P = AVC + (D + T + sK)/Q where AVC is average variable cost, Q is output, s is the allowed “fair” rate of return, D is depreciation, T is taxes, and K is the firm’s current capital stock. • rate-of-return regulation Maximum price allowed by a regulatory agency is based on the (expected) rate of return that a firm will earn. 382 PART 3 • Market Structure and Competitive Strategy return must be based on the firm’s actual cost of capital, that cost depends in turn on the behavior of the regulatory agency (and on investors’ perceptions of what allowed rates of return will be in the future). The difficulty of agreeing on a set of numbers to be used in rate-of-return calculations often leads to delays in the regulatory response to changes in cost and other market conditions (not to mention long and expensive regulatory hearings). The major beneficiaries are usually lawyers, accountants, and, occasionally, economic consultants. The net result is regulatory lag—the delays of a year or more usually entailed in changing regulated prices. Another approach to regulation is setting price caps based on the firm’s variable costs, past prices, and possibly inflation and productivity growth. A price cap can allow for more flexibility than rate-of-return regulation. Under price cap regulation, for example, a firm would typically be allowed to raise its prices each year (without having to get approval from the regulatory agency) by an amount equal to the actual rate of inflation, minus expected productivity growth. Price cap regulation of this sort has been used to control prices of long distance and local telephone service. By the 1990s, the regulatory environment in the United States had changed dramatically. Many parts of the telecommunications industry had been deregulated, as had electric utilities in many states. Because scale economies had been largely exhausted, there was no reason to regard these firms as natural monopolies. In addition, technological change made entry by new firms relatively easy. 10.5 Monopsony So far, our discussion of market power has focused entirely on the seller side of the market. Now we turn to the buyer side. We will see that if there are not too many buyers, they can also have market power and use it profitably to affect the price they pay for a product. First, a few terms. • Monopsony refers to a market in which there is a single buyer. • An oligopsony is a market with only a few buyers. • With one or only a few buyers, some buyers may have monopsony power: a buyer’s ability to affect the price of a good. Monopsony power enables the buyer to purchase a good for less than the price that would prevail in a competitive market. Suppose you are trying to decide how much of a good to purchase. You could apply the basic marginal principle—keep purchasing units of the good until the last unit purchased gives additional value, or utility, just equal to the cost of that last unit. In other words, on the margin, additional benefit should just be offset by additional cost. Let’s look at this additional benefit and additional cost in more detail. We use the term marginal value to refer to the additional benefit from purchasing one more unit of a good. How do we determine marginal value? Recall from Chapter 4 that an individual demand curve determines marginal value, or marginal utility, as a function of the quantity purchased. Therefore, your marginal value schedule is your demand curve for the good. An individual’s demand curve slopes downward because the marginal value obtained from buying one more unit of a good declines as the total quantity purchased increases. • oligopsony Market with only a few buyers. • monopsony power Buyer’s ability to affect the price of a good. • marginal value Additional benefit derived from purchasing one more unit of a good. In §4.1, we explain that as we move down along a demand curve, the value the consumer places on an additional unit of the good falls. CHAPTER 10 • Market Power: Monopoly and Monopsony 383 • marginal expenditure Additional cost of buying one more unit of a good. • average expenditure Price paid per unit of a good. The additional cost of buying one more unit of a good is called the marginal expenditure. What that marginal expenditure is depends on whether you are a competitive buyer or a buyer with monopsony power. Suppose you are a competitive buyer—in other words, you have no influence over the price of the good. In that case, the cost of each unit you buy is the same no matter how many units you purchase; it is the market price of the good. Figure 10.13(a) illustrates this principle. The price you pay per unit is your average expenditure per unit, and it is the same for all units. But what is your marginal expenditure per unit? As a competitive buyer, your marginal expenditure is equal to your average expenditure, which in turn is equal to the market price of the good. Figure 10.13(a) also shows your marginal value schedule (i.e., your demand curve). How much of the good should you buy? You should buy until the marginal value of the last unit is just equal to the marginal expenditure on that unit. Thus you should purchase quantity Q* at the intersection of the marginal expenditure and demand curves. We introduced the concepts of marginal and average expenditure because they will make it easier to understand what happens when buyers have monopsony power. But before considering that situation, let’s look at the analogy between competitive buyer conditions and competitive seller conditions. Figure 10.13(b) shows how a perfectly competitive seller decides how much to produce and sell. Because the seller takes the market price as given, both average and marginal revenue are equal to the price. The profit-maximizing quantity is at the intersection of the marginal revenue and marginal cost curves. Now suppose that you are the only buyer of the good. Again you face a market supply curve, which tells you how much producers are willing to sell as a function of the price you pay. Should the quantity you purchase be at the point where your marginal value curve intersects the market supply curve? No. If $/Q P* $/Q MC ME AE P* AR MR D MV Q* (a) Quantity Q* (b) Quantity FIGURE 10.13 COMPETITIVE BUYER COMPARED TO COMPETITIVE SELLER In (a), the competitive buyer takes market price P* as given. Therefore, marginal expenditure and average expenditure are constant and equal; quantity purchased is found by equating price to marginal value (demand). In (b), the competitive seller also takes price as given. Marginal revenue and average revenue are constant and equal; quantity sold is found by equating price to marginal cost. 384 PART 3 • Market Structure and Competitive Strategy you want to maximize your net benefit from purchasing the good, you should purchase a smaller quantity, which you will obtain at a lower price. To determine how much to buy, set the marginal value from the last unit purchased equal to the marginal expenditure on that unit.14 Note, however, that the market supply curve is not the marginal expenditure curve. The market supply curve shows how much you must pay per unit, as a function of the total number of units you buy. In other words, the supply curve is the average expenditure curve. And because this average expenditure curve is upward sloping, the marginal expenditure curve must lie above it. The decision to buy an extra unit raises the price that must be paid for all units, not just the extra one.15 Figure 10.14 illustrates this principle. The optimal quantity for the monopso* , is found at the intersection of the demand and marginal expennist to buy, Qm diture curves. The price that the monopsonist pays is found from the supply * . Finally, note that this * that brings forth the supply Qm curve: It is the price Pm * is lower, than the quantity and price that * is less, and the price Pm quantity Qm would prevail in a competitive market, Qc and Pc. FIGURE 10.14 MONOPSONIST BUYER The market supply curve is monopsonist’s average expenditure curve AE. Because average expenditure is rising, marginal expenditure lies above it. The monopso* , where marginal expenditure nist purchases quantity Qm and marginal value (demand) intersect. The price paid * is then found from the average expenditure per unit Pm (supply) curve. In a competitive market, price and quantity, Pc and Qc, are both higher. They are found at the point where average expenditure (supply) and marginal value (demand) intersect. $/Q Pc P*m ME S AE MV Q*m Qc Quantity 14Mathematically, we can write the net benefit NB from the purchase as NB V − E, where V is the value to the buyer of the purchase and E is the expenditure. Net benefit is maximized when NB/Q = 0. Then NB/Q = V/Q - E/Q = MV - ME = 0 so that MV ME. 15To obtain the marginal expenditure curve algebraically, write the supply curve with price on the left-hand side: P P(Q). Then total expenditure E is price times quantity, or E P(Q)Q, and marginal expenditure is ME = E/Q = P(Q) + Q(P/Q) Because the supply curve is upward sloping, P/Q is positive, and marginal expenditure is greater than average expenditure. CHAPTER 10 • Market Power: Monopoly and Monopsony 385 Monopsony and Monopoly Compared Monopsony is easier to understand if you compare it with monopoly. Figures 10.15(a) and 10.15(b) illustrate this comparison. Recall that a monopolist can charge a price above marginal cost because it faces a downward-sloping demand, or average revenue curve, so that marginal revenue is less than average revenue. Equating marginal cost with marginal revenue leads to a quantity Q* that is less than what would be produced in a competitive market, and to a price P* that is higher than the competitive price Pc. The monopsony situation is exactly anal |
ogous. As Figure 10.15(b) illustrates, the monopsonist can purchase a good at a price below its marginal value because it faces an upward-sloping supply, or average expenditure, curve. Thus for a monopsonist, marginal expenditure is greater than average expenditure. Equating marginal value with marginal expenditure leads to a quantity Q* that is less than what would be bought in a competitive market, and to a price P* that is lower than the competitive price Pc. 10.6 Monopsony Power Much more common than pure monopsony are markets with only a few firms competing among themselves as buyers, so that each firm has some monopsony power. For example, the major U.S. automobile manufacturers compete with one another as buyers of tires. Because each of them accounts for a large $/Q P* Pc $/Q MC AR Pc P* ME S AE MV MR Q* (a) FIGURE 10.15 MONOPOLY AND MONOPSONY Qc Quantity Q* (b) Qc Quantity These diagrams show the close analogy between monopoly and monopsony. (a) The monopolist produces where marginal revenue intersects marginal cost. Average revenue exceeds marginal revenue, so that price exceeds marginal cost. (b) The monopsonist purchases up to the point where marginal expenditure intersects marginal value. Marginal expenditure exceeds average expenditure, so that marginal value exceeds price. 386 PART 3 • Market Structure and Competitive Strategy share of the tire market, each has some monopsony power in that market. General Motors, the largest, might be able to exert considerable monopsony power when contracting for supplies of tires (and other automotive parts). In a competitive market, price and marginal value are equal. A buyer with monopsony power, however, can purchase a good at a price below marginal value. The extent to which price is marked down below marginal value depends on the elasticity of supply facing the buyer.16 If supply is very elastic (ES is large), the markdown will be small and the buyer will have little monopsony power. Conversely, if supply is very inelastic, the markdown will be large and the buyer will have considerable monopsony power. Figures 10.16(a) and 10.16(b) illustrate these two cases. Sources of Monopsony Power What determines the degree of monopsony power in a market? Again, we can draw analogies with monopoly and monopoly power. We saw that monopoly power depends on three things: the elasticity of market demand, the number of sellers in the market, and the way those sellers interact. Monopsony power depends on three similar things: The elasticity of market supply, the number of buyers in the market, and the way those buyers interact. ELASTICITY OF MARKET SUPPLY A monopsonist benefits because it faces an upward-sloping supply curve, so that marginal expenditure exceeds average $/Q P* MV – P* $/Q ME ME S AE MV – P* P* MV S AE MV Q* (a) Quantity Q* (b) Quantity FIGURE 10.16 MONOPSONY POWER: ELASTIC VERSUS INELASTIC SUPPLY Monopsony power depends on the elasticity of supply. When supply is elastic, as in (a), marginal expenditure and average expenditure do not differ by much, so price is close to what it would be in a competitive market. The opposite is true when supply is inelastic, as in (b). 16The exact relationship (analogous to equation (10.1)) is given by (MV − P)/P 1/Es. This equation follows because MV ME and ME (PQ)/Q P Q(P/Q). CHAPTER 10 • Market Power: Monopoly and Monopsony 387 expenditure. The less elastic the supply curve, the greater the difference between marginal expenditure and average expenditure and the more monopsony power the buyer enjoys. If only one buyer is in the market—a pure monopsonist—its monopsony power is completely determined by the elasticity of market supply. If supply is highly elastic, monopsony power is small and there is little gain in being the only buyer. NUMBER OF BUYERS Most markets have more than one buyer, and the number of buyers is an important determinant of monopsony power. When the number of buyers is very large, no single buyer can have much influence over price. Thus each buyer faces an extremely elastic supply curve, so that the market is almost completely competitive. The potential for monopsony power arises when the number of buyers is limited. INTERACTION AMONG BUYERS Finally, suppose three or four buyers are in the market. If those buyers compete aggressively, they will bid up the price close to their marginal value of the product, and will thus have little monopsony power. On the other hand, if those buyers compete less aggressively, or even collude, prices will not be bid up very much, and the buyers’ degree of monopsony power might be nearly as high as if there were only one buyer. So, as with monopoly power, there is no simple way to predict how much monopsony power buyers will have in a market. We can count the number of buyers, and we can often estimate the elasticity of supply, but that is not enough. Monopsony power also depends on the interaction among buyers, which can be more difficult to ascertain. The Social Costs of Monopsony Power Because monopsony power results in lower prices and lower quantities purchased, we would expect it to make the buyer better off and sellers worse off. But suppose we value the welfare of buyers and sellers equally. How is aggregate welfare affected by monopsony power? We can find out by comparing the buyer and seller surplus that results from a competitive market to the surplus that results when a monopsonist is the sole buyer. Figure 10.17 shows the average and marginal expenditure curves and marginal value curve for the monopsonist. The monopsonist’s net benefit is maximized by purchasing a quantity Qm at a price Pm such that marginal value equals marginal expenditure. In a competitive market, price equals marginal value. Thus the competitive price and quantity, Pc and Qc, are found where the average expenditure and marginal value curves intersect. Now let’s see how surplus changes if we move from the competitive price and quantity, Pc and Qc, to the monopsony price and quantity, Pm and Qm. With monopsony, the price is lower and less is sold. Because of the lower price, sellers lose an amount of surplus given by rectangle A. In addition, sellers lose the surplus given by triangle C because of the reduced sales. The total loss of producer (seller) surplus is therefore A C. By buying at a lower price, the buyer gains the surplus given by rectangle A. However, the buyer buys less, Qm instead of Qc, and so loses the surplus given by triangle B. The total gain in surplus to the buyer is therefore A − B. Altogether, there is a net loss of surplus given by B C. This is the deadweight loss from monopsony power. Even if the monopsonist’s gains were taxed away and redistributed to the producers, there would be an inefficiency because output would be lower than under competition. The deadweight loss is the social cost of this inefficiency. Note the similarity with the deadweight loss from monopoly power discussed in §10.4. 388 PART 3 • Market Structure and Competitive Strategy $/Q Pc Pm FIGURE 10.17 DEADWEIGHT LOSS FROM MONOPSONY POWER The shaded rectangle and triangles show changes in buyer and seller surplus when moving from competitive price and quantity, Pc and Qc, to the monopsonist’s price and quantity, Pm and Qm. Because both price and quantity are lower, there is an increase in buyer (consumer) surplus given by A − B. Producer surplus falls by A C, so there is a deadweight loss given by triangles B and C. ME S AE Deadweight Loss B C A MV Qm Qc Quantity • bilateral monopoly Market with only one seller and one buyer. Bilateral Monopoly What happens when a monopolist meets a monopsonist? It’s hard to say. We call a market with only one seller and only one buyer a bilateral monopoly. If you think about such a market, you’ll see why it is difficult to predict the price and quantity. Both the buyer and the seller are in a bargaining situation. Unfortunately, no simple rule determines which, if either, will get the better part of the bargain. One party might have more time and patience, or might be able to convince the other party that it will walk away if the price is too low or too high. Bilateral monopoly is rare. Markets in which a few producers have some monopoly power and sell to a few buyers who have some monopsony power are more common. Although bargaining may still be involved, we can apply a rough principle here: Monopsony power and monopoly power will tend to counteract each other. In other words, the monopsony power of buyers will reduce the effective monopoly power of sellers, and vice versa. This tendency does not mean that the market will end up looking perfectly competitive; if, for example, monopoly power is large and monopsony power small, the residual monopoly power would still be significant. But in general, monopsony power will push price closer to marginal cost, and monopoly power will push price closer to marginal value. E XAM PLE 10.5 MONOPSONY POWER IN U.S. MANUFACTURING Monopoly power, as measured by the price-cost margin (P − MC)/P, varies considerably across manufacturing industries in the United States. Some industries have price-cost margins close to zero, while in others margins are as high as 0.4 or 0.5. These variations are due in part to differences in the determinants of monopoly power: In some industries, market demand is more elastic than in others; some industries have more sellers than others; and in some industries, sellers compete more aggressively than in others. But something else can help explain these variations in monopoly CHAPTER 10 • Market Power: Monopoly and Monopsony 389 power—differences in monopsony power among the firms’ customers. The role of monopsony power was investigated in a statistical study of 327 U.S. manufacturing industries.17 The study sought to determine the extent to which variations in price–cost margins could be attributed to variations in monopsony power by buyers in each industry. Although the degree of buyers’ monopsony |
power could not be measured directly, data were available for variables that help determine monopsony power, such as buyer concentration (the fraction of total sales going to the three or four largest firms) and the average annual size of buyers’ orders. The study found that buyers’ monopsony power had an important effect on the price–cost margins of sellers and could significantly reduce any monopoly power that sellers might otherwise have. Take, for example, the concentration of buyers, an important determinant of monopsony power. In industries where only four or five buyers account for all or nearly all sales, the price–cost margins of sellers would on average be as much as 10 percentage points lower than in comparable industries with hundreds of buyers accounting for sales. A good example of monopsony power in manufacturing is the market for automobile parts and components, such as brakes and radiators. Each major car producer in the United States typically buys an individual part from at least three, and often as many as a dozen, suppliers. In addition, for a standardized product, such as brakes, each automobile company usually produces part of its needs itself, so that it is not totally reliant on outside firms. This puts companies like General Motors and Ford in an excellent bargaining position with respect to their suppliers. Each supplier must compete for sales against five or 10 other suppliers, but each can sell to only a few buyers. For a specialized part, a single auto company may be the only buyer. As a result, the automobile companies have considerable monopsony power. This monopsony power becomes evident from the conditions under which suppliers must operate. To obtain a sales contract, a supplier must have a track record of reliability, in terms of both product quality and ability to meet tight delivery schedules. Suppliers are also often required to respond to changes in volume as auto sales and production levels fluctuate. Finally, pricing negotiations are notoriously difficult; a potential supplier will sometimes lose a contract because its bid is a penny per item higher than those of its competitors. Not surprisingly, producers of parts and components usually have little or no monopoly power. 10.7 Limiting Market Power: The Antitrust Laws We have seen that market power—whether wielded by sellers or buyers—harms potential purchasers who could have bought at competitive prices. In addition, market power reduces output, which leads to a deadweight loss. Excessive market power also raises problems of equity and fairness: If a firm has significant monopoly power, it will profit at the expense of consumers. In theory, a firm’s excess profits could be taxed away and redistributed to the buyers of its products, but such a redistribution is often impractical. It is difficult to determine what portion of a firm’s profit is attributable to monopoly power, and it is even more difficult to locate all the buyers and reimburse them in proportion to their purchases. How, then, can society limit market power and prevent it from being used anticompetitively? For a natural monopoly, such as an electric utility company, direct price regulation is the answer. But more generally, the answer is to prevent firms from obtaining excessive market power through mergers and acquisitions, and to prevent firms that already have market power from using it to restrict competition. In the United States and most other countries, this is done 17The study was by Steven H. Lustgarten, “The Impact of Buyer Concentration in Manufacturing Industries,” Review of Economics and Statistics 57 (May 1975): 125–32. 390 PART 3 • Market Structure and Competitive Strategy • antitrust laws Rules and regulations prohibiting actions that restrain, or are likely to restrain, competition. • parallel conduct Form of implicit collusion in which one firm consistently follows actions of another. • predatory pricing Practice of pricing to drive current competitors out of business and to discourage new entrants in a market so that a firm can enjoy higher future profits. via antitrust laws: rules and regulations designed to promote a competitive economy by prohibiting actions that are likely to restrain competition. Antitrust laws differ from country to country, and we will focus mostly on how those laws work in the United States. But it is important to stress at the outset that in the United States and elsewhere, while there are limitations (such as colluding with other firms), in general, it is not illegal to be a monopolist or to have market power. On the contrary, we have seen that patent and copyright laws protect the monopoly positions of firms that developed unique innovations. Thus Microsoft has a near-monopoly in personal computer operating systems because other firms are prohibited from copying Windows. Even if Microsoft had a complete monopoly in operating systems (it doesn’t—the Apple and Linux operating systems also compete in the market), that would not be illegal. What might be illegal, however, is if Microsoft used its monopoly power in personal computer operating systems to prevent other firms from entering with new operating systems, or to leverage its power and reduce competition in other markets. As we will see in Example 10.8, that was the basis for lawsuits brought against Microsoft by the U.S. Department of Justice and the European Commission. Restricting What Firms Can Do Innovation drives economic growth and enhances consumer welfare, so we are delighted when Apple gains market power by inventing the iPhone and iPad, or when a pharmaceutical company gains market power through its invention of a new life-saving drug. But there are other ways in which firms can gain market power that are not so laudable, and this is where the antitrust laws come into play. At a fundamental level, the laws work as follows. Section 1 of the Sherman Act (which was passed in 1890) prohibits contracts, combinations, or conspiracies in restraint of trade. One obvious example of an illegal combination is an explicit agreement among producers to restrict their output and/or to “fix” price above the competitive level. There have been numerous instances of such illegal combinations and conspiracies, as Example 10.7 illustrates. Implicit collusion in the form of parallel conduct can also be construed as violating the law. For example, if Firm B consistently follows Firm A’s pricing (parallel pricing), and if the firm’s conduct is contrary to what one would expect companies to do in the absence of collusion (such as raising prices in the face of decreased demand and over-supply), an implicit understanding may be inferred.18 Section 2 of the Sherman Act makes it illegal to monopolize or to attempt to monopolize a market and prohibits conspiracies that result in monopolization. The Clayton Act (1914) did much to pinpoint the kinds of practices that are likely to be anticompetitive. For example, the act makes it unlawful for a firm with a large market share to require the buyer or lessor of a good not to buy from a competitor. It also makes it illegal to engage in predatory pricing— pricing designed to drive current competitors out of business and to discourage new entrants (so that the predatory firm can enjoy higher prices in the future). Monopoly power can also be achieved by a merger of firms into a larger and more dominant firm, or by one firm acquiring or taking control of another firm 18The Sherman Act applies to all firms that do business in the United States (to the extent that a conspiracy to restrain trade could affect U.S. markets). However, foreign governments (or firms operating under their government’s control) are not subject to the act, so OPEC need not fear the wrath of the Justice Department. Also, firms can collude with respect to exports. The Webb-Pomerene Act (1918) allows price fixing and related collusion with respect to export markets, as long as domestic markets are unaffected by such collusion. Firms operating in this manner must form a “Webb-Pomerene Association” and register it with the government. CHAPTER 10 • Market Power: Monopoly and Monopsony 391 by purchasing its stock. The Clayton Act prohibits mergers and acquisitions if they “substantially lessen competition” or “tend to create a monopoly.” The antitrust laws also limit possible anticompetitive conduct by firms in other ways. For example, the Clayton Act, as amended by the Robinson-Patman Act (1936), makes it illegal to discriminate by charging buyers of essentially the same product different prices if those price differences are likely to injure competition. Even then, firms are not liable if they can show that the price differences were necessary to meet competition. (As we will see in the next chapter, price discrimination is a common practice. It becomes the target of antitrust action only when buyers suffer economic damages and competition is reduced.) Another important component of the antitrust laws is the Federal Trade Commission Act (1914, amended in 1938, 1973, 1975), which created the Federal Trade Commission (FTC). This act supplements the Sherman and Clayton acts by fostering competition through a whole set of prohibitions against unfair and anticompetitive practices, such as deceptive advertising and labeling, agreements with retailers to exclude competing brands, and so on. Because these prohibitions are interpreted and enforced in administrative proceedings before the FTC, the act provides broad powers that reach further than those of other antitrust laws. The antitrust laws are actually phrased vaguely in terms of what is and what is not allowed. They are intended to provide a general statutory framework to give the Justice Department, the FTC, and the courts wide discretion in interpreting and applying them. This approach is important because it is difficult to know in advance what might be an impediment to competition. Such ambiguity creates a need for |
common law (i.e., the practice whereby courts interpret statutes) and supplemental provisions and rulings (e.g., by the FTC or the Justice Department). Enforcement of the Antitrust Laws The antitrust laws are enforced in three ways: 1. Through the Antitrust Division of the Department of Justice. As an arm of the executive branch, its enforcement policies closely reflect the view of the administration in power. Responding to an external complaint or an internal study, the department can institute a criminal proceeding, bring a civil suit, or both. The result of a criminal action can be fines for the corporation and fines or jail sentences for individuals. For example, individuals who conspire to fix prices or rig bids can be charged with a felony and, if found guilty, may be sentenced to jail—something to remember if you are planning to parlay your knowledge of microeconomics into a successful business career! Losing a civil action forces a corporation to cease its anticompetitive practices and often to pay damages. 2. Through the administrative procedures of the Federal Trade Commission. Again, action can result from an external complaint or from the FTC’s own initiative. Should the FTC decide that action is required, it can either request a voluntary understanding to comply with the law or seek a formal commission order requiring compliance. 3. Through private proceedings. Individuals or companies can sue for treble (three-fold) damages inflicted on their businesses or property. The prospect of treble damages can be a strong deterrent to would-be violators. Individuals or companies can also ask the courts for injunctions to force wrongdoers to cease anticompetitive actions. 392 PART 3 • Market Structure and Competitive Strategy U.S. antitrust laws are more stringent and far-reaching than those of most other countries. In fact, some people have argued that they have prevented American industry from competing effectively in international markets. The laws certainly constrain American business and may at times have put American firms at a disadvantage in world markets. But this criticism must be weighed against their benefits: Antitrust laws have been crucial for maintaining competition, and competition is essential for economic efficiency, innovation, and growth. Antitrust in Europe As the European Union has grown, its methods of antitrust enforcement have evolved. The responsibility for the enforcement of antitrust concerns that involve two or more member states resides in a single entity, the Competition Directorate, located in Brussels. Separate and distinct antitrust authorities within individual member states are responsible for those issues whose effects are felt largely or entirely within particular countries. At first glance, the antitrust laws of the European Union are quite similar to those of the United States. Article 101 of the Treaty of the European Community concerns restraints of trade, much like Section 1 of the Sherman Act. Article 102, which focuses on abuses of market power by dominant firms, is similar in many ways to Section 2 of the Sherman Act. Finally, with respect to mergers, the European Merger Control Act is similar in spirit to Section 7 of the Clayton Act. Nevertheless, there remain a number of procedural and substantive differences between antitrust laws in Europe and the United States. Merger evaluations typically are conducted more quickly in Europe, and it is easier in practice to prove that a European firm is dominant than it is to show that a U.S. firm has monopoly power. Both the European Union and the U.S. have been actively enforcing laws against price fixing, but Europe imposes only civil penalties, whereas the U.S. can impose prison sentences as well as fines. Antitrust enforcement has grown rapidly through the world in the past decade. Today, there are active enforcement agencies in over one hundred countries. While there is no formal world-wide antitrust enforcement body, all enforcement agencies meet at least once each year through the auspices of the International Competition Network. E XAM PLE 10.6 A PHONE CALL ABOUT PRICES In 1981 and early 1982, American Airlines and Braniff Airways were competing fiercely with each other for passengers. A fare war broke out as the firms undercut each other’s prices to capture market share. On February 21, 1982, Robert Crandall, president and CEO of American, made a phone call to Howard Putnam, president and chief executive of Braniff. To Crandall’s later surprise, the call had been taped. It went like this:19 Crandall I think it’s dumb as hell for Christ’s sake, all right, to sit here and pound the @!#$%&! out of each other and neither one of us making a @!#$%&! dime. 19According to the New York Times, February 24, 1983. CHAPTER 10 • Market Power: Monopoly and Monopsony 393 Putnam Well… Crandall I mean, you know, @!#$%&!, what the hell is the point of it? Putnam But if you’re going to overlay every route of American’s on top of every route that Braniff has—I just can’t sit here and allow you to bury us without giving our best effort. Crandall Oh sure, but Eastern and Delta do the same thing in Atlanta and have for years. Putnam Do you have a suggestion for me? Crandall Yes, I have a suggestion for you. Raise your @!#$%&! fares 20 percent. I’ll raise mine the next morning. Putnam Robert, we… Crandall You’ll make more money and I will, too. Putnam We can’t talk about pricing! Crandall Oh @!#$%&!, Howard. We can talk about any @!#$%&! thing we want to talk about. Crandall was wrong. Corporate executives cannot talk about anything they want. Talking about prices and agreeing to fix them is a clear violation of Section 1 of the Sherman Act. Putnam must have known this because he promptly rejected Crandall’s suggestion. After learning about the call, the Justice Department filed a suit accusing Crandall of violating the antitrust laws by proposing to fix prices. However, proposing to fix prices is not enough to violate Section 1 of the Sherman Act: For the law to be violated, the two parties must agree to collude. Therefore, because Putnam had rejected Crandall’s proposal, Section 1 was not violated. The court later ruled, however, that a proposal to fix prices could be an attempt to monopolize part of the airline industry and, if so, would violate Section 2 of the Sherman Act. American Airlines promised the Justice Department never again to engage in such activity. EXAM PLE 10.7 GO DIRECTLY TO JAIL. DON’T PASS GO. Corporate executives sometimes forget that price fixing is a criminal act in the United States that can lead not only to stiff fines, but also a prison sentence. Sitting in a prison cell is no fun. The Internet and cell phone service is terrible, there is no cable TV, and the food leaves much to be desired. So if you become a successful business executive, think twice before picking up the phone. And if your company happens to be located in Europe or Asia, don’t think that will keep you out of a U.S. jail. For example: • In 1996 Archer Daniels Midland (ADM) and two other producers of lysine (an animal feed additive) pled guilty to charges of price fixing. In 1999 three ADM executives were sentenced to prison terms of two to three years.20 • In 1999 four of the world’s largest drug and chemical companies—Hoffman-La Roche of Switzerland, BASF of Germany, Rhone Poulenc of France, and Takeda of Japan—pled guilty to fixing the prices of vitamins sold in the U.S. and Europe. The companies paid about $1.5 billion in penalties to the U.S. Department of Justice (DOJ), $1 billion to the European Commission, and over $4 billion to settle civil suits. Executives from each of the companies did prison time in the U.S. • During 2002 to 2009, Horizon Lines engaged in price fixing with Sea Star Lines (Puerto Ricobased shipping companies). Five executives got prison terms ranging from one to four years. 20Of course, it is always possible that you could be portrayed in a movie. In the 2009 movie, The Informant, actor Matt Damon played the role of Mark Whitacre, the ADM executive who blew the whistle on the price-fixing conspiracy, and then served a prison term for embezzlement. 394 PART 3 • Market Structure and Competitive Strategy • Eight companies, mostly in Korea and Japan, fixed DRAM (memory chip) prices from 1998 to 2002. In 2007, 18 executives from these companies were sentenced to prison terms in the United States. • In 2009, five companies pled guilty to fixing prices of LCD displays during 2001 to 2006. 22 executives received prison sentences in the United States (on top of $1 billion in fines). • In 2011, two companies were convicted of fixing prices and rigging bids for ready-mix concrete in Iowa. One executive was sentenced to one year in prison, another to four years. Get the idea? Don’t make the mistake of doing what these business people did. Stay out of jail. E XAM PLE 10.8 THE UNITED STATES AND THE EUROPEAN UNION VERSUS MICROSOFT Over the past two decades Microsoft has grown to become the largest computer software company in the world. Its Windows operating system for personal computers has maintained over a 90 percent market share. Microsoft has also continued to dominate the office productivity market. Its Office Suite, which includes Word (word processing), Excel (spreadsheets), and Powerpoint (presentations), has held over a 95 percent worldwide market share for nearly a decade. Microsoft’s incredible success has been due in good part to the creative technological and marketing decisions of the company and its now-retired CEO, Bill Gates. Is there anything wrong as a matter of either economics or law with being so successful and dominant? It all depends. Under the antitrust laws of the United States and the European Union, efforts by firms to restrain trade or to engage in activities that inappropriately maintain monopolies are illegal. Did Microsoft engage in anticompetitive, illegal practices? In 1998, the U.S. governm |
ent said yes; Microsoft disagreed. The Antitrust Division of the U.S. DOJ filed suit, claiming that Microsoft had illegally bundled its Internet browser, Internet Explorer, with its operating system for the purpose of maintaining its dominant operating system monopoly. The DOJ claimed that Microsoft viewed Netscape’s Internet browser (Netscape Navigator) as a threat to its monopoly over the PC operating system market. The threat existed because Netscape’s browser included Sun’s Java software, which can run programs that have been written for any operating system, including those that compete with Windows. Following an eight-month trial that was hard-fought on a range of economic issues, the District Court found that Microsoft did have monopoly power in the market for PC operating systems, which it had maintained illegally in violation of Section 2 of the Sherman Act. However, the court did find that certain exclusionary agreements with computer manufacturers and Internet service providers had not foreclosed competition sufficiently to violate Section 1 of the Sherman Act. On appeal, the D.C. Circuit Court of Appeals supported these aspects of the District Court’s opinion while leaving undecided whether bundling Internet Explorer in the operating system was itself illegal. The U.S. case was ultimately settled in 2004, with (among other things) Microsoft agreeing to give computer manufacturers (1) the ability to offer an operating system without Internet Explorer and (2) the option of loading competing browser programs on the PCs that they sell. Microsoft’s problems did not end with the U.S. settlement, however. In 2004, the European Commission ordered Microsoft to pay $794 million in fines for its anticompetitive practices and to produce a version of Windows without the Windows Media Player to be sold alongside its standard editions. In 2008, the European Commission levied an additional fine of $1.44 billion, claiming that Microsoft had not complied with the earlier decision. Even more recently, CHAPTER 10 • Market Power: Monopoly and Monopsony 395 in response to a concern relating to the bundling of browsers, Microsoft agreed to offer customers a choice of browsers when first booting up their new operating system. As of 2011, the European case against Microsoft remains on appeal. There is strong evidence that the European-imposed remedies have had little impact on the market for media players or browsers. However, Microsoft is facing an even stronger threat than U.S. or E.U. enforcement, such as competition from the powerful Google search engine and social media sites such as Facebook. SUMMARY 1. Market power is the ability of sellers or buyers to affect the price of a good. 2. Market power comes in two forms. When sellers charge a price that is above marginal cost, we say that they have monopoly power, which we measure by the extent to which price exceeds marginal cost. When buyers can obtain a price below their marginal value of the good, we say they have monopsony power, which we measure by the extent to which marginal value exceeds price. 3. Monopoly power is determined in part by the number of firms competing in a market. If there is only one firm—a pure monopoly—monopoly power depends entirely on the elasticity of market demand. The less elastic the demand, the more monopoly power the firm will have. When there are several firms, monopoly power also depends on how the firms interact. The more aggressively they compete, the less monopoly power each firm will have. 4. Monopsony power is determined in part by the number of buyers in a market. If there is only one buyer— a pure monopsony—monopsony power depends on the elasticity of market supply. The less elastic the supply, the more monopsony power the buyer will have. When there are several buyers, monopsony power also depends on how aggressively they compete for supplies. 5. Market power can impose costs on society. Because monopoly and monopsony power both cause production to fall below the competitive level, there is a deadweight loss of consumer and producer surplus. There can be additional social costs from rent seeking. 6. Sometimes, scale economies make pure monopoly desirable. But the government will still want to regulate price to maximize social welfare. 7. More generally, we rely on the antitrust laws to prevent firms from obtaining excessive market power. QUESTIONS FOR REVIEW 1. A monopolist is producing at a point at which marginal cost exceeds marginal revenue. How should it adjust its output to increase profit? 2. We write the percentage markup of price over marginal cost as (P − MC)/P. For a profit-maximizing monopolist, how does this markup depend on the elasticity of demand? Why can this markup be viewed as a measure of monopoly power? 3. Why is there no market supply curve under conditions of monopoly? 4. Why might a firm have monopoly power even if it is not the only producer in the market? 5. What are some of the different types of barriers to entry that give rise to monopoly power? Give an example of each. 6. What factors determine the amount of monopoly power an individual firm is likely to have? Explain each one briefly. 7. Why is there a social cost to monopoly power? If the gains to producers from monopoly power could be redistributed to consumers, would the social cost of monopoly power be eliminated? Explain briefly. 8. Why will a monopolist’s output increase if the government forces it to lower its price? If the government wants to set a price ceiling that maximizes the monopolist’s output, what price should it set? 9. How should a monopsonist decide how much of a product to buy? Will it buy more or less than a competitive buyer? Explain briefly. 10. What is meant by the term “monopsony power”? Why might a firm have monopsony power even if it is not the only buyer in the market? 11. What are some sources of monopsony power? What determines the amount of monopsony power an individual firm is likely to have? 12. Why is there a social cost to monopsony power? If the gains to buyers from monopsony power could be redistributed to sellers, would the social cost of monopsony power be eliminated? Explain briefly. 13. How do the antitrust laws limit market power in the United States? Give examples of major provisions of these laws. 14. Explain briefly how the U.S. antitrust laws are actually enforced. 396 PART 3 • Market Structure and Competitive Strategy EXERCISES 1. Will an increase in the demand for a monopolist’s product always result in a higher price? Explain. Will an increase in the supply facing a monopsonist buyer always result in a lower price? Explain. 2. Caterpillar Tractor, one of the largest producers of farm machinery in the world, has hired you to advise it on pricing policy. One of the things the company would like to know is how much a 5-percent increase in price is likely to reduce sales. What would you need to know to help the company with this problem? Explain why these facts are important. 3. A monopolist firm faces a demand with constant elasticity of 2.0. It has a constant marginal cost of $20 per unit and sets a price to maximize profit. If marginal cost should increase by 25 percent, would the price charged also rise by 25 percent? 4. A firm faces the following average revenue (demand) curve: P = 120 - 0.02Q where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C 60Q 25,000. Assume that the firm maximizes profits. a. What is the level of production, price, and total profit per week? b. If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit? 5. The following table shows the demand curve facing a monopolist who produces at a constant marginal cost of $10: PRICE QUANTITY 18 16 14 12 10 8 6 4 2 0 0 4 8 12 16 20 24 28 32 36 a. Calculate the firm’s marginal revenue curve. b. What are the firm’s profit-maximizing output and price? What is its profit? c. What would the equilibrium price and quantity be in a competitive industry? d. What would the social gain be if this monopolist were forced to produce and price at the competitive equilibrium? Who would gain and lose as a result? 6. Suppose that an industry is characterized as follows: C 100 2q2 MC 4q P 90 − 2Q MR 90 − 4Q each firm’s total cost function firm’s marginal cost function industry demand curve industry marginal revenue curve a. If there is only one firm in the industry, find the monopoly price, quantity, and level of profit. b. Find the price, quantity, and level of profit if the industry is competitive. c. Graphically illustrate the demand curve, marginal revenue curve, marginal cost curve, and average cost curve. Identify the difference between the profit level of the monopoly and the profit level of the competitive industry in two different ways. Verify that the two are numerically equivalent. 7. Suppose a profit-maximizing monopolist is producing 800 units of output and is charging a price of $40 per unit. a. If the elasticity of demand for the product is −2, find the marginal cost of the last unit produced. b. What is the firm’s percentage markup of price over marginal cost? c. Suppose that the average cost of the last unit produced is $15 and the firm’s fixed cost is $2000. Find the firm’s profit. 8. A firm has two factories, for which costs are given by: Factory # 1: C1 (Q1) = 10Q1 2 Factory # 2: C2 (Q2) = 20Q2 2 The firm faces the following demand curve: P = 700 - 5Q where Q is total output—i.e., Q Q1 Q2. a. On a diagram, draw the marginal cost curves for the two factories, the average and marginal revenue curves, and the total marginal cost curve (i.e., the marginal cost of producing Q Q1 Q2). Indicate the profit-maximizing output for each factory, total output, and price. b. Calculate the values of Q1, Q2, Q, and P that maxi- mize profit. c. Suppose that labor costs increase in Factory 1 but not in Factory 2. H |
ow should the firm adjust (i.e., raise, lower, or leave unchanged) the following: Output in Factory 1? Output in Factory 2? Total output? Price? CHAPTER 10 • Market Power: Monopoly and Monopsony 397 9. A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The costs of production for the two plants are MC1 20 2Q1 and MC2 10 5 Q2. The firm’s estimate of demand for the product is P 20 3(Q1 Q2). How much should the firm plan to produce in each plant? At what price should it plan to sell the product? 10. One of the more important antitrust cases of the 20th century involved the Aluminum Company of America (Alcoa) in 1945. At that time, Alcoa controlled about 90 percent of primary aluminum production in the United States, and the company had been accused of monopolizing the aluminum market. In its defense, Alcoa argued that although it indeed controlled a large fraction of the primary market, secondary aluminum (i.e., aluminum produced from the recycling of scrap) accounted for roughly 30 percent of the total supply of aluminum and that many competitive firms were engaged in recycling. Therefore, Alcoa argued, it did not have much monopoly power. a. Provide a clear argument in favor of Alcoa’s posi- tion. b. Provide a clear argument against Alcoa’s position. c. The 1945 decision by Judge Learned Hand has been called “one of the most celebrated judicial opinions of our time.” Do you know what Judge Hand’s ruling was? 11. A monopolist faces the demand curve P 11 Q, where P is measured in dollars per unit and Q in thousands of units. The monopolist has a constant average cost of $6 per unit. a. Draw the average and marginal revenue curves and the average and marginal cost curves. What are the monopolist’s profit-maximizing price and quantity? What is the resulting profit? Calculate the firm’s degree of monopoly power using the Lerner index. b. A government regulatory agency sets a price ceiling of $7 per unit. What quantity will be produced, and what will the firm’s profit be? What happens to the degree of monopoly power? c. What price ceiling yields the largest level of output? What is that level of output? What is the firm’s degree of monopoly power at this price? 12. Michelle’s Monopoly Mutant Turtles (MMMT) has the exclusive right to sell Mutant Turtle t-shirts in the United States. The demand for these t-shirts is Q 10,000/P2. The firm’s short-run cost is SRTC 2000 5Q, and its long-run cost is LRTC 6Q. a. What price should MMMT charge to maximize profit in the short run? What quantity does it sell, and how much profit does it make? Would it be better off shutting down in the short run? b. What price should MMMT charge in the long run? What quantity does it sell and how much profit does it make? Would it be better off shutting down in the long run? c. Can we expect MMMT to have lower marginal cost in the short run than in the long run? Explain why. 13. You produce widgets for sale in a perfectly competitive market at a market price of $10 per widget. Your widgets are manufactured in two plants, one in Massachusetts and the other in Connecticut. Because of labor problems in Connecticut, you are forced to raise wages there, so that marginal costs in that plant increase. In response to this, should you shift production and produce more in your Massachusetts plant? 14. The employment of teaching assistants (TAs) by major universities can be characterized as a monopsony. Suppose the demand for TAs is W 30,000 125n, where W is the wage (as an annual salary) and n is the number of TAs hired. The supply of TAs is given by W 1000 75n. a. If the university takes advantage of its monopsonist position, how many TAs will it hire? What wage will it pay? b. If, instead, the university faced an infinite supply of TAs at the annual wage level of $10,000, how many TAs would it hire? *15. Dayna’s Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is C 100 5Q Q2, and demand is P 55 2Q. a. What price should DD set to maximize profit? What output does the firm produce? How much profit and consumer surplus does DD generate? b. What would output be if DD acted like a perfect competitor and set MC P? What profit and consumer surplus would then be generated? c. What is the deadweight loss from monopoly power in part (a)? d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at $27. How does this affect price, quantity, consumer surplus, and DD’s profit? What is the resulting deadweight loss? e. Now suppose the government sets the maximum price at $23. How does this decision affect price, quantity, consumer surplus, DD’s profit, and deadweight loss? f. Finally, consider a maximum price of $12. What will this do to quantity, consumer surplus, profit, and deadweight loss? *16. There are 10 households in Lake Wobegon, Minnesota, each with a demand for electricity of Q 50 P. Lake Wobegon Electric’s (LWE) cost of producing electricity is TC 500 Q. a. If the regulators of LWE want to make sure that there is no deadweight loss in this market, what price will they force LWE to charge? What will 398 PART 3 • Market Structure and Competitive Strategy output be in that case? Calculate consumer surplus and LWE’s profit with that price. b. If regulators want to ensure that LWE doesn’t lose money, what is the lowest price they can impose? Calculate output, consumer surplus, and profit. Is there any deadweight loss? c. Kristina knows that deadweight loss is something that this small town can do without. She suggests that each household be required to pay a fixed amount just to receive any electricity at all, and then a per-unit charge for electricity. Then LWE can break even while charging the price calculated in part (a). What fixed amount would each household have to pay for Kristina’s plan to work? Why can you be sure that no household will choose instead to refuse the payment and go without electricity? 17. A certain town in the Midwest obtains all of its electricity from one company, Northstar Electric. Although the company is a monopoly, it is owned by the citizens of the town, all of whom split the profits equally at the end of each year. The CEO of the company claims that because all of the profits will be given back to the citizens, it makes economic sense to charge a monopoly price for electricity. True or false? Explain. 18. A monopolist faces the following demand curve: Q = 144/P2 where Q is the quantity demanded and P is price. Its average variable cost is AVC = Q1/2 and its fixed cost is 5. a. What are its profit-maximizing price and quantity? What is the resulting profit? b. Suppose the government regulates the price to be no greater than $4 per unit. How much will the monopolist produce? What will its profit be? c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal? C H A P T E R 11 Pricing with Market Power As we explained in Chapter 10, market power is quite common. Many industries have only a few producers, so that each producer has some monopoly power. And many firms, as buyers of raw materials, labor, or specialized capital goods, have some monopsony power in the markets for these factor inputs. The problem faced by the managers of these firms is how to use their market power most effectively. They must decide how to set prices, choose quantities of factor inputs, and determine output in both the short and long run to maximize profit. Managers of firms with market power have a harder job than those who manage perfectly competitive firms. A firm that is perfectly competitive in output markets has no influence over market price. As a result, its managers need worry only about the cost side of the firm’s operations, choosing output so that price is equal to marginal cost. But the managers of a firm with monopoly power must also worry about the characteristics of demand. Even if they set a single price for the firm’s output, they must obtain at least a rough estimate of the elasticity of demand to determine what that price (and corresponding output level) should be. Furthermore, firms can often do much better by using a more complicated pricing strategy—for example, charging different prices to different customers. To design such pricing strategies, managers need ingenuity and even more information about demand. This chapter explains how firms with market power set prices. We begin with the basic objective of every pricing strategy: capturing consumer surplus and converting it into additional profit for the firm. Then we discuss how this goal can be achieved using price discrimination—charging different prices to different customers, sometimes for the same product and sometimes for small variations in the product. Because price discrimination is widely practiced in one form or another, it is important to understand how it works. Next, we discuss the two-part tariff—requiring customers to pay in advance for the right to purchase units of a good at a later time (and at additional cost). The classic example of this is an amusement park, where customers pay a fee to enter and then additional fees for each ride. Although amusement parks may seem like a rather specialized market, there are many other examples of two-part tariffs: the price of a Gillette razor, which gives the owner the opportunity to purchase Gillette razor blades; a tennis club, where members pay an annual fee and then an hourly rate for court time; or the monthly subscription 11.1 Capturing Consumer Surplus 400 11.2 Price Discrimination 401 11.3 Intertemporal Price Discrimination and Peak-Load Pricing 410 11.4 The Two-Part Tariff 414 *11.5 Bundling 419 *11.6 Advertising 429 Appendix: The Vertically Integrated Firm 439 11.1 The Economics of Coupons and Rebates 408 11.2 Airline Fares 409 11.3 How to Price a Best-Selling Novel 413 11.4 Pricing Cellular Phone Servi |
ce 417 11.5 The Complete Dinner versus à la Carte: A Restaurant’s Pricing Problem 427 11.6 Advertising in Practice 432 399 400 PART 3 • Market Structure and Competitive Strategy cost of long-distance telephone service, which gives users the opportunity to make long-distance calls, paying by the minute as they do so. We will also discuss bundling, a pricing strategy that involves tying products together and selling them as a package. For example: a personal computer that comes bundled with several software packages; a one-week vacation in which the airfare, rental car, and hotel are bundled and sold at a single package price; or a luxury car, in which the sun roof, power windows, and leather seats are “standard” features. Finally, we will examine the use of advertising by firms with market power. As we will see, deciding how much money to spend on advertising requires information about demand and is closely related to the firm’s pricing decision. We will derive a simple rule of thumb for determining the profit-maximizing advertising-to-sales ratio. 11.1 Capturing Consumer Surplus All the pricing strategies that we will examine have one thing in common: They are means of capturing consumer surplus and transferring it to the producer. You can see this more clearly in Figure 11.1. Suppose the firm sold all its output at a single price. To maximize profit, it would pick a price P* and corresponding output Q* at the intersection of its marginal cost and marginal revenue curves. Although the firm would then be profitable, its managers might still wonder if they could make it even more profitable. They know that some customers (in region A of the demand curve) would pay more than P*. But raising the price would mean losing some customers, selling less, and earning smaller profits. Similarly, other potential customers are not buying the firm’s product because they will not pay a price as high as P*. Many of them, however, would pay prices higher than the firm’s marginal cost. (These customers are in region B of the demand curve.) By lowering its price, the firm Consumer surplus is explained in §4.4 and reviewed in §9.1. FIGURE 11.1 CAPTURING CONSUMER SURPLUS If a firm can charge only one price for all its customers, that price will be P* and the quantity produced will be Q*. Ideally, the firm would like to charge a higher price to consumers willing to pay more than P*, thereby capturing some of the consumer surplus under region A of the demand curve. The firm would also like to sell to consumers willing to pay prices lower than P*, but only if doing so does not entail lowering the price to other consumers. In that way, the firm could also capture some of the surplus under region B of the demand curve. A Pmax $/Q P1 P* P2 Pc B MC D MR Q* Quantity CHAPTER 11 • Pricing with Market Power 401 could sell to some of these customers. Unfortunately, it would then earn less revenue from its existing customers, and again profits would shrink. How can the firm capture the consumer surplus (or at least part of it) from its customers in region A, and perhaps also sell profitably to some of its potential customers in region B? Charging a single price clearly will not do the trick. However, the firm might charge different prices to different customers, according to where the customers are along the demand curve. For example, some customers in the upper end of region A would be charged the higher price P1, some in region B would be charged the lower price P2, and some in between would be charged P*. This is the basis of price discrimination: charging different prices to different customers. The problem, of course, is to identify the different customers, and to get them to pay different prices. We will see how this can be done in the next section. The other pricing techniques that we will discuss in this chapter—two-part tariffs and bundling—also expand the range of a firm’s market to include more customers and to capture more consumer surplus. In each case, we will examine both the amount by which the firm’s profit can be increased and the effect on consumer welfare. (As we will see, when there is a high degree of monopoly power, these pricing techniques can sometimes make both consumers and the producer better off.) We turn first to price discrimination. 11.2 Price Discrimination Price discrimination can take three broad forms, which we call first-, second-, and third-degree price discrimination. We will examine them in turn. First-Degree Price Discrimination Ideally, a firm would like to charge a different price to each of its customers. If it could, it would charge each customer the maximum price that the customer is willing to pay for each unit bought. We call this maximum price the customer’s reservation price. The practice of charging each customer his or her reservation price is called perfect first-degree price discrimination.1 Let’s see how it affects the firm’s profit. First, we need to know the profit that the firm earns when it charges only the single price P* in Figure 11.2. To find out, we can add the profit on each incremental unit produced and sold, up to the total quantity Q*. This incremental profit is the marginal revenue less the marginal cost for each unit. In Figure 11.2, this marginal revenue is highest and marginal cost lowest for the first unit. For each additional unit, marginal revenue falls and marginal cost rises. Thus the firm produces the total output Q*, at which point marginal revenue and marginal cost are equal. If we add up the profits on each incremental unit produced, we obtain the firm’s variable profit; the firm’s profit, ignoring its fixed costs. In Figure 11.2, variable profit is given by the yellow-shaded area between the marginal revenue and marginal cost curves.2 Consumer surplus, which is the area between the average revenue curve and the price P* that customers pay, is outlined as a black triangle. 1We are assuming that each customer buys one unit of the good. If a customer buys more than one unit, the firm will have to charge different prices for each of the units. 2Recall from Chapter 10 that because total profit p is the difference between total revenue R and total cost C, incremental profit is just p = R - C = MR - MC. Variable profit is found by summing all the ps, and thus it is the area between the MR and MC curves. This ignores fixed costs, which are independent of the firm’s output and pricing decisions. Thus, total profit equals variable profit minus fixed cost. • price discrimination Practice of charging different prices to different consumers for similar goods. • reservation price Maximum price that a customer is willing to pay for a good. • first-degree price discrimination Practice of charging each customer her reservation price. In §8.3, we explain that a firm’s profit-maximizing output is the output at which marginal revenue is equal to marginal cost. • variable profit Sum of profits on each incremental unit produced by a firm; i.e., profit ignoring fixed costs. 402 PART 3 • Market Structure and Competitive Strategy Pmax $/Q P* Pc FIGURE 11.2 ADDITIONAL PROFIT FROM PERFECT FIRST-DEGREE PRICE DISCRIMINATION Because the firm charges each consumer her reservation price, it is profitable to expand output to Q**. When only a single price, P*, is charged, the firm’s variable profit is the area between the marginal revenue and marginal cost curves. With perfect price discrimination, this profit expands to the area between the demand curve and the marginal cost curve. Consumer surplus when a single price P* is charged Variable profit when a single price P* is charged Additional profit from perfect price discrimination MC D AR MR Q* Q** Quantity PERFECT PRICE DISCRIMINATION What happens if the firm can perfectly price discriminate? Because each consumer is charged exactly what he or she is willing to pay, the marginal revenue curve is no longer relevant to the firm’s output decision. Instead, the incremental revenue earned from each additional unit sold is simply the price paid for that unit; it is therefore given by the demand curve. Since price discrimination does not affect the firm’s cost structure, the cost of each additional unit is again given by the firm’s marginal cost curve. Therefore, the additional profit from producing and selling an incremental unit is now the difference between demand and marginal cost. As long as demand exceeds marginal cost, the firm can increase its profit by expanding production. It will do so until it produces a total output Q**. At Q**, demand is equal to marginal cost, and producing any more reduces profit. Variable profit is now given by the area between the demand and marginal cost curves.3 Observe from Figure 11.2 how the firm’s profit has increased. (The additional profit resulting from price discrimination is shown by the purple-shaded area.) Note also that because every customer is being charged the maximum amount that he or she is willing to pay, all consumer surplus has been captured by the firm. IMPERFECT PRICE DISCRIMINATION In practice, perfect first-degree price discrimination is almost never possible. First, it is usually impractical to charge each and every customer a different price (unless there are only a few customers). Second, a firm usually does not know the reservation price of each customer. Even if it could ask how much each customer would be willing to pay, 3Incremental profit is again p = R - C, but R is given by the price to each customer (i.e., the average revenue curve), so p = AR - MC. Variable profit is the sum of these ps and is given by the area between the AR and MC curves. CHAPTER 11 • Pricing with Market Power 403 it probably would not receive honest answers. After all, it is in the customers’ interest to claim that they would pay very little. Sometimes, however, firms can discriminate imperfectly by charging a few different prices based on estimates of customers’ reservation prices. This practice is often use |
d by professionals, such as doctors, lawyers, accountants, or architects, who know their clients reasonably well. In such cases, the client’s willingness to pay can be assessed and fees set accordingly. For example, a doctor may offer a reduced fee to a low-income patient whose willingness to pay or insurance coverage is low, but charge higher fees to upper-income or better-insured patients. And an accountant, having just completed a client’s tax returns, is in an excellent position to estimate how much the client is willing to pay for the service. Another example is a car salesperson, who typically works with a 15-percent profit margin. The salesperson can give part of this margin away to the customer by making a “deal,” or can insist that the customer pay the full sticker price. A good salesperson knows how to size up customers: A customer who is likely to look elsewhere for a car is given a large discount (from the salesperson’s point of view, a small profit is better than no sale and no profit), but the customer in a hurry is offered little or no discount. In other words, a successful car salesperson knows how to price discriminate! Still another example is college and university tuition. Colleges don’t charge different tuition rates to different students in the same degree programs. Instead, they offer financial aid, in the form of scholarships or subsidized loans, which reduces the net tuition that the student must pay. By requiring those who seek aid to disclose information about family income and wealth, colleges can link the amount of aid to ability (and hence willingness) to pay. Thus students who are financially well off pay more for their education, while students who are less well off pay less. Figure 11.3 illustrates imperfect first-degree price discrimination. If only a sin*. Instead, six different prices are charged, gle price were charged, it would be P4 the lowest of which, P6, is set at about the point where marginal cost intersects the demand curve. Note that those customers who would not have been willing to * or greater are actually better off in this situation—they are now pay a price of P4 in the market and may be enjoying at least some consumer surplus. In fact, if price $/Q P1 P2 P3 P*4 P5 P6 FIGURE 11.3 FIRST-DEGREE PRICE DISCRIMINATION IN PRACTICE Firms usually don’t know the reservation price of every consumer, but sometimes reservation prices can be roughly identified. Here, six different prices are charged. The firm earns higher profits, but some con*, there sumers may also benefit. With a single price P4 are fewer consumers. The consumers who now pay P5 or P6 enjoy a surplus. MC D MR Quantity 404 PART 3 • Market Structure and Competitive Strategy discrimination brings enough new customers into the market, consumer welfare can increase to the point that both the producer and consumers are better off. Second-Degree Price Discrimination In some markets, as each consumer purchases many units of a good over any given period, his reservation price declines with the number of units purchased. Examples include water, heating fuel, and electricity. Consumers may each purchase a few hundred kilowatt-hours of electricity a month, but their willingness to pay declines with increasing consumption. The first 100 kilowatt-hours may be worth a lot to the consumer—operating a refrigerator and providing for minimal lighting. Conservation becomes easier with the additional units and may be worthwhile if the price is high. In this situation, a firm can discriminate according to the quantity consumed. This is called second-degree price discrimination, and it works by charging different prices for different quantities of the same good or service. Quantity discounts are an example of second-degree price discrimination. A single light bulb might be priced at $5, while a box containing four of the same bulb might be priced at $14, making the average price per bulb $3.50. Similarly, the price per ounce for breakfast cereal is likely to be smaller for the 24-ounce box than for the 16-ounce box. Another example of second-degree price discrimination is block pricing by electric power companies, natural gas utilities, and municipal water companies. With block pricing, the consumer is charged different prices for different quantities or “blocks” of a good. If scale economies cause average and marginal costs to decline, the government agency that controls rates may encourage block pricing. Because it leads to expanded output and greater scale economies, this policy can increase consumer welfare while allowing for greater profit to the company: While prices are reduced overall, the savings from the lower unit cost still permits the company to increase its profit. Figure 11.4 illustrates second-degree price discrimination for a firm with declining average and marginal costs. If a single price were charged, it would be P0, and the quantity produced would be Q0. Instead, three different prices are charged, based on the quantities purchased. The first block of sales is priced at P1, the second at P2, and the third at P3. Third-Degree Price Discrimination A well-known liquor company has what seems to be a strange pricing practice. The company produces a vodka that it advertises as one of the smoothest and best-tasting available. This vodka is called “Three Star Golden Crown” and sells for about $16 a bottle.4 However, the company also takes some of this same vodka and bottles it under the name “Old Sloshbucket,” which is sold for about $8 a bottle. Why does it do this? Has the president of the company been spending too much time near the vats? Perhaps, but this company is also practicing third-degree price discrimination, and it does so because the practice is profitable. This form of price discrimination divides consumers into two or more groups with separate demand curves for each group. It is the most prevalent form of price discrimination, and examples abound: regular versus “special” airline fares; premium versus nonpremium brands of liquor, canned food or frozen vegetables; discounts to students and senior citizens; and so on. 4We have changed the names to protect the innocent. • second-degree price discrimination Practice of charging different prices per unit for different quantities of the same good or service. • block pricing Practice of charging different prices for different quantities or “blocks” of a good. • third-degree price discrimination Practice of dividing consumers into two or more groups with separate demand curves and charging different prices to each group. $/Q P1 P0 P2 P3 CHAPTER 11 • Pricing with Market Power 405 FIGURE 11.4 SECOND-DEGREE PRICE DISCRIMINATION Different prices are charged for different quantities, or “blocks,” of the same good. Here, there are three blocks, with corresponding prices P1, P2, and P3. There are also economies of scale, and average and marginal costs are declining. Second-degree price discrimination can then make consumers better off by expanding output and lowering cost. AC MC D MR Q1 Q0 Q2 Q3 Quantity 1st Block 2nd Block 3rd Block CREATING CONSUMER GROUPS In each case, some characteristic is used to divide consumers into distinct groups. For many goods, for example, students and senior citizens are usually willing to pay less on average than the rest of the population (because their incomes are lower), and identity can be readily established (via a college ID or driver’s license). Likewise, to separate vacationers from business travelers (whose companies are usually willing to pay higher fares), airlines can put restrictions on special low-fare tickets, such as requiring advance purchase or a Saturday night stay. With the liquor company, or the premium versus nonpremium (e.g., supermarket label) brand of food, the label itself divides consumers; many consumers are willing to pay more for a name brand even though the nonpremium brand is identical or nearly identical (and might be manufactured by the same company that produced the premium brand). If third-degree price discrimination is feasible, how should the firm decide what price to charge each group of consumers? Let’s think about this in two steps. 1. We know that however much is produced, total output should be divided between the groups of customers so that marginal revenues for each group are equal. Otherwise, the firm would not be maximizing profit. For example, if there are two groups of customers and the marginal revenue for the first group, MR1, exceeds the marginal revenue for the second group, MR2, the firm could clearly do better by shifting output from the second group to the first. It would do this by lowering the price to the first group and raising the price to the second group. Thus, whatever the two prices, they must be such that the marginal revenues for the different groups are equal. 2. We know that total output must be such that the marginal revenue for each group of consumers is equal to the marginal cost of production. Again, if this were not the case, the firm could increase its profit by raising or lowering total output (and lowering or raising its prices to both groups). For example, suppose that marginal revenues were the same for each group of consumers but that marginal revenue exceeded marginal cost. The firm could then make 406 PART 3 • Market Structure and Competitive Strategy a greater profit by increasing its total output. It would lower its prices to both groups of consumers, so that marginal revenues for each group would fall (but would still be equal to each other) and would approach marginal cost. Let’s look at this problem algebraically. Let P1 be the price charged to the first group of consumers, P2 the price charged to the second group, and C(QT) the total cost of producing output QT Q1 Q2. Total profit is then p = P1Q1 + P2Q2 - C(QT) The firm should increase its sales to each group of consumers, Q1 and Q2, until the incremental profit from the last unit sold is zero. |
First, we set incremental profit for sales to the first group of consumers equal to zero: p Q1 = (P1Q1) Q1 - C Q1 = 0 Here, (P1Q1)/Q1 is the incremental revenue from an extra unit of sales to the first group of consumers (i.e., MR1). The next term, C/Q1, is the incremental cost of producing this extra unit—i.e., marginal cost, MC. We thus have MR1 = MC Similarly, for the second group of consumers, we must have MR2 = MC Putting these relations together, we see that prices and output must be set so that MR1 = MR2 = MC (11.1) Again, marginal revenue must be equal across groups of consumers and must equal marginal cost. DETERMINING RELATIVE PRICES Managers may find it easier to think in terms of the relative prices that should be charged to each group of consumers and to relate these prices to the elasticities of demand. Recall from Section 10.1 that we can write marginal revenue in terms of the elasticity of demand: MR = P(1 + 1/Ed) Thus MR1 P1(1 1/E1) and MR2 P2(1 1/E2), where E1 and E2 are the elasticities of demand for the firm’s sales in the first and second markets, respectively. Now equating MR1 and MR2 as in equation (11.1) gives the following relationship that must hold for the prices: P1 P2 = (1 + 1/E2) (1 + 1/E1) (11.2) In our discussion of a rule of thumb for pricing in §10.1, we explained that a profitmaximizing firm chooses an output at which its marginal revenue is equal to the price of the product plus the ratio of the price to the price elasticity of demand. CHAPTER 11 • Pricing with Market Power 407 As you would expect, the higher price will be charged to consumers with the lower demand elasticity. For example, if the elasticity of demand for consumers in group 1 is 2 and the elasticity for consumers in group 2 is 4, we will have = (1 - 1/4)/(1 - 1/2) = (3/4)/(1/2) = 1.5. In other words, the price P1/P2 charged to the first group of consumers should be 1.5 times as high as the price charged to the second group. Figure 11.5 illustrates third-degree price discrimination. Note that the demand curve D1 for the first group of consumers is less elastic than the curve for the second group; thus the price charged to the first group is higher. The total quantity produced, QT Q1 Q2, is found by summing the marginal revenue curves MR1 and MR2 horizontally, which yields the dashed curve MRT, and finding its intersection with the marginal cost curve. Because MC must equal MR1 and MR2, we can draw a horizontal line leftward from this intersection to find the quantities Q1 and Q2. It may not always be worthwhile for the firm to try to sell to more than one group of consumers. In particular, if demand is small for the second group and marginal cost is rising steeply, the increased cost of producing and selling to this group may outweigh the increase in revenue. In Figure 11.6, the firm is better off charging a single price P* and selling only to the larger group of consumers: The additional cost of serving the smaller market would outweigh the additional revenue that might come from selling to it. $/Q P1 P2 MC D2 AR2 MRT MR1 D1 AR1 MR2 Q1 Q2 QT Quantity FIGURE 11.5 THIRD-DEGREE PRICE DISCRIMINATION Consumers are divided into two groups, with separate demand curves for each group. The optimal prices and quantities are such that the marginal revenue from each group is the same and equal to marginal cost. Here group 1, with demand curve D1, is charged P1, and group 2, with the more elastic demand curve D2, is charged the lower price P2. Marginal cost depends on the total quantity produced QT. Note that Q1 and Q2 are chosen so that MR1 MR2 MC. 408 PART 3 • Market Structure and Competitive Strategy $/Q P* FIGURE 11.6 NO SALES TO SMALLER MARKET Even if third-degree price discrimination is feasible, it may not pay to sell to both groups of consumers if marginal cost is rising. Here the first group of consumers, with demand D1, are not willing to pay much for the product. It is unprofitable to sell to them because the price would have to be too low to compensate for the resulting increase in marginal cost. MC D2 MR2 D1 MR1 Q* Quantity E XAM PLE 11.1 THE ECONOMICS OF COUPONS AND REBATES Producers of processed foods and related consumer goods often issue coupons that let customers buy products at discounts. These coupons are usually distributed as part of an advertisement for the product. They may appear in newspapers or magazines or in promotional mailings. For example, a coupon for a particular breakfast cereal might be worth 50 cents toward the purchase of a box of the cereal. Why do firms issue these coupons? Why not just lower the price of the product and thereby save the costs of printing and collecting the coupons? Coupons provide a means of price discrimination. Studies show that only about 20 to 30 percent of all consumers regularly bother to clip, save, and use coupons. These consumers tend to be more sensitive to price than those who ignore coupons. They generally have more price-elastic demands and lower reservation prices. By issuing coupons, therefore, a cereal company can separate its customers into two groups and, in effect, charge the more price-sensitive customers a lower price than the other customers. Rebate programs work the same way. For example, Hewlett-Packard ran a program in which a consumer could mail in a form together with the proof of purchase of an ink-jet printer and receive a rebate of $10.00. Why not just lower the price of the printer by $10.00? Because only those consumers with relatively price-sensitive demands bother to send in the materials and request rebates. Again, the program is a means of price discrimination. Can consumers really be divided into distinct groups in this way? Table 11.1 shows the results of a statistical study in which, for a variety of products, price elasticities of demand were estimated for users and nonusers of coupons.5 This study confirms that users of coupons tend to have more price-sensitive demands. It also shows the extent to which the elasticities differ for the two groups of consumers and how the difference varies from one product to another. 5The study is by Chakravarthi Narasimhan, “A Price Discrimination Theory of Coupons,” Marketing Science (Spring 1984). A recent study of coupons for breakfast cereals finds that contrary to the predictions of the price-discrimination model, shelf prices for cereals tend to be lower during periods when coupons are more widely available. This might occur because couponing spurs more price competition among cereal manufacturers. See Aviv Nevo and Catherine Wolfram, “Prices and Coupons for Breakfast Cereals,” RAND Journal of Economics 33 (2002): 319–39. CHAPTER 11 • Pricing with Market Power 409 By themselves, these elasticity estimates do not tell a firm what price to set and how large a discount to offer because they pertain to market demand, not to the demand for the firm’s particular brand. For example, Table 11.1 indicates that the elasticity of demand for cake mix is −0.21 for nonusers of coupons and −0.43 for users. But the elasticity of demand for any of the five or six major brands of cake mix on the market will be much larger than either of these numbers—about five or six times as large, as a rule of thumb.6 So for any one brand of cake mix— say, Pillsbury—the elasticity of demand for users of coupons might be about −2.4, versus about −1.2 for nonusers. From equation (11.2), therefore, we can determine that the price to nonusers of coupons should be about 1.5 times the price to users. In other words, if a box of cake mix sells for $3.00, the company should offer coupons that give a $1.00 discount. TABLE 11.1 PRICE ELASTICITIES OF DEMAND FOR USERS VERSUS NONUSERS OF COUPONS PRODUCT NONUSERS PRICE ELASTICITY Toilet tissue Stuffing/dressing Shampoo Cooking/salad oil Dry mix dinners Cake mix Cat food Frozen entrees Gelatin Spaghetti sauce Creme rinse/conditioner Soups Hot dogs −0.60 −0.71 −0.84 −1.22 −0.88 −0.21 −0.49 −0.60 −0.97 −1.65 −0.82 −1.05 −0.59 USERS −0.66 −0.96 −1.04 −1.32 −1.09 −0.43 −1.13 −0.95 −1.25 −1.81 −1.12 −1.22 −0.77 EXAM PLE 11.2 AIRLINE FARES Travelers are often amazed at the variety of fares available for round-trip flights from New York to Los Angeles. Recently, for example, the first-class fare was around $2000; the regular (unrestricted) economy fare was about $1000, and special discount fares (often requiring the purchase of a ticket two weeks in advance and/or a Saturday night stayover) could be bought for as little as $200. Although firstclass service is not the same as economy service with a minimum stay requirement, the difference would not seem to warrant a price that is so much higher. Why do airlines set such fares? These fares provide a profitable form of price discrimination. The gains from discriminating are 6This rule of thumb applies if interfirm competition can be described by the Cournot model, which we will discuss in Chapter 12. 410 PART 3 • Market Structure and Competitive Strategy TABLE 11.2 ELASTICITIES OF DEMAND FOR AIR TRAVEL FARE CATEGORY ELASTICITY FIRST CLASS UNRESTRICTED COACH DISCOUNTED Price Income −0.3 1.2 −0.4 1.2 −0.9 1.8 large because different types of customers, with very different elasticities of demand, purchase these different types of tickets. Table 11.2 shows price (and income) elasticities of demand for three categories of service within the United States: first class, unrestricted coach, and discounted tickets (which often have restrictions and may be partly nonrefundable). Note that the demand for discounted fares is about two or three times as price elastic as firstclass or unrestricted coach service. Why the difference? While discounted tickets are usually used by families and other leisure travelers, first-class and unrestricted coach tickets are more often bought by business travelers, who have little choice about when they travel and whose companies pick up the tab. Of course, these elasticities pertain to market demand, and with several |
airlines competing for customers, the elasticities of demand for each airline will be larger. But the relative sizes of elasticities across the three categories of service should be about the same. When elasticities of demand differ so widely, it should not be surprising that airlines set such different fares for different categories of service. Airline price discrimination has become increasingly sophisticated. A wide variety of fares is available, depending on how far in advance the ticket is bought, the percentage of the fare that is refundable if the trip is changed or cancelled, and whether the trip includes a weekend stay.7 The objective of the airlines has been to discriminate more finely among travelers with different reservation prices. As one industry executive puts it, “You don’t want to sell a seat to a guy for $69 when he is willing to pay $400.”8 At the same time, an airline would rather sell a seat for $69 than leave it empty. • intertemporal price discrimination Practice of separating consumers with different demand functions into different groups by charging different prices at different points in time. • peak-load pricing Practice of charging higher prices during peak periods when capacity constraints cause marginal costs to be high. 11.3 Intertemporal Price Discrimination and Peak-Load Pricing Two other closely related forms of price discrimination are important and widely practiced. The first of these is intertemporal price discrimination: separating consumers with different demand functions into different groups by charging different prices at different points in time. The second is peak-load pricing: charging higher prices during peak periods when capacity constraints cause marginal costs to be high. Both of these strategies involve charging different prices at different times, but the reasons for doing so are somewhat different in each case. We will take each in turn. 7Airlines also allocate the number of seats on each flight that will be available for each fare category. The allocation is based on the total demand and mix of passengers expected for each flight, and can change as the departure of the flight nears and estimates of demand and passenger mix change. 8“The Art of Devising Air Fares,” New York Times, March 4, 1987. CHAPTER 11 • Pricing with Market Power 411 Intertemporal Price Discrimination The objective of intertemporal price discrimination is to divide consumers into high-demand and low-demand groups by charging a price that is high at first but falls later. To see how this strategy works, think about how an electronics company might price new, technologically advanced equipment, such as highperformance digital cameras or LCD television monitors. In Figure 11.7, D1 is the (inelastic) demand curve for a small group of consumers who value the product highly and do not want to wait to buy it (e.g., photography buffs who want the latest camera). D2 is the demand curve for the broader group of consumers who are more willing to forgo the product if the price is too high. The strategy, then, is to offer the product initially at the high price P1, selling mostly to consumers on demand curve D1. Later, after this first group of consumers has bought the product, the price is lowered to P2, and sales are made to the larger group of consumers on demand curve D2.9 There are other examples of intertemporal price discrimination. One involves charging a high price for a first-run movie and then lowering the price after the movie has been out a year. Another, practiced almost universally by publishers, is to charge a high price for the hardcover edition of a book and then to release the paperback version at a much lower price about a year later. Many people think that the lower price of the paperback is due to a much lower cost of production, but this is not true. Once a book has been edited and typeset, the $/Q P1 P2 D2 AR2 AC MC MR2 D1 AR1 MR1 Q1 Q2 Quantity FIGURE 11.7 INTERTEMPORAL PRICE DISCRIMINATION Consumers are divided into groups by changing the price over time. Initially, the price is high. The firm captures surplus from consumers who have a high demand for the good and who are unwilling to wait to buy it. Later the price is reduced to appeal to the mass market. 9The prices of new electronic products also come down over time because costs fall as producers start to achieve greater scale economies and move down the learning curve. But even if costs did not fall, producers can make more money by first setting high prices and then reducing them over time, thereby discriminating and capturing consumer surplus. 412 PART 3 • Market Structure and Competitive Strategy marginal cost of printing an additional copy, whether hardcover or paperback, is quite low, perhaps a dollar or so. The paperback version is sold for much less not because it is much cheaper to print but because high-demand consumers have already purchased the hardbound edition. The remaining consumers— paperback buyers—generally have more elastic demands. Peak-Load Pricing Peak-load pricing also involves charging different prices at different points in time. Rather than capturing consumer surplus, however, the objective is to increase economic efficiency by charging consumers prices that are close to marginal cost. For some goods and services, demand peaks at particular times—for roads and tunnels during commuter rush hours, for electricity during late summer afternoons, and for ski resorts and amusement parks on weekends. Marginal cost is also high during these peak periods because of capacity constraints. Prices should thus be higher during peak periods. This is illustrated in Figure 11.8, where D1 is the demand curve for the peak period and D2 the demand curve for the nonpeak period. The firm sets marginal revenue equal to marginal cost for each period, obtaining the high price P1 for the peak period and the lower price P2 for the nonpeak period, selling corresponding quantities Q1 and Q2. This strategy increases the firm’s profit above what it would be if it charged one price for all periods. It is also more efficient: The sum of producer and consumer surplus is greater because prices are closer to marginal cost. The efficiency gain from peak-load pricing is important. If the firm were a regulated monopolist (e.g., an electric utility), the regulatory agency should set the prices P1 and P2 at the points where the demand curves, D1 and D2, intersect the marginal cost curve, rather than where the marginal revenue curves intersect marginal cost. In that case, consumers realize the entire efficiency gain. Note that peak-load pricing is different from third-degree price discrimination. With third-degree price discrimination, marginal revenue must be equal for In §9.2, we explain that economic efficiency means that aggregate consumer and producer surplus is maximized. $/Q P1 P2 FIGURE 11.8 PEAK-LOAD PRICING Demands for some goods and services increase sharply during particular times of the day or year. Charging a higher price P1 during the peak periods is more profitable for the firm than charging a single price at all times. It is also more efficient because marginal cost is higher during peak periods. MC D1 AR1 MR1 D2 AR2 MR2 Q 2 Q1 Quantity CHAPTER 11 • Pricing with Market Power 413 each group of consumers and equal to marginal cost. Why? Because the costs of serving the different groups are not independent. For example, with unrestricted versus discounted air fares, increasing the number of seats sold at discounted fares affects the cost of selling unrestricted tickets—marginal cost rises rapidly as the airplane fills up. But this is not so with peak-load pricing (or for that matter, with most instances of intertemporal price discrimination). Selling more tickets for ski lifts or amusement parks on a weekday does not significantly raise the cost of selling tickets on the weekend. Similarly, selling more electricity during offpeak periods will not significantly increase the cost of selling electricity during peak periods. As a result, price and sales in each period can be determined independently by setting marginal cost equal to marginal revenue for each period. Movie theaters, which charge more for evening shows than for matinees, are another example. For most movie theaters, the marginal cost of serving customers during the matinee is independent of marginal cost during the evening. The owner of a movie theater can determine the optimal prices for the evening and matinee shows independently, using estimates of demand and marginal cost in each period. EXAM PLE 11.3 HOW TO PRICE A BEST-SELLING NOVEL Publishing both hardbound and paperback editions of a book allows publishers to price discriminate. As they do with most goods, consumers differ considerably in their willingness to pay for books. For example, some consumers want to buy a new bestseller as soon as it is released, even if the price is $25. Other consumers, however, will wait a year until the book is available in paperback for $10. But how does a publisher decide that $25 is the right price for the new hardbound edition and $10 is the right price for the paperback edition? And how long should it wait before bringing out the paperback edition? The key is to divide consumers into two groups, so that those who are willing to pay a high price do so and only those unwilling to pay a high price wait and buy the paperback. This means that significant time must be allowed to pass before the paperback is released. If consumers know that the paperback will be available within a few months, they will have little incentive to buy the hardbound edition.10 On the other hand, if the publisher waits too long to bring out the paperback edition, interest will wane and the market will dry up. As a result, publishers typically wait 12 to 18 months before releasing paperback editions. What about price? Setting the price of the hardbound edition is difficult: Except for a few autho |
rs whose books always seem to sell, publishers have little data with which to estimate demand for a book that is about to be published. Often, they can judge only from the past sales of similar books. But usually only aggregate data are available for each category of book. Most new novels, therefore, are released at similar prices. It is clear, however, that those consumers willing to wait for the paperback edition have demands that are far more elastic than those of bibliophiles. It is not surprising, then, that paperback editions sell for so much less than hardbacks.11 10Some consumers will buy the hardbound edition even if the paperback is already available because it is more durable and more attractive on a bookshelf. This must be taken into account when setting prices, but it is of secondary importance compared with intertemporal price discrimination. 11Hardbound and paperback editions are often published by different companies. The author’s agent auctions the rights to the two editions, but the contract for the paperback specifies a delay to protect the sales of the hardbound edition. The principle still applies, however. The length of the delay and the prices of the two editions are chosen to price discriminate intertemporally. 414 PART 3 • Market Structure and Competitive Strategy 11.4 The Two-Part Tariff • two-part tariff Form of pricing in which consumers are charged both an entry and a usage fee. The two-part tariff is related to price discrimination and provides another means of extracting consumer surplus. It requires consumers to pay a fee up front for the right to buy a product. Consumers then pay an additional fee for each unit of the product they wish to consume. The classic example of this strategy is an amusement park.12 You pay an admission fee to enter, and you also pay a certain amount for each ride. The owner of the park must decide whether to charge a high entrance fee and a low price for the rides or, alternatively, to admit people for free but charge high prices for the rides. The two-part tariff has been applied in many settings: tennis and golf clubs (you pay an annual membership fee plus a fee for each use of a court or round of golf); the rental of large mainframe computers (a flat monthly fee plus a fee for each unit of processing time consumed); telephone service (a monthly hook-up fee plus a fee for minutes of usage). The strategy also applies to the sale of products like safety razors (you pay for the razor, which lets you consume the blades that fit that brand of razor). The problem for the firm is how to set the entry fee (which we denote by T) versus the usage fee (which we denote by P). Assuming that the firm has some market power, should it set a high entry fee and low usage fee, or vice versa? To solve this problem, we need to understand the basic principles involved. SINGLE CONSUMER Let’s begin with the artificial but simple case illustrated in Figure 11.9. Suppose there is only one consumer in the market (or many consumers with identical demand curves). Suppose also that the firm knows this consumer’s demand curve. Now, remember that the firm wants to capture as much consumer surplus as possible. In this case, the solution is straightforward: Set the usage fee P equal to marginal cost and the entry fee T equal to the total consumer surplus for each consumer. Thus, the consumer pays T* (or a bit less) to use the product, and P* MC per unit consumed. With the fees set in this way, the firm captures all the consumer surplus as its profit. T* $/Q P* FIGURE 11.9 TWO-PART TARIFF WITH A SINGLE CONSUMER The consumer has demand curve D. The firm maximizes profit by setting usage fee P equal to marginal cost and entry fee T* equal to the entire surplus of the consumer. MC D Quantity 12This pricing strategy was first analyzed by Walter Oi, “A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly,” Quarterly Journal of Economics (February 1971): 77–96. $/Q A P* B T* C CHAPTER 11 • Pricing with Market Power 415 FIGURE 11.10 TWO-PART TARIFF WITH TWO CONSUMERS The profit-maximizing usage fee P* will exceed marginal cost. The entry fee T* is equal to the surplus of the consumer with the smaller demand. The resulting profit is 2T* (P* − MC)(Q1 Q2). Note that this profit is larger than twice the area of triangle ABC. MC D1 D2 Q2 Q1 Quantity TWO CONSUMERS Now suppose that there are two different consumers (or two groups of identical consumers). The firm, however, can set only one entry fee and one usage fee. It would thus no longer want to set the usage fee equal to marginal cost. If it did, it could make the entry fee no larger than the consumer surplus of the consumer with the smaller demand (or else it would lose that consumer), and this would not yield a maximum profit. Instead, the firm should set the usage fee above marginal cost and then set the entry fee equal to the remaining consumer surplus of the consumer with the smaller demand. Figure 11.10 illustrates this. With the optimal usage fee at P* greater than MC, the firm’s profit is 2T* (P* − MC)(Q1 Q2). (There are two consumers, and each pays T*.) You can verify that this profit is more than twice the area of triangle ABC, the consumer surplus of the consumer with the smaller demand when P MC. To determine the exact values of P* and T*, the firm would need to know (in addition to its marginal cost) the demand curves D1 and D2. It would then write down its profit as a function of P and T and choose the two prices that maximize this function. (See Exercise 10 for an example of how to do this.) MANY CONSUMERS Most firms, however, face a variety of consumers with different demands. Unfortunately, there is no simple formula to calculate the optimal two-part tariff in this case, and some trial-and-error experiments might be required. But there is always a trade-off: A lower entry fee means more entrants and thus more profit from sales of the item. On the other hand, as the entry fee becomes smaller and the number of entrants larger, the profit derived from the entry fee will fall. The problem, then, is to pick an entry fee that results in the optimum number of entrants—that is, the fee that allows for maximum profit. In principle, we can do this by starting with a price for sales of the item P, finding the optimum entry fee T, and then estimating the resulting profit. The price P is then changed, and the corresponding entry fee calculated, along with the new profit level. By iterating this way, we can approach the optimal two-part tariff. 416 PART 3 • Market Structure and Competitive Strategy Profit FIGURE 11.11 TWO-PART TARIFF WITH MANY DIFFERENT CONSUMERS Total profit p is the sum of the profit from the entry fee p a and p a and the profit from sales p s depend on T, the entry fee. Therefore s. Both (T)T + (P - MC)Q(n) where n is the number of entrants, which depends on the entry fee T, and Q is the rate of sales, which is greater the larger is n. Here T* is the profit-maximizing entry fee, given P. To calculate optimum values for P and T, we can start with a number for P, find the optimum T, and then estimate the resulting profit. P is then changed and the corresponding T recalculated, along with the new profit level. Total a s T* T Figure 11.11 illustrates this principle. The firm’s profit p is divided into two components, each of which is plotted as a function of the entry fee T, assuming a fixed sales price P. The first component, p a, is the profit from the entry fee and is equal to the revenue n(T)T, where n(T) is the number of entrants. (Note that a high T implies a small n.) Initially, as T is increased from zero, revenue n(T)T rises. Eventually, however, further increases in T will make n so small that n(T)T falls. The second component, p s, is the profit from sales of the item itself at price P and is equal to (P − MC)Q, where Q is the rate at which entrants purchase the item. The larger the number of entrants n, the larger Q will be. Thus p s falls when T is increased because a higher T reduces n. Starting with a number for P, we determine the optimal (profit-maximizing) T*. We then change P, find a new T*, and determine whether profit is now higher or lower. This procedure is repeated until profit has been maximized. Obviously, more data are needed to design an optimal two-part tariff than to choose a single price. Knowing marginal cost and the aggregate demand curve is not enough. It is impossible (in most cases) to determine the demand curve of every consumer, but one would at least like to know by how much individual demands differ from one another. If consumers’ demands for your product are fairly similar, you would want to charge a price P that is close to marginal cost and make the entry fee T large. This is the ideal situation from the firm’s point of view because most of the consumer surplus could then be captured. On the other hand, if consumers have different demands for your product, you would probably want to set P well above marginal cost and charge a lower entry fee T. In that case, however, the two-part tariff is a less effective means of capturing consumer surplus; setting a single price may do almost as well. At Disneyland in California and Walt Disney World in Florida, the strategy is to charge a high entry fee and charge nothing for the rides. This policy makes sense because consumers have reasonably similar demands for Disney vacations. Most people visiting the parks plan daily budgets (including expenditures for food and beverages) that, for most consumers, do not differ very much. CHAPTER 11 • Pricing with Market Power 417 Firms are perpetually searching for innovative pricing strategies, and a few have devised and introduced a two-part tariff with a “twist”—the entry fee T entitles the customer to a certain number of free units. For example, if you buy a Gillette razor, several blades are usually included in the package. The monthly lease fee for a mainframe computer usually includes s |
ome free usage before usage is charged. This twist lets the firm set a higher entry fee T without losing as many small customers. Because these small customers might pay little or nothing for usage under this scheme, the higher entry fee will capture their surplus without driving them out of the market, while also capturing more of the surplus of the large customers. EXAM PLE 11.4 PRICING CELLULAR PHONE SERVICE Most telephone service is priced using a two-part tariff: a monthly access fee, which may include some free minutes, plus a per-minute charge for additional minutes. This is also true for cellular phone service, which has grown explosively, both in the United States and around the world. In the case of cellular service, providers have taken the two-part tariff and turned it into an art form. In most parts of the United States, consumers can choose among four national network providers— Verizon, T-Mobile, AT&T, and Sprint. These providers compete among themselves for customers, but each has some market power. This market power arises in part from oligopolistic pricing and output decisions, as we will explain in Chapters 12 and 13. Market power also arises because consumers face switching costs: When they sign up for a cellular plan, they must typically make a commitment to stay for at least one year, and breaking the contract is quite expensive. Most service providers impose a penalty upwards of $200 for early termination. Because providers have market power, they must think carefully about profit-maximizing pricing strategies. The two-part tariff provides an ideal means by which cellular providers can capture consumer surplus and turn it into profit. Table 11.3 shows cellular rate plans (for 2011) offered by Verizon Wireless, Sprint, and AT&T, as well as Orange (a subsidiary of France Telecom that operates in several countries) and China Mobile. Note that all of these cellular providers give consumers a choice of alternative two-part tariffs, and the plans are structured in similar ways. Let’s focus on the Verizon plans. The least expensive Verizon plan has a monthly access charge of $39.99 and includes 450 “anytime” minutes (i.e., 450 minutes of talk time per month that can be used at any hour of the day). The plan also includes an unlimited amount of talk time during nights and weekends (periods when demand is generally lower). A subscriber who uses more than the 450 “anytime” minutes is charged $0.45 for each additional minute. A customer who uses her cell phone more frequently could sign up for a more expensive plan, e.g., one that costs $59.99 per month but includes 900 “anytime” minutes and a charge of $0.40 for additional minutes. And if you, the reader, use your cell phone constantly (and thus have time for little else), you could sign up for a plan that includes unlimited “anytime” minutes, at a monthly cost of $69.99. Why do cellular phone providers offer several different types of plans and options within each? Why don’t they simply offer a single two-part tariff with a monthly access charge and a per-minute usage charge? Offering several different plans and options allows companies to combine thirddegree price discrimination with the two-part tariff. The plans are structured so that consumers sort themselves into groups based on their plan choices. A different two-part tariff is then applied to each group. 418 PART 3 • Market Structure and Competitive Strategy TABLE 11.3 CELLULAR RATE PLANS (2011) ANYTIME MINUTES MONTHLY ACCESS CHARGES NIGHT & WEEKEND MINUTES PER-MINUTE RATE AFTER ALLOWANCE A. VERIZON: AMERICA’S CHOICE BASIC 450 900 Unlimited $39.99 $59.99 $69.99 Unlimited Unlimited Unlimited 200 450 900 450 900 Unlimited 100 200 300 None 100 400 150 450 800 1200 1800 B. SPRINT: BASIC TALK PLANS $29.99 $39.99 $59.99 Unlimited Unlimited Unlimited C. AT&T INDIVIDUAL PLANS $39.99 $59.99 $69.99 £10.00 £15.00 £20.00 28.00 NIS 38.00 NIS 61.90 NIS 58 RMB 158 RMB 258 RMB 358 RMB 458 RMB 5000 Unlimited Unlimited D. ORANGE (UK) None None None E. ORANGE (ISRAEL) None None None F. CHINA MOBILE None None None None None $0.45 $0.40 Included $0.45 $0.45 $0.40 $0.45 $0.40 Included 25 pence 25 pence 25 pence 0.59 NIS 0.59 NIS 0.59 NIS 0.40 RMB 0.35 RMB 0.32 RMB 0.30 RMB 0.25 RMB To convert the international prices to U.S. dollars (as of August 2011), use the following conversion factors: 1£ $1.60, 1 NIS $0.30, and 1 RMB $0.13. Data from various cellular providers. To see how this sorting works, consider the plan choices of different types of consumers. People who use a cell phone only occasionally will want to spend as little as possible on the service and will choose the least expensive plan (with the fewest “anytime” minutes). The most expensive plans are best suited to very heavy users (perhaps a salesperson who travels extensively and makes call throughout the day), who will want to minimize their per-minute cost. Other plans are better suited to consumers with moderate calling needs. Consumers will choose a plan that best matches their needs. Thus they will sort themselves into CHAPTER 11 • Pricing with Market Power 419 groups, and the consumers in each group will be relatively homogeneous in terms of demands for cellular service. Remember that the two-part tariff works best when consumers have identical or very similar demands. (Recall from Figure 11.9 that with identical consumers, the two-part tariff can be used to capture all consumer surplus.) Creating a situation in which consumers sort themselves into groups in this way makes best use of the two-part tariff. • bundling Practice of selling two or more products as a package. *11.5 Bundling You have probably seen the 1939 film Gone with the Wind. It is a classic that is nearly as popular now as it was then.13 Yet we would guess that you have not seen Getting Gertie’s Garter, a flop that the same company (MGM, a division of Loews) also distributed. And we would also guess that you did not know that these two films were priced in what was then an unusual and innovative way.14 Movie theaters that leased Gone with the Wind also had to lease Getting Gertie’s Garter. (Movie theaters pay the film companies or their distributors a daily or weekly fee for the films they lease.) In other words, these two films were bundled—i.e., sold as a package.15 Why would the film company do this? You might think that the answer is obvious: Gone with the Wind was a great film and Gertie was a lousy film, so bundling the two forced movie theaters to lease Gertie. But this answer doesn’t make economic sense. Suppose a theater’s reservation price (the maximum price it will pay) for Gone with the Wind is $12,000 per week, and its reservation price for Gertie is $3000 per week. Then the most it would pay for both films is $15,000, whether it takes the films individually or as a package. Bundling makes sense when customers have heterogeneous demands and when the firm cannot price discriminate. With films, different movie theaters serve different groups of patrons and therefore different theaters may face different demands for films. For example, different theaters might appeal to different age groups, who in turn have different relative film preferences. To see how a film company can use customer heterogeneity to its advantage, suppose that there are two movie theaters and that their reservation prices for our two films are as follows: GONE WITH THE WIND GETTING GERTIE’S GARTER Theater A Theater B $12,000 $10,000 $3000 $4000 13Adjusted for inflation, Gone with the Wind was also the largest grossing film of all time. Titanic, released in 1997, made $601 million. Gone with the Wind grossed $81.5 million in 1939 dollars, which is equivalent to $941 million in 1997 dollars. 14For those readers who claim to know all this, our final trivia question is: Who played the role of Gertie in Getting Gertie’s Garter? 15The major Hollywood studios were forced to stop bundling their films in 1948, when the Supreme Court decided that the studios were acting in violation of antitrust laws by forcing theaters to buy their films on an all-or-nothing basis. In addition, the studios were forced to sell their theater chains, ending decades of monopolistic vertical integration that had made the studios economic powerhouses. 420 PART 3 • Market Structure and Competitive Strategy If the films are rented separately, the maximum price that could be charged for Wind is $10,000 because charging more would exclude Theater B. Similarly, the maximum price that could be charged for Gertie is $3000. Charging these two prices would yield $13,000 from each theater, for a total of $26,000 in revenue. But suppose the films are bundled. Theater A values the pair of films at $15,000 ($12,000 $3000), and Theater B values the pair at $14,000 ($10,000 $4000). Therefore, we can charge each theater $14,000 for the pair of films and earn a total revenue of $28,000. Clearly, we can earn more revenue ($2000 more) by bundling the films. Relative Valuations Why is bundling more profitable than selling the films separately? Because (in this example) the relative valuations of the two films are reversed. In other words, although both theaters would pay much more for Wind than for Gertie, Theater A would pay more than Theater B for Wind ($12,000 vs. $10,000), while Theater B would pay more than Theater A for Gertie ($4000 vs. $3000). In technical terms, we say that the demands are negatively correlated—the customer willing to pay the most for Wind is willing to pay the least for Gertie. To see why this is critical, suppose demands were positively correlated—that is, Theater A would pay more for both films: GONE WITH THE WIND GETTING GERTIE’S GARTER Theater A Theater B $12,000 $10,000 $4000 $3000 The most that Theater A would pay for the pair of films is now $16,000, but the most that Theater B would pay is only $13,000. Thus if we bundled the films, the maximum price that could be charged for the package is $13,000, yielding a to |
tal revenue of $26,000, the same as by renting the films separately. Now, suppose a firm is selling two different goods to many consumers. To analyze the possible advantages of bundling, we will use a simple diagram to describe the preferences of the consumers in terms of their reservation prices and their consumption decisions given the prices charged. In Figure 11.12 the horizontal axis is r1, which is the reservation price of a consumer for good 1, and FIGURE 11.12 RESERVATION PRICES Reservation prices r1 and r2 for two goods are shown for three consumers, labeled A, B, and C. Consumer A is willing to pay up to $3.25 for good 1 and up to $6 for good 2. r2 $10 $6 $5 $3.25 C A B $3.25 $5 $8.25 $10 r1 r2 P2 II I Consumers buy only good 2 Consumers buy both goods III IV Consumers buy neither good Consumers buy only good 1 P1 r1 CHAPTER 11 • Pricing with Market Power 421 FIGURE 11.13 CONSUMPTION DECISIONS WHEN PRODUCTS ARE SOLD SEPARATELY The reservation prices of consumers in region I exceed the prices P1 and P2 for the two goods, so these consumers buy both goods. Consumers in regions II and IV buy only one of the goods, and consumers in region III buy neither good. the vertical axis is r2, which is the reservation price for good 2. The figure shows the reservation prices for three consumers. Consumer A is willing to pay up to $3.25 for good 1 and up to $6 for good 2; consumer B is willing to pay up to $8.25 for good 1 and up to $3.25 for good 2; and consumer C is willing to pay up to $10 for each of the goods. In general, the reservation prices for any number of consumers can be plotted this way. Suppose that there are many consumers and that the products are sold separately, at prices P1 and P2, respectively. Figure 11.13 shows how consumers can be divided into groups. Consumers in region I of the graph have reservation prices that are above the prices being charged for each of the goods, so they will buy both goods. Consumers in region II have a reservation price for good 2 that is above P2, but a reservation price for good 1 that is below P1; they will buy only good 2. Similarly, consumers in region IV will buy only good 1. Finally, consumers in region III have reservation prices below the prices charged for each of the goods, and so will buy neither. Now suppose the goods are sold only as a bundle, for a total price of PB. We can then divide the graph into two regions, as in Figure 11.14. Any given r2 PB I Consumers buy bundle r2 = PB – r1 II Consumers do not buy bundle PB r1 FIGURE 11.14 CONSUMPTION DECISIONS WHEN PRODUCTS ARE BUNDLED Consumers compare the sum of their reservation prices r1 + r2, with the price of the bundle PB. They buy the bundle only if r1 + r2 is at least as large as PB. 422 PART 3 • Market Structure and Competitive Strategy consumer will buy the bundle only if its price is less than or equal to the sum of that consumer’s reservation prices for the two goods. The dividing line is therefore the equation PB r1 r2 or, equivalently, r2 PB − r1. Consumers in region I have reservation prices that add up to more than PB, so they will buy the bundle. Consumers in region II, who have reservation prices that add up to less than PB, will not buy the bundle. Depending on the prices, some of the consumers in region II of Figure 11.14 might have bought one of the goods if they had been sold separately. These consumers are lost to the firm, however, when it sells the goods only as a bundle. The firm, then, must determine whether it can do better by bundling. In general, the effectiveness of bundling depends on the extent to which demands are negatively correlated. In other words, it works best when consumers who have a high reservation price for good 1 have a low reservation price for good 2, and vice versa. Figure 11.15 shows two extremes. In part (a), each point represents the two reservation prices of a consumer. Note that the demands for the two goods are perfectly positively correlated—consumers with a high reservation price for good 1 also have a high reservation price for good 2. If the firm bundles and charges a price PB P1 P2, it will make the same profit that it would make by selling the goods separately at prices P1 and P2. In part (b), on the other hand, demands are perfectly negatively correlated—a higher reservation price for good 2 implies a proportionately lower one for good 1. In this case, bundling is the ideal strategy. By charging the price PB the firm can capture all the consumer surplus. Figure 11.16, which shows the movie example that we introduced at the beginning of this section, illustrates how the demands of the two movie theaters are negatively correlated. (Theater A will pay relatively more for Gone with the r2 PB r2 P2 P1 (a) r1 PB r1 (b) FIGURE 11.15 RESERVATION PRICES In (a), because demands are perfectly positively correlated, the firm does not gain by bundling: It would earn the same profit by selling the goods separately. In (b), demands are perfectly negatively correlated. Bundling is the ideal strategy—all the consumer surplus can be extracted. (Gertie) r2 $10,000 5000 4000 3000 CHAPTER 11 • Pricing with Market Power 423 FIGURE 11.16 MOVIE EXAMPLE Consumers A and B are two movie theaters. The diagram shows their reservation prices for the films Gone with the Wind and Getting Gertie’s Garter. Because the demands are negatively correlated, bundling pays. B A $5000 10,000 12,000 14,000 r1 (Wind) Wind, but Theater B will pay relatively more for Getting Gertie’s Garter.) This makes it more profitable to rent the films as a bundle priced at $14,000. Mixed Bundling So far, we have assumed that the firm has two options: to sell the goods either separately or as a bundle. But there is a third option, called mixed bundling. As the name suggests, the firm offers its products both separately and as a bundle, with a package price below the sum of the individual prices. (We use the term pure bundling to refer to the strategy of selling the products only as a bundle.) Mixed bundling is often the ideal strategy when demands are only somewhat negatively correlated and/or when marginal production costs are significant. (Thus far, we have assumed that marginal production costs are zero.) In Figure 11.17, mixed bundling is the most profitable strategy. Although demands are perfectly negatively correlated, there are significant marginal costs. (The marginal cost of producing good 1 is $20, and the marginal cost of producing good 2 is $30.) We have four consumers, labeled A through D. Now, let’s compare three strategies: 1. Selling the goods separately at prices P1 $50 and P2 $90 2. Selling the goods only as a bundle at a price of $100 3. Mixed bundling, whereby the goods are offered separately at prices P1 P2 $89.95, or as a bundle at a price of $100. Table 11.4 shows these three strategies and the resulting profits. (You can try other prices for P1, P2, and PB to verify that those given in the table maximize profit for each strategy.) When the goods are sold separately, only consumers B, C, and D buy good 1, and only consumer A buys good 2; total profit is 3($50 − $20) 1($90 − $30) $150. With pure bundling, all four consumers buy the bundle for $100, so that total profit is 4($100 − $20 − $30) $200. As we should expect, pure bundling is better than selling the goods separately because consumers’ demands are negatively correlated. But what about mixed bundling? • mixed bundling Selling two or more goods both as a package and individually. • pure bundling Selling products only as a package. 424 PART 3 • Market Structure and Competitive Strategy c1 $20 A FIGURE 11.17 MIXED VERSUS PURE BUNDLING With positive marginal costs, mixed bundling may be more profitable than pure bundling. Consumer A has a reservation price for good 1 that is below marginal cost c1, and consumer D has a reservation price for good 2 that is below marginal cost c2. With mixed bundling, consumer A is induced to buy only good 2, and consumer D is induced to buy only good 1, thus reducing the firm’s cost. r2 $100 90 80 70 60 50 40 30 20 10 B C c2 $30 D $10 20 30 40 50 60 70 80 90 100 r1 Consumer D buys only good 1 for $89.95, consumer A buys only good 2 for $89.95, and consumers B and C buy the bundle for $100. Total profit is now ($89.95 − $20) ($89.95 − $30) 2($100 − $20 − $30) $229.90.16 In this case, mixed bundling is the most profitable strategy, even though demands are perfectly negatively correlated (i.e., all four consumers have reservation prices on the line r2 100 − r1). Why? For each good, marginal production cost exceeds the reservation price of one consumer. For example, consumer A has a reservation price of $90 for good 2 but a reservation price of only $10 for good 1. Because the cost of producing a unit of good 1 is $20, the firm would prefer that consumer A buy only good 2, not the bundle. It can achieve this goal by offering good 2 separately for a price just below consumer A’s reservation price, while also offering the bundle at a price acceptable to consumers B and C. Mixed bundling would not be the preferred strategy in this example if marginal costs were zero: In that case, there would be no benefit in excluding TABLE 11.4 BUNDLING EXAMPLE Sold separately Pure bundling P1 $50 — P2 $90 — Mixed bundling $89.95 $89.95 PB — $100 $100 PROFIT $150 $200 $229.90 16Note that in the mixed bundling strategy, goods 1 and 2 are priced at $89.95 rather than at $90. If they were priced at $90, consumers A and D would be indifferent between buying a single good and buying the bundle, and if they buy the bundle, total profit will be lower. r2 $120 100 90 80 60 40 20 10 A B C D CHAPTER 11 • Pricing with Market Power 425 FIGURE 11.18 MIXED BUNDLING WITH ZERO MARGINAL COSTS If marginal costs are zero, and if consumers’ demands are not perfectly negatively correlated, mixed bundling is still more profitable than pure bundling. In this example, consumers B and C are willing to pay $20 more for the bundle than are c |
onsumers A and D. With pure bundling, the price of the bundle is $100. With mixed bundling, the price of the bundle can be increased to $120 and consumers A and D can still be charged $90 for a single good. $10 20 40 60 80 90 100 120 r1 consumer A from buying good 1 and consumer D from buying good 2. We leave it to you to demonstrate this (see Exercise 12).17 If marginal costs are zero, mixed bundling can still be more profitable than pure bundling if consumers’ demands are not perfectly negatively correlated. (Recall that in Figure 11.17, the reservation prices of the four consumers are perfectly negatively correlated.) This is illustrated by Figure 11.18, in which we have modified the example of Figure 11.17. In Figure 11.18, marginal costs are zero, but the reservation prices for consumers B and C are now higher. Once again, let’s compare three strategies: selling the two goods separately, pure bundling, and mixed bundling. Table 11.5 shows the optimal prices and the resulting profits for each strategy. (Once again, you should try other prices for P1, P2, and PB to verify that those given in the table maximize profit for each strategy.) When the goods are sold separately, only consumers C and D buy good 1, and only consumers A and B buy good 2; total profit is thus $320. With pure bundling, all four TABLE 11.5 MIXED BUNDLING WITH ZERO MARGINAL COSTS Sell separately Pure bundling Mixed bundling P1 $80 — $90 P2 $80 — $90 PB — $100 $120 PROFIT $320 $400 $420 17Sometimes a firm with monopoly power will find it profitable to bundle its product with the product of another firm; see Richard L. Schmalensee, “Commodity Bundling by Single-Product Monopolies,” Journal of Law and Economics 25 (April 1982): 67–71. Bundling can also be profitable when the products are substitutes or complements. See Arthur Lewbel, “Bundling of Substitutes or Complements,” International Journal of Industrial Organization 3 (1985): 101–7. 426 PART 3 • Market Structure and Competitive Strategy consumers buy the bundle for $100, so that total profit is $400. As expected, pure bundling is better than selling the goods separately because consumers’ demands are negatively correlated. But mixed bundling is better still. With mixed bundling, consumer A buys only good 2, consumer D buys only good 1, and consumers B and C buy the bundle at a price of $120. Total profit is now $420. Why does mixed bundling give higher profits than pure bundling even though marginal costs are zero? The reason is that demands are not perfectly negatively correlated: The two consumers who have high demands for both goods (B and C) are willing to pay more for the bundle than are consumers A and D. With mixed bundling, therefore, we can increase the price of the bundle (from $100 to $120), sell this bundle to two consumers, and charge the remaining consumers $90 for a single good. Bundling in Practice Bundling is a widely used pricing strategy. When you buy a new car, for example, you can purchase such options as power windows, power seats, or a sunroof separately, or you can purchase a “luxury package” in which these options are bundled. Manufacturers of luxury cars (such as Lexus, BMW, or Infiniti) tend to include such “options” as standard equipment; this practice is pure bundling. For more moderately priced cars, however, these items are optional, but are usually offered as part of a bundle. Automobile companies must decide which items to include in such bundles and how to price them. Another example is vacation travel. If you plan a vacation to Europe, you might make your own hotel reservations, buy an airplane ticket, and order a rental car. Alternatively, you might buy a vacation package in which airfare, land arrangements, hotels, and even meals are all bundled together. Still another example is cable television. Cable operators typically offer a basic service for a low monthly fee, plus individual “premium” channels, such as Cinemax, Home Box Office, and the Disney Channel, on an individual basis for additional monthly fees. However, they also offer packages in which two or more premium channels are sold as a bundle. Bundling cable channels is profitable because demands are negatively correlated. How do we know that? Given that there are only 24 hours in a day, the time that a consumer spends watching HBO is time that cannot be spent watching the Disney Channel. Thus consumers with high reservation prices for some channels will have relatively low reservation prices for others. How can a company decide whether to bundle its products, and determine the profit-maximizing prices? Most companies do not know their customers’ reservation prices. However, by conducting market surveys, they may be able to estimate the distribution of reservation prices, and then use this information to design a pricing strategy. This is illustrated in Figure 11.19. The dots are estimates of reservation prices or a representative sample of consumers (obtained, say, from a market survey). The company might first choose a price for the bundle, PB, such that a diagonal line connecting these prices passes roughly midway through the dots in the figure. It could then try individual prices P1 and P2. Given P1, P2, and PB, we can separate consumers into four regions, as shown in the figure. Consumers in Region I buy nothing (because r1 < P1, r2 < P2, and r1 r2 < PB). Consumers in Region II buy the bundle (because r1 r2> PB). Consumers in Region III buy only good 2 (because r2> P2 but r1 < PB − P2). Likewise, consumers in Region IV buy only good 1. Given this distribution, we can calculate the resulting profits. We III—Buy Only Good 2 r2 PB P2 I—Buy Nothing CHAPTER 11 • Pricing with Market Power 427 FIGURE 11.19 MIXED BUNDLING IN PRACTICE The dots in this figure are estimates of reservation prices for a representative sample of consumers. A company could first choose a price for the bundle, PB, such that a diagonal line connecting these prices passes roughly midway through the dots. The company could then try individual prices P1 and P2. Given P1, P2, and PB, profits can be calculated for this sample of consumers. Managers can then raise or lower P1, P2, and PB and see whether the new pricing leads to higher profits. This procedure is repeated until total profit is roughly maximized. II—Buy Bundle IV—Buy Only Good 1 P1 PB r1 can then raise or lower P1, P2, and PB and see whether doing so leads to higher profits. This can be done repeatedly (on a computer) until prices are found that roughly maximize total profit. EXAM PLE 11.5 THE COMPLETE DINNER VERSUS À LA CARTE: A RESTAURANT’S PRICING PROBLEM Many restaurants offer both complete dinners and à la carte menus. Why? Most customers go out to eat knowing roughly how much they are willing to spend for dinner (and choose the restaurant accordingly). Diners, however, have different preferences. For example, some value appetizers highly but could happily skip dessert. Others attach little value to the appetizer but regard dessert as essential. And some customers attach moderate values to both appetizers and desserts. What pricing strategy lets the restaurant capture as much consumer surplus as possible from these heterogeneous customers? The answer, of course, is mixed bundling. For a restaurant, mixed bundling means offering both complete dinners (the appetizer, main course, and dessert come as a package) and an à la carte menu (the customer buys the appetizer, main course, and dessert separately). This strategy allows the à la carte menu to be priced to capture consumer surplus from customers who value some dishes much more highly than others. (Such customers would correspond to consumers A and D in Figure 11.17 (page 424).) At the same time, the complete dinner retains those customers who have lower variations in their reservation prices for different dishes (e.g., customers who attach moderate values to both appetizers and desserts). For example, if the restaurant expects to attract customers willing to spend about $20 for dinner, it might charge about $5 for appetizers, $14 for a typical main dish, and $4 for dessert. It could also offer a complete dinner, which includes an appetizer, 428 PART 3 • Market Structure and Competitive Strategy main course, and dessert, for $20. Then, the customer who loves dessert but couldn’t care less about an appetizer will order only the main dish and dessert, and spend $18 (saving the restaurant the cost of preparing an appetizer). At the same time, another customer who attaches a moderate value (say, $3 or $3.50) to both the appetizer and dessert will buy the complete dinner. You don’t have to go an expensive French restaurant to experience mixed bundling. Table 11.6 shows the prices of some individual items at McDonald’s, as well as the prices of “super meals” that include meat or fish items along with a large order of French fries and a large soda. Note that you can buy a Big Mac, a large fries, and a large soda separately for a total of $9.27, or you can buy them as a bundle for $6.99. You say you don’t care for fries? Then just buy the Big Mac and large soda separately, for a total of $6.68, which is $0.31 less than the price of the bundle. Unfortunately for consumers, perhaps, creative pricing is sometimes more important than creative cooking for the financial success of a restaurant. Successful restaurateurs know their customers’ demand characteristics and use that knowledge to design a pricing strategy that extracts as much consumer surplus as possible. TABLE 11.6 MIXED BUNDLING AT MCDONALD’S (2011) INDIVIDUAL ITEM Chicken Sandwich Filet-O-Fish Big Mac Quarter Pounder Double Quarter Pounder 10-piece Chicken McNuggets Large French Fries Large Soda PRICE $5.49 $4.39 $4.69 $4.69 $6.09 $5.19 $2.59 $1.99 Data from McDonald’s restaurant menu. MEAL (INCLUDES SODA AND FRIES) UNBUNDLED PRICE PRICE OF BUNDLE SAVINGS Chicken Sandwich Filet-O-Fish Big Mac Quarter Pounder Double Quarter Pounder 10-piece Chicken McNugg |
ets $10.07 $8.97 $9.27 $9.27 $10.67 $9.77 $7.89 $6.79 $6.99 $7.19 $8.39 $7.59 $2.18 $2.18 $2.28 $2.08 $2.28 $2.18 • tying Practice of requiring a customer to purchase one good in order to purchase another. Tying Tying is a general term that refers to any requirement that products be bought or sold in some combination. Pure bundling is a common form of tying, but tying can also take other forms. For example, suppose a firm sells a product (such as a copying machine) that requires the consumption of a secondary product (such as paper). The consumer who buys the first product is also required to buy the secondary product from the same company. This requirement is usually imposed through a contract. Note that this is different from the examples of bundling discussed earlier. In those examples, the consumer might have been happy to buy just one of the products. In this case, however, the first product is useless without access to the secondary product. Why might firms use this kind of pricing practice? One of the main benefits of tying is that it often allows a firm to meter demand and thereby practice price discrimination more effectively. During the 1950s, for example, when Xerox had a monopoly on copying machines but not on paper, customers who leased Xerox CHAPTER 11 • Pricing with Market Power 429 copiers also had to buy Xerox paper. This allowed Xerox to meter consumption (customers who used a machine intensively bought more paper), and thereby apply a two-part tariff to the pricing of its machines. Also during the 1950s, IBM required customers who leased its mainframe computers to use paper computer cards made only by IBM. By pricing cards well above marginal cost, IBM was effectively charging higher prices for computer usage to customers with larger demands.18 Tying can also be used to extend a firm’s market power. As we discussed in Example 10.8 (page 394), in 1998 the Department of Justice brought suit against Microsoft, claiming that the company had tied its Internet Explorer Web browser to its Windows 98 operating system in order to maintain its monopoly power in the market for PC operating systems. Tying can have other uses. An important one is to protect customer goodwill connected with a brand name. This is why franchises are often required to purchase inputs from the franchiser. For example, Mobil Oil requires its service stations to sell only Mobil motor oil, Mobil batteries, and so on. Similarly, until recently, a McDonald’s franchisee had to purchase all materials and supplies— from the hamburgers to the paper cups—from McDonald’s, thus ensuring product uniformity and protecting the brand name.19 *11.6 Advertising We have seen how firms can utilize their market power when making pricing decisions. Pricing is important for a firm, but most firms with market power have another important decision to make: how much to advertise. In this section, we will see how firms with market power can make profit-maximizing advertising decisions, and how those decisions depend on the characteristics of demand for the firm’s product.20 For simplicity, we will assume that the firm sets only one price for its product. We will also assume that having done sufficient market research, it knows how its quantity demanded depends on both its price P and its advertising expenditures in dollars A; that is, it knows Q(P, A). Figure 11.20 shows the firm’s demand and cost curves with and without advertising. AR and MR are the firm’s average and marginal revenue curves when it does not advertise, and AC and MC are its average and marginal cost curves. It produces a quantity Q0, where MR MC, and receives a price P0. Its profit per unit is the difference between P0 and average cost, so its total profit p 0 is given by the gray-shaded rectangle. Now suppose the firm advertises. This causes its demand curve to shift out and to the right; the new average and marginal revenue curves are given by AR and MR. Advertising is a fixed cost, so the firm’s average cost curve rises (to AC). Marginal cost, however, remains the same. With advertising, the firm produces Q1 (where MR MC) and receives a price P1. Its total profit p 1, given by the purple-shaded rectangle, is now much larger. 18Antitrust actions ultimately forced IBM to discontinue this pricing practice. 19In some cases, the courts have ruled that tying is not necessary to protect customer goodwill and is anticompetitive. Today, a McDonald’s franchisee can buy supplies from any McDonald’s-approved source. For a discussion of some of the antitrust issues involved in franchise tying, see Benjamin Klein and Lester F. Saft, “The Law and Economics of Franchise Tying Contracts,” Journal of Law and Economics 28 (May 1985): 345–61. 20A perfectly competitive firm has little reason to advertise: By definition it can sell as much as it produces at a market price that it takes as given. That is why it would be unusual to see a producer of corn or soybeans advertise. In §7.1, marginal cost—the increase in cost that results from producing one extra unit of output—is distinguished from average cost— the cost per unit of output. 430 PART 3 • Market Structure and Competitive Strategy $/Q P1 P0 π 0 π 1 MC AR′ AC ′ AC MR ′ AR MR Q0 Q1 Quantity FIGURE 11.20 EFFECTS OF ADVERTISING AR and MR are average and marginal revenue when the firm doesn’t advertise, and AC and MC are average and marginal cost. The firm produces Q0 and receives a price P0. Its total profit p 0 is given by the gray-shaded rectangle. If the firm advertises, its average and marginal revenue curves shift to the right. Average cost rises (to AC) but marginal cost remains the same. The firm now produces Q1 (where MR = MC), and receives a price P1. Its total profit, p 1, is now larger. Although the firm in Figure 11.20 is clearly better off when it advertises, the figure does not help us determine how much advertising it should do. It must choose its price P and advertising expenditure A to maximize profit, which is now given by: p = PQ(P, A) - C(Q) - A Given a price, more advertising will result in more sales and thus more revenue. But what is the firm’s profit-maximizing advertising expenditure? You might be tempted to say that the firm should increase its advertising expenditures until the last dollar of advertising just brings forth an additional dollar of revenue—that is, until the marginal revenue from advertising, (PQ)/A, is just equal to 1. But as Figure 11.20 shows, this reasoning omits an important element. Remember that advertising leads to increased output (in the figure, output increased from Q0 to Q1). But increased output in turn means increased production costs, and this must be taken into account when comparing the costs and benefits of an extra dollar of advertising. The correct decision is to increase advertising until the marginal revenue from an additional dollar of advertising, MRAds, just equals the full marginal CHAPTER 11 • Pricing with Market Power 431 cost of that advertising. That full marginal cost is the sum of the dollar spent directly on the advertising and the marginal production cost resulting from the increased sales that advertising brings about. Thus the firm should advertise up to the point that MRAds = P Q A = 1 + MC Q A (11.3) = full marginal cost of advertising This rule is often ignored by managers, who justify advertising budgets by comparing the expected benefits (i.e., added sales) only with the cost of the advertising. But additional sales mean increased production costs that must also be taken into account.21 A Rule of Thumb for Advertising Like the rule MR = MC, equation (11.3) is sometimes difficult to apply in practice. In Chapter 10, we saw that MR MC implies the following rule of thumb for pricing: (P − MC)/P −1/ED, where ED is the firm’s price elasticity of demand. We can combine this rule of thumb for pricing with equation (11.3) to obtain a rule of thumb for advertising. First, rewrite equation (11.3) as follows: (P - MC) Q A = 1 Now multiply both sides of this equation by A/PQ, the advertising-to-sales ratio: P - MC P c A Q Q A d = A PQ In equation (10.1), we offer a rule of thumb for pricing for a profit-maximizing firm—the markup over marginal cost as a percentage of price should equal minus the inverse of the price elasticity of demand. • advertising-to-sales ratio Ratio of a firm’s advertising expenditures to its sales. The term in brackets, (A/Q)(Q/A), is the advertising elasticity of demand, the percentage change in the quantity demanded that results from a 1-percent increase in advertising expenditures. We will denote this elasticity by EA. Because (P − MC)/P must equal −1/EP, we can rewrite this equation as follows: • advertising elasticity of demand Percentage change in quantity demanded resulting from a 1-percent increase in advertising expenditures. A/PQ = -(EA/EP) (11.4) Equation (11.4) is a rule of thumb for advertising. It says that to maximize profit, the firm’s advertising-to-sales ratio should be equal to minus the ratio of 21To derive this result using calculus, differentiate p(Q,A) with respect to A, and set the derivative equal to zero: 0p/0A = P(0Q/0A) - MC(0Q/0A) - 1 = 0 Rearranging gives equation (11.3). 432 PART 3 • Market Structure and Competitive Strategy the advertising and price elasticities of demand. Given information (from, say, market research studies) on these two elasticities, the firm can use this rule to check that its advertising budget is not too small or too large. To put this rule into perspective, assume that a firm is generating sales revenue of $1 million per year while allocating only $10,000 (1 percent of its revenues) to advertising. The firm knows that its advertising elasticity of demand is .2, so that a doubling of its advertising budget from $10,000 to $20,000 should increase sales by 20 percent. The firm also knows that the price elasticity of demand for its product is −4. Should it increase its advertising budget, knowing that wit |
h a price elasticity of demand of −4, its markup of price over marginal cost is substantial? The answer is yes; equation (11.4) tells us that the firm’s advertising-to-sales ratio should be −(.2/−4) = 5 percent, so the firm should increase its advertising budget from $10,000 to $50,000. This rule makes intuitive sense. It says firms should advertise a lot if (i) demand is very sensitive to advertising (EA is large), or if (ii) demand is not very price elastic (EP is small). Although (i) is obvious, why should firms advertise more when the price elasticity of demand is small? A small elasticity of demand implies a large markup of price over marginal cost. Therefore, the marginal profit from each extra unit sold is high. In this case, if advertising can help sell a few more units, it will be worth its cost.22 E XAM PLE 11.6 ADVERTISING IN PRACTICE In Example 10.2 (page 370), we looked at the use of markup pricing by supermarkets, convenience stores, and makers of designer jeans. We saw in each case how the markup of price over marginal cost depended on the firm’s price elasticity of demand. Now let’s see why these firms, as well as producers of other goods, advertise as much (or as little) as they do. First, supermarkets. We said that the price elasticity of demand for a typical supermarket is around −10. To determine the advertising-to-sales ratio, we also need to know the advertising elasticity of demand. This number can vary considerably depending on what part of the country the supermarket is located in and whether it is in a city, suburb, or rural area. A reasonable range, however, would be 0.1 to 0.3. Substituting these numbers into equation (11.4), we find that the manager of a typical supermarket should have an advertising budget of around 1 to 3 percent of sales—which is indeed what many supermarkets spend on advertising. Convenience stores have lower price elasticities of demand (around −5), but their advertising-to-sales ratios are usually less than those for supermarkets (and are often zero). Why? Because convenience stores mostly serve customers who live nearby; they may need a few items late at night or may simply not want to drive to the supermarket. These customers already know about the convenience store and are unlikely to change their buying habits if the store 22Advertising often affects the price elasticity of demand, and this fact must be taken into account. For some products, advertising broadens the market by attracting a large range of customers, or by creating a bandwagon effect. This is likely to make demand more price elastic than it would have been otherwise. (But EA is likely to be large, so that advertising will still be worthwhile.) Sometimes advertising is used to differentiate a product from others (by creating an image, allure, or brand identification), making the product’s demand less price elastic than it would otherwise be. CHAPTER 11 • Pricing with Market Power 433 advertises. Thus EA is very small, and advertising is not worthwhile. Advertising is quite important for makers of designer jeans, who will have advertising-to-sales ratios as high as 10 or 20 percent. Advertising helps to make consumers aware of the label and gives it an aura and image. We said that price elasticities of demand in the range of −3 to −4 are typical for the major labels, and advertising elasticities of demand can range from .3 to as high as 1. So, these levels of advertising would seem to make sense. Laundry detergents have among the highest advertising-to-sales ratios of all products, sometimes exceeding 30 percent, even though demand for any one brand is at least as price elastic as it is for designer jeans. What justifies all the advertising? A very large advertising elasticity. The demand for any one brand of laundry detergent depends crucially on advertising; without it, consumers would have little basis for selecting that particular brand.23 Finally, Table 11.7 shows sales, advertising expenditures, and the ratio of the two for leading brands of over-the-counter drugs. Observe that overall, the ratios are quite high. As with laundry detergents, the advertising elasticity for name-brand drugs is very high. Alka-Seltzer, Mylanta, and Tums, for instance, are all antacids that do much the same thing. Sales depend on consumer identification with a particular brand, which requires advertising. TABLE 11.7 SALES AND ADVERTISING EXPENDITURES FOR LEADING BRANDS OF OVER-THE-COUNTER DRUGS (IN MILLIONS OF DOLLARS) SALES ADVERTISING RATIO (%) Pain Medications Tylenol Advil Bayer Excedrin Antacids Alka-Seltzer Mylanta Tums 855 360 170 130 160 135 135 Cold Remedies (decongestants) Benadryl Sudafed Cough Medicine Vicks Robitussin Halls 130 115 350 205 130 143.8 91.7 43.8 26.7 52.2 32.8 27.6 30.9 28.6 26.6 37.7 17.4 17 26 26 21 33 24 20 24 25 8 19 13 Data from Milt Freudenheim, “Rearranging Drugstore Shelves,” THE NEW YORK TIMES, September 27, 1994. 23For an overview of statistical approaches to estimating the advertising elasticity of demand, see Ernst R. Berndt, The Practice of Econometrics (Reading, MA: Addison-Wesley, 1991), ch. 8. 434 PART 3 • Market Structure and Competitive Strategy SUMMARY 1. Firms with market power are in an enviable position because they have the potential to earn large profits. Realizing that potential, however, may depend critically on pricing strategy. Even if the firm sets a single price, it needs an estimate of the elasticity of demand for its output. More complicated strategies, which can involve setting several different prices, require even more information about demand. 2. A pricing strategy aims to enlarge the customer base that the firm can sell to and capture as much consumer surplus as possible. There are a number of ways to do this, and they usually involve setting more than a single price. 3. Ideally, the firm would like to price discriminate perfectly—i.e., to charge each customer his or her reservation price. In practice, this is almost always impossible. On the other hand, various forms of imperfect price discrimination are often used to increase profits. 4. The two-part tariff is another means of capturing consumer surplus. Customers must pay an “entry” fee that allows them to buy the good at a per-unit price. The two-part tariff is most effective when customer demands are relatively homogeneous. 5. When demands are heterogeneous and negatively correlated, bundling can increase profits. With pure bundling, two or more different goods are sold only as a package. With mixed bundling, the customer can buy the goods individually or as a package. Mixed bundling can be more profitable than pure bundling if marginal costs are significant or if demands are not perfectly negatively correlated. 6. Bundling is a special case of tying, a requirement that products be bought or sold in some combination. Tying can be used to meter demand or to protect customer goodwill associated with a brand name. 7. Advertising can further increase profits. The profit-maximizing advertising-to-sales ratio is equal in magnitude to the ratio of the advertising and price elasticities of demand. QUESTIONS FOR REVIEW 1. Suppose a firm can practice perfect, first-degree price discrimination. What is the lowest price it will charge, and what will its total output be? 2. How does a car salesperson practice price discrimination? How does the ability to discriminate correctly affect his or her earnings? 3. Electric utilities often practice second-degree price discrimination. Why might this improve consumer welfare? 4. Give some examples of third-degree price discrimination. Can third-degree price discrimination be effective if the different groups of consumers have different levels of demand but the same price elasticities? 5. Show why optimal, third-degree price discrimination requires that marginal revenue for each group of consumers equals marginal cost. Use this condition to explain how a firm should change its prices and total output if the demand curve for one group of consumers shifts outward, causing marginal revenue for that group to increase. 6. When pricing automobiles, American car companies typically charge a much higher percentage markup over cost for “luxury option” items (such as leather trim, etc.) than for the car itself or for more “basic” options such as power steering and automatic transmission. Explain why. 7. How is peak-load pricing a form of price discrimination? Can it make consumers better off? Give an example. 8. How can a firm determine an optimal two-part tariff if it has two customers with different demand curves? (Assume that it knows the demand curves.) 9. Why is the pricing of a Gillette safety razor a form of two-part tariff? Must Gillette be a monopoly producer of its blades as well as its razors? Suppose you were advising Gillette on how to determine the two parts of the tariff. What procedure would you suggest? 10. In the town of Woodland, California, there are many dentists but only one eye doctor. Are senior citizens more likely to be offered discount prices for dental exams or for eye exams? Why? 11. Why did MGM bundle Gone with the Wind and Getting Gertie’s Garter? What characteristic of demands is needed for bundling to increase profits? 12. How does mixed bundling differ from pure bundling? Under what conditions is mixed bundling preferable to pure bundling? Why do many restaurants practice mixed bundling (by offering a complete dinner as well as an à la carte menu) instead of pure bundling? 13. How does tying differ from bundling? Why might a firm want to practice tying? 14. Why is it incorrect to advertise up to the point that the last dollar of advertising expenditures generates another dollar of sales? What is the correct rule for the marginal advertising dollar? 15. How can a firm check that its advertising-to-sales ratio is not too high or too low? What information does it need? EXERCISES 1. Price discrimination requires the ability to sort customers an |
d the ability to prevent arbitrage. Explain how the following can function as price discrimination schemes and discuss both sorting and arbitrage: a. Requiring airline travelers to spend at least one Saturday night away from home to qualify for a low fare. b. Insisting on delivering cement to buyers and basing prices on buyers’ locations. c. Selling food processors along with coupons that can be sent to the manufacturer for a $10 rebate. d. Offering temporary price cuts on bathroom tissue. e. Charging high-income patients more than low- income patients for plastic surgery. 2. If the demand for drive-in movies is more elastic for couples than for single individuals, it will be optimal for theaters to charge one admission fee for the driver of the car and an extra fee for passengers. True or false? Explain. 3. In Example 11.1 (page 408), we saw how producers of processed foods and related consumer goods use coupons as a means of price discrimination. Although coupons are widely used in the United States, that is not the case in other countries. In Germany, coupons are illegal. a. Does prohibiting the use of coupons in Germany make German consumers better off or worse off? b. Does prohibiting the use of coupons make German producers better off or worse off? 4. Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $20,000 and a fixed cost of $10 billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States. The demand for BMWs in each market is given by and QE = 4,000,000 - 100PE QU = 1,000,000 - 20PU where the subscript E denotes Europe, the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be? b. If BMW were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company’s profit? 5. A monopolist is deciding how to allocate output between two geographically separated markets (East CHAPTER 11 • Pricing with Market Power 435 Coast and Midwest). Demand and marginal revenue for the two markets are P1 P2 = 15 - Q1 MR1 = 25 - 2Q2 MR2 = 15 - 2Q1 = 25 - 4Q2 The monopolist’s total cost is C 5 3(Q1 Q2). What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions? *6. Elizabeth Airlines (EA) flies only one route: Chicago– Honolulu. The demand for each flight is Q 500 − P. EA’s cost of running each flight is $30,000 plus $100 per passenger. a. What is the profit-maximizing price that EA will charge? How many people will be on each flight? What is EA’s profit for each flight? b. EA learns that the fixed costs per flight are in fact $41,000 instead of $30,000. Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA’s average cost curve when fixed costs are $30,000, and EA’s average cost curve when fixed costs are $41,000. c. Wait! EA finds out that two different types of people fly to Honolulu. Type A consists of business people with a demand of QA 260 − 0.4P. Type B consists of students whose total demand is QB 240 − 0.6P. Because the students are easy to spot, EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight? d. What would EA’s profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus? e. Before EA started price discriminating, how much consumer surplus was the Type A demand getting from air travel to Honolulu? Type B? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged? 7. Many retail video stores offer two alternative plans for renting films: • A two-part tariff: Pay an annual membership fee (e.g., $40) and then pay a small fee for the daily rental of each film (e.g., $2 per film per day). • A straight rental fee: Pay no membership fee, but pay a higher daily rental fee (e.g., $4 per film per day). 436 PART 3 • Market Structure and Competitive Strategy What is the logic behind the two-part tariff in this case? Why offer the customer a choice of two plans rather than simply a two-part tariff? 8. Sal’s satellite company broadcasts TV to subscribers in Los Angeles and New York. The demand functions for each of these two groups are profits? Explain why price would not be equal to marginal cost. 10. As the owner of the only tennis club in an isolated wealthy community, you must decide on membership dues and fees for court time. There are two types of tennis players. “Serious” players have demand QNY QLA = 60 - 0.25PNY = 100 - 0.50PLA where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by C = 1000 + 40Q where Q QNY QLA. a. What are the profit-maximizing prices and quantities for the New York and Los Angeles markets? b. As a consequence of a new satellite that the Pentagon recently deployed, people in Los Angeles receive Sal’s New York broadcasts and people in New York receive Sal’s Los Angeles broadcasts. As a result, anyone in New York or Los Angeles can receive Sal’s broadcasts by subscribing in either city. Thus Sal can charge only a single price. What price should he charge, and what quantities will he sell in New York and Los Angeles? c. In which of the above situations, (a) or (b), is Sal better off? In terms of consumer surplus, which situation do people in New York prefer and which do people in Los Angeles prefer? Why? *9. You are an executive for Super Computer, Inc. (SC), which rents out super computers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of P cents per second. SC has two types of potential customers of equal number—10 businesses and 10 academic institutions. Each business customer has the demand function Q 10 − P, where Q is in millions of seconds per month; each academic institution has the demand Q 8 − P. The marginal cost to SC of additional computing is 2 cents per second, regardless of volume. a. Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What would be your profits? b. Suppose you were unable to keep the two types of customers separate and charged a zero rental fee. What usage fee would maximize your profits? What would be your profits? c. Suppose you set up one two-part tariff—that is, you set one rental and one usage fee that both business and academic customers pay. What usage and rental fees would you set? What would be your Q1 = 10 - P where Q1 is court hours per week and P is the fee per hour for each individual player. There are also “occasional” players with demand Q2 = 4 - 0.25P Assume that there are 1000 players of each type. Because you have plenty of courts, the marginal cost of court time is zero. You have fixed costs of $10,000 per week. Serious and occasional players look alike, so you must charge them the same prices. a. Suppose that to maintain a “professional” atmosphere, you want to limit membership to serious players. How should you set the annual membership dues and court fees (assume 52 weeks per year) to maximize profits, keeping in mind the constraint that only serious players choose to join? What would profits be (per week)? b. A friend tells you that you could make greater profits by encouraging both types of players to join. Is your friend right? What annual dues and court fees would maximize weekly profits? What would these profits be? c. Suppose that over the years, young, upwardly mobile professionals move to your community, all of whom are serious players. You believe there are now 3000 serious players and 1000 occasional players. Would it still be profitable to cater to the occasional player? What would be the profit- maximizing annual dues and court fees? What would profits be per week? 11. Look again at Figure 11.12 (p. 420), which shows the reservation prices of three consumers for two goods. Assuming that marginal production cost is zero for both goods, can the producer make the most money by selling the goods separately, by using pure bundling, or by using mixed bundling? What prices should be charged? 12. Look again at Figure 11.17 (p. 424). Suppose that the marginal costs c1 and c2 were zero. Show that in this case, pure bundling, not mixed bundling, is the most profitable pricing strategy. What price should be charged for the bundle? What will the firm’s profit be? 13. Some years ago, an article appeared in the New York Times about IBM’s pricing policy. The previous day, IBM had announced major price cuts on most of its small and medium-sized computers. The article said: IBM probably has no choice but to cut prices periodically to get its customers to purchase more and lease less. If they succeed, this could make life more difficult for IBM’s major competitors. Outright purchases of computers are needed for ever larger IBM revenues and profits, says Morgan Stanley’s Ulric Weil in his new book, Information Systems in the 80’s. Mr. Weil declares that IBM cannot revert to an emphasis on leasing. a. Provide a brief but clear argument in support of the claim that IBM should try “to get its customers to purchase more and lease less.” b. Provide a brief but clear argument against this claim. c. What factors determine whether leasing or selling is preferable for a company like IBM? Explain briefly. 14. You are selling two goods, 1 and 2, to a market co |
nsisting of three consumers with reservation prices as follows: RESERVATION PRICE ($) CONSUMER FOR 1 FOR 2 A B C 20 60 100 100 60 20 The unit cost of each product is $30. a. Compute the optimal prices and profits for (i) selling the goods separately, (ii) pure bundling, and (iii) mixed bundling. b. Which strategy would be most profitable? Why? 15. Your firm produces two products, the demands for which are independent. Both products are produced at zero marginal cost. You face four consumers (or groups of consumers) with the following reservation prices: CHAPTER 11 • Pricing with Market Power 437 b. Now suppose that the production of each good entails a marginal cost of $30. How does this information change your answers to (a)? Why is the optimal strategy now different? 16. A cable TV company offers, in addition to its basic service, two products: a Sports Channel (Product 1) and a Movie Channel (Product 2). Subscribers to the basic service can subscribe to these additional services individually at the monthly prices P1 and P2, respectively, or they can buy the two as a bundle for the price PB, where PB < P1 P2. They can also forgo the additional services and simply buy the basic service. The company’s marginal cost for these additional services is zero. Through market research, the cable company has estimated the reservation prices for these two services for a representative group of consumers in the company’s service area. These reservation prices are plotted (as x’s) in Figure 11.21, as are the prices P1, P2, and PB that the cable company is currently charging. The graph is divided into regions I, II, III, and IV. a. Which products, if any, will be purchased by the consumers in region I? In region II? In region III? In region IV? Explain briefly. b. Note that as drawn in the figure, the reservation prices for the Sports Channel and the Movie Channel are negatively correlated. Why would you, or why would you not, expect consumers’ reservation prices for cable TV channels to be negatively correlated? c. The company’s vice president has said: “Because the marginal cost of providing an additional channel is zero, mixed bundling offers no advantage over pure bundling. Our profits would be just r1 PB P1 II XX X X X X X X X X IV III X X PB X r2 X P2 CONSUMER GOOD 1($) GOOD 2($) A B C D 25 40 80 100 100 80 40 25 PB–P2 X I a. Consider three alternative pricing strategies: (i) selling the goods separately; (ii) pure bundling; (iii) mixed bundling. For each strategy, determine the optimal prices to be charged and the resulting profits. Which strategy would be best? PB–P1 FIGURE 11.21 FIGURE FOR EXERCISE 16 438 PART 3 • Market Structure and Competitive Strategy as high if we offered the Sports Channel and the Movie Channel together as a bundle, and only as a bundle.” Do you agree or disagree? Explain why. d. Suppose the cable company continues to use mixed bundling to sell these two services. Based on the distribution of reservation prices shown in Figure 11.21, do you think the cable company should alter any of the prices that it is now charging? If so, how? *17. Consider a firm with monopoly power that faces the demand curve P = 100 - 3Q + 4A1/2 and has the total cost function C = 4Q2 + 10Q + A where A is the level of advertising expenditures, and P and Q are price and output. a. Find the values of A, Q, and P that maximize the firm’s profit. b. Calculate the Lerner index, L (P − MC)/P, for this firm at its profit-maximizing levels of A, Q, and P. CHAPTER 11 • Pricing with Market Power 439 • horizontal integration Organizational form in which several plants produce the same or related products for a firm. • vertical integration Organizational form in which a firm contains several divisions, with some producing parts and components that others use to produce finished products. Internal • transfer prices prices at which parts and components from upstream divisions are “sold” to downstream divisions within a firm. Appendix to Chapter 11 The Vertically Integrated Firm Many firms are integrated—they consist of several divisions, each with its own managers. Some firms are horizontally integrated: There are several divisions that produce the same or closely related products. We saw an example of this when we discussed the multi-plant firm in Section 10.1. Some firms are vertically integrated: They have several divisions, with some divisions producing parts and components which other divisions use to produce the finished product. For example, automobile companies have “upstream” divisions that produce engines, brakes, radiators and other components that the “downstream” divisions use to produce the finished cars. (Some firms are both vertically and horizontally integrated.) This appendix explains the economic issues that arise in a vertically integrated firm. As we will see, vertical integration has important benefits, but it also introduces complex pricing decisions: How should the firm value the parts and components that are transferred from the upstream to the downstream divisions? The firm must determine transfer prices, the internal prices at which the parts and components from upstream divisions are “sold” to downstream divisions. Transfer prices must be chosen correctly because they are the signals that divisional managers use to determine output levels. We will begin by explaining the advantages of vertical integration—advantages to the firm, as well as to the consumers who buy the end products of the firm. Some firms, however, are not vertically integrated; they simply buy parts and components from other independent firms. To understand why, we will explain some of the problems associated with vertical integration. Next, we will explain transfer pricing, and show how a vertically integrated firm should choose its transfer prices in a way that maximizes the firm’s total profit. Why Vertically Integrate? There are a number of advantages to vertical integration. If upstream and downstream divisions are part of the same firm, it might be easier to guarantee that parts and components are produced and delivered on time, and are made to the precise specifications needed by the downstream division. (On the other hand, a carefully written and enforced contract between independent upstream and downstream firms can often achieve the same thing.) The biggest advantage of vertical integration, however, is that it avoids the problem of “double marginalization,” i.e., it avoids a double markup. Market Power and Double Marginalization Often, one or more firms selling to each other along a vertical chain will have market power. For example, United Technologies and General Electric have monopoly power in the production of jet aircraft engines, which they sell to Boeing and Airbus, which in turn have monopoly power in the market for commercial aircraft. How do firms along a vertical chain exercise such monopoly power, and how are prices and output affected? Would the firms benefit from a vertical merger that integrates an upstream and a related downstream business? Would consumers? 440 PART 3 • Market Structure and Competitive Strategy To answer these questions, consider the following example. Suppose an engine manufacturer has monopoly power in the market for engines, and an automobile manufacturer that buys these engines has monopoly power in the market for its cars. Would this market power cause these two firms to benefit in any way if they were to merge? Would consumers of the final product—automobiles—be better or worse off if the two companies merged? Many people (who haven’t read this book) would answer “maybe” to the first question, and “worse off” to the second question. It turns out, however, that when there is market power of this sort, a vertical merger can be beneficial to the two firms, and also beneficial to consumers. SEPARATE FIRMS To see this, consider the following simple example. Suppose a monopolist producer of specialty engines produces those engines at a constant marginal cost cE, and sells the engines at a price PE. The engines are bought by a monopolist producer of sports cars, which sells the cars at the price P. Demand for the cars is given by Q = A - P (A11.1) with the constant A > cE. To keep this example as simple as possible, we will assume that the automobile manufacturer has no additional costs other than the cost of the engine. (As an exercise, you can repeat this example assuming that there is an additional constant marginal cost cA to assemble the cars.) If the two companies are independent of each other, the automobile manufacturer will take the price of engines as given, and choose a price for its cars to maximize its profits: p A = (P - PE)(A - P) (A11.2) You can check that given PE, the profit maximizing price of cars is:1 P* = 1 2 (A + PE) (A11.3) Then the number of cars sold and the automobile company’s profit are:2 and A - PE) (A11.4) (A - PE)2 (A11.5) 1Take the derivative of p A with respect to P and set it equal to zero. 2Substitute expression (A11.3) for P* into equations (A11.1) for Q and (A11.2) for p A. What about the engine manufacturer? It chooses the price of engines, PE, to maximize its profit: CHAPTER 11 • Pricing with Market Power 441 p E = (PE - cE)Q(PE) = (PE - cE) 1 2 (A - PE) You can confirm that the profit-maximizing price of engines is:3 PE* = 1 2 (A + cE) The profit to the engine manufacturer is then equal to: E* = 1 p 8 (A - cE)2 (A11.6) (A11.7) (A11.8) Now go back to Equation (A11.5) for the profit to the automobile manufacturer, and substitute in Equation (A11.7) for the price of engines. You will see that the automobile company’s profit is then: A* = 1 p 16 (A - cE)2 Hence the total profit for the two companies is: p TOT* = p A* + p E* = 3 16 (A - cE)2 Also, the price of cars paid by consumers is: P* = 1 4 (3A + cE) (A11.9) (A11.10) (A11.11) VERTICAL INTEGRATION Now suppose that the engine company and the automobile company merge to form a vertically integrated firm. Th |
e management of this firm would choose a price of automobiles to maximize the firm’s profit: p = (P - cE)(A - P) (A11.12) The profit-maximizing price of cars is now: P* = (A + cE)/2 (A11.13) which yields a profit of: p* = 1 4 (A - cE)2 (A11.14) 3Now take the derivative of p E with respect to PE and set it equal to zero. 442 PART 3 • Market Structure and Competitive Strategy • double marginalization When each firm in a vertical chain marks up its price above its marginal cost, thereby increasing the price of the final product. Observe that the profit for the integrated firm is greater than the total profit for the two individual firms that operate independently. Furthermore, the price to consumers for automobiles is lower. (To confirm that this is indeed the case, compare (A11.11) with (A11.13) and remember that A > cE.) Hence, in this case vertical integration benefits not only the merging firms, but also consumers. DOUBLE MARGINALIZATION Why would a vertical merger make both the merging firms and consumers better off? The reason is that vertical integration avoids the problem of double marginalization. When the two firms operate independently, each one exercises its monopoly power by marking up its price above its marginal cost. But to do this, each firm must contract its output. The engine producer contracts its output to mark up its price above its marginal cost, and then the automobile manufacturer does likewise. This “double marginalization” pushes the price above the “single marginalization” or single markup over price of the integrated firm. This example of double marginalization is illustrated graphically in Figure A11.1, which shows the demand curve (average revenue curve) for cars, and the corresponding marginal revenue curve. For the automobile company, the marginal revenue curve for cars is the demand curve for engines (effectively, the net marginal revenue for engines). It describes the number of engines that the auto maker will buy as a function of price. From the point of view of the engine company, it is the average revenue curve for engines (i.e., the demand curve for engines that the engine company faces). Corresponding to that demand curve is the engine company’s marginal revenue curve for engines, labeled MRE in the figure. If the engine company and automobile company are separate entities, the engine company will produce a quantity of engines at the point where its marginal revenue curve intersects its marginal cost curve. That $/Q A ′ PA PA cE FIGURE A11.1 EXAMPLE OF DOUBLE MARGINALIZATION For the automobile company, the marginal revenue curve for cars is the demand curve for engines (the net marginal revenue for engines). Corresponding to that demand curve is the engine company’s marginal revenue curve, MRE. If the engine company and automobile company are separate entities, the engine company will produce a quantity of engines QE at the point where its marginal revenue curve intersects its marginal cost curve. The automobile maker will buy those engines and produce an equal number of cars. Hence, the price of cars will be P’A. But if the firms merge, the integrated company will have the demand curve ARCARS and marginal revenue curve MRCARS. It produces a number of engines and equal number of cars at the point where MRCARS equals the marginal cost of producing cars, which is MCE. Thus more engines and cars are produced, and the price of cars is lower. MCE ARCARS MRCARS = NMRE Q ′ ′ QE = QA QE = QA MRE CHAPTER 11 • Pricing with Market Power 443 • quantity forcing Use of a sales quota or other incentives to make downstream firms sell as much as possible. quantity of engines is labeled Q’E. The automobile maker will buy those engines and produce an equal number of cars. Hence, the price of cars will be P’A. What happens if the two companies merge? The integrated company will have the demand curve ARCARS and the corresponding marginal revenue curve MRCARS. It will produce a number of engines and equal number of cars at the point where the marginal revenue curve for cars intersects the marginal cost of producing cars, which in this example is simply the marginal cost of engines. As shown in the figure, there will be a larger quantity of engines and cars produced at a correspondingly lower price. ALTERNATIVES TO VERTICAL INTEGRATION What can firms do to reduce the problem of double marginalization if a vertical merger is not an option? One solution is for the upstream firm to try to make the downstream market as competitive as possible, thereby reducing any double marginalization. Thus, Intel, which has monopoly power in processors, would like to do everything it can to make sure that the market for personal computers remains highly competitive, and might even help computer firms that are in danger of going out of business. A second method of dealing with double marginalization is called quantity forcing. The idea is to impose a sales quota or other restriction on downstream firms so that they cannot reduce their output in an attempt to marginalize. For example, automobile companies will create financial incentives to push dealerships (which have some monopoly power) to sell as many cars as possible. Transfer Pricing in the Integrated Firm We now turn to the profit-maximizing vertically integrated firm and see how it should choose its transfer prices and divisional output levels. We begin with the simplest case: There is no outside market for the output of the upstream division; i.e., the upstream division produces a good that is neither produced nor used by any other firm. Later we will consider what happens when there is an outside market for the upstream division’s output. Transfer Pricing When There Is No Outside Market Look again at Figure A11.1. We saw that if the firm is integrated, the profit- maximizing number of engines and cars it will produce is QE QA, at the point where MRCARS equals the marginal cost of producing cars, which is MCE. Now suppose the downstream automobile division had to “pay” the upstream engine division a transfer price for each engine it used. What should that transfer price be? It should equal the marginal cost of producing engines, i.e., MCE. Why? Because then the automobile division will have a marginal cost of producing cars equal to MCE, so that even if it is left to maximize its own divisional profit, it will produce the correct number of cars. Another way to see this is in terms of opportunity cost. What is the opportunity cost to the integrated firm of utilizing one more engine (to produce one more car)? It is the marginal cost of engines. Thus we have a simple rule: Set the transfer price of any upstream parts and components equal to the marginal cost of producing those parts and components. You might argue that the example illustrated in Figure A11.1 is oversimplified because the only cost of producing a car is the cost of an engine. So now consider a firm with three divisions: Two upstream divisions produce inputs to 444 PART 3 • Market Structure and Competitive Strategy In §10.1, we explain that a firm maximizes its profit at the output at which marginal revenue is equal to marginal cost. a downstream processing division. The two upstream divisions produce quantities Q1 and Q2 and have total costs C1(Q1) and C2(Q2). The downstream division produces a quantity Q using the production function Q = f(K, L, Q1, Q2) where K and L are capital and labor inputs, and Q1 and Q2 are the intermediate inputs from the upstream divisions. Excluding the costs of the inputs Q1 and Q2, the downstream division has a total production cost Cd(Q). Total revenue from sales of the final product is R(Q). We assume there are no outside markets for the intermediate inputs Q1and Q2; they can be used only by the downstream division. Then the firm has two problems: 1. What quantities Q1, Q2, and Q will maximize its profit? 2. Is there an incentive scheme that will decentralize the firm’s management? In particular, is there a set of transfer prices P1 and P2, so that if each division maximizes its own divisional profit, the profit of the overall firm will also be maximized? To solve these problems, we note that the firm’s total profit is p(Q) = R(Q) - Cd(Q) - C1(Q1) - C2(Q2) (A11.15) What is the level of Q1 that maximizes this profit? It is the level at which the cost of the last unit of Q1 is just equal to the additional revenue it brings to the firm. The cost of producing one extra unit of Q1 is the marginal cost C1/Q1 MC1. How much extra revenue results from that one extra unit? An extra unit of Q1 allows the firm to produce more final output Q of an amount Q/Q1 MP1, the marginal product of Q1. An extra unit of final output results in additional revenue R/Q MR, but it also results in additional cost to the downstream division of an amount Cd/Q MCd. Thus the net marginal revenue NMR1 that the firm earns from an extra unit of Q1 is (MR − MCd)MP1. Setting this equal to the marginal cost of the unit, we obtain the following rule for profit maximization4: NMR1 = (MR - MCd)MP1 = MC1 (A11.16) Going through the same steps for the second intermediate input gives NMR2 = (MR - MCd)MP2 = MC2 (A11.17) Note from equations (A11.16) and (A11.17) that it is incorrect to determine the firm’s final output level Q by setting marginal revenue equal to marginal cost for the downstream division—i.e., by setting MR MCd. Doing so ignores the cost of producing the intermediate input. (MR exceeds MCd because this cost is positive.) Also, note that equations (A11.16) and (A11.17) are standard 4Using calculus, we can obtain this rule by differentiating equation (A11.15) with respect to Q1: dp/dQ1 = (dR/dQ)(0Q/0Q1) - (dCd/dQ)(0Q/0Q1) - dC1/dQ1 = (MR - MCd)MP1 - MC1 Setting dp/dQ 0 to maximize profit gives equation (A11.4). conditions of marginal analysis: The output of each upstream division should be such that its marginal cost is equal to its marginal contribution to the profit of the overall firm. CHAPTE |
R 11 • Pricing with Market Power 445 Now, what transfer prices P1 and P2 should be “charged” to the downstream division for its use of the intermediate inputs? Remember that if each of the three divisions uses these transfer prices to maximize its own divisional profit, the profit of the overall firm should be maximized. The two upstream divisions will maximize their divisional profits, p 2, which are given by 1 and p and p 1 = P1Q1 - C1(Q1) p 2 = P2Q2 - C2(Q2) Because the upstream divisions take P1 and P2 as given, they will choose Q1 and Q2 so that P1 MC1 and P2 MC2. Similarly, the downstream division will maximize p(Q) = R(Q) - Cd(Q) - P1Q1 - P2Q2 Because the downstream division also takes P1 and P2 as given, it will choose Q1 and Q2 so that (MR - MCd)MP1 = NMR1 = P1 (A11.18) and (MR - MCd)MP2 = NMR2 = P2 (A11.19) Note that by setting the transfer prices equal to the respective marginal costs (P1 MC1 and P2 MC2), the profit-maximizing conditions given by equations (A11.16) and (A11.17) will be satisfied. We therefore have a simple solution to the transfer pricing problem: Set each transfer price equal to the marginal cost of the respective upstream division. Then when each division is required to maximize its own profit, the quantities Q1 and Q2 that the upstream divisions will want to produce will be the same quantities that the downstream division will want to “buy,” and they will maximize the firm’s total profit. To illustrate this graphically, suppose Race Car Motors, Inc., has two divisions. The upstream Engine Division produces engines, and the downstream Assembly Division puts together automobiles, using one engine (and a few other parts) in each car. In Figure A11.2, the average revenue curve AR is Race Car Motors’ demand curve for cars. (Note that the firm has monopoly power in the automobile market.) MCA is the marginal cost of assembling automobiles, given the engines (i.e., it does not include the cost of the engines). Because the car requires one engine, the marginal product of the engines is one. Thus the curve labeled MR − MCA is also the net marginal revenue curve for engines: NMRE = (MR - MCA)MPE = MR - MCA The profit-maximizing number of engines (and number of cars) is given by the intersection of the net marginal revenue curve NMRE with the marginal cost curve for engines MCE. Having determined the number of cars that it will produce, and knowing its divisional cost functions, the management of Race Car 446 PART 3 • Market Structure and Competitive Strategy $/Q PA PE FIGURE A11.2 RACE CAR MOTORS, INC. The firm’s upstream division should produce a quantity of engines QE that equates its marginal cost of engine production MCE with the downstream division’s net marginal revenue of engines NMRE. Because the firm uses one engine in every car, NMRE is the difference between the marginal revenue from selling cars and the marginal cost of assembling them, i.e., MR − MCA. The optimal transfer price for engines PE equals the marginal cost of producing them. Finished cars are sold at price PA. MCE AR MCA MR Quantity Q A = Q E NMRE = (MR – MCA) Motors can now set the transfer price PE that correctly values the engines used to produce its cars. This is the transfer price that should be used to calculate divisional profit (and year-end bonuses for divisional managers). Transfer Pricing with a Competitive Outside Market Now suppose there is a competitive outside market for the intermediate good produced by an upstream division. Because the outside market is competitive, there is a single market price at which one can buy or sell the good. Therefore, the marginal cost of the intermediate good is simply the market price. Because the optimal transfer price must equal marginal cost, it must also equal the competitive market price. To see this, suppose there is a competitive market for the engines that Race Car Motors produces. If the market price is low, Race Car Motors may want to buy some or all of its engines in the market; if it is high, it may want to sell engines in the market. Figure A11.3 illustrates the first case. For quantities below QE,1, the upstream division’s marginal cost of producing engines MCE is below the market price PE,M; for quantities above QE,1, it is above the market price. The * firm should obtain engines at the least cost, so the marginal cost of engines MCE will be the upstream division’s marginal cost for quantities up to QE,1 and the market price for quantities above QE,1. Note that Race Car Motors uses more engines and produces more cars than it would have had there been no outside engine market. The downstream division now buys QE,2 engines and produces an equal number of automobiles. However, it “buys” only QE,1 of these engines from the upstream division and the rest on the open market. It might seem strange that Race Car Motors must go into the open market to buy engines that it can make itself. If it made all of its own engines, however, its marginal cost of producing them would exceed the competitive market price. Although the profit of the upstream division would be higher, the total profit of the firm would be lower. $/Q PA PE,M CHAPTER 11 • Pricing with Market Power 447 MCE AR MC* E MCA MR FIGURE A11.3 BUYING ENGINES IN A COMPETITIVE OUTSIDE MARKET Race Car Motors’ marginal cost of engines * is the upstream division’s marginal cost MCE for quantities up to QE,1 and the market price PE,M for quantities above QE,1. The downstream division should use a total of QE,2 engines to produce an equal number of cars; in that case, the marginal cost of engines equals net marginal revenue. QE,2 − QE,1 of these engines are bought in the outside market. The downstream division “pays” the upstream division the transfer price PE,M for the remaining QE,1 engines. QE,1 Q E,2 QE Quantity NMRE = (MR MCA) Figure A11.4 shows the case where Race Car Motors sells engines in the outside market. Now the competitive market price PE,M is above the transfer price that the firm would have set had there been no outside market. In this case, although the upstream Engine Division produces QE,1 engines, only QE,2 engines $/Q PA PE,M MCE AR MC*E MCA MR FIGURE A11.4 SELLING ENGINES IN A COMPETITIVE OUTSIDE MARKET The optimal transfer price for Race Car Motors is again the market price PE,M. This price is above the point at which MCE intersects NMRE, so the upstream division sells some of its engines in the outside market. The upstream division produces QE,1 engines, the quantity at which MCE equals PE,M. The downstream division uses only QE,2 of these engines, the quantity at which NMRE equals PE,M. Compared with Figure A11.2, in which there is no outside market, more engines but fewer cars are produced. Q E,2 QA QE,1 NMRE = (MR Quantity MCA) 448 PART 3 • Market Structure and Competitive Strategy are used by the downstream division to produce automobiles. The rest are sold in the outside market at the price PE,M. Note that compared with a situation in which there is no outside engine market, Race Car Motors is producing more engines but fewer cars. Why not produce this larger number of engines but use all of them to produce more cars? Because the engines are too valuable. On the margin, the net revenue that can be earned from selling them in the outside market is higher than the net revenue from using them to build additional cars. Transfer Pricing with a Noncompetitive Outside Market Now suppose there is an outside market for the output of the upstream division, but that market is not competitive. Suppose that the engines produced by the upstream Engine Division is a special one that only Race Car Motors can make, so that Race Car Motors can be a monopoly supplier to that outside market while also producing engines for its own use. We will not work through the details of this case, but you should be able to see that the transfer price paid to the Engine Division will be below the price at which engines are bought in the outside market. Why “pay” the Engine Division a price that is lower than that paid in the outside market? The reason is that the opportunity cost of utilizing an engine internally is just the marginal cost of producing the engine, whereas the opportunity cost of selling it outside is higher, because it includes a monopoly markup. Sometimes a vertically integrated firm can buy components in an outside market in which it has monopsony power. Suppose, for example, that Race Car Motors is the only company that uses the engines produced by its upstream Engine Division, but other companies also make that engine. Thus Race Car Motors can obtain its engines from its upstream Engine Division, or can purchase them as a monopsonist in the outside market. You should be able to see that in this case, the transfer price paid to the Engine Division will be above the price at which engines are bought in the outside market. Why “pay” the upstream division a price that is higher than that paid in the outside market? With monopsony power, purchasing one additional engine in the outside market incurs a marginal expenditure that is greater than the actual price paid in that market. (The marginal expenditure is higher because purchasing an additional unit raises the average expenditure paid for all units bought in the outside market.) The marginal expenditure is the opportunity cost of buying an engine outside, and therefore should equal the transfer price paid to the Engine Division, so the transfer price will be greater than the price paid outside. Taxes and Transfer Pricing So far we have ignored taxes in our discussion of transfer pricing. But in fact taxes can play an important role in determining transfer prices when the objective is to maximize the after-tax profits of the integrated firm. This is especially the case when the upstream and downstream divisions of the firm operate in different countries. To see this, suppose that the upstream Engine Division of Race Car Motors happens to be located in |
an Asian country with a low corporate profits tax rate, while the downstream Assembly Division is located in the United States, with a higher tax rate. Suppose that in the absence of taxes, the marginal cost and thus the optimal transfer price for an engine is $5000. How would this transfer price be affected by taxes? CHAPTER 11 • Pricing with Market Power 449 In our example, the difference in tax rates will cause the opportunity cost of using an engine downstream to exceed $5000. Why? Because the downstream profit generated by the use of the engine will be taxed at a relatively high rate. Thus, taking taxes into account, the firm will want to set a higher transfer price, perhaps $7000. This will reduce the downstream profits in the United States (so that the firm will pay less in taxes) and increase the profits of the upstream division, which faces a lower tax rate. In §10.5, we explain that when a buyer has monopsony power, its marginal expenditure curve lies above its average expenditure curve because the decision to buy an extra unit of the good raises the price that must be paid on all units. A Numerical Example Suppose Race Car Motors has the following demand for its automobiles: Its marginal revenue is thus P = 20,000 - Q MR = 20,000 - 2Q The downstream division’s cost of assembling cars is CA(Q) = 8000Q so that the division’s marginal cost is MCA 8000. The upstream division’s cost of producing engines is CE(QE) = 2QE 2 The division’s marginal cost is thus MCE(QE) 4QE. First, suppose there is no outside market for the engines. How many engines and cars should the firm produce? What should be the transfer price for engines? To solve this problem, we set the net marginal revenue for engines equal to the marginal cost of producing engines. Because each car has one engine, QE Q. The net marginal revenue of engines is thus NMRE = MR - MCA = 12,000 - 2QE Now set NMRE equal to MCE: 12,000 - 2QE = 4QE Thus 6QE 12,000 and QE 2000. The firm should therefore produce 2000 engines and 2000 cars. The optimal transfer price is the marginal cost of these 2000 engines: PE = 4QE = $8000 Second, suppose that engines can be bought or sold for $6000 in an outside competitive market. This is below the $8000 transfer price that is optimal when there is no outside market, so the firm should buy some engines outside. Its marginal cost of engines, and the optimal transfer price, is now $6000. Set this $6000 marginal cost equal to the net marginal revenue of engines: 6000 = NMRE = 12,000 - 2QE 450 PART 3 • Market Structure and Competitive Strategy Thus the total quantity of engines and cars is now 3000. The company now produces more cars (and sells them at a lower price) because its cost of engines is lower. Also, since the transfer price for the engines is now $6000, the upstream Engine Division supplies only 1500 engines (because MCE(1500) $6000). The remaining 1500 engines are bought in the outside market. EXERCISES 1. Suppose Boeing faces the following demand curve for the monthly sales of its 787 aircraft: Q = 120 - 0.5p Where Q is airplanes sold per month and P is the price in millions of dollars. The airplane uses a set of engines made by General Electric, and Boeing pays GE a price PE (in millions of dollars) for each set of engines. The marginal cost to GE of producing a set of engines is 20 (million dollars). In addition to paying for engines, Boeing incurs a marginal cost of 100 (million dollars) per plane. a. What is Boeing’s profit-maximizing price of airplanes, given a price PE for the engines? What is the profit-maximizing price that GE will charge for each set of engines? Given that price of engines, what price will Boeing charge for its airplanes? b. Suppose Boeing were to acquire GE’s engine division, so that now the engines and airplanes are made by a single company. Now what price will the company charge for its airplanes? 2. Review the numerical example about Race Car Motors. Calculate the profit earned by the upstream division, the downstream division, and the firm as a whole in each of the three cases examined: (a) there is no outside market for engines; (b) there is a competitive market for engines in which the market price is $6000; and (c) the firm is a monopoly supplier of engines to an outside market. In which case does Race Car Motors earn the most profit? In which case does the upstream division earn the most? The downstream division? 3. Ajax Computer makes a computer for climate control in office buildings. The company uses a microprocessor produced by its upstream division, along with other parts bought in outside competitive markets. The microprocessor is produced at a constant marginal cost of $500, and the marginal cost of assembling the computer (including the cost of the other parts) by the downstream division is a constant $700. The firm has been selling the computer for $2000, and until now there has been no outside market for the microprocessor. a. Suppose an outside market for the microprocessor develops and that Ajax has monopoly power in that market, selling microprocessors for $1000 each. Assuming that demand for the microprocessor is unrelated to the demand for the Ajax computer, what transfer price should Ajax apply to the microprocessor for its use by the downstream computer division? Should production of computers be increased, decreased, or left unchanged? Explain briefly. b. How would your answer to (a) change if the demands for the computer and the microprocessors were competitive; i.e., if some of the people who buy the microprocessors use them to make climate control systems of their own? 4. Reebok produces and sells running shoes. It faces a market demand schedule P 11 − 1.5Qs, where Qs is the number of pairs of shoes sold and P is the price in dollars per pair of shoes. Production of each pair of shoes requires 1 square yard of leather. The leather is shaped and cut by the Form Division of Reebok. The cost function for leather is TCL = 1 + QL + 0.5QL 2 where QL is the quantity of leather (in square yards) produced. Excluding leather, the cost function for running shoes is TCs = 2Qs a. What is the optimal transfer price? b. Leather can be bought and sold in a competitive market at the price of PF 1.5. In this case, how much leather should the Form Division supply internally? How much should it supply to the outside market? Will Reebok buy any leather in the outside market? Find the optimal transfer price. c. Now suppose the leather is unique and of extremely high quality. Therefore, the Form Division may act as a monopoly supplier to the outside market as well as a supplier to the downstream division. Suppose the outside demand for leather is given by P 32 − QL. What is the optimal transfer price for the use of leather by the downstream division? At what price, if any, should leather be sold to the outside market? What quantity, if any, will be sold to the outside market? C H A P T E R 12 Monopolistic Competition and Oligopoly In the last two chapters, we saw how firms with monopoly power can choose prices and output levels to maximize profit. We also saw that monopoly power does not require a firm to be a pure monopolist. In many industries, even though several firms compete with each other, each firm has at least some monopoly power: It has control over price and can profitably charge a price that exceeds marginal cost. In this chapter, we examine market structures other than pure monopoly that can give rise to monopoly power. We begin with what might seem like an oxymoron: monopolistic competition. A monopolistically competitive market is similar to a perfectly competitive market in two key respects: There are many firms, and entry by new firms is not restricted. But it differs from perfect competition in that the product is differentiated: Each firm sells a brand or version of the product that differs in quality, appearance, or reputation, and each firm is the sole producer of its own brand. The amount of monopoly power wielded by a firm depends on its success in differentiating its product from those of other firms. Examples of monopolistically competitive industries abound: Toothpaste, laundry detergent, and packaged coffee are a few. The second form of market structure we will examine is oligopoly: a market in which only a few firms compete with one another, and entry by new firms is impeded. The product that the firms produce might be differentiated, as with automobiles, or it might not be, as with steel. Monopoly power and profitability in oligopolistic industries depend in part on how the firms interact. For example, if the interaction is more cooperative than competitive, firms could charge prices well above marginal cost and earn large profits. In some oligopolistic industries, firms do cooperate, but in others, they compete aggressively, even though this means lower profits. To see why, we need to consider how oligopolistic firms decide on output and prices. These decisions are complicated because each firm must operate strategically—when making a decision, it must weigh the probable reactions of its competitors. To understand oligopolistic markets, we must therefore introduce some basic concepts of gaming and strategy. We develop these concepts more fully in Chapter 13. The third form of market structure that we examine is a cartel. In a cartelized market, some or all firms explicitly collude: They coordinate prices and output levels to maximize joint profits. Cartels can arise in markets that would otherwise be competitive, as with the OPEC oil cartel, or oligopolistic, as with the international bauxite cartel 12.1 Monopolistic Competition 452 12.2 Oligopoly 456 12.3 Price Competition 464 12.4 Competition versus Collusion: The Prisoners’ Dilemma 469 12.5 Implications of the Prisoners’ Dilemma for Oligopolistic Pricing 472 12.6 Cartels 477 12.1 Monopolistic Competition in the Markets for Colas and Coffee 455 12.2 A Pricing Problem for Procter & Gamble 467 12.3 P |
rocter & Gamble in a Prisoners’ Dilemma 471 12.4 Price Leadership and Price Rigidity in Commercial Banking 475 12.5 The Prices of College Textbooks 476 12.6 The Cartelization of Intercollegiate Athletics 480 12.7 The Milk Cartel 481 451 452 PART 3 • Market Structure and Competitive Strategy • monopolistic competition Market in which firms can enter freely, each producing its own brand or version of a differentiated product. • oligopoly Market in which only a few firms compete with one another, and entry by new firms is impeded. • cartel Market in which some or all firms explicitly collude, coordinating prices and output levels to maximize joint profits. In §10.2, we explain that a seller of a product has some monopoly power if it can profitably charge a price greater than marginal cost. At first glance, a cartel may seem like a pure monopoly. After all, the firms in a cartel appear to operate as though they were parts of one big company. But a cartel differs from a monopoly in two important respects. First, because cartels rarely control the entire market, they must consider how their pricing decisions will affect noncartel production levels. Second, because the members of a cartel are not part of one big company, they may be tempted to “cheat” their partners by undercutting prices and grabbing bigger shares of the market. As a result, many cartels tend to be unstable and short-lived. 12.1 Monopolistic Competition In many industries, the products are differentiated. For one reason or another, consumers view each firm’s brand as different from other brands. Crest toothpaste, for example, is perceived to be different from Colgate, Aim, and other toothpastes. The difference is partly flavor, partly consistency, and partly reputation—the consumer’s image (correct or incorrect) of the relative decay-preventing efficacy of Crest. As a result, some consumers (but not all) will pay more for Crest. Because Procter & Gamble is the sole producer of Crest, it has monopoly power. But its monopoly power is limited because consumers can easily substitute other brands if the price of Crest rises. Although consumers who prefer Crest will pay more for it, most of them will not pay much more. The typical Crest user might pay 25 or 50 cents a tube more, but probably not one or two dollars more. For most consumers, toothpaste is toothpaste, and the differences among brands are small. Therefore, the demand curve for Crest toothpaste, though downward sloping, is fairly elastic. (A reasonable estimate of the elasticity of demand for Crest is −5.) Because of its limited monopoly power, Procter & Gamble will charge a price that is higher, but not much higher, than marginal cost. The situation is similar for Tide detergent or Scott paper towels. The Makings of Monopolistic Competition A monopolistically competitive market has two key characteristics: 1. Firms compete by selling differentiated products that are highly substitutable for one another but not perfect substitutes. In other words, the crossprice elasticities of demand are large but not infinite. 2. There is free entry and exit: It is relatively easy for new firms to enter the market with their own brands and for existing firms to leave if their products become unprofitable. To see why free entry is an important requirement, let’s compare the markets for toothpaste and automobiles. The toothpaste market is monopolistically competitive, but the automobile market is better characterized as an oligopoly. It is relatively easy for other firms to introduce new brands of toothpaste, and this limits the profitability of producing Crest or Colgate. If the profits were large, other firms would spend the necessary money (for development, production, advertising, and promotion) to introduce new brands of their own, which would reduce the market shares and profitability of Crest and Colgate. The automobile market is also characterized by product differentiation. However, the large-scale economies involved in production make entry by new firms difficult. Thus, until the mid-1970s, when Japanese producers became important competitors, the three major U.S. automakers had the market largely to themselves. CHAPTER 12 • Monopolistic Competition and Oligopoly 453 There are many other examples of monopolistic competition besides toothpaste. Soap, shampoo, deodorants, shaving cream, cold remedies, and many other items found in a drugstore are sold in monopolistically competitive markets. The markets for many sporting goods are likewise monopolistically competitive. So is most retail trade, because goods are sold in many different stores that compete with one another by differentiating their services according to location, availability and expertise of salespeople, credit terms, etc. Entry is relatively easy, so if profits are high in a neighborhood because there are only a few stores, new stores will enter. Equilibrium in the Short Run and the Long Run As with monopoly, in monopolistic competition firms face downward-sloping demand curves. Therefore, they have some monopoly power. But this does not mean that monopolistically competitive firms are likely to earn large profits. Monopolistic competition is also similar to perfect competition: Because there is free entry, the potential to earn profits will attract new firms with competing brands, driving economic profits down to zero. To make this clear, let’s examine the equilibrium price and output level for a monopolistically competitive firm in the short and long run. Figure 12.1(a) shows the short-run equilibrium. Because the firm’s product differs from its competitors’, its demand curve DSR is downward sloping. (This is the firm’s demand curve, not the market demand curve, which is more steeply sloped.) The profitmaximizing quantity QSR is found at the intersection of the marginal revenue $/Q PSR $/Q PLR AC DSR MC MRSR AC DLR MC MRLR QSR (a) Quantity QLR (b) Quantity FIGURE 12.1 A MONOPOLISTICALLY COMPETITIVE FIRM IN THE SHORT AND LONG RUN Because the firm is the only producer of its brand, it faces a downward-sloping demand curve. Price exceeds marginal cost and the firm has monopoly power. In the short run, described in part (a), price also exceeds average cost, and the firm earns profits shown by the yellow-shaded rectangle. In the long run, these profits attract new firms with competing brands. The firm’s market share falls, and its demand curve shifts downward. In long-run equilibrium, described in part (b), price equals average cost, so the firm earns zero profit even though it has monopoly power. 454 PART 3 • Market Structure and Competitive Strategy In §10.1, we explain that a monopolist maximizes profit by choosing an output at which marginal revenue is equal to marginal cost. Recall from §8.7 that with the possibility of entry and exit, firms will earn zero economic profit in long-run equilibrium. In §9.2, we explain that competitive markets are efficient because they maximize the sum of consumers’ and producers’ surplus. In §10.4, we discuss the deadweight loss from monopoly power. and marginal cost curves. Because the corresponding price PSR exceeds average cost, the firm earns a profit, as shown by the shaded rectangle in the figure. In the long run, this profit will induce entry by other firms. As they introduce competing brands, our firm will lose market share and sales; its demand curve will shift down, as in Figure 12.1(b). (In the long run, the average and marginal cost curves may also shift. We have assumed for simplicity that costs do not change.) The long-run demand curve DLR will be just tangent to the firm’s average cost curve. Here, profit maximization implies the quantity QLR and the price PLR. It also implies zero profit because price is equal to average cost. Our firm still has monopoly power: Its long-run demand curve is downward sloping because its particular brand is still unique. But the entry and competition of other firms have driven its profit to zero. More generally, firms may have different costs, and some brands will be more distinctive than others. In this case, firms may charge slightly different prices, and some will earn small profits. Monopolistic Competition and Economic Efficiency Perfectly competitive markets are desirable because they are economically efficient: As long as there are no externalities and nothing impedes the workings of the market, the total surplus of consumers and producers is as large as possible. Monopolistic competition is similar to competition in some respects, but is it an efficient market structure? To answer this question, let’s compare the long-run equilibrium of a monopolistically competitive industry to the long-run equilibrium of a perfectly competitive industry. Figure 12.2 shows that there are two sources of inefficiency in a monopolisti- cally competitive industry: 1. Unlike perfect competition, with monopolistic competition the equilibrium price exceeds marginal cost. This means that the value to consumers of additional units of output exceeds the cost of producing those units. If output were expanded to the point where the demand curve intersects the marginal cost curve, total surplus could be increased by an amount equal to the yellow-shaded area in Figure 12.2(b). This should not be surprising. We saw in Chapter 10 that monopoly power creates a deadweight loss, and monopoly power exists in monopolistically competitive markets. 2. Note in Figure 12.2(b) that for the monopolistically competitive firm, output is below that which minimizes average cost. Entry of new firms drives profits to zero in both perfectly competitive and monopolistically competitive markets. In a perfectly competitive market, each firm faces a horizontal demand curve, so the zero-profit point occurs at minimum average cost, as Figure 12.2(a) shows. In a monopolistically competitive market, however, the demand curve is downward sloping, so the zero-profit point is to the left of minimum average c |
ost. Excess capacity is inefficient because average cost would be lower with fewer firms. These inefficiencies make consumers worse off. Is monopolistic competition then a socially undesirable market structure that should be regulated? The answer—for two reasons—is probably no: 1. In most monopolistically competitive markets, monopoly power is small. Usually enough firms compete, with brands that are sufficiently substitutable, so that no single firm has much monopoly power. Any resulting deadweight CHAPTER 12 • Monopolistic Competition and Oligopoly 455 Pc MC AC PMC D MR Qc (a) Quantity QMC MC AC D Quantity MR Qc (b) FIGURE 12.2 COMPARISON OF MONOPOLISTICALLY COMPETITIVE EQUILIBRIUM AND PERFECTLY COMPETITIVE EQUILIBRIUM Under perfect competition, as in (a), price equals marginal cost, but under monopolistic competition, price exceeds marginal cost. Thus there is a deadweight loss, as shown by the yellow-shaded area in (b). In both types of markets, entry occurs until profits are driven to zero. Under perfect competition, the demand curve facing the firm is horizontal, so the zero-profit point occurs at the point of minimum average cost. Under monopolistic competition the demand curve is downward-sloping, so the zero-profit point is to the left of the point of minimum average cost. In evaluating monopolistic competition, these inefficiencies must be balanced against the gains to consumers from product diversity. loss will therefore be small. And because firms’ demand curves will be fairly elastic, average cost will be close to the minimum. 2. Any inefficiency must be balanced against an important benefit from monopolistic competition: product diversity. Most consumers value the ability to choose among a wide variety of competing products and brands that differ in various ways. The gains from product diversity can be large and may easily outweigh the inefficiency costs resulting from downwardsloping demand curves. EXAM PLE 12.1 MONOPOLISTIC COMPETITION IN THE MARKETS FOR COLAS AND COFFEE The markets for soft drinks and coffee illustrate the characteristics of monopolistic competition. Each market has a variety of brands that differ slightly but are close substitutes for one another. Each brand of cola, for example, tastes a little different from the next. (Can you tell the difference between Coke and Pepsi? Between Coke and RC Cola?) And each brand of ground coffee has a slightly different flavor, fragrance, and caffeine content. Most consumers develop their own preferences; you might prefer Maxwell House coffee to 456 PART 3 • Market Structure and Competitive Strategy other brands and buy it regularly. Brand loyalties, however, are usually limited. If the price of Maxwell House were to rise substantially above those of other brands, you and most other consumers who had been buying it would probably switch brands. Just how much monopoly power does General Foods, the producer of Maxwell House, have with this brand? In other words, how elastic is the demand for Maxwell House? Most large companies carefully study product demands as part of their market research. Company estimates are usually proprietary, but two published studies of the demands for various brands of colas and ground coffees used simulated shopping experiments to determine how market shares for each brand would change in response to specific changes in price. Table 12.1 summarizes the results by showing the elasticities of demand for several brands.1 First, note that among colas, RC Cola is much less price elastic than Coke. Although it has a small share of the cola market, its taste is more distinctive than that of Coke, Pepsi, and other brands, so consumers who buy it have stronger brand loyalty. But even though RC Cola has more monopoly power than Coke, it is not necessarily more profitable. Profits depend on fixed costs and volume, as well as price. Even if its average profit is smaller, Coke will generate more profit because it has a much larger share of the market. Second, note that coffees as a group are more price elastic than colas. There is less brand loyalty among coffee buyers than among cola buyers because the differences among coffees are less perceptible than the differences among colas. Note that the demand for Chock Full o’ Nuts is less price elastic than its competitors. Why? Because Chock Full o’ Nuts, like RC Cola, has a more distinctive taste than Folgers or Maxwell House, and so consumers who buy it tend to remain loyal. Fewer consumers notice or care about the taste differences between Folgers and Maxwell House. With the exception of RC Cola and Chock Full o’ Nuts, all the colas and coffees are quite price elastic. With elasticities on the order of −4 to −8, each brand has only limited monopoly power. This is typical of monopolistic competition. TABLE 12.1 ELASTICITIES OF DEMAND FOR BRANDS OF COLAS AND COFFEE BRAND ELASTICITY OF DEMAND Colas Ground coffee RC Cola Coke Folgers Maxwell House Chock Full o’Nuts −2.4 −5.2 to −5.7 −6.4 −8.2 −3.6 12.2 Oligopoly In oligopolistic markets, the products may or may not be differentiated. What matters is that only a few firms account for most or all of total production. In some oligopolistic markets, some or all firms earn substantial profits over the long run because barriers to entry make it difficult or impossible for new firms to enter. Oligopoly is a prevalent form of market structure. Examples of 1The elasticity estimates in Table 12.1 are from John R. Nevin, “Laboratory Experiments for Estimating Consumer Demand: A Validation Study,” Journal of Marketing Research 11 (August 1974): 261–68; and Lakshman Krishnamurthi and S. P. Raj, “A Model of Brand Choice and Purchase Quantity Price Sensitivities,” Marketing Science (1991). In typical simulated shopping experiments, consumers are asked to choose the brands that they prefer from a variety of prepriced brands. This trial is repeated several times, with different prices each time. CHAPTER 12 • Monopolistic Competition and Oligopoly 457 oligopolistic industries include automobiles, steel, aluminum, petrochemicals, electrical equipment, and computers. Why might barriers to entry arise? We discussed some of the reasons in Chapter 10. Scale economies may make it unprofitable for more than a few firms to coexist in the market; patents or access to a technology may exclude potential competitors; and the need to spend money for name recognition and market reputation may discourage entry by new firms. These are “natural” entry barriers—they are basic to the structure of the particular market. In addition, incumbent firms may take strategic actions to deter entry. For example, they might threaten to flood the market and drive prices down if entry occurs, and to make the threat credible, they can construct excess production capacity. Managing an oligopolistic firm is complicated because pricing, output, advertising, and investment decisions involve important strategic considerations. Because only a few firms are competing, each firm must carefully consider how its actions will affect its rivals, and how its rivals are likely to react. Suppose that because of sluggish car sales, Ford is considering a 10-percent price cut to stimulate demand. It must think carefully about how competing auto companies will react. They might not react at all, or they might cut their prices only slightly, in which case Ford could enjoy a substantial increase in sales, largely at the expense of its competitors. Or they might match Ford’s price cut, in which case all of the firms will sell more cars, but might make much lower profits because of the lower prices. Another possibility is that some firms will cut their prices by even more than Ford to punish Ford for rocking the boat, and this in turn might lead to a price war and to a drastic fall in profits for the entire industry. Ford must carefully weigh all these possibilities. In fact, for almost any major economic decision that a firm makes—setting price, determining production levels, undertaking a major promotion campaign, or investing in new production capacity—it must try to determine the most likely response of its competitors. These strategic considerations can be complex. When making decisions, each firm must weigh its competitors’ reactions, knowing that these competitors will also weigh its reactions to their decisions. Furthermore, decisions, reactions, reactions to reactions, and so forth are dynamic, evolving over time. When the managers of a firm evaluate the potential consequences of their decisions, they must assume that their competitors are as rational and intelligent as they are. Then, they must put themselves in their competitors’ place and consider how they would react. Equilibrium in an Oligopolistic Market When we study a market, we usually want to determine the price and quantity that will prevail in equilibrium. For example, we saw that in a perfectly competitive market, the equilibrium price equates the quantity supplied with the quantity demanded. Then we saw that for a monopoly, an equilibrium occurs when marginal revenue equals marginal cost. Finally, when we studied monopolistic competition, we saw how a long-run equilibrium results as the entry of new firms drives profits to zero. In these markets, each firm could take price or market demand as given and largely ignore its competitors. In an oligopolistic market, however, a firm sets price or output based partly on strategic considerations regarding the behavior of its competitors. At the same time, competitors’ decisions depend on the first firm’s decision. How, then, can we figure out what the market price and output will be in equilibrium—or whether there will even be an equilibrium? To answer 458 PART 3 • Market Structure and Competitive Strategy In §8.7, we explain that in a competitive market, longrun equilibrium occurs when no firm has an incentive to enter or exit because firms are earning zero economic profit and the quantity |
demanded is equal to the quantity supplied. • Nash equilibrium Set of strategies or actions in which each firm does the best it can given its competitors’ actions. • duopoly Market in which two firms compete with each other. Recall from §8.8 that when firms produce homogeneous or identical goods, consumers consider only price when making their purchasing decisions. • Cournot model Oligopoly model in which firms produce a homogeneous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how much to produce. these questions, we need an underlying principle to describe an equilibrium when firms make decisions that explicitly take each other’s behavior into account. Remember how we described an equilibrium in competitive and monopolistic markets: When a market is in equilibrium, firms are doing the best they can and have no reason to change their price or output. Thus a competitive market is in equilibrium when the quantity supplied equals the quantity demanded: Each firm is doing the best it can—it is selling all that it produces and is maximizing its profit. Likewise, a monopolist is in equilibrium when marginal revenue equals marginal cost because it, too, is doing the best it can and is maximizing its profit. NASH EQUILIBRIUM With some modification, we can apply this same principle to an oligopolistic market. Now, however, each firm will want to do the best it can given what its competitors are doing. And what should the firm assume that its competitors are doing? Because the firm will do the best it can given what its competitors are doing, it is natural to assume that these competitors will do the best they can given what that firm is doing. Each firm, then, takes its competitors into account, and assumes that its competitors are doing likewise. This may seem a bit abstract at first, but it is logical, and as we will see, it gives us a basis for determining an equilibrium in an oligopolistic market. The concept was first explained clearly by the mathematician John Nash in 1951, so we call the equilibrium it describes a Nash equilibrium. It is an important concept that we will use repeatedly: Nash Equilibrium: Each firm is doing the best it can given what its competitors are doing. We discuss this equilibrium concept in more detail in Chapter 13, where we show how it can be applied to a broad range of strategic problems. In this chapter, we will apply it to the analysis of oligopolistic markets. To keep things as uncomplicated as possible, this chapter will focus largely on markets in which two firms are competing with each other. We call such a market a duopoly. Thus each firm has just one competitor to take into account in making its decisions. Although we focus on duopolies, our basic results will also apply to markets with more than two firms. The Cournot Model We will begin with a simple model of duopoly first introduced by the French economist Augustin Cournot in 1838. Suppose the firms produce a homogeneous good and know the market demand curve. Each firm must decide how much to produce, and the two firms make their decisions at the same time. When making its production decision, each firm takes its competitor into account. It knows that its competitor is also deciding how much to produce, and the market price will depend on the total output of both firms. The essence of the Cournot model is that each firm treats the output level of its competitor as fixed when deciding how much to produce. To see how this works, let’s consider the output decision of Firm 1. Suppose Firm 1 thinks that Firm 2 will produce nothing. In that case, Firm 1’s demand curve is the market demand curve. In Figure 12.3 this is shown as D1(0), which means the demand curve for Firm 1, assuming Firm 2 produces zero. Figure 12.3 also shows the corresponding marginal revenue curve MR1(0). We have assumed that Firm 1’s marginal P1 D1(0) MR1(0) CHAPTER 12 • Monopolistic Competition and Oligopoly 459 FIGURE 12.3 FIRM 1’S OUTPUT DECISION Firm 1’s profit-maximizing output depends on how much it thinks that Firm 2 will produce. If it thinks Firm 2 will produce nothing, its demand curve, labeled D1(0), is the market demand curve. The corresponding marginal revenue curve, labeled MR1(0), intersects Firm 1’s marginal cost curve MC1 at an output of 50 units. If Firm 1 thinks that Firm 2 will produce 50 units, its demand curve, D1(50), is shifted to the left by this amount. Profit maximization now implies an output of 25 units. Finally, if Firm 1 thinks that Firm 2 will produce 75 units, Firm 1 will produce only 12.5 units. MC1 MR1(75) MR1(50) D1(75) D1(50) 12.5 25 50 75 Q1 cost MC1 is constant. As shown in the figure, Firm 1’s profit-maximizing output is 50 units, the point where MR1(0) intersects MC1. So if Firm 2 produces zero, Firm 1 should produce 50. Suppose, instead, that Firm 1 thinks Firm 2 will produce 50 units. Then Firm 1’s demand curve is the market demand curve shifted to the left by 50. In Figure 12.3, this curve is labeled D1(50), and the corresponding marginal revenue curve is labeled MR1(50). Firm 1’s profit-maximizing output is now 25 units, the point where MR1(50) = MC1. Now, suppose Firm 1 thinks that Firm 2 will produce 75 units. Then Firm 1’s demand curve is the market demand curve shifted to the left by 75. It is labeled D1(75) in Figure 12.3, and the corresponding marginal revenue curve is labeled MR1(75). Firm 1’s profit-maximizing output is now 12.5 units, the point where MR1(75) = MC1. Finally, suppose Firm 1 thinks that Firm 2 will produce 100 units. Then Firm 1’s demand and marginal revenue curves (which are not shown in the figure) would intersect its marginal cost curve on the vertical axis; if Firm 1 thinks that Firm 2 will produce 100 units or more, it should produce nothing. REACTION CURVES To summarize: If Firm 1 thinks that Firm 2 will produce nothing, it will produce 50; if it thinks Firm 2 will produce 50, it will produce 25; if it thinks Firm 2 will produce 75, it will produce 12.5; and if it thinks Firm 2 will produce 100, then it will produce nothing. Firm 1’s profit-maximizing output is thus a decreasing schedule of how much it thinks Firm 2 will produce. We call this schedule Firm 1’s reaction curve and denote it by Q*1(Q2). This curve is plotted in Figure 12.4, where each of the four output combinations that we found above is shown as an x. • reaction curve Relationship between a firm’s profitmaximizing output and the amount it thinks its competitor will produce. 460 PART 3 • Market Structure and Competitive Strategy FIGURE 12.4 REACTION CURVES AND COURNOT EQUILIBRIUM Firm 1’s reaction curve shows how much it will produce as a function of how much it thinks Firm 2 will produce. (The xs at Q2 = 0, 50, and 75 correspond to the examples shown in Figure 12.3.) Firm 2’s reaction curve shows its output as a function of how much it thinks Firm 1 will produce. In Cournot equilibrium, each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits. Therefore, neither firm will move from this equilibrium. Q1 100 75 50 x 25 12.5 Firm 2’s Reaction Curve Q*2(Q1) x Firm 1’s Reaction Curve Q*1(Q2) 25 50 Cournot Equilibrium x 75 100 Q2 • Cournot equilibrium Equilibrium in the Cournot model in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly. We can go through the same kind of analysis for Firm 2; that is, we can determine Firm 2’s profit-maximizing quantity given various assumptions about how much Firm 1 will produce. The result will be a reaction curve for Firm *(Q1) that relates its output to the output that it thinks Firm 2—i.e., a schedule Q 2 1 will produce. If Firm 2’s marginal revenue or marginal cost curve is different from that of Firm 1, its reaction curve will also differ in form. For example, Firm 2’s reaction curve might look like the one drawn in Figure 12.4. COURNOT EQUILIBRIUM How much will each firm produce? Each firm’s reaction curve tells it how much to produce, given the output of its competitor. In equilibrium, each firm sets output according to its own reaction curve; the equilibrium output levels are therefore found at the intersection of the two reaction curves. We call the resulting set of output levels a Cournot equilibrium. In this equilibrium, each firm correctly assumes how much its competitor will produce, and it maximizes its profit accordingly. Note that this Cournot equilibrium is an example of a Nash equilibrium (and thus it is sometimes called a Cournot-Nash equilibrium). Remember that in a Nash equilibrium, each firm is doing the best it can given what its competitors are doing. As a result, no firm would individually want to change its behavior. In the Cournot equilibrium, each firm is producing an amount that maximizes its profit given what its competitor is producing, so neither would want to change its output. Suppose the two firms are initially producing output levels that differ from the Cournot equilibrium. Will they adjust their outputs until the Cournot equilibrium is reached? Unfortunately, the Cournot model says nothing about the dynamics of the adjustment process. In fact, during any adjustment process, the model’s central assumption that each firm can assume that its competitor’s output is fixed will not hold. Because both firms would be adjusting their outputs, neither output would be fixed. We need different models to understand dynamic adjustment, and we will examine some in Chapter 13. When is it rational for each firm to assume that its competitor’s output is fixed? It is rational if the two firms are choosing their outputs only once because CHAPTER 12 • Monopolistic Competition and Oligopoly 461 then their outputs cannot change. It is also rational once they are in Cournot equilibrium because then neither firm will have any incentive to change its output. When using the Cournot model, we must therefore con |
fine ourselves to the behavior of firms in equilibrium. The Linear Demand Curve—An Example Let’s work through an example—two identical firms facing a linear market demand curve. This will help clarify the meaning of a Cournot equilibrium and let us compare it with the competitive equilibrium and the equilibrium that results if the firms collude and choose their output levels cooperatively. Suppose our duopolists face the following market demand curve: P = 30 - Q where Q is the total production of both firms (i.e., Q = Q1 + Q2). Also, suppose that both firms have zero marginal cost: MC 1 = MC 2 = 0 We can determine the reaction curve for Firm 1 as follows. To maximize profit, it sets marginal revenue equal to marginal cost. Its total revenue R1 is given by R1 = PQ1 = 30Q1 = 30Q1 = (30 - Q)Q1 - (Q1 - Q 1 + Q2)Q1 2 - Q2Q1 Its marginal revenue MR1 is just the incremental revenue R1 resulting from an incremental change in output Q1: MR1 = R1/Q1 = 30 - 2Q1 - Q2 Now, setting MR1 equal to zero (the firm’s marginal cost) and solving for Q1, we find = Firm 1 s reaction curve: Q1 = 15 - The same calculation applies to Firm 2: = Firm 2 s reaction curve: Q2 = 15 - 1 2 Q2 1 2 Q1 (12.1) (12.2) The equilibrium output levels are the values for Q1 and Q2 at the intersection of the two reaction curves—i.e., the levels that solve equations (12.1) and (12.2). By replacing Q2 in equation (12.1) with the expression on the righthand side of (12.2), you can verify that the equilibrium output levels are Cournot equilibrium: Q1 = Q2 = 10 462 PART 3 • Market Structure and Competitive Strategy FIGURE 12.5 DUOPOLY EXAMPLE The demand curve is P = 30 − Q, and both firms have zero marginal cost. In Cournot equilibrium, each firm produces 10. The collusion curve shows combinations of Q1 and Q2 that maximize total profits. If the firms collude and share profits equally, each will produce 7.5. Also shown is the competitive equilibrium, in which price equals marginal cost and profit is zero. Q1 30 15 10 7.5 Collusion Curve Firm 2’s Reaction Curve Competitive Equilibrium Cournot Equilibrium Collusive Equilibrium Firm 1’s Reaction Curve 7.5 10 15 30 Q2 The total quantity produced is therefore Q = Q1 + Q2 = 20, so the equilibrium market price is P = 30 − Q = 10, and each firm earns a profit of 100. Figure 12.5 shows the firms’ reaction curves and this Cournot equilibrium. Note that Firm 1’s reaction curve shows its output Q1 in terms of Firm 2’s output Q2. Likewise, Firm 2’s reaction curve shows Q2 in terms of Q1. (Because the firms are identical, the two reaction curves have the same form. They look different because one gives Q1 in terms of Q2 and the other gives Q2 in terms of Q1.) The Cournot equilibrium is at the intersection of the two curves. At this point, each firm is maximizing its own profit, given its competitor’s output. We have assumed that the two firms compete with each other. Suppose, instead, that the antitrust laws were relaxed and the two firms could collude. They would set their outputs to maximize total profit, and presumably they would split that profit evenly. Total profit is maximized by choosing total output Q so that marginal revenue equals marginal cost, which in this example is zero. Total revenue for the two firms is R = PQ = (30 - Q)Q = 30Q - Q 2 Marginal revenue is therefore MR = R/Q = 30 - 2Q Setting MR equal to zero, we see that total profit is maximized when Q = 15. Any combination of outputs Q1 and Q2 that add up to 15 maximizes total profit. The curve Q1 + Q2 = 15, called the collusion curve, therefore gives all pairs of outputs Q1 and Q2 that maximize total profit. This curve is also shown in CHAPTER 12 • Monopolistic Competition and Oligopoly 463 Figure 12.5. If the firms agree to share profits equally, each will produce half of the total output: Q1 = Q2 = 7.5 As you would expect, both firms now produce less—and earn higher profits (112.50)—than in the Cournot equilibrium. Figure 12.5 shows this collusive equilibrium and the competitive output levels found by setting price equal to marginal cost. (You can verify that they are Q1 = Q2 = 15, which implies that each firm makes zero profit.) Note that the Cournot outcome is much better (for the firms) than perfect competition, but not as good as the outcome from collusion. First Mover Advantage—The Stackelberg Model We have assumed that our two duopolists make their output decisions at the same time. Now let’s see what happens if one of the firms can set its output first. There are two questions of interest. First, is it advantageous to go first? Second, how much will each firm produce? Continuing with our example, we assume that both firms have zero marginal cost, and that market demand is given by P = 30 − Q, where Q is total output. Suppose Firm 1 sets its output first and then Firm 2, after observing Firm 1’s output, makes its output decision. In setting output, Firm 1 must therefore consider how Firm 2 will react. This Stackelberg model of duopoly is different from the Cournot model, in which neither firm has any opportunity to react. Let’s begin with Firm 2. Because it makes its output decision after Firm 1, it takes Firm 1’s output as fixed. Therefore, Firm 2’s profit-maximizing output is given by its Cournot reaction curve, which we derived above as equation (12.2): = Firm 2 s reaction curve: Q2 = 15 - 1 2 Q1 (12.2) What about Firm 1? To maximize profit, it chooses Q1 so that its marginal rev- enue equals its marginal cost of zero. Recall that Firm 1’s revenue is R1 = PQ1 = 30Q1 - Q 1 2 - Q2Q1 (12.3) Because R1 depends on Q2, Firm 1 must anticipate how much Firm 2 will produce. Firm 1 knows, however, that Firm 2 will choose Q2 according to the reaction curve (12.2). Substituting equation (12.2) for Q2 into equation (12.3), we find that Firm 1’s revenue is R1 = 30Q1 - Q1 2 - Q1 a 15 - 1 2 b Q1 = 15Q1 - 1 2 2 Q1 Its marginal revenue is therefore MR1 = R1/Q1 = 15 - Q1 (12.4) • Stackelberg model Oligopoly model in which one firm sets its output before other firms do. 464 PART 3 • Market Structure and Competitive Strategy Setting MR1 = 0 gives Q1 = 15. And from Firm 2’s reaction curve (12.2), we find that Q2 = 7.5. Firm 1 produces twice as much as Firm 2 and makes twice as much profit. Going first gives Firm 1 an advantage. This may appear counterintuitive: It seems disadvantageous to announce your output first. Why, then, is going first a strategic advantage? The reason is that announcing first creates a fait accompli: No matter what your competitor does, your output will be large. To maximize profit, your competitor must take your large output level as given and set a low level of output for itself. If your competitor produced a large level of output, it would drive price down and you would both lose money. So unless your competitor views “getting even” as more important than making money, it would be irrational for it to produce a large amount. As we will see in Chapter 13, this kind of “firstmover advantage” occurs in many strategic situations. The Cournot and Stackelberg models are alternative representations of oligopolistic behavior. Which model is the more appropriate depends on the industry. For an industry composed of roughly similar firms, none of which has a strong operating advantage or leadership position, the Cournot model is probably the more appropriate. On the other hand, some industries are dominated by a large firm that usually takes the lead in introducing new products or setting price; the mainframe computer market is an example, with IBM the leader. Then the Stackelberg model may be more realistic. 12.3 Price Competition We have assumed that our oligopolistic firms compete by setting quantities. In many oligopolistic industries, however, competition occurs along price dimensions. For example, automobile companies view price as a key strategic variable, and each one chooses its price with its competitors in mind. In this section, we use the Nash equilibrium concept to study price competition, first in an industry that produces a homogeneous good and then in an industry with some degree of product differentiation. Price Competition with Homogeneous Products—The Bertrand Model The Bertrand model was developed in 1883 by another French economist, Joseph Bertrand. Like the Cournot model, it applies to firms that produce the same homogeneous good and make their decisions at the same time. In this case, however, the firms choose prices instead of quantities. As we will see, this change can dramatically affect the market outcome. Let’s return to the duopoly example of the last section, in which the market demand curve is P = 30 - Q where Q = Q1 + Q2 is again total production of a homogeneous good. This time, however, we will assume that both firms have a marginal cost of $3: MC 1 = MC 2 = $3 As an exercise, you can show that the Cournot equilibrium for this duopoly, which results when both firms choose output simultaneously, is Q1 = Q2 = 9. You • Bertrand model Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge. CHAPTER 12 • Monopolistic Competition and Oligopoly 465 can also check that in this Cournot equilibrium, the market price is $12, so that each firm makes a profit of $81. Now suppose that these two duopolists compete by simultaneously choosing a price instead of a quantity. What price will each firm choose, and how much profit will each earn? To answer these questions, note that because the good is homogeneous, consumers will purchase only from the lowest-price seller. Thus, if the two firms charge different prices, the lower-price firm will supply the entire market and the higher-price firm will sell nothing. If both firms charge the same price, consumers will be indifferent as to which firm they buy from and each firm will supply half the market. What is the Nash equilibrium in this case? If you think about this probl |
em a little, you will see that because of the incentive to cut prices, the Nash equilibrium is the competitive outcome—i.e., both firms set price equal to marginal cost: P1 = P2 = $3. Then industry output is 27 units, of which each firm produces 13.5 units. And because price equals marginal cost, both firms earn zero profit. To check that this outcome is a Nash equilibrium, ask whether either firm would have any incentive to change its price. Suppose Firm 1 raised its price. It would then lose all of its sales to Firm 2 and therefore be no better off. If, instead, it lowered its price, it would capture the entire market but would lose money on every unit it produced; again, it would be worse off. Therefore, Firm 1 (and likewise Firm 2) has no incentive to deviate: It is doing the best it can to maximize profit, given what its competitor is doing. Why couldn’t there be a Nash equilibrium in which the firms charged the same price, but a higher one (say, $5), so that each made some profit? Because if either firm lowered its price just a little, it could capture the entire market and nearly double its profit. Thus each firm would want to undercut its competitor. Such undercutting would continue until the price dropped to $3. By changing the strategic choice variable from output to price, we get a dramatically different outcome. In the Cournot model, because each firm produces only 9 units, the market price is $12. Now the market price is $3. In the Cournot model, each firm made a profit; in the Bertrand model, the firms price at marginal cost and make no profit. The Bertrand model has been criticized on several counts. First, when firms produce a homogeneous good, it is more natural to compete by setting quantities rather than prices. Second, even if firms do set prices and choose the same price (as the model predicts), what share of total sales will go to each one? We assumed that sales would be divided equally among the firms, but there is no reason why this must be the case. Despite these shortcomings, the Bertrand model is useful because it shows how the equilibrium outcome in an oligopoly can depend crucially on the firms’ choice of strategic variable.2 Price Competition with Differentiated Products Oligopolistic markets often have at least some degree of product differentiation.3 Market shares are determined not just by prices, but also by differences in the design, performance, and durability of each firm’s product. In such cases, it is natural for firms to compete by choosing prices rather than quantities. 2Also, it has been shown that if firms produce a homogeneous good and compete by first setting output capacities and then setting price, the Cournot equilibrium in quantities again results. See David Kreps and Jose Scheinkman, “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes,” Bell Journal of Economics 14 (1983): 326–38. 3Product differentiation can exist even for a seemingly homogeneous product. Consider gasoline, for example. Although gasoline itself is a homogeneous good, service stations differ in terms of location and services provided. As a result, gasoline prices may differ from one service station to another. 466 PART 3 • Market Structure and Competitive Strategy To see how price competition with differentiated products can work, let’s go through the following simple example. Suppose each of two duopolists has fixed costs of $20 but zero variable costs, and that they face the same demand curves: = = Firm 1 Firm 2 s demand: Q1 s demand: Q2 = 12 - 2P1 = 12 - 2P2 + P2 + P1 (12.5a) (12.5b) where P1 and P2 are the prices that Firms 1 and 2 charge, respectively, and Q1 and Q2 are the resulting quantities that they sell. Note that the quantity that each firm can sell decreases when it raises its own price but increases when its competitor charges a higher price. CHOOSING PRICES We will assume that both firms set their prices at the same time and that each firm takes its competitor’s price as fixed. We can therefore use the Nash equilibrium concept to determine the resulting prices. Let’s begin with Firm 1. Its profit p 1 is its revenue P1Q1 less its fixed cost of $20. Substituting for Q1 from the demand curve of equation (12.5a), we have p 1 = P1Q1 - 20 = 12P1 - 2P1 2 + P1P2 - 20 At what price P1 is this profit maximized? The answer depends on P2, which Firm 1 assumes to be fixed. However, whatever price Firm 2 is charging, Firm 1’s profit is maximized when the incremental profit from a very small increase in its own price is just zero. Taking P2 as fixed, Firm 1’s profit-maximizing price is therefore given by p 1/P1 = 12 - 4P1 + P2 = 0 This equation can be rewritten to give the following pricing rule, or reaction curve, for Firm 1: = Firm 1 s reaction curve: P1 = 3 + 1 4 P2 This equation tells Firm 1 what price to set, given the price P2 that Firm 2 is setting. We can similarly find the following pricing rule for Firm 2: = Firm 2 s reaction curve: P2 = 3 + 1 4 P1 These reaction curves are drawn in Figure 12.6. The Nash equilibrium is at the point where the two reaction curves cross; you can verify that each firm is then charging a price of $4 and earning a profit of $12. At this point, because each firm is doing the best it can given the price its competitor has set, neither firm has an incentive to change its price. Now suppose the two firms collude: Instead of choosing their prices independently, they both decide to charge the same price—namely, the price that maximizes both of their profits. You can verify that the firms would then charge $6, and that they would be better off colluding because each would now earn a profit of $16.4 Figure 12.6 shows this collusive equilibrium. Firm 2’s reaction curve P1 $6 $4 CHAPTER 12 • Monopolistic Competition and Oligopoly 467 Collusive equilibrium Firm 1’s reaction curve Nash equilibrium FIGURE 12.6 NASH EQUILIBRIUM IN PRICES Here two firms sell a differentiated product, and each firm’s demand depends both on its own price and on its competitor’s price. The two firms choose their prices at the same time, each taking its competitor’s price as given. Firm 1’s reaction curve gives its profit-maximizing price as a function of the price that Firm 2 sets, and similarly for Firm 2. The Nash equilibrium is at the intersection of the two reaction curves: When each firm charges a price of $4, it is doing the best it can given its competitor’s price and has no incentive to change price. Also shown is the collusive equilibrium: If the firms cooperatively set price, they will choose $6. $4 $6 P2 Finally, suppose Firm 1 sets its price first and that, after observing Firm 1’s decision, Firm 2 makes its pricing decision. Unlike the Stackelberg model in which the firms set their quantities, in this case Firm 1 would be at a distinct disadvantage by moving first. (To see this, calculate Firm 1’s profit-maximizing price, taking Firm 2’s reaction curve into account.) Why is moving first now a disadvantage? Because it gives the firm that moves second an opportunity to undercut slightly and thereby capture a larger market share. (See Exercise 11 at the end of the chapter.) EXAM PLE 12.2 A PRICING PROBLEM FOR PROCTER & GAMBLE When Procter & Gamble (P&G) planned to enter the Japanese market for Gypsy Moth Tape, it knew its production costs and understood the market demand curve but found it hard to determine the right price to charge because two other firms—Kao, Ltd., and Unilever, Ltd.—were also planning to enter the market. All three firms would be choosing their prices at about the same time, and P&G had to take this into account when setting its own price.5 4The firms have the same costs, so they will charge the same price P. Total profit is given by p T = p + p 2 1 = 24P - 4P2 + 2P2 - 40 = 24P - 2P2 - 40. This is maximized when p P = $6. Each firm’s profit is therefore T/P = 0. p T/P = 24 − 4P, so the joint profit-maximizing price is p 1 = p 2 = 12P - P2 - 20 = 72 - 36 - 20 = $16 5This example is based on classroom material developed by Professor John Hauser of MIT. To protect P&G’s proprietary interests, some of the facts about the product and the market have been altered. The fundamental description of P&G’s problem, however, is accurate. 468 PART 3 • Market Structure and Competitive Strategy Because all three firms were using the same technology for producing Gypsy Moth Tape, they had the same production costs. Each firm faced a fixed cost of $480,000 per month and a variable cost of $1 per unit. From market research, P&G ascertained that its demand curve for monthly sales was Q = 3375P -3.5(PU).25(PK).25 where Q is monthly sales in thousands of units, and P, PU, and PK are P&G’s, Unilever’s, and Kao’s prices, respectively. Now, put yourself in P&G’s position. Assuming that Unilever and Kao face the same demand conditions, with what price should you enter the market, and how much profit should you expect to earn? You might begin by calculating the profit you would earn as a function of the price you charge, under alternative assumptions about the prices that Unilever and Kao will charge. Using the demand curve and cost numbers given above, we have done these calculations and tabulated the results in Table 12.2. Each entry shows your profit, in thousands of dollars per month, for a particular combination of prices (while assuming in each case that Unilever and Kao set the same price). For example, if you charge $1.30 and Unilever and Kao both charge $1.50, you will earn a profit of $15,000 per month. But remember that in all likelihood, the managers of Unilever and Kao are making the same calculations that you are and probably have their own versions of Table 12.2. Now suppose your competitors charge $1.50 or more. As the table shows, you would want to charge only $1.40, because that price gives you the highest profit. (For example, if they charged $1.50, you would make $29,000 per month by charging $1.40 but only $20,000 by charging $1.50, and $15,000 by |
charging $1.30.) Consequently, you would not want to charge $1.50 (or more). Assuming that your competitors have followed the same reasoning, you should not expect them to charge $1.50 (or more) either. What if your competitors charge $1.30? In that case, you will lose money, but you will lose the least amount of money ($6000 per month) by charging TABLE 12.2 P&G’S PROFIT (IN THOUSANDS OF DOLLARS PER MONTH) COMPETITOR’S (EQUAL) PRICES ($) P&G’S PRICE ($) 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 −226 −106 −56 −44 −52 −70 −93 −215 −204 −194 −183 −174 −165 −155 −89 −37 −25 −32 −51 −76 −73 −19 −6 −15 −34 −59 −87 −58 −43 −28 −15 2 12 3 −18 −44 −72 15 29 20 −1 −28 −57 31 46 36 14 −13 −44 47 62 52 30 1 −2 62 78 68 44 15 −118 −102 −30 −17 CHAPTER 12 • Monopolistic Competition and Oligopoly 469 $1.40. Your competitors would therefore not expect you to charge $1.30, and by the same reasoning, you should not expect them to charge a price this low. What price lets you do the best you can, given your competitors’ prices? It is $1.40. This is also the price at which your competitors are doing the best they can, so it is a Nash equilibrium.6 As the table shows, in this equilibrium you and your competitors each make a profit of $12,000 per month. If you could collude with your competitors, you could make a larger profit. You would all agree to charge $1.50, and each of you would earn $20,000. But this collusive agreement might be hard to enforce: You could increase your profit further at your competitor’s expense by dropping your price below theirs, and of course your competitors could do the same thing to you. 12.4 Competition versus Collusion: The Prisoners’ Dilemma A Nash equilibrium is a noncooperative equilibrium: Each firm makes the decisions that give it the highest possible profit, given the actions of its competitors. As we have seen, the resulting profit earned by each firm is higher than it would be under perfect competition but lower than if the firms colluded. Collusion, however, is illegal, and most managers prefer to stay out of jail. But if cooperation can lead to higher profits, why don’t firms cooperate without explicitly colluding? In particular, if you and your competitor can both figure out the profit-maximizing price you would agree to charge if you were to collude, why not just set that price and hope your competitor will do the same? If your competitor does do the same, you will both make more money. The problem is that your competitor probably won’t choose to set price at the collusive level. Why not? Because your competitor would do better by choosing a lower price, even if it knew that you were going to set price at the collusive level. To understand this, let’s go back to our example of price competition from the last section. The firms in that example each have a fixed cost of $20, have zero variable cost, and face the following demand curves: = = Firm 1 Firm 2 s demand: Q1 s demand: Q2 = 12 - 2P1 = 12 - 2P2 + P2 + P1 We found that in the Nash equilibrium each firm will charge a price of $4 and earn a profit of $12, whereas if the firms collude, they will charge a price of $6 and earn a profit of $16. Now suppose that the firms do not collude, but that Firm 1 charges the $6 collusive price, hoping that Firm 2 will do the same. If Firm 2 does do the same, it will earn a profit of $16. But what if it charges the $4 price instead? In that case, Firm 2 would earn a profit of p 2 = P2Q2 - 20 = (4)[12 - (2)(4) + 6] - 20 = $20 6This Nash equilibrium can also be derived algebraically from the demand curve and cost data above. We leave this to you as an exercise. 470 PART 3 • Market Structure and Competitive Strategy • noncooperative game Game in which negotiation and enforcement of binding contracts are not possible. • payoff matrix Table showing profit (or payoff) to each firm given its decision and the decision of its competitor. • prisoners’ dilemma Game theory example in which two prisoners must decide separately whether to confess to a crime; if a prisoner confesses, he will receive a lighter sentence and his accomplice will receive a heavier one, but if neither confesses, sentences will be lighter than if both confess. Firm 1, on the other hand, will earn a profit of only p 1 = P1Q1 - 20 = (6)[12 - (2)(6) + 4] - 20 = $4 So if Firm 1 charges $6 but Firm 2 charges only $4, Firm 2’s profit will increase to $20. And it will do so at the expense of Firm 1’s profit, which will fall to $4. Clearly, Firm 2 does best by charging only $4. Similarly, Firm 1 does best by charging only $4. If Firm 2 charges $6 and Firm 1 charges $4, Firm 1 will earn a $20 profit and Firm 2 only $4. PAYOFF MATRIX Table 12.3 summarizes the results of these different possibilities. In deciding what price to set, the two firms are playing a noncooperative game: Each firm independently does the best it can, taking its competitor into account. Table 12.3 is called the payoff matrix for this game because it shows the profit (or payoff) to each firm given its decision and the decision of its competitor. For example, the upper left-hand corner of the payoff matrix tells us that if both firms charge $4, each will make a $12 profit. The upper right-hand corner tells us that if Firm 1 charges $4 and Firm 2 charges $6, Firm 1 will make $20 and Firm 2 $4. This payoff matrix can clarify the answer to our original question: Why don’t firms behave cooperatively, and thereby earn higher profits, even if they can’t collude? In this case, cooperating means both firms charging $6 instead of $4 and thereby earning $16 instead of $12. The problem is that each firm always makes more money by charging $4, no matter what its competitor does. As the payoff matrix shows, if Firm 2 charges $4, Firm 1 does best by charging $4. And if Firm 2 charges $6, Firm 1 still does best by charging $4. Similarly, Firm 2 always does best by charging $4, no matter what Firm 1 does. As a result, unless the two firms can sign an enforceable agreement to charge $6, neither firm can expect its competitor to charge $6, and both will charge $4. THE PRISONERS’ DILEMMA A classic example in game theory, called the prisoners’ dilemma, illustrates the problem faced by oligopolistic firms. It goes as follows: Two prisoners have been accused of collaborating in a crime. They are in separate jail cells and cannot communicate with each other. Each has been asked to confess. If both prisoners confess, each will receive a prison term of five years. If neither confesses, the prosecution’s case will be difficult to make, so the prisoners can expect to plea bargain and receive terms of two years. On the other hand, if one prisoner confesses and the other does not, the one who confesses will receive a term of only one year, while the other will go to prison for 10 years. If you were one of these prisoners, what would you do—confess or not confess? The payoff matrix in Table 12.4 summarizes the possible outcomes. (Note that the “payoffs” are negative; the entry in the lower right-hand corner means a TABLE 12.3 PAYOFF MATRIX FOR PRICING GAME FIRM 2 CHARGE $4 CHARGE $6 Firm 1 Charge $4 Charge $6 $12, $12 $20, $4 $4, $20 $16, $16 CHAPTER 12 • Monopolistic Competition and Oligopoly 471 TABLE 12.4 PAYOFF MATRIX FOR PRISONERS’ DILEMMA PRISONER B CONFESS DON’T CONFESS Prisoner A Confess Don’t confess −5, −5 −10, −1 −1, −10 −2, −2 two-year sentence for each prisoner.) As the table shows, our prisoners face a dilemma. If they could both agree not to confess (in a way that would be binding), then each would go to jail for only two years. But they can’t talk to each other, and even if they could, can they trust each other? If Prisoner A does not confess, he risks being taken advantage of by his former accomplice. After all, no matter what Prisoner A does, Prisoner B comes out ahead by confessing. Likewise, Prisoner A always comes out ahead by confessing, so Prisoner B must worry that by not confessing, she will be taken advantage of. Therefore, both prisoners will probably confess and go to jail for five years. Oligopolistic firms often find themselves in a prisoners’ dilemma. They must decide whether to compete aggressively, attempting to capture a larger share of the market at their competitor’s expense, or to “cooperate” and compete more passively, coexisting with their competitors and settling for their current market share, and perhaps even implicitly colluding. If the firms compete passively, setting high prices and limiting output, they will make higher profits than if they compete aggressively. Like our prisoners, however, each firm has an incentive to “fink” and undercut its competitors, and each knows that its competitors have the same incentive. As desirable as cooperation is, each firm worries—with good reason—that if it competes passively, its competitor might decide to compete aggressively and seize the lion’s share of the market. In the pricing problem illustrated in Table 12.3, both firms do better by “cooperating” and charging a high price. But the firms are in a prisoners’ dilemma, where neither can trust its competitor to set a high price. EXAM PLE 12.3 PROCTER & GAMBLE IN A PRISONERS’ DILEMMA In Example 12.2, we examined the problem that arose when P&G, Unilever, and Kao Soap all planned to enter the Japanese market for Gypsy Moth Tape at the same time. They all faced the same cost and demand conditions, and each firm had to decide on a price that took its competitors into account. In Table 12.2, (page 468) we tabulated the profits to P&G corresponding to alternative prices that the firm and its competitors might charge. We argued that P&G should expect its competitors to charge a price of $1.40 and should do the same.7 P&G would be better off if it and its competitors all charged a price of $1.50. This is clear from the payoff matrix in Table 12.5. This payoff matrix is the portion of Table 12.2 corresponding to prices of $1.40 and $1.50, with |
the payoffs to P&G’s competitors also tabulated.8 If all the firms charge $1.50, each will make a profit of $20,000 per month, 7As in Example 12.2, some of the facts about the product and the market have been altered to protect P&G’s proprietary interests. 472 PART 3 • Market Structure and Competitive Strategy TABLE 12.5 PAYOFF MATRIX FOR PRICING PROBLEM UNILEVER AND Kao CHARGE $1.40 CHARGE $1.50 P&G Charge $1.40 Charge $1.50 $12, $12 $3, $21 $29, $11 $20, $20 instead of the $12,000 per month they make by charging $1.40. So why don’t they charge $1.50? Because these firms are in a prisoners’ dilemma. No matter what Unilever and Kao do, P&G makes more money by charging $1.40. For example, if Unilever and Kao charge $1.50, P&G can make $29,000 per month by charging $1.40, versus $20,000 by charging $1.50. Unilever and Kao are in the same boat. For example, if P&G charges $1.50 and Unilever and Kao both charge $1.40, P&G’s competitors will each make $21,000, instead of $20,000.9 As a result, P&G knows that if it sets a price of $1.50, its competitors will have a strong incentive to undercut and charge $1.40. P&G will then have only a small share of the market and make only $3000 per month profit. Should P&G make a leap of faith and charge $1.50? If you were faced with this dilemma, what would you do? 12.5 Implications of the Prisoners’ Dilemma for Oligopolistic Pricing Does the prisoners’ dilemma doom oligopolistic firms to aggressive competition and low profits? Not necessarily. Although our imaginary prisoners have only one opportunity to confess, most firms set output and price over and over again, continually observing their competitors’ behavior and adjusting their own accordingly. This allows firms to develop reputations from which trust can arise. As a result, oligopolistic coordination and cooperation can sometimes prevail. Take, for example, an industry made up of three or four firms that have coexisted for a long time. Over the years, the managers of those firms might grow tired of losing money because of price wars, and an implicit understanding might arise by which all the firms maintain high prices and no firm tries to take market share from its competitors. Although each firm might be tempted to undercut its competitors, its managers know that the resulting gains will be short lived: Competitors will retaliate, and the result will be renewed warfare and lower profits over the long run. This resolution of the prisoners’ dilemma occurs in some industries, but not in others. Sometimes managers are not content with the moderately high profits resulting from implicit collusion and prefer to compete aggressively in order to increase market share. Sometimes implicit understandings are difficult to reach. For example, firms with different costs and different assessments of market demand might disagree about the “correct” collusive price. Firm A might think 8This payoff matrix assumes that Unilever and Kao both charge the same price. Entries represent profits in thousands of dollars per month. 9If P&G and Kao both charged $1.50 and only Unilever undercut and charged $1.40, Unilever would make $29,000 per month. It is especially profitable to be the only firm charging the low price. CHAPTER 12 • Monopolistic Competition and Oligopoly 473 the “correct” price is $10, while Firm B thinks it is $9. When it sets a $9 price, Firm A might view this as an attempt to undercut and retaliate by lowering its price to $8. The result is a price war. In many industries, therefore, implicit collusion is short lived. There is often a fundamental layer of mistrust, so warfare erupts as soon as one firm is perceived by its competitors to be “rocking the boat” by changing its price or increasing advertising. Price Rigidity Because implicit collusion tends to be fragile, oligopolistic firms often have a strong desire for price stability. This is why price rigidity can be a characteristic of oligopolistic industries. Even if costs or demand change, firms are reluctant to change price. If costs fall or market demand declines, they fear that lower prices might send the wrong message to their competitors and set off a price war. And if costs or demand rises, they are reluctant to raise prices because they are afraid that their competitors may not raise theirs. Price rigidity is the basis of the kinked demand curve model of oligopoly. According to this model, each firm faces a demand curve kinked at the currently prevailing price P*. (See Figure 12.7.) At prices above P*, the demand curve is very elastic. The reason is that the firm believes that if it raises its price above P*, other firms will not follow suit, and it will therefore lose sales and much of its market share. On the other hand, the firm believes that if it lowers its price below P*, other firms will follow suit because they will not want to lose their shares of the market. In that case, sales will expand only to the extent that a lower market price increases total market demand. Because the firm’s demand curve is kinked, its marginal revenue curve is discontinuous. (The bottom part of the marginal revenue curve corresponds to the less elastic part of the demand curve, as shown by the solid portions of each curve.) As a result, the firm’s costs can change without resulting in a change in • price rigidity Characteristic of oligopolistic markets by which firms are reluctant to change prices even if costs or demands change. • kinked demand curve model Oligopoly model in which each firm faces a demand curve kinked at the currently prevailing price: at higher prices demand is very elastic, whereas at lower prices it is inelastic. $/Q P* MC′ MC D FIGURE 12.7 THE KINKED DEMAND CURVE Each firm believes that if it raises its price above the current price P*, none of its competitors will follow suit, so it will lose most of its sales. Each firm also believes that if it lowers price, everyone will follow suit, and its sales will increase only to the extent that market demand increases. As a result, the firm’s demand curve D is kinked at price P*, and its marginal revenue curve MR is discontinuous at that point. If marginal cost increases from MC to MC’, the firm will still produce the same output level Q* and charge the same price P*. Q* Quantity MR 474 PART 3 • Market Structure and Competitive Strategy • price signaling Form of implicit collusion in which a firm announces a price increase in the hope that other firms will follow suit. • price leadership Pattern of pricing in which one firm regularly announces price changes that other firms then match. price. As shown in Figure 12.7, marginal cost could increase but still equal marginal revenue at the same output level, so that price stays the same. Although the kinked demand curve model is attractively simple, it does not really explain oligopolistic pricing. It says nothing about how firms arrived at price P* in the first place, and why they didn’t arrive at some different price. It is useful mainly as a description of price rigidity rather than as an explanation of it. The explanation for price rigidity comes from the prisoners’ dilemma and from firms’ desires to avoid mutually destructive price competition. Price Signaling and Price Leadership A big impediment to implicitly collusive pricing is the fact that it is difficult for firms to agree (without talking to each other) on what the price should be. Coordination is particularly difficult when cost and demand conditions—and thus the “correct” price—are changing. Price signaling is a form of implicit collusion that sometimes gets around this problem. For example, a firm might announce that it has raised its price (perhaps through a press release) and hope that its competitors will take this announcement as a signal that they should also raise prices. If competitors follow suit, all of the firms will earn higher profits. Sometimes a pattern is established whereby one firm regularly announces price changes and other firms in the industry follow suit. This pattern is called price leadership: One firm is implicitly recognized as the “leader,” while the other firms, the “price followers,” match its prices. This behavior solves the problem of coordinating price: Everyone charges what the leader is charging. Suppose, for example, that three oligopolistic firms are currently charging $10 for their product. (If they all know the market demand curve, this might be the Nash equilibrium price.) Suppose that by colluding, they could all set a price of $20 and greatly increase their profits. Meeting and agreeing to set a price of $20 is illegal. But suppose instead that Firm A raises its price to $15, and announces to the business press that it is doing so because higher prices are needed to restore economic vitality to the industry. Firms B and C might view this as a clear message—namely, that Firm A is seeking their cooperation in raising prices. They might then raise their own prices to $15. Firm A might then increase price further—say, to $18—and Firms B and C might raise their prices as well. Whether or not the profit-maximizing price of $20 is reached (or surpassed), a pattern of coordination has been established that, from the firm’s point of view, may be nearly as effective as meeting and formally agreeing on a price.10 This example of signaling and price leadership is extreme and might lead to an antitrust lawsuit. But in some industries, a large firm might naturally emerge as a leader, with the other firms deciding that they are best off just matching the leader’s prices, rather than trying to undercut the leader or each other. An example is the U.S. automobile industry, where General Motors has traditionally been the price leader. Price leadership can also serve as a way for oligopolistic firms to deal with the reluctance to change prices, a reluctance that arises out of the fear of being undercut or “rocking the boat.” As cost and demand conditions change, firms may find it in |
creasingly necessary to change prices that have remained rigid for some time. In that case, they might look to a price leader to signal when and by how much price should change. Sometimes a large firm will naturally act as leader; sometimes different firms will act as leader from time to time. The example that follows illustrates this. 10For a formal model of how such price leadership can facilitate collusion, see Julio J. Rotemberg and Garth Saloner, “Collusive Price Leadership,” Journal of Industrial Economics, 1990; 93–111. CHAPTER 12 • Monopolistic Competition and Oligopoly 475 EXAM PLE 12.4 PRICE LEADERSHIP AND PRICE RIGIDITY IN COMMERCIAL BANKING Commercial banks borrow money from individuals and companies who deposit funds in checking accounts, savings accounts, and certificates of deposit. They then use this money to make loans to household and corporate borrowers. By lending at an interest rate higher than the rate that they pay on their deposits, they earn a profit. The largest commercial banks in the United States compete with each other to make loans to large corporate clients. The main form of competition is over price—in this case, the interest rates they charge. If competition becomes aggressive, the interest rates fall, and so do profits. The incentive to avoid aggressive competition leads to price rigidity, and to a form of price leadership. The interest rate that banks charge large corporate clients is called the prime rate. Because it is widely known, it is a convenient focal point for price leadership. Most large banks charge the same or nearly the same prime rate; they avoid making frequent changes in the rate that might be destabilizing and lead to competitive warfare. The prime rate changes only when money market conditions cause other interest rates to rise or fall substantially. When that happens, one of the major banks announces a change in its rate and other banks quickly follow suit. Different banks act as leader from time to time, but when one bank announces a change, the others follow within two or three days. Figure 12.8 compares the prime rate with the interest rate on high-grade (AAA) corporate bonds. Observe that although the corporate bond rate fluctuated continuously, there were extended periods during which the prime rate did the change. This is an example of price rigidity—banks are reluctant to change their lending rate for fear of being undercut and losing business to their competitors. 10 Prime Rate AAA Corporate Bond Yield 3 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 FIGURE 12.8 PRIME RATE VERSUS CORPORATE BOND RATE The prime rate is the rate that major banks charge large corporate customers for short-term loans. It changes only infrequently because banks are reluctant to undercut one another. When a change does occur, it begins with one bank, and other banks quickly follow suit. The corporate bond rate is the return on long-term corporate bonds. Because these bonds are widely traded, this rate fluctuates with market conditions. 476 PART 3 • Market Structure and Competitive Strategy E XAM PLE 12.5 THE PRICES OF COLLEGE TEXTBOOKS If you bought this book new at a college bookstore in the United States, you probably paid something close to $200 for it. Now, there’s no doubt about it—this is a fantastic book! But $200? Why so much?11 These publishers have an incentive to avoid a price war that could drive prices down. The best way to avoid a price war is to avoid discounting and to increase prices in lockstep on a regular basis. A quick visit to the bookstore will prove that the price of this book is not at all unusual. Most textbooks sold in the United States have retail prices in the $200 range. In fact even other microeconomics textbooks—which are clearly inferior to this one—sell for around $200. Publishing companies set the prices of their textbooks, so should we expect competition among publishers to drive down prices? Partly because of mergers and acquisitions over the last decade or so, college textbook publishing is an oligopoly. (Pearson, the publisher of this book, is the largest college textbook publisher, followed by Cengage Learning and McGraw-Hill.) The retail bookstore industry is also highly concentrated, and the retail markup on textbooks is around 30 percent. Thus a $200 retail price implies that the publisher is receiving a net (wholesale) price of about $150. The elasticity of demand is low, because the instructor chooses the textbook, often disregarding the price. On the other hand, if the price is too high, some students will buy a used book or decide not to buy the book at all. In fact, it might be the case that publishers could earn more money by lowering textbook prices. So why don’t they do that? First, that might lead to a dreaded price war. Second, publishers might not have read this book! • dominant firm Firm with a large share of total sales that sets price to maximize profits, taking into account the supply response of smaller firms. The Dominant Firm Model In some oligopolistic markets, one large firm has a major share of total sales while a group of smaller firms supplies the remainder of the market. The large firm might then act as a dominant firm, setting a price that maximizes its own profits. The other firms, which individually could have little influence over price, would then act as perfect competitors: They take the price set by the dominant firm as given and produce accordingly. But what price should the dominant firm set? To maximize profit, it must take into account how the output of the other firms depends on the price it sets. Figure 12.9 shows how a dominant firm sets its price. Here, D is the market demand curve, and SF is the supply curve (i.e., the aggregate marginal cost curve) of the smaller fringe firms. The dominant firm must determine its demand curve DD. As the figure shows, this curve is just the difference between market demand and the supply of fringe firms. For example, at price P1, the supply of fringe firms is just equal to market demand; thus the dominant firm can sell nothing at this price. At a price P2 or less, fringe firms will not supply any of the good, so the dominant firm faces the market demand curve. At prices between P1 and P2, the dominant firm faces the demand curve DD. 11You might have saved some money by buying the book via the Internet. If you bought the book used, or if you rented an electronic edition, you probably paid about half the U.S. retail price. And if you bought the International Student Edition of the book, which is paperback and only sold outside the U.S., you probably paid much less. For an updated list of the prices of intermediate microeconomics textbooks, go to http://theory.economics.utoronto.ca/poet/. CHAPTER 12 • Monopolistic Competition and Oligopoly 477 Price D P1 P* P2 SF MCD DD FIGURE 12.9 PRICE SETTING BY A DOMINANT FIRM The dominant firm sets price, and the other firms sell all they want at that price. The dominant firm’s demand curve, DD, is the difference between market demand D and the supply of fringe firms SF . The dominant firm produces a quantity QD at the point where its marginal revenue MRD is equal to its marginal cost MCD. The corresponding price is P*. At this price, fringe firms sell QF, so that total sales equal QT. QF QD QT Quantity MRD Corresponding to DD is the dominant firm’s marginal revenue curve MRD. MCD is the dominant firm’s marginal cost curve. To maximize its profit, the dominant firm produces quantity QD at the intersection of MRD and MCD. From the demand curve DD, we find price P*. At this price, fringe firms sell a quantity QF; thus the total quantity sold is QT = QD + QF. 12.6 Cartels Producers in a cartel explicitly agree to cooperate in setting prices and output levels. Not all the producers in an industry need to join the cartel, and most cartels involve only a subset of producers. But if enough producers adhere to the cartel’s agreements, and if market demand is sufficiently inelastic, the cartel may drive prices well above competitive levels. Cartels are often international. While U.S. antitrust laws prohibit American companies from colluding, those of other countries are much weaker and are sometimes poorly enforced. Furthermore, nothing prevents countries, or companies owned or controlled by foreign governments, from forming cartels. For example, the OPEC cartel is an international agreement among oil-producing countries which has succeeded in raising world oil prices above competitive levels. Other international cartels have also succeeded in raising prices. During the mid-1970s, for example, the International Bauxite Association (IBA) quadrupled bauxite prices, and a secretive international uranium cartel pushed up uranium prices. Some cartels had longer successes: From 1928 through the early 1970s, 478 PART 3 • Market Structure and Competitive Strategy Recall from §10.2 that monopoly power refers to market power on the part of a seller—the ability of a firm to price its product above its marginal cost of production. a cartel called Mercurio Europeo kept the price of mercury close to monopoly levels, and an international cartel monopolized the iodine market from 1878 through 1939. However, most cartels have failed to raise prices. An international copper cartel operates to this day, but it has never had a significant impact on copper prices. Cartel attempts to drive up the prices of tin, coffee, tea, and cocoa have also failed.12 CONDITIONS FOR CARTEL SUCCESS Why do some cartels succeed while others fail? There are two conditions for cartel success. First, a stable cartel organization must be formed whose members agree on price and production levels and then adhere to that agreement. Unlike our prisoners in the prisoners’ dilemma, cartel members can talk to each other to formalize an agreement. This does not mean, however, that agreeing is easy. Different members may have differen |
t costs, different assessments of market demand, and even different objectives, and they may therefore want to set price at different levels. Furthermore, each member of the cartel will be tempted to “cheat” by lowering its price slightly to capture a larger market share than it was allotted. Most often, only the threat of a long-term return to competitive prices deters cheating of this sort. But if the profits from cartelization are large enough, that threat may be sufficient. The second condition is the potential for monopoly power. Even if a cartel can solve its organizational problems, there will be little room to raise price if it faces a highly elastic demand curve. Potential monopoly power may be the most important condition for success; if the potential gains from cooperation are large, cartel members will have more incentive to solve their organizational problems. Analysis of Cartel Pricing Only rarely do all the producers of a good combine to form a cartel. A cartel usually accounts for only a portion of total production and must take into account the supply response of competitive (noncartel) producers when it sets price. Cartel pricing can thus be analyzed by using the dominant firm model discussed earlier. We will apply this model to two cartels, the OPEC oil cartel and the CIPEC copper cartel.13 This will help us understand why OPEC was successful in raising price while CIPEC was not. ANALYZING OPEC Figure 12.10 illustrates the case of OPEC. Total demand TD is the total world demand curve for crude oil, and Sc is the competitive (non-OPEC) supply curve. The demand for OPEC oil DOPEC is the difference between total demand and competitive supply, and MROPEC is the corresponding marginal revenue curve. MCOPEC is OPEC’s marginal cost curve; as you can see, OPEC has much lower production costs than do non-OPEC producers. OPEC’s marginal revenue and marginal cost are equal at quantity QOPEC, which is the quantity that OPEC will produce. We see from OPEC’s demand curve that the price will be P*, at which competitive supply is Qc. Suppose petroleum-exporting countries had not formed a cartel but had instead produced competitively. Price would then have equaled marginal cost. We can therefore determine the competitive price from the point where OPEC’s 12See Jeffrey K. MacKie-Mason and Robert S. Pindyck, “Cartel Theory and Cartel Experience in International Minerals Markets,” in Energy: Markets and Regulation (Cambridge, MA: MIT Press, 1986). 13CIPEC is the French acronym for International Council of Copper Exporting Countries. CHAPTER 12 • Monopolistic Competition and Oligopoly 479 Price TD Sc FIGURE 12.10 THE OPEC OIL CARTEL TD is the total world demand curve for oil, and Sc is the competitive (non-OPEC) supply curve. OPEC’s demand DOPEC is the difference between the two. Because both total demand and competitive supply are inelastic, OPEC’s demand is inelastic. OPEC’s profit-maximizing quantity QOPEC is found at the intersection of its marginal revenue and marginal cost curves; at this quantity, OPEC charges price P*. If OPEC producers had not cartelized, price would be Pc, where OPEC’s demand and marginal cost curves intersect. DOPEC MC OPEC P* ′ Pc MR OPEC Qc QOPEC QT Quantity demand curve intersects its marginal cost curve. That price, labeled Pc, is much lower than the cartel price P*. Because both total demand and non-OPEC supply are inelastic, the demand for OPEC oil is also fairly inelastic. Thus the cartel has substantial monopoly power, and it has used that power to drive prices well above competitive levels. In Chapter 2, we stressed the importance of distinguishing between short-run and long-run supply and demand. That distinction is important here. The total demand and non-OPEC supply curves in Figure 12.10 apply to a short- or intermediate-run analysis. In the long run, both demand and supply will be much more elastic, which means that OPEC’s demand curve will also be much more elastic. We would thus expect that in the long run OPEC would be unable to maintain a price that is so much above the competitive level. Indeed, during 1982–1989, oil prices fell in real terms, largely because of the long-run adjustment of demand and non-OPEC supply. ANALYZING CIPEC Figure 12.11 provides a similar analysis of CIPEC, which consists of four copper-producing countries: Chile, Peru, Zambia, and Congo (formerly Zaire), that collectively account for less than half of world copper production. In these countries, production costs are lower than those of non-CIPEC producers, but except for Chile, not much lower. In Figure 12.11, CIPEC’s marginal cost curve is therefore drawn only a little below the non-CIPEC supply curve. CIPEC’s demand curve DCIPEC is the difference between total demand TD and non-CIPEC supply Sc. CIPEC’s marginal cost and marginal revenue curves intersect at quantity QCIPEC, with the corresponding price P*. Again, the competitive price Pc is found at the point where CIPEC’s demand curve intersects its marginal cost curve. Note that this price is very close to the cartel price P*. Why can’t CIPEC increase copper prices much? As Figure 12.11 shows, the total demand for copper is more elastic than that for oil. (Other materials, such 480 PART 3 • Market Structure and Competitive Strategy Price TD FIGURE 12.11 THE CIPEC COPPER CARTEL TD is the total demand for copper and Sc is the competitive (non-CIPEC) supply. CIPEC’s demand DCIPEC is the difference between the two. Both total demand and competitive supply are relatively elastic, so CIPEC’s demand curve is elastic, and CIPEC has very little monopoly power. Note that CIPEC’s optimal price P* is close to the competitive price Pc. P* Pc Sc MCCIPEC DCIPEC MR CIPEC QCIPEC Qc QT Quantity as aluminum, can easily be substituted for copper.) Also, competitive supply is much more elastic. Even in the short run, non-CIPEC producers can easily expand supply if prices should rise (in part because of the availability of supply from scrap metal). Thus CIPEC’s potential monopoly power is small. As the examples of OPEC and CIPEC illustrate, successful cartelization requires two things. First, the total demand for the good must not be very price elastic. Second, either the cartel must control nearly all the world’s supply or, if it does not, the supply of noncartel producers must not be price elastic. Most international commodity cartels have failed because few world markets meet both conditions. E XAM PLE 12.6 THE CARTELIZATION OF INTERCOLLEGIATE ATHLETICS Many people think of intercollegiate athletics as an extracurricular activity for college students and a diversion for fans. They assume that universities support athletics because it not only gives amateur athletes a chance to develop their skills and play football or basketball before large audiences but also provides entertainment and promotes school spirit and alumni support. Although it does these things, intercollegiate athletics is also a big—and an extremely profitable—industry. Like any industry, intercollegiate athletics has firms and consumers. The “firms” are the universities that support and finance teams. The inputs to production are the coaches, student athletes, and capital in the form of stadiums and playing fields. The consumers, many of whom are current or former college students, are the fans who buy tickets to games and the TV and radio networks that pay to broadcast them. There are many firms and consumers, which suggests that the industry is competitive. But the persistently high level of profits in this industry is inconsistent with competition—a large state university can regularly earn more than $6 million a year in profits from football games CHAPTER 12 • Monopolistic Competition and Oligopoly 481 alone.14 This profitability is the result of monopoly power, obtained via cartelization. The cartel organization is the National Collegiate Athletic Association (NCAA). The NCAA restricts competition in a number of important ways. To reduce bargaining power by student athletes, the NCAA creates and enforces rules regarding eligibility and terms of compensation. To reduce competition by universities, it limits the number of games that can be played each season and the number of teams that can participate in each division. And to limit price competition, the NCAA positioned itself as the sole negotiator of all football television contracts, thereby monopolizing one of the main sources of industry revenues. The NCAA was forced to end this practice in 1984. Has the NCAA been a successful cartel? Like most cartels, its members have occasionally broken its rules and regulations. But until 1984, it was successful in increasing the monopoly power of the college basketball industry well above what it would have been otherwise. In 1984, however, the Supreme Court ruled that the NCAA’s monopolization of football television contracts was illegal, allowing individual universities to negotiate their own contracts. The ensuing competition led to an increase in the amount of college football shown on television, but a drop in the contract fees paid to schools, which has resulted in a decrease in the total revenues to schools. All in all, although the Supreme Court’s ruling reduced the NCAA’s monopoly power, it did not eliminate it. The NCAA still negotiates fees for other televised collegiate sports; in 2010, CBS and Turner Broadcasting signed a $10.8 billion deal with the NCAA to cover the Division I Men’s Basketball Championship for 14 years. At the same time, the Association continued a 2001 deal with ESPN to allow coverage of 11 nonrevenue sports (including the Division I Women’s Basketball Championship, soccer, men’s ice hockey, and the College World Series). The original deal called for ESPN to pay the NCAA $200 million over 11 years. The NCAA’s anticompetitive practices have come under numerous attacks. In 2005, the National Invitation Tournament (NIT), a college basketball tournament operated b |
y the Metropolitan Intercollegiate Basketball Committee, challenged the NCAA’s rule that effectively forced schools invited to its tournament to boycott the NIT. The NIT claimed that this practice was anticompetitive and an illegal use of the NCAA’s powers. The parties ultimately settled the lawsuit for nearly $60 million. In 2007, the NCAA was sued by 11,500 Division I football and basketball players claiming that it illegally fixed the price of an athletic scholarship below the cost of a college education. According to the players, the NCAA shortchanged them, on average, $2,500 a year because of its arbitrary limit on scholarships. EX AM PLE 12.7 THE MILK CARTEL The U.S. government has supported the price of milk since the Great Depression and continues to do so today. The government, however, scaled back price supports during the 1990s, and as a result, wholesale prices of milk have fluctuated more widely. Not surprisingly, farmers have been complaining. In response to these complaints, in 1996 the federal government allowed milk producers in the six New England states to cartelize. The cartel—called the Northeast Interstate Dairy Compact—set minimum wholesale prices for milk, and was exempt from the antitrust laws. The result was that consumers in New England paid more for a gallon of milk than consumers elsewhere in the nation. In 1999, Congress responded to the lobbying efforts of farmers in other states by attempting to expand the milk cartel. introduced Legislation was that would have allowed dairy farmers in New York, New Jersey, Maryland, Delaware, and Pennsylvania to join the New England states and thereby form a cartel covering most of the northeast United States.15 Not wanting to be left out, dairy 14See “In Big-Time College Athletics, the Real Score Is in Dollars,” New York Times, March 1, 1987. 482 PART 3 • Market Structure and Competitive Strategy farmers in the South also lobbied Congress for higher milk prices. As a result, the 1999 legislation also authorized 16 southern states, including Texas, Florida, and Georgia, to create their own regional cartel. Studies have suggested that the original cartel (covering only the New England states) has caused retail prices of milk to rise by only a few cents a gallon. Why so little? The reason is that the New England cartel is surrounded by a fringe of noncartel producers—namely, dairy farmers in New York, New Jersey, and other states. Expanding the cartel, however, would have shrunk the competitive fringe, thereby giving the cartel a greater influence over milk prices. Recognizing the political headaches and regional conflict caused by these attempts at cartelization, Congress ended the Northeast Interstate Dairy Compact in October 2001. Although proponents of the Compact attempted to revive the cartel, opposition in Congress has been strong and, as of 2011, the cartel has not been re-authorized. Nonetheless, milk production continues to benefit from federal price supports. SUMMARY 1. In a monopolistically competitive market, firms compete by selling differentiated products, which are highly substitutable. New firms can enter or exit easily. Firms have only a small amount of monopoly power. In the long run, entry will occur until profits are driven to zero. Firms then produce with excess capacity (i.e., at output levels below those that minimize average cost). 2. In an oligopolistic market, only a few firms account for most or all of production. Barriers to entry allow some firms to earn substantial profits, even over the long run. Economic decisions involve strategic considerations—each firm must consider how its actions will affect its rivals, and how they are likely to react. 3. In the Cournot model of oligopoly, firms make their output decisions at the same time, each taking the other’s output as fixed. In equilibrium, each firm is maximizing its profit, given the output of its competitor, so no firm has an incentive to change its output. The firms are therefore in a Nash equilibrium. Each firm’s profit is higher than it would be under perfect competition but less than what it would earn by colluding. 4. In the Stackelberg model, one firm sets its output first. That firm has a strategic advantage and earns a higher profit. It knows that it can choose a large output and QUESTIONS FOR REVIEW that its competitors will have to choose smaller outputs if they want to maximize profits. 5. The Nash equilibrium concept can also be applied to markets in which firms produce substitute goods and compete by setting price. In equilibrium, each firm maximizes its profit, given the prices of its competitors, and so has no incentive to change price. 6. Firms would earn higher profits by collusively agreeing to raise prices, but the antitrust laws usually prohibit this. They might all set high prices without colluding, each hoping its competitors will do the same, but they are in a prisoners’ dilemma, which makes this unlikely. Each firm has an incentive to cheat by lowering its price and capturing sales from competitors. 7. The prisoners’ dilemma creates price rigidity in oligopolistic markets. Firms are reluctant to change prices for fear of setting off price warfare. 8. Price leadership is a form of implicit collusion that sometimes gets around the prisoners’ dilemma. One firm sets price and other firms follow suit. 9. In a cartel, producers explicitly collude in setting prices and output levels. Successful cartelization requires that the total demand not be very price elastic, and that either the cartel control most supply or else the supply of noncartel producers be inelastic. 1. What are the characteristics of a monopolistically competitive market? What happens to the equilibrium price and quantity in such a market if one firm introduces a new, improved product? 2. Why is the firm’s demand curve flatter than the total market demand curve in monopolistic competition? Suppose a monopolistically competitive firm is making a profit in the short run. What will happen to its demand curve in the long run? 3. Some experts have argued that too many brands of breakfast cereal are on the market. Give an argument to support this view. Give an argument against it. 15“Congress Weighs an Expanded Milk Cartel That Would Aid Farmers by Raising Prices,” New York Times, May 2, 1999. For an update, go to the following Web site: www.dairycompact.org. CHAPTER 12 • Monopolistic Competition and Oligopoly 483 4. Why is the Cournot equilibrium stable? (i.e., Why don’t firms have any incentive to change their output levels once in equilibrium?) Even if they can’t collude, why don’t firms set their outputs at the joint profitmaximizing levels (i.e., the levels they would have chosen had they colluded)? 5. In the Stackelberg model, the firm that sets output first has an advantage. Explain why. 6. What do the Cournot and Bertrand models have in common? What is different about the two models? 7. Explain the meaning of a Nash equilibrium when firms are competing with respect to price. Why is the equilibrium stable? Why don’t the firms raise prices to the level that maximizes joint profits? EXERCISES 1. Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain. 2. Consider two firms facing the demand curve P = 50 − 5Q, where Q = Q1 + Q2. The firms’ cost functions are C1(Q1) = 20 + 10 Q1 and C2(Q2) = 10 + 12 Q2. a. Suppose both firms have entered the industry. What is the joint profit-maximizing level of output? How much will each firm produce? How would your answer change if the firms have not yet entered the industry? b. What is each firm’s equilibrium output and profit if they behave noncooperatively? Use the Cournot model. Draw the firms’ reaction curves and show the equilibrium. c. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but a takeover is not? 3. A monopolist can produce at a constant average (and marginal) cost of AC = MC = $5. It faces a market demand curve given by Q = 53 − P. a. Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. b. Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1 + Q2 = 53 - P 8. The kinked demand curve describes price rigidity. Explain how the model works. What are its limitations? Why does price rigidity occur in oligopolistic markets? 9. Why does price leadership sometimes evolve in oligopolistic markets? Explain how the price leader determines a profit-maximizing price. 10. Why has the OPEC oil cartel succeeded in raising prices substantially while the CIPEC copper cartel has not? What conditions are necessary for successful cartelization? What organizational problems must a cartel overcome? d. Calculate the Cournot equilibrium (i.e., the values of Q1 and Q2 for which each firm is doing as well as it can given its competitor’s output). What are the resulting market price and profits of each firm? *e. Suppose there are N firms in the industry, all with the same constant marginal cost, MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as N becomes large, the market price approaches the price that would prevail under perfect competition. 4. This exercise is a continuation of Exercise 3. We return to two firms with the same constant average and marginal cost, AC = MC = 5, facing the market demand curve Q1 + Q2 = 53 − P. Now we will use the Stackelberg model to analyze what will happen if one of the firms makes its output decision before the other. a. Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2). Find the reaction curves that tell each firm how much to produce in terms of the output of its c |
ompetitor. b. How much will each firm produce, and what will its profit be? 5. Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of Q1 and Q2. c. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of output on the assumption that its competitor’s output is fixed. Find each firm’s “reaction curve” (i.e., the rule that gives its desired output in terms of its competitor’s output). where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level. 6. Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs 484 PART 3 • Market Structure and Competitive Strategy are given by C1 = 60Q1 and C2 = 60Q2, where Q1 is the output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve: of lights, Everglow and Dimlit. They have identical cost functions: P = 300 - Q Ci = 10Qi + 1 2 Q = QE 2(i = E, D) Q i + QD where Q = Q1 + Q2. a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit. c. Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1’s profit differ from that found in part (b) above? d. Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm’s profits? 7. Suppose that two competing firms, A and B, produce a homogeneous good. Both firms have a marginal cost of MC = $50. Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium, and (iii) Bertrand equilibrium. a. Because Firm A must increase wages, its MC increases to $80. b. The marginal cost of both firms increases. c. The demand curve shifts to the right. 8. Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) = 40q. Assume that the demand curve for the industry is given by P = 100 − Q and that each firm expects the other to behave as a Cournot competitor. a. Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes its profits when taking its rival’s output as given. What are the profits of each firm? b. What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $25 and American had constant marginal and average costs of $40? c. Assuming that both firms have the original cost function, C(q) = 40q, how much should Texas Air be willing to invest to lower its marginal cost from 40 to 25, assuming that American will not follow suit? How much should American be willing to spend to reduce its marginal cost to 25, assuming that Texas Air will have marginal costs of 25 regardless of American’s actions? *9. Demand for light bulbs can be characterized by Q = 100 − P, where Q is in millions of boxes of lights sold and P is the price per box. There are two producers a. Unable to recognize the potential for collusion, the two firms act as short-run perfect competitors. What are the equilibrium values of QE, QD, and P? What are each firm’s profits? b. Top management in both firms is replaced. Each new manager independently recognizes the oligopolistic nature of the light bulb industry and plays Cournot. What are the equilibrium values of QE, QD, and P? What are each firm’s profits? c. Suppose the Everglow manager guesses correctly that Dimlit is playing Cournot, so Everglow plays Stackelberg. What are the equilibrium values of QE, QD, and P? What are each firm’s profits? d. If the managers of the two companies collude, what are the equilibrium values of QE, QD, and P? What are each firm’s profits? 10. Two firms produce luxury sheepskin auto seat covers: Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by C(q) = 30q + 1.5q 2 The market demand for these seat covers is represented by the inverse demand equation P = 300 - 3Q where Q = q1 + q2, total output. a. If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm? b. It occurs to the managers of WW and BBBS that they could do a lot better by colluding. If the two firms collude, what will be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case? c. The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. To aid in making the decision, the manager of WW constructs a payoff CHAPTER 12 • Monopolistic Competition and Oligopoly 485 matrix like the one below. Fill in each box with the profit of WW and the profit of BBBS. Given this payoff matrix, what output strategy is each firm likely to pursue? PROFIT PAYOFF MATRIX BBBS (WW PROFIT, BBBS PROFIT) PRODUCE COURNOT q PRODUCE CARTEL q WW Produce Cournot q Produce Cartel q d. Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much will BBBS produce? What is the market price, and what is the profit for each firm? Is WW better off by choosing its output first? Explain why or why not. *11. Two firms compete by choosing price. Their demand functions are and Q1 = 20 - P1 + P2 Q2 = 20 + P1 - P2 where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why. *12. The dominant firm model can help us understand the behavior of some cartels. Let’s apply this model to the OPEC oil cartel. We will use isoelastic curves to describe world demand W and noncartel (competitive) supply S. Reasonable numbers for the price elasticities of world demand and noncartel supply are −1/2 and 1/2, respectively. Then, expressing W and S in millions of barrels per day (mb/d), we could write and W = 160P -1/2 S = (3 1 3 )P1/2 Note that OPEC’s net demand is D = W − S. a. Draw the world demand curve W, the non-OPEC supply curve S, OPEC’s net demand curve D, and OPEC’s marginal revenue curve. For purposes of approximation, assume OPEC’s production cost is zero. Indicate OPEC’s optimal price, OPEC’s optimal production, and non-OPEC production on the diagram. Now, show on the diagram how the various curves will shift and how OPEC’s optimal price will change if non-OPEC supply becomes more expensive because reserves of oil start running out. b. Calculate OPEC’s optimal (profit-maximizing) price. (Hint: Because OPEC’s cost is zero, just write the expression for OPEC revenue and find the price that maximizes it.) c. Suppose the oil-consuming countries were to unite and form a “buyers’ cartel” to gain monopsony power. What can we say, and what can’t we say, about the impact this action would have on price? 13. Suppose the market for tennis shoes has one dominant firm and five fringe firms. The market demand is Q = 400 − 2 P. The dominant firm has a constant marginal cost of 20. The fringe firms each have a marginal cost of MC = 20 + 5q. a. Verify that the total supply curve for the five fringe firms is Qf = P − 20. b. Find the dominant firm’s demand curve. c. Find the profit-maximizing quantity produced and price charged by the dominant firm, and the quantity produced and price charged by each of the fringe firms. d. Suppose there are 10 fringe firms instead of five. How does this change your results? e. Suppose there continue to be five fringe firms but that each manages to reduce its marginal cost to MC = 20 + 2q. How does this change your results? 486 PART 3 • Market Structure and Competitive Strategy *14. A lemon-growing cartel consists of four orchards. Their total cost functions are TC 1 TC 2 TC 3 TC 4 = 20 + 5Q 1 2 = 25 + 3Q 2 2 = 15 + 4Q 3 2 = 20 + 6Q 4 2 TC is in hundreds of dollars, and Q is in cartons per month picked and shipped. a. Tabulate total, average, and marginal costs for each firm for output levels between 1 and 5 cartons per month (i.e., for 1, 2, 3, 4, and 5 cartons). b. If the cartel decided to ship 10 cartons per month and set a price of $25 per carton, how should output be allocated among the firms? c. At this shipping level, which firm has the most incentive to cheat? Does any firm not have an incentive to cheat? C H A P T E R 13 Game Theory and Competitive Strategy I |
n Chapter 12, we began to explore some of the strategic output and pricing decisions that firms must often make. We saw how a firm can take into account the likely responses of its competitors when it makes these decisions. However, there are many questions about market structure and firm behavior that we have not yet addressed. For example, why do firms tend to collude in some markets and to compete aggressively in others? How do some firms manage to deter entry by potential competitors? And how should firms make pricing decisions when demand or cost conditions are changing or new competitors are entering the market? To answer these questions, we will use game theory to extend our analysis of strategic decision making. The application of game theory has been an important development in microeconomics. This chapter explains some key aspects of this theory and shows how it can be used to understand how markets evolve and operate, and how managers should think about the strategic decisions they continually face. We will see, for example, what happens when oligopolistic firms must set and adjust prices strategically over time, so that the prisoners’ dilemma, which we discussed in Chapter 12, is repeated over and over. We will show how firms can make strategic moves that give them advantages over competitors or an edge in bargaining situations, and how they can use threats, promises, or more concrete actions to deter entry. Finally, we will turn to auctions and see how game theory can be applied to auction design and bidding strategies. 13.1 Gaming and Strategic Decisions First, we should clarify what gaming and strategic decision making are all about. A game is any situation in which players (the participants) make strategic decisions—i.e., decisions that take into account each other’s actions and responses. Examples of games include firms competing with each other by setting prices, or a group of consumers bidding against each other at an auction for a work of art. Strategic decisions result in payoffs to the players: outcomes that generate rewards or benefits. For the price-setting firms, the payoffs are profits 13.1 Gaming and Strategic Decisions 487 13.2 Dominant Strategies 490 13.3 The Nash Equilibrium Revisited 492 13.4 Repeated Games 498 13.5 Sequential Games 502 13.6 Threats, Commitments, and Credibility 505 13.7 Entry Deterrence 510 *13.8 Auctions 516 13.1 Acquiring a Company 490 13.2 Oligopolistic Cooperation in the Water Meter Industry 501 13.3 Competition and Collusion in the Airline Industry 501 13.4 Wal-Mart Stores’ Preemptive Investment Strategy 509 13.5 DuPont Deters Entry in the Titanium Dioxide Industry 514 13.6 Diaper Wars 515 13.7 Auctioning Legal Services 522 13.8 Internet Auctions 522 487 488 PART 3 • Market Structure and Competitive Strategy • game Situation in which players (participants) make strategic decisions that take into account each other’s actions and responses. • payoff Value associated with a possible outcome. • strategy Rule or plan of action for playing a game. • optimal strategy Strategy that maximizes a player’s expected payoff. • cooperative game Game in which participants can negotiate binding contracts that allow them to plan joint strategies. • noncooperative game Game in which negotiation and enforcement of binding contracts are not possible. for the bidders at the auction, the winner’s payoff is her consumer surplus—i.e., the value she places on the artwork less the amount she must pay. A key objective of game theory is to determine the optimal strategy for each player. A strategy is a rule or plan of action for playing the game. For our pricesetting firms, a strategy might be: “I’ll keep my price high as long as my competitors do the same, but once a competitor lowers his price, I’ll lower mine even more.” For a bidder at an auction, a strategy might be: “I’ll make a first bid of $2000 to convince the other bidders that I’m serious about winning, but I’ll drop out if other bidders push the price above $5000.” The optimal strategy for a player is the one that maximizes the expected payoff. We will focus on games involving players who are rational, in the sense that they think through the consequences of their actions. In essence, we are concerned with the following question: If I believe that my competitors are rational and act to maximize their own payoffs, how should I take their behavior into account when making my decisions? In real life, of course, you may encounter competitors who are irrational, or are less capable than you of thinking through the consequences of their actions. Nonetheless, a good place to start is by assuming that your competitors are just as rational and just as smart as you are.1 As we will see, taking competitors’ behavior into account is not as simple as it might seem. Determining optimal strategies can be difficult, even under conditions of complete symmetry and perfect information (i.e., my competitors and I have the same cost structure and are fully informed about each others’ costs, about demand, etc.). Moreover, we will be concerned with more complex situations in which firms face different costs, different types of information, and various degrees and forms of competitive “advantage” and “disadvantage.” Noncooperative versus Cooperative Games The economic games that firms play can be either cooperative or noncooperative. In a cooperative game, players can negotiate binding contracts that allow them to plan joint strategies. In a noncooperative game, negotiation and enforcement of binding contracts are not possible. An example of a cooperative game is the bargaining between a buyer and a seller over the price of a rug. If the rug costs $100 to produce and the buyer values the rug at $200, a cooperative solution to the game is possible: An agreement to sell the rug at any price between $101 and $199 will maximize the sum of the buyer’s consumer surplus and the seller’s profit, while making both parties better off. Another cooperative game would involve two firms negotiating a joint investment to develop a new technology (assuming that neither firm would have enough know-how to succeed on its own). If the firms can sign a binding contract to divide the profits from their joint investment, a cooperative outcome that makes both parties better off is possible.2 An example of a noncooperative game is a situation in which two competing firms take each other’s likely behavior into account when independently 1When we asked, 80 percent of our students told us that they were smarter and more capable than most of their classmates. We hope that you don’t find it too much of a strain to imagine competing against people who are as smart and capable as you are. 2Bargaining over a rug is called a constant sum game because no matter what the selling price, the sum of consumer surplus and profit will be the same. Negotiating over a joint venture is a nonconstant sum game: The total profit that results from the venture will depend on the outcome of the negotiations (e.g., the resources that each firm devotes to the venture). CHAPTER 13 • Game Theory and Competitive Strategy 489 setting their prices. Each firm knows that by undercutting its competitor, it can capture more market share. But it also knows that in doing so, it risks setting off a price war. Another noncooperative game is the auction mentioned above: Each bidder must take the likely behavior of the other bidders into account when determining an optimal bidding strategy. Note that the fundamental difference between cooperative and noncooperative games lies in the contracting possibilities. In cooperative games, binding contracts are possible; in noncooperative games, they are not. We will be concerned mostly with noncooperative games. Whatever the game, however, keep in mind the following key point about strategic decision making: It is essential to understand your opponent’s point of view and to deduce his or her likely responses to your actions. This point may seem obvious—of course, one must understand an opponent’s point of view. Yet even in simple gaming situations, people often ignore or misjudge opponents’ positions and the rational responses that those positions imply. HOW TO BUY A DOLLAR BILL Consider the following game devised by Martin Shubik.3 A dollar bill is auctioned, but in an unusual way. The highest bidder receives the dollar in return for the amount bid. However, the secondhighest bidder must also hand over the amount that he or she bid—and get nothing in return. If you were playing this game, how much would you bid for the dollar bill? Classroom experience shows that students often end up bidding more than a dollar for the dollar. In a typical scenario, one player bids 20 cents and another 30 cents. The lower bidder now stands to lose 20 cents but figures he can earn a dollar by raising his bid, and so bids 40 cents. The escalation continues until two players carry the bidding to a dollar against 90 cents. Now the 90-cent bidder has to choose between bidding $1.10 for the dollar or paying 90 cents to get nothing. Most often, he raises his bid, and the bidding escalates further. In some experiments, the “winning” bidder has ended up paying more than $3 for the dollar! How could intelligent students put themselves in this position? By failing to think through the likely response of the other players and the sequence of events it implies. In the rest of this chapter, we will examine simple games that involve pricing, advertising, and investment decisions. The games are simple in that, given some behavioral assumptions, we can determine the best strategy for each firm. But even for these simple games, we will find that the correct behavioral assumptions are not always easy to make. Often they will depend on how the game is played (e.g., how long the firms stay in business, their reputations, etc.). Therefore, when reading this chapter, you should try to understand the basic iss |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.