The Pearson Series in Economics - 8th Edition

276 PART 2 • Producers, Consumers, and Competitive Markets This is the same result as (A7.5)—that is, the necessary condition for cost minimization. • Cobb-Douglas production The Cobb-Douglas Cost and Production Functions function Production function of the form q ϭ AKa Lb, where Given a specific production function F(K, L), conditions (A7.13) and (A7.14) can be q is the rate of output, K is the used to derive the cost function C(q). To understand this principle, let’s work through quantity of capital, and L is the the example of a Cobb-Douglas production function. This production function is quantity of labor, and where A, a, and b are positive constants. F(K,L) = AKaLb 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 Cobb- Douglas 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(AKaLb - q0) (A7.15) Differentiating with respect to L, K, and l, and setting those derivatives equal to 0, we obtain 0⌽/0L = w - l(bAKaLb-1) = 0 (A7.16) 0⌽/0K = r - l(aAKa-1Lb) = 0 (A7.17) 0⌽/0l = AKaLb - q0 = 0 (A7.18) From equation (A7.16) we have l = w/AbKaLb-1 (A7.19) Substituting this formula into equation (A7.17) gives us (A7.20) rbAKaLb-1 = waAKa -1Lb or br (A7.21) L = aw K 2For example, the marginal product of labor is given by MPL = 0[F(K,L)]/0L = bAKaLb-1. Thus, MPL falls as L increases.

CHAPTER 7 • The Cost of Production 277 (A7.21) is the expansion path. Now use Equation (A7.21) to substitute for L in equation (A7.18): AKa a br b - q0 = 0 (A7.22) aw Kb We can rewrite the new equation as: Ka + b = a aw b bq0 (A7.23) br A (A7.24) or = a aw b a b b a q0 b a 1 b + + K br A (A7.24) is the factor demand for capital. We have now determined the cost-min- imizing 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): = br = br a aw b a b b a q0 b a 1 b aw K aw + + L £ br A § (A7.25) = a br b a a b a q0 b a 1 b aw + A + L (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 ϭ wL ϩ rK. After some algebraic manipulation we find that b/(a + b)r a/(a + b) a b/(a + b) a -a/(a + b) q 1/(a + b) b C = w £ a b + a b§ a b (A7.26) bA 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 = wbra[(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 1 2b ra a b a -a 1 2b wb ra a b a -a 1 2bC0 b b A b b A C1 = 2w £ a b + a b § a b q0 = £ a b + a b § a b q0 = (+++1++)+++1++* C0 Recall that at the beginning of this section, we assumed that a < 1 and ß < 1. Therefore, C1 6 2C0. Even though wages doubled, the cost of producing q0 less 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 pro- duced 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 ⌽ = AKaLb - o(wL + rK - C0). EXERCISES to capital and labor, $10 worth of raw materials is used in the production of each parka. 1. Of the following production functions, which exhibit a. By minimizing cost subject to the production func- increasing, constant, or decreasing returns to scale? a. F(K, L) ϭ K2L tion, derive the cost-minimizing demands for K and L b. F(K, L) ϭ 10K ϩ 5L as a function of output (q), wage rates (w), and rental c. F(K, L) ϭ (KL).5 rates on machines (r). Use these results to derive the total cost function: that is, costs as a function of q, r, w, 2. The production function for a product is given by q ϭ and the constant $10 per unit materials cost. 100KL. If the price of capital is $120 per day and the b. This process requires skilled workers, who earn $32 price of labor $30 per day, what is the minimum cost of per hour. The rental rate on the machines used in producing 1000 units of output? the process is $64 per hour. At these factor prices, what are total costs as a function of q? Does this 3. Suppose a production function is given by F(K, L) ϭ technology exhibit decreasing, constant, or increas- KL2; the price of capital is $10 and the price of labor ing returns to scale? $15. What combination of labor and capital minimizes c. Polly’s Parkas plans to produce 2000 parkas per the cost of producing any given output? week. At the factor prices given above, how many workers should the firm hire (at 40 hours per week) 4. Suppose the process of producing lightweight parkas and how many machines should it rent (at 40 by Polly’s Parkas is described by the function machine-hours per week)? What are the marginal and average costs at this level of production? 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

8C H A P T E R Profit Maximization and Competitive Supply CHAPTER OUTLINE Acost curve describes the minimum cost at which a firm can pro- 8.1 Perfectly Competitive 279 duce various amounts of output. Once we know its cost curve, Markets 282 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 8.2 Profit Maximization 284 chooses the level of output that maximizes its profit. We will also see 287 how the output choices of individual firms lead to a supply curve for 8.3 Marginal Revenue, 292 an entire industry. Marginal Cost, and 295 Profit Maximization 300 Because our discussion of production and cost in Chapters 6 and 7 306 applies to firms in all kinds of markets, we will begin by explaining the 8.4 Choosing Output in the profit-maximizing output decision in a general setting. However, we Short Run 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 8.5 The Competitive Firm’s relation to the industry that its production decisions have no effect on Short-Run Supply Curve 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. 8.6 The Short-Run Market Supply Curve We begin by explaining exactly what is meant by a competitive mar- ket. We then explain why it makes sense to assume that firms (in any 8.7 Choosing Output in the market) have the objective of maximizing profit. We provide a rule for Long Run choosing the profit-maximizing output for firms in all markets, com- petitive or otherwise. Following this we show how a competitive firm 8.8 The Industry’s Long-Run chooses its output in the short and long run. Supply Curve We next examine how the firm’s output choice changes as the cost LIST OF EXAMPLES 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 8.1 Condominiums versus of individual firms to obtain the industry supply curve. In the short run, Cooperatives in New York firms in an industry choose which level of output to produce in order City 283 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 8.2 The Short-Run Output the prospect of high profits encourages firms to enter an industry, losses encourage them to leave. Decision of an Aluminum 8.1 Perfectly Competitive Markets Smelting Plant 290 In Chapter 2, we used supply–demand analysis to explain how chang- 8.3 Some Cost Considerations ing market conditions affect the market price of such products as wheat and gasoline. We saw that the equilibrium price and quantity of each for Managers 291 8.4 The Short-Run Production of Petroleum Products 294 8.5 The Short-Run World 297 Supply of Copper 8.6 Constant-, Increasing-, 310 and Decreasing-Cost Industries: Coffee, Oil, and Automobiles 8.7 The Supply of Taxicabs in New York 312 8.8 The Long-Run Supply of Housing 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 encoun- tered these assumptions earlier in the book; here we summarize and elaborate on them. • price taker Firm that has no PRICE TAKING Because many firms compete in the market, each firm faces a influence over market price and significant number of direct competitors for its products. Because each individual thus takes the price as given. 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 dis- tribution 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 per- fectly 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. • free entry (or exit) PRODUCT HOMOGENEITY Price-taking behavior typically occurs in markets Condition under which there where firms produce identical, or nearly identical, products. When the products are no special costs that make it of all of the firms in a market are perfectly substitutable with one another—that is, difficult for a firm to enter (or exit) when they are homogeneous—no firm can raise the price of its product above the an industry. 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 opportu- nity 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

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 mar- ket 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 rights to pro- duce drugs. Any new entrant would either have to invest in research and devel- opment 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 mar- kets 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? In §2.4, we explain that demand is price elastic when Apart from agriculture, few real-world markets are perfectly competitive in the the percentage decline sense that each firm faces a perfectly horizontal demand curve for a homoge- in quantity demanded is neous product in an industry that it can freely enter or exit. Nevertheless, many greater than the percentage markets are highly competitive in the sense that firms face highly elastic demand increase in price. curves and relatively easy entry and exit. A simple rule of thumb to describe whether a market is close to being per- fectly 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 implic- itly 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 behav- ior. 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 oper- ating 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.

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 unnec- essary 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 maximiza- tion, 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 informa- tion. On some occasions they may engage in acquisition and/or growth strate- gies 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 maximiza- tion 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 maximiza- tion 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 maxi- mization 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 • cooperative Association of businesses or people jointly Now that we’ve underscored the fact that profit maximization is a fundamental owned and operated by assumption in most economic analyses of firm behavior, let’s pause to consider members for mutual benefit. an important qualifier to this assumption: Some forms of organizations have objectives that are quite different from profit maximization. An important such • condominium A housing organization is the cooperative—an association of businesses or people jointly unit that is individually owned owned and operated by members for mutual benefit. For example, several farms but provides access to common might decide to enter into a cooperative agreement by which they pool their facilities that are paid for resources in order to distribute and market milk to consumers. Because each par- and controlled jointly by an ticipating member of the milk cooperative is an autonomous economic unit, each association of owners. farm will act to maximize its own profits (rather than the profits of the coopera- tive 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 supermar- ket. 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 pro- portion to their purchases). Housing cooperatives, or co-ops, are another example of this form of organi- zation. 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 partici- pate 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 condo- minium. A condominium (or “condo”) is a housing unit (an apartment, con- nected 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 oper- ation 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. E X A M P L E 8 . 1 CONDOMINIUMS VERSUS COOPERATIVES IN NEW YORK CITY While owners of condominiums must join with fel- of the governance is usually delegated to a board low condo owners to manage common spaces that represents all co-op members, members must (e.g., entry areas), they can make their own deci- often spend substantial time in the governance of sions as to how to manage their individual units so the association. In addition, condo members can as to achieve the greatest value possible. In con- sell their units whenever and to whomever they trast, co-ops share joint liability on any outstanding choose, whereas co-op members must get per- mortgage on the co-op building and are subject to mission from the co-op board before a sale can be more complex governance rules. Although much made.

284 PART 2 • Producers, Consumers, and Competitive Markets Nationwide, condos are far more common than But that’s history. The building restrictions in New co-ops, outnumbering them by a factor of nearly 10 York have long disappeared, and yet the conver- to 1. In this regard, New York City is very different sion of apartments from co-ops to condos has been from the rest of the nation—co-ops are more popu- relatively slow. Why? A recent study provides some lar, and outnumber condos by a factor of about 4 to interesting answers.2 The authors find that the typi- 1. What accounts for the relative popularity of hous- cal condominium apartment is worth about 15.5 ing cooperatives in New York City? Part of the answer percent more than an equivalent apartment held is historical. Housing cooperatives are a much older in the form of a co-op. Clearly, holding an apart- form of organization in the U.S., dating back to the ment in the form of a co-op is not the best way to mid-nineteenth century, whereas the development maximize the apartment’s value. On the other hand, of condominiums began only in the 1960s, at which co-op owners can be more selective in choosing point a large number of buildings in New York were their neighbors when sales are made—something already co-ops. In addition, while condominiums that New Yorkers seem to care a great deal about. It were becoming increasingly popular in other parts of appears that in New York, many owners have been the country, building regulations in New York made willing to forgo substantial amounts of money in the co-op the required governance structure. order to achieve non-monetary benefits. • profit Difference between 8.3 Marginal Revenue, Marginal Cost, total revenue and total cost. and Profit Maximization • marginal revenue Change in revenue resulting from a one- We now return to our working assumption of profit maximization and exam- unit increase in output. ine 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 differ- ence 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 one- unit increase in output. Also shown is the total cost curve C(q). The slope of this curve, which mea- sures 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, C(q) FIGURE 8.1 revenue, R(q) A PROFIT MAXIMIZATION IN THE profit B SHORT RUN (dollars per year) q* q1 A firm chooses output q*, so that profit, the 0 q0 π (q) difference AB between revenue R and cost C, is maximized. At that output, marginal Output (units per year) revenue (the slope of the revenue curve) is equal to marginal cost (the slope of the cost curve). For the firm illustrated in Figure 8.1, profit is negative at low levels of out- put 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 con- clude 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 Often we will want to distinguish between market demand curves and the demand curve relates the demand curves faced by individual firms. In this chapter we will denote mar- quantity of a good that a ket output and demand by capital letters (Q and D) and the firm’s output and consumer will buy to the demand by lowercase letters (q and d). price of that good. 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 cor- responds 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 mar- ket 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 Firm Price Industry (dollars per (dollars per bushel) bushel) $4 d $4 100 200 q 2,000 D (a) Output (bushels) (b) 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 impor- tant 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 Marginal, average, and total cost are discussed in §7.1. 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* ϭ 8 and the price is $40, because marginal revenue is equal to marginal cost at this point. To see that q* ϭ 8 is indeed the profit-maximizing output, note that at a lower output, say q1 ϭ 7, marginal revenue is greater than marginal cost; profit could thus be increased by increasing output. The shaded area between q1 ϭ 7 and q* shows the lost profit associated with producing at q1. At a higher output, say q2, mar- ginal 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 ϭ 9 shows the lost profit associated with producing at q2. When output is q* ϭ 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

288 PART 2 • Producers, Consumers, and Competitive Markets Price 60 MC (dollars per Lost profit for unit) q2 > q* AR = MR = P 50 ATC D Lost profit for A AVC 40 q1 < q* C B 30 20 10 0 1 2 3 4 5 67 8 9 10 11 q0 q1 q* q2 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 mar- kets 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*,

CHAPTER 8 • Profit Maximization and Competitive Supply 289 Price MC ATC (dollars per B unit of P = MR output) A C AVC D E F 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 busi- ness 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 deci- sion 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 Remember from §7.1 that fixed costs do not change with the level of output, but they can be eliminated a fixed cost is an ongoing if the firm shuts down. (Examples of fixed costs include the salaries of plant cost that does not change managers and security personnel, and the electricity to keep the lights and with the level of output but heat running.) is eliminated if the firm shuts down. 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 profit- able 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 illus- tration. 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 cus- tomers 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 busi- ness 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. E X A M P L E 8 . 2 THE SHORT-RUN OUTPUT DECISION OF AN ALUMINUM SMELTING PLANT How should the manager of an day. Running a third shift would aluminum smelting plant deter- involve overtime, and the price mine the plant’s profit-maximizing of the aluminum is insufficient output? Recall from Example 7.3 to make the added production (page 240) that the smelting plant’s profitable. Suppose, however, short-run marginal cost of produc- that the price of aluminum were tion depends on whether it is run- to increase to P2 ϭ $1360 per ning two or three shifts per day. As ton. This price is greater than shown in Figure 8.5, marginal cost the $1300 marginal cost of the is $1140 per ton for output levels third shift, making it profitable up to 600 tons per day and $1300 to increase output to 900 tons per ton for output levels between per day. 600 and 900 tons per day. Finally, suppose the price drops Suppose that the price of alu- to only $1100 per ton. In this case, minum is initially P1 ϭ $1250 per the firm should stop producing, ton. In that case, the profit-maxi- but it should probably stay in busi- mizing output is 600 tons; the firm ness. By taking this step, it could can make a profit above its variable cost of $110 resume producing in the future should the price per ton by employing workers for two shifts a increase.

CHAPTER 8 • Profit Maximization and Competitive Supply 291 Cost MC (dollars per ton) P2 P1 1400 1300 1200 1140 1100 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. E X A M P L E 8 . 3 SOME COST CONSIDERATIONS FOR MANAGERS The application of the rule that marginal revenue for marginal cost. When marginal and average vari- should equal marginal cost depends on a man- able cost are nearly constant, there is little difference ager’s ability to estimate marginal cost.3 To obtain between them. However, if both marginal and aver- useful measures of cost, managers should keep age cost are increasing sharply, the use of average three guidelines in mind. variable cost can be misleading in deciding how much to produce. Suppose for example, that a company First, except under limited circumstances, aver- has the following cost information: age variable cost should not be used as a substitute 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 Labor cost $8 per unit for all output $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 involves marginal cost. Suppose that a manager for the first 80 units of output and then see how both is trying to cut back production. She reduces the cost measures change when we include the additional number of hours that some employees work and 20 units produced with overtime labor. For the first 80 lays off others. But the salary of an employee who units, average variable cost is simply the labor cost is laid off may not be an accurate measure of the ($2400 ϭ $30 per unit ϫ 80 units) plus the materials marginal cost of production when cuts are made. cost ($640 ϭ $8 per unit ϫ 80 units) divided by the Union contracts, for example, often require the firm 80 units—($2400 ϩ $640)/80 ϭ $38 per unit. Because to pay laid-off employees part of their salaries. In average variable cost is the same for each unit of out- this case, the marginal cost of increasing produc- put, marginal cost is also equal to $38 per unit. tion is not the same as the savings in marginal cost when production is decreased. The savings is the When output increases to 100 units per day, both labor cost after the required layoff salary has been average variable cost and marginal cost change. subtracted. The variable cost has now increased; it includes the additional materials cost of $160 (20 units ϫ Third, all opportunity costs should be included in $8 per unit) and the additional labor cost of $1000 determining marginal cost. Suppose a department (20 units ϫ $50 per unit). Average variable cost is store wants to sell children’s furniture. Instead of therefore the total labor cost plus the materials cost building a new selling area, the manager decides ($2400 ϩ $1000 ϩ $640 ϩ $160) divided by the to use part of the third floor, which had been used 100 units of output, or $42 per unit. for appliances, for the furniture. The marginal cost of this space is the $90 per square foot per day in What about marginal cost? While the materials cost profit that would have been earned had the store per unit has remained unchanged at $8 per unit, the continued to sell appliances there. This opportunity marginal cost of labor has now increased to $50 per cost measure may be much greater than what the unit, so that the marginal cost of each unit of overtime store actually paid for that part of the building. output is $58 per day. Because marginal cost is higher than average variable cost, a manager who relies on These three guidelines can help a manager to average variable cost will produce too much. measure marginal cost correctly. Failure to do so can cause production to be too high or too low and Second, a single item on a firm’s accounting led- thereby reduce profit. ger may have two components, only one of which 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 pos- sible 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 mar- ginal 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 rea- son 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.

CHAPTER 8 • Profit Maximization and Competitive Supply 293 Price MC FIGURE 8.6 (dollars per AC THE SHORT-RUN unit) AVC SUPPLY CURVE FOR P2 A COMPETITIVE FIRM P1 In the short run, the firm chooses its output so that P = AVC marginal cost MC is equal to price as long as the firm cov- ers its average variable cost. The short-run supply curve is given by the crosshatched portion of the marginal cost curve. 0 q1 q2 Output The higher price not only makes the additional production profitable, but also In §6.2, we explain that increases the firm’s total profit because it applies to all units that the firm produces. diminishing marginal returns occurs when each additional The Firm’s Response to an Input Price Change increase in an input results in a smaller and smaller When the price of its product changes, the firm changes its output level to increase in output. 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 Price, cost MC2 (dollars per unit) MC1 $5 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 ϭ 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 X A M P L E 8 . 4 THE SHORT-RUN PRODUCTION OF PETROLEUM PRODUCTS Suppose you are managing an ity of the refinery and the cost of oil refinery that converts crude oil production. How much should you into a particular mix of products, produce each day?4 including gasoline, jet fuel, and residual fuel oil for home heat- Information about the refin- ing. Although plenty of crude oil ery’s marginal cost of produc- is available, the amount that you tion is essential for this decision. refine depends on the capac- Figure 8.8 shows the short-run marginal cost curve (SMC). Cost 77 SMC (dollars per barrel) 76 75 74 73 9000 10,000 11,000 8000 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 products can be sold for $73 per barrel. Because of uneven segments rather than as a smooth curve. the marginal cost of production is close to $74 The increase occurs in segments because the refin- for the first unit of output, no crude oil should be ery uses different processing units to turn crude oil run through the refinery when the price is $73. into finished products. When a particular process- If, however, price is between $74 and $75, the ing unit reaches capacity, output can be increased refinery should produce 9700 barrels a day (filling only by substituting a more expensive process. the thermal cracker). Finally, if the price is above For example, gasoline can be produced from light $75, the more expensive refining unit should be crude oils rather inexpensively in a processing unit used and production expanded toward 10,700 called a “thermal cracker.” When this unit becomes barrels a day. full, additional gasoline can still be produced (from heavy as well as light crude oil), but only at a higher Because the cost function rises in steps, you cost. In the case illustrated by Figure 8.8, the first know that your production decisions need not capacity constraint comes into effect when produc- change much in response to small changes in tion reaches about 9700 barrels a day. A second price. You will typically use sufficient crude oil capacity constraint becomes important when pro- to fill the appropriate processing unit until price duction increases beyond 10,700 barrels a day. increases (or decreases) substantially. In that case, you need simply calculate whether the increased Deciding how much output to produce now price warrants using an additional, more expensive becomes relatively easy. Suppose that refined processing unit. The shaded area in the figure gives the total savings to the firm (or equiv- alently, the reduction in lost profit) associated with the reduction in output from q1 to q2. 8.6 The 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 indus- try’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 pro- duction 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 sup- ply 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 Dollars MC1 MC2 MC3 per unit S P3 P2 P1 2 45 78 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. In §2.4, we define the elas- Elasticity of Market Supply ticity of supply as the per- centage change in quantity Unfortunately, finding the industry supply curve is not always as simple as add- supplied resulting from a ing up a set of individual supply curves. As price rises, all firms in the industry 1-percent increase in price. 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 out- put to market price. The elasticity of supply Es is the percentage change in quan- tity 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

CHAPTER 8 • Profit Maximization and Competitive Supply 297 cost increases slowly in response to increases in output, supply is relatively elas- tic; 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 indus- try’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. E X A M P L E 8 . 5 THE SHORT-RUN WORLD SUPPLY OF COPPER In the short run, the shape of the market supply as fixed. Figure 8.10 shows how the curve is con- curve for a mineral such as copper depends on structed for the nine countries listed in the table. how the cost of mining varies within and among the (The curve is incomplete because there are a few world’s major producers. Costs of mining, smelting, smaller and higher-cost producers that we have not and refining copper differ because of differences included.) Note that the curve in Figure 8.10 is an in labor and transportation costs and because approximation. The marginal cost number for each of differences in the copper content of the ore. country is an average for all copper producers in Table 8.1 summarizes some of the relevant cost that country, and we are assuming that marginal cost and production data for the nine largest copper- and average cost are approximately the same. In the producing nations.5 Remember that in the short United States, for example, some producers have a run, because the costs of building mines, smelters, marginal cost greater than $1.70 and some less. and refineries are taken as sunk, the marginal cost numbers in Table 8.1 reflect the costs of operating The lowest-cost copper is mined in Russia, where (but not building) these facilities. the marginal cost of refined copper is roughly $1.30 per pound. The line segment labeled MCR These data can be used to plot the short-run represents the marginal cost curve for Russia. The world supply curve for copper. It is a short-run curve curve is horizontal until the total capacity for mining because it takes the existing mines and refineries and refining copper in Russia is reached. (That point TABLE 8.1 THE WORLD COPPER INDUSTRY (2010) COUNTRY ANNUAL PRODUCTION MARGINAL COST (THOUSAND METRIC TONS) (DOLLARS PER POUND) Australia 900 2.30 Canada 480 2.60 Chile 5,520 1.60 Indonesia 840 1.80 Peru 1285 1.70 Poland 430 2.40 Russia 750 1.30 US 1120 1.70 Zambia 770 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 2.8 MCCa 2.6 MCPo 2.4 MCA 2.2 Price (dollars per pound) 2.0 MCPe MCUS MCI 1.8 1.6 MCZ MCCh 1.4 MCR 1.2 3000 4500 6000 7500 9000 10,500 12,000 1.0 0.8 0.6 0.4 0.2 0 0 1500 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 mar- ginal 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 on the price of copper. At relatively low prices, such as metric tons per year.) Line segment MCZ represents $1.30 and $1.80 per pound, the curve is quite elastic the marginal cost curve for Zambia, segment MCCh because small price increases lead to large increases the marginal cost curve for Chile, and so on. in the quantity of copper supplied. At higher prices— say, above $2.40 per pound—the curve becomes The world supply curve is obtained by summing more inelastic because, at those prices, most produc- each nation’s supply curve horizontally. As can be ers would be operating close to or at capacity. seen from the figure, the elasticity of supply depends For a review of consumer Producer Surplus in the Short Run surplus, see §4.4, where it is defined as the difference In Chapter 4, we measured consumer surplus as the difference between the maxi- between what a consumer is mum that a person would pay for an item and its market price. An analogous willing to pay for a good and concept applies to firms. If marginal cost is rising, the price of the product is what the consumer actually greater than marginal cost for every unit produced except the last one. As a pays when buying it. result, firms earn a surplus on all but the last unit of output. The producer sur- plus of a firm is the sum over all units produced of the differences between the • producer surplus Sum over market price of the good and the marginal cost of production. Just as consumer all units produced by a firm of surplus measures the area below an individual’s demand curve and above the differences between the market market price of the product, producer surplus measures the area above a pro- price of a good and the marginal ducer’s supply curve and below the market price. cost of production.

CHAPTER 8 • Profit Maximization and Competitive Supply 299 Price MC (dollars per Producer AVC FIGURE 8.11 unit of Surplus P output) PRODUCER SURPLUS FOR A FIRM B A The producer surplus for a firm is measured by the C yellow area below the market price and above the D marginal cost curve, between outputs 0 and q*, the profit-maximizing output. Alternatively, it is equal 0 to rectangle ABCD because the sum of all mar- ginal 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-maxi- mizing output is q*, where P ϭ MC. The surplus that the producer obtains from selling each unit is the difference between the price and the marginal cost of pro- ducing the unit. The producer surplus is then the sum of these “unit surpluses” over all units that the firm produces. It is given by the 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 produc- tion. 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) ϭ TC − FC ϭ VC.

300 PART 2 • Producers, Consumers, and Competitive Markets FIGURE 8.12 Price S (dollars per PRODUCER SURPLUS FOR D A MARKET unit of Output output) The producer surplus for a market is the area below the market price and above P* the market supply curve, between 0 and output Q*. Producer Surplus 0 Q* In §7.4, we explain that surplus for a market. This can be seen in Figure 8.12. The market supply curve begins economies of scale arise at the vertical axis at a point representing the average variable cost of the lowest-cost when a firm can double its firm in the market. Producer surplus is the area that lies below the market price of the output for less than twice product and above the supply curve between the output levels 0 and Q*. the cost. 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 ϭ P ϭ 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.

CHAPTER 8 • Profit Maximization and Competitive Supply 301 Dollars per LMC LAC unit of output SMC SAC E FIGURE 8.13 A F $40 D P = MR OUTPUT CHOICE IN THE C B LONG RUN G The firm maximizes its profit by $30 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 ϭ 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 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 ZERO ECONOMIC PROFIT When a firm goes into a business, it does so in A firm is earning a normal the expectation that it will earn a return on its investment. A zero economic return on its investment—i.e., profit means that the firm is earning a normal—i.e., competitive—return on that it is doing as well as it could by investment. This normal return, which is part of the user cost of capital, is the investing its money elsewhere. 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 prod- uct 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 long- run average cost remains $30 but the market price falls to $20. Recall our discus- sion 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 positive long- run 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 Firm Industry LMC Dollars Dollars S1 per unit of per unit of output output $40 P1 P1 S2 LAC P2 $30 P2 q2 Output Q1 Q2 D (a) (b) Output 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 sup- ply 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. When a firm earns zero economic profit, it has no incentive to exit the indus- • long-run competitive try. Likewise, other firms have no special incentive to enter. A long-run com- equilibrium All firms in an petitive equilibrium occurs when three conditions hold: industry are maximizing profit, no firm has an incentive to enter 1. All firms in the industry are maximizing profit. or exit, and price is such that 2. No firm has an incentive either to enter or exit the industry because all quantity supplied equals quantity demanded. 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 opportu- nity 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 opportu- nity 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 con- tinue 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 indus- try 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 eco- nomic 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 pos- sess 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 tal- ent. 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 rent that is earned by the scarce factors. Economic rent is what firms are willing • economic rent Amount that to pay for an input less the minimum amount necessary to buy it. In competitive firms are willing to pay for an markets, in both the short and the long run, economic rent is often positive even input less the minimum amount though profit is zero. necessary to obtain it. 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 dif- ference 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 sup- ply 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 eco- nomic 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 oper- ate 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 base- ball 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 LMC LAC Ticket Economic Rent LMC LAC price price $7 $10 $7.20 1.0 Season ticket 1.3 (a) sales (millions) 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 produc- tion 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 fran- chise 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 gener- ated 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 vol- umes 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 • constant-cost industry Industry whose long-run supply Figure 8.16 shows the derivation of the long-run supply curve for a constant- curve is horizontal. cost 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 intersec- tion 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. Dollars per Firm Dollars per Industry S2 unit of MC unit of SL output output S1 C P2 AC AB P2 P1 P1 D1 D2 q1 q2 Output Q1 Q2 Output (a) (b) 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 short- run equilibrium. This profit will be attractive to investors and will cause exist- ing 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 equilib- rium at the intersection of D2 and S2. For this intersection to be a long-run equi- librium, 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 mar- ket. Constant-cost industries can have horizontal long-run average cost curves. • increasing-cost Increasing-Cost Industry industry Industry whose long-run supply curve is upward In an increasing-cost industry the prices of some or all inputs to produc- sloping. tion 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 long- run supply, which is similar to the previous constant-cost derivation. The indus- try is initially in equilibrium at A in part (b). When the demand curve unexpect- edly 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 equi- librium. 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

CHAPTER 8 • Profit Maximization and Competitive Supply 309 Dollars per Firm Dollars per Industry S2 unit of MC2 MC1 unit of S1 SL output output AC2 B P2 AC1 P2 A P3 P3 P1 P1 D1 D2 q1 q2 Q1 Q2 Q3 (a) (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 sup- ply 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 • decreasing-cost industry Industry whose The industry supply curve can also be downward sloping. In this case, the long-run supply curve is unexpected increase in demand causes industry output to expand as before. downward sloping. 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 net- work. 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 long- run 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.

310 PART 2 • Producers, Consumers, and Competitive Markets E X A M P L E 8 . 6 CONSTANT-, INCREASING-, AND DECREASING-COST INDUSTRIES: COFFEE, OIL, AND AUTOMOBILES As you have progressed through this book, you have availability of easily accessible, large-volume oil been introduced to industries that have constant, fields. Consequently, as oil companies increase out- increasing, and decreasing long-run costs. Let’s look put, they are forced to obtain oil from increasingly back at some of these industries, beginning with one expensive fields. that has constant long-run costs. In Example 2.7, we saw that the supply of coffee is extremely elastic in Finally, a decreasing-cost industry. We discussed the long run (see Figure 2.18c). The reason is that the demand for automobiles in Examples 3.1 and land for growing coffee is widely available and the 3.3, but what about supply? In the automobile indus- costs of planting and caring for trees remains con- try, certain cost advantages arise because inputs can stant as the volume of coffee produced grows. Thus, be acquired more cheaply as the volume of produc- coffee is a constant-cost industry. tion increases. Indeed, the major automobile manu- facturers—such as General Motors, Toyota, Ford, Now consider the case of an increasing-cost and Honda—acquire batteries, engines, brake sys- industry. We explained in Example 2.9 that the oil tems, and other key inputs from firms that specialize industry is an increasing cost industry with an upward- in producing those inputs efficiently. As a result, the sloping long-run supply curve (see Figure 2.23b). average cost of automobile production decreases Why are costs increasing? Because there is a limited 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 produc- tion 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 encour- ages 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 ϭ MC1 ϩ 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 mar- ginal 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 to S2ϭ S1 ϩ t, causes the market price of the product to increase (by less than 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.

CHAPTER 8 • Profit Maximization and Competitive Supply 311 Dollars per MC2 = MC1 + t unit of MC1 output t FIGURE 8.18 P1 EFFECT OF AN OUTPUT TAX ON A COMPETITIVE FIRM’S OUTPUT AVC1 + t An output tax raises the firm’s marginal cost AVC1 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. q2 q1 Output 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 S2 = S1 + t FIGURE 8.19 unit of S1 output EFFECT OF AN OUTPUT TAX t ON INDUSTRY OUTPUT P2 P1 D An output tax placed on all firms in a com- petitive 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 elas- ticity 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 X A M P L E 8 . 7 THE SUPPLY OF TAXICABS IN NEW YORK The price of a taxi ride depends, of course, on the at a rate that is also regulated by the city: $110 per distance. Most cities regulate the fares that a taxicab 12-hour shift. Driving 6 shifts per week and 50 weeks can charge, and typically the price of a ride begins per year, the cab driver must therefore pay an addi- with a fixed fee to enter the cab, and then a charge tional 162 1502 11102 = $33,000 per year to lease per mile driven. In 2011 there were 13,150 taxicabs the medallion. This leaves the driver with a net income operating in New York City. One would expect that of only $72,000 - $10,000 - $33,000 = $29,000 if fares went down, fewer drivers would want to per year. operate cabs and the quantity supplied would fall. Likewise, one would expect that if fares went up, Suppose New York City reduced the fare sched- more drivers would want to operate cabs and the ule, so that a 5-mile trip only brought the driver $10 quantity would increase. Let’s see if that’s right. instead of $15. Then the driver’s annual gross revenue would drop from $72,000 to $48,000. After cover- Driving a cab is not an easy job. Most drivers work ing the costs of leasing the medallion as well as gas, a 12-hour shift six days per week. What annual income etc., the driver would be left with only $5,000 of net can the driver expect to earn? Assuming the driver annual income. Under those circumstances, hardly works 50 weeks per year, the total hours worked will anyone would want to drive a cab. And now sup- be 11221621502 = 3600 hours per year. But part of pose that New York instead raised taxi fares so that that time is spent waiting at a cab stand or cruising a 5-mile trip brought in $20 instead of $15. Now the for passengers; only about 2/3 of the time will there driver’s annual gross revenue will be $96,000, and his actually be a paying passenger inside, i.e., about net income after expenses would be $53,000. That’s 2400 hours per year. Driving about 10 miles per hour not bad for a job that requires little education and (remember, this is New York), the cabbie will drive no special skills, so many more people will want to about 24,000 “paid” miles per year. Some rides are drive cabs. Thus we would expect the supply curve longer than others, but the average taxi ride in New for taxis to be very elastic—small reductions in the York is about 5 miles, and (in 2011) the average cost price (the fare earned on an average five-mile ride) was about $12.60 on the meter, or about $15 with tip. will cause a sharp reduction in quantity, and small Based on 5-mile average trips, the driver will therefore increases in price will cause a sharp increase in quan- make about 124,0002>152 = 4,800 trips and earn a tity (the number of operating taxicabs). This is illus- gross income of 1$152 14,8002 = $72,000 per year. trated by the supply curve labeled S in Figure 8.20. From this, the driver must pay for gas, insurance, Something is missing, however. While reducing and maintenance and depreciation on the cab, which fares will indeed cause a reduction in the quantity can add up to $10,000 per year. But that is not the supplied, raising the price will not cause an increase only cost. As in most cities, driving a taxi in New York in the quantity supplied. Why not? Because the num- requires a medallion. The medallions, which were ber of medallions is fixed at 13,150, roughly the same issued by the city, are owned by taxicab compa- number that were in circulation in 1937. By refusing nies. The companies lease the medallions to drivers 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 FIGURE 8.20 P S′ S 13,150 Q THE SUPPLY CURVE FOR NEW $20 YORK TAXICABS $15 $10 If there were no restriction on the num- ber 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 an- other job. Likewise, an increase in price would bring many new drivers into the market. But the number of medallions—and therefore the num- ber 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 Many cities require taxis to have medallions and the supply curve becomes vertical at the quantity restrict the number of medallions. You’ll find out 13,150 (and is labeled S’ in the figure). why in Chapter 9, when you read Example 9.5. E X A M P L E 8 . 8 THE LONG-RUN SUPPLY OF HOUSING Owner-occupied and rental not increase substantially as the housing provide interesting quantity of housing supplied examples of the range of pos- increases. Likewise, costs asso- sible supply elasticities. People ciated with construction are not buy or rent housing to obtain likely to increase because there the services that a house pro- is a national market for lumber vides—a place to eat and sleep, and other materials. Therefore, comfort, and so on. If the price the long-run elasticity of the of housing services were to rise housing supply is likely to be in one area of the country, the very large, approximating that quantity of services provided of a constant-cost industry. In could increase substantially. fact, many studies find the long- run supply curve to be nearly horizontal.10 To begin, consider the supply of owner-occu- The market for rental housing is different, how- pied housing in suburban or rural areas where land ever. The construction of rental housing is often is not scarce. In this case, the price of land does 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 renovated—a practice that increases the quantity outlaw it entirely, while others limit it to certain areas. of rental services. With urban land becoming more Because urban land on which most rental housing valuable as housing density increases, and with the is located is restricted and valuable, the long-run cost of construction soaring with the height of build- elasticity of supply of rental housing is much lower ings, increased demand causes the input costs of than the elasticity of supply of owner-occupied hous- rental housing to rise. In this increasing-cost case, ing. As the price of rental-housing services rises, new the elasticity of supply can be much less than 1; in high-rise rental units are built and older units are one study, the authors found it to be 0.36.11 SUMMARY be necessary to produce the profit-maximizing out- put. In both the short run and the long run, producer 1. Managers can operate in accordance with a com- surplus is the area under the horizontal price line and plex set of objectives and under various constraints. above the marginal cost of production. However, we can assume that firms act as if they are 7. Economic rent is the payment for a scarce factor of pro- maximizing long-run profit. duction less the minimum amount necessary to hire that factor. In the long run in a competitive market, 2. Many markets may approximate perfect competition producer surplus is equal to the economic rent gener- in that one or more firms act as if they face a nearly ated by all scarce factors of production. horizontal demand curve. In general, the number of 8. In the long run, profit-maximizing competitive firms firms in an industry is not always a good indicator of choose the output at which price is equal to long-run the extent to which that industry is competitive. marginal cost. 9. A long-run competitive equilibrium occurs under 3. Because a firm in a competitive market accounts for a these conditions: (a) when firms maximize profit; (b) small share of total industry output, it makes its out- when all firms earn zero economic profit, so that there put choice under the assumption that its production is no incentive to enter or exit the industry; and (c) decision will have no effect on the price of the product. when the quantity of the product demanded is equal In this case, the demand curve and the marginal rev- to the quantity supplied. enue curve are identical. 10. The long-run supply curve for a firm is horizontal when the industry is a constant-cost industry in which 4. In the short run, a competitive firm maximizes its the increased demand for inputs to production (associ- profit by choosing an output at which price is equal ated with an increased demand for the product) has no to (short-run) marginal cost. Price must, however, be effect on the market price of the inputs. But the long- greater than or equal to the firm’s minimum average run supply curve for a firm is upward sloping in an variable cost of production. increasing-cost industry, where the increased demand for inputs causes the market price of some or all inputs 5. The short-run market supply curve is the horizontal to rise. 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 5. Why do firms enter an industry when they know that in the long run economic profit will be zero? 1. Why would a firm that incurs losses choose to produce rather than shut down? 6. At the beginning of the twentieth century, there were many small American automobile manufacturers. At 2. Explain why the industry supply curve is not the long- the end of the century, there were only three large ones. run industry marginal cost curve. Suppose that this situation is not the result of lax fed- eral enforcement of antimonopoly laws. How do you 3. In long-run equilibrium, all firms in the industry earn explain the decrease in the number of manufacturers? zero economic profit. Why is this true? 4. What is the difference between economic profit and producer surplus? 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 automo- are the steps by which a competitive market ensures bile industry?) increased output? Will your answer change if the gov- 7. Because industry X is characterized by perfect com- ernment imposes a price ceiling? petition, every firm in the industry is earning zero 13. The government passes a law that allows a substantial economic profit. If the product price falls, no firm can subsidy for every acre of land used to grow tobacco. survive. Do you agree or disagree? Discuss. How does this program affect the long-run supply 8. An increase in the demand for movies also increases curve for tobacco? the salaries of actors and actresses. Is the long-run sup- 14. A certain brand of vacuum cleaners can be purchased ply curve for films likely to be horizontal or upward from several local stores as well as from several cata- sloping? Explain. logues or websites. 9. True or false: A firm should always produce at an output a. If all sellers charge the same price for the vacuum at which long-run average cost is minimized. Explain. 10. Can there be constant returns to scale in an industry cleaner, will they all earn zero economic profit in with an upward-sloping supply curve? Explain. the long run? 11. What assumptions are necessary for a market to be b. If all sellers charge the same price and one local perfectly competitive? In light of what you have seller owns the building in which he does busi- learned in this chapter, why is each of these assump- ness, paying no rent, is this seller earning a positive tions important? economic profit? 12. Suppose a competitive industry faces an increase in c. Does the seller who pays no rent have an incentive demand (i.e., the demand curve shifts upward). What to lower the price that he charges for the vacuum cleaner? EXERCISES $200. Assume that the price of the output remains at $60 per unit. What general conclusion can you reach 1. The data in the table below give information about the about the effects of fixed costs on the firm’s output price (in dollars) for which a firm can sell a unit of out- choice? put and the total cost of production. 3. Use the same information as in Exercise 1. a. Fill in the blanks in the table. a. Derive the firm’s short-run supply curve. (Hint: b. Show what happens to the firm’s output choice and profit if the price of the product falls from $60 to $50. You may want to plot the appropriate cost curves.) b. If 100 identical firms are in the market, what is the R P MC MR R MR P industry supply curve? q P P ‫ ؍‬60 C P ‫ ؍‬60 P ‫ ؍‬60 P ‫ ؍‬60 P ‫ ؍‬50 P ‫ ؍‬50 P ‫ ؍‬50 4. Suppose you are the manager of a watchmaking firm 0 60 100 operating in a competitive market. Your cost of pro- 1 60 150 duction is given by C ϭ 200 ϩ 2q2, where q is the level 2 60 178 of output and C is total cost. (The marginal cost of pro- 3 60 198 duction is 4q; the fixed cost is $200.) 4 60 212 a. If the price of watches is $100, how many watches 5 60 230 6 60 250 should you produce to maximize profit? 7 60 272 b. What will the profit level be? 8 60 310 c. At what minimum price will the firm produce a 9 60 355 10 60 410 positive output? 11 60 475 5. Suppose that a competitive firm’s marginal cost of pro- 2. Using the data in the table, show what happens to ducing output q is given by MC(q) ϭ 3 ϩ 2q. Assume the firm’s output choice and profit if the fixed cost of that the market price of the firm’s product is $9. production increases from $100 to $150 and then to 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) ϭ 3 ϩ 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 ϭ 50 ϩ 4q ϩ 2q2 and a marginal cost function MC ϭ 4 ϩ 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 quan- *11. Suppose that a competitive firm has a total cost func- tity of output should the firm produce in the long run? tion C(q) ϭ 450 ϩ 15q ϩ 2q2 and a marginal cost function 7. Suppose the same firm’s cost function is C(q) ϭ 4q2 ϩ 16. MC(q) ϭ 15 ϩ 4q. If the market price is P ϭ $115 per a. Find variable cost, fixed cost, average cost, aver- unit, find the level of output produced by the firm. Find the level of profit and the level of producer surplus. age variable cost, and average fixed cost. (Hint: Marginal cost is given by MC ϭ 8q.) *12. A number of stores offer film developing as a service to b. Show the average cost, marginal cost, and average their customers. Suppose that each store offering this variable cost curves on a graph. service has a cost function C(q) ϭ 50 ϩ 0.5q ϩ 0.08q2 and c. Find the output that minimizes average cost. a marginal cost MC ϭ 0.5 ϩ 0.16q. d. At what range of prices will the firm produce a pos- a. If the going rate for developing a roll of film is $8.50, itive output? is the industry in long-run equilibrium? If not, find e. At what range of prices will the firm earn a nega- the price associated with long-run equilibrium. tive profit? b. Suppose now that a new technology is developed f. At what range of prices will the firm earn a positive which will reduce the cost of film developing by profit? 25 percent. Assuming that the industry is in long- *8. A competitive firm has the following short-run cost run equilibrium, how much would any one store be function: C(q) ϭ q3 − 8q2 ϩ 30q ϩ 5. willing to pay to purchase this new technology? a. Find MC, AC, and AVC and sketch them on a graph. b. At what range of prices will the firm supply zero *13. Consider a city that has a number of hot dog stands output? operating throughout the downtown area. Suppose that c. Identify the firm’s supply curve on your graph. each vendor has a marginal cost of $1.50 per hot dog d. At what price would the firm supply exactly 6 units sold and no fixed cost. Suppose the maximum number of output? of hot dogs that any one vendor can sell is 100 per day. *9. a. Suppose that a firm’s production function is q ϭ a. If the price of a hot dog is $2, how many hot dogs 9x1/2 in the short run, where there are fixed costs does each vendor want to sell? of $1000, and x is the variable input whose cost is b. If the industry is perfectly competitive, will the $4000 per unit. What is the total cost of producing a price remain at $2 for a hot dog? If not, what will level of output q? In other words, identify the total the price be? cost function C(q). c. If each vendor sells exactly 100 hot dogs a day and b. Write down the equation for the supply curve. the demand for hot dogs from vendors in the city c. If price is $1000, how many units will the firm pro- is Q ϭ 4400 − 1200P, how many vendors are there? duce? What is the level of profit? Illustrate your d. Suppose the city decides to regulate hot dog ven- answer on a cost-curve graph. dors by issuing permits. If the city issues only 20 *10. Suppose you are given the following information permits and if each vendor continues to sell 100 hot about a particular industry: dogs a day, what price will a hot dog sell for? e. Suppose the city decides to sell the permits. What QD = 6500 - 100P Market demand is the highest price that a vendor would pay for a Market supply permit? QS = 1200P Firm total cost function q2 *14. A sales tax of $1 per unit of output is placed on a par- Firm marginal cost function ticular firm whose product sells for $5 in a competitive C(q) = 722 + 200 industry with many firms. 2q a. How will this tax affect the cost curves for the firm? b. What will happen to the firm’s price, output, and MC(q) = 200 profit? c. Will there be entry or exit in the industry? Assume that all firms are identical and that the market is characterized by perfect competition. *15. A sales tax of 10 percent is placed on half the firms (the a. Find the equilibrium price, the equilibrium quan- polluters) in a competitive industry. The revenue is paid to the remaining firms (the nonpolluters) as a 10 tity, the output supplied by the firm, and the profit percent subsidy on the value of output sold. of each firm. a. Assuming that all firms have identical constant b. Would you expect to see entry into or exit from the long-run average costs before the sales tax-subsidy industry in the long run? Explain. What effect will policy, what do you expect to happen (in both the entry or exit have on market equilibrium? short run and the long run), to the price of the c. What is the lowest price at which each firm would product, the output of firms, and industry output? sell its output in the long run? Is profit positive, (Hint: How does price relate to industry input?) negative, or zero at this price? Explain. b. Can such a policy always be achieved with a bal- d. What is the lowest price at which each firm would anced budget in which tax revenues are equal to sell its output in the short run? Is profit positive, subsidy payments? Why or why not? Explain. negative, or zero at this price? Explain.

9C H A P T E R The Analysis of Competitive Markets In Chapter 2, we saw how supply and demand curves can help us CHAPTER OUTLINE describe and understand the behavior of competitive markets. In Chapters 3 to 8, we saw how these curves are derived and what 9.1 Evaluating the Gains and determines their shapes. Building on this foundation, we return to sup- Losses from Government ply–demand analysis and show how it can be applied to a wide vari- Policies—Consumer and ety of economic problems—problems that might concern a consumer Producer Surplus faced with a purchasing decision, a firm faced with a long-range plan- 317 ning problem, or a government agency that has to design a policy and evaluate its likely impact. 9.2 The Efficiency of a Competitive Market We begin by showing how consumer and producer surplus can be 323 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 9.3 Minimum Prices use consumer and producer surplus to demonstrate the efficiency of 328 a competitive market—why the equilibrium price and quantity in a competitive market maximizes the aggregate economic welfare of pro- 9.4 Price Supports and ducers and consumers. Production Quotas 332 Then we apply supply–demand analysis to a variety of problems. Because very few markets in the United States have been untouched 9.5 Import Quotas and Tariffs by government interventions of one kind or another, most of the prob- 340 lems 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 9.6 The Impact of a Tax to use the tools of economic analysis to deal with them and others like or Subsidy them on your own. We hope that by working through the examples 345 we provide, you will see how to calculate the response of markets to changing economic conditions or government policies and to evaluate LIST OF EXAMPLES the resulting gains and losses to consumers and producers. 9.1 Price Controls and Natural 9.1 Evaluating the Gains and Losses Gas Shortages 322 from Government Policies— Consumer and Producer Surplus 9.2 The Market for Human Kidneys 325 We saw at the end of Chapter 2 that a government-imposed price ceil- ing causes the quantity of a good demanded to rise (at the lower price, 9.3 Airline Regulation consumers want to buy more) and the quantity supplied to fall (pro- 330 ducers are not willing to supply as much at the lower price). The result 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 is a shortage—i.e., excess demand. Of course, those consumers who can still under price controls, the buy the good will be better off because they will now pay less. (Presumably, price of a product can be this was the objective of the policy in the first place.) But if we also take into no higher than a maximum account those who cannot obtain the good, how much better off are consumers allowable ceiling price. as a whole? Might they be worse off? And if we lump consumers and produc- ers 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. For a review of consumer Review of Consumer and Producer Surplus surplus, see §4.4, where it is defined as the difference In an unregulated, competitive market, consumers and producers buy and sell between what a consumer is at the prevailing market price. But remember, for some consumers the value of willing to pay for a good and the good exceeds this market price; they would pay more for the good if they had what the consumer actually to. Consumer surplus is the total benefit or value that consumers receive beyond pays when buying it. 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 FIGURE 9.1 Price Consumer S $10 Surplus CONSUMER AND PRODUCER SURPLUS D 7 Quantity Consumer A would pay $10 for a good whose mar- 5 ket price is $5 and therefore enjoys a benefit of $5. Consumer B enjoys a benefit of $2, and Consum- Producer er C, who values the good at exactly the market Surplus price, enjoys no benefit. Consumer surplus, which measures the total benefit to all consumers, is the Q0 yellow-shaded area between the demand curve Consumer A Consumer B Consumer C 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, con- sumer and producer surplus measure the welfare benefit of a competitive market.

CHAPTER 9 • The Analysis of Competitive Markets 319 thus enjoys a $2 net benefit. Finally, Consumer C values the good at exactly the For a review of producer market price, $5. He is indifferent between buying or not buying the good, and if surplus, see §8.6, where it is the market price were one cent higher, he would forgo the purchase. Consumer defined as the sum over all C, therefore, obtains no net benefit.1 units produced of the differ- ence between the market For consumers in the aggregate, consumer surplus is the area between the price of the good and the demand curve and the market price (i.e., the yellow-shaded area in Figure 9.1). marginal cost of its production. Because consumer surplus measures the total net benefit to consumers, we can mea- sure the gain or loss to consumers from a government intervention by measur- ing 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 ben- efit—a surplus—from selling those units. For each unit, this surplus is the dif- ference 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 pro- ducer 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 • welfare effects Gains and losses to consumers and With consumer and producer surplus, we can evaluate the welfare effects of a producers. 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 pro- duction 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 reduc- tion 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.

320 PART 2 • Producers, Consumers, and Competitive Markets Price FIGURE 9.2 Deadweight Loss S CHANGE IN CONSUMER AND D PRODUCER SURPLUS FROM PRICE Quantity CONTROLS The price of a good has been regulated to be P0 A B Pmax C no higher than Pmax, which is below the market- clearing 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 mea- Shortage sure the deadweight loss from price controls. Q1 Q0 Q2 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 who have stayed in the market but are producing less. Therefore, the total • deadweight loss Net loss of change in producer surplus is −A − C. Producers clearly lose as a result of total (consumer plus producer) price controls. surplus. 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) ϩ (−A − C) ϭ −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 dead- weight loss from price controls may not carry much political weight. However, if the demand curve is very 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 increas- ing to rising world levels. Consumers spent hours waiting in line to buy gaso- line. This was a good example of price controls making consumers—the group whom the policy was presumably intended to protect—worse off. Price D P0 A B S FIGURE 9.3 Pmax C EFFECT OF PRICE CONTROLS WHEN DEMAND IS INELASTIC If demand is sufficiently inelastic, triangle B can be larger than rectangle A. In this case, consum- ers suffer a net loss from price controls. Q1 Q2 Quantity

322 PART 2 • Producers, Consumers, and Competitive Markets E X A M P L E 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 whole- sale price of natural gas. Specifically, we saw that, in 2007, the free-mar- ket 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 maxi- mum 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 sub- stituting 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 P= $19.20 Supply 18 Demand 16 14 PG ($/mcf ) 12 10 $7.73 8 6 B 4 PO = $6.40 C A 2 QS = 20.6 QD = 29.1 Pmax = $3.00 10 20 30 40 0 Quantity (Tcf) Q* = 23 0 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 • economic efficiency efficiency—the maximization of aggregate consumer and producer surplus. Maximization of aggregate We just saw how price controls create a deadweight loss. The policy therefore consumer and producer surplus. imposes an efficiency cost on the economy: Taken together, producer and con- sumer 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,

324 PART 2 • Producers, Consumers, and Competitive Markets • market failure Situation but not always, the case. In some situations, a market failure occurs: Because in which an unregulated prices fail to provide the proper signals to consumers and producers, the competitive market is inefficient unregulated competitive market is inefficient—i.e., does not maximize aggre- because prices fail to provide gate consumer and producer surplus. There are two important instances in proper signals to consumers and which market failure can occur: producers. 1. Externalities: Sometimes the actions of either consumers or producers • externality Action taken by result in costs or benefits that do not show up as part of the market price. either a producer or a consumer Such costs or benefits are called externalities because they are “external” which affects other producers or to the market. One example is the cost to society of environmental pollu- consumers but is not accounted tion by a producer of industrial chemicals. Without government interven- for by the market price. tion, 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 informa- tion is discussed in detail in Chapter 17. In the absence of externalities or a lack of information, an unregulated com- petitive 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), produc- tion 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 Price FIGURE 9.5 P2 B S C WELFARE LOSS WHEN PRICE IS HELD A D ABOVE MARKET-CLEARING LEVEL P0 Q2 Quantity 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. Q3 Q0

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. EXAMPLE 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 prohibits the sale of organs for transplanta- tion. 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) wait- ing 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.