Daniel l. Rubinfeld

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254 Part 2 Producers, Consumers, and Competitive Markets miaht compete very aaaressiveiv (as we will see in Chapter 13). The important o _ 00 _ point to remember is that although firms may behave competitively in many situations, there is no simple indicator to tell us w'hen a market is highly competi_ tive. Often it is necessary to analyze both the firms themselves and their strategic interactions, as we do in Chapters 12 and 13. bsidizes public television may seem public-spirited and altruistic. Yet this ~uneficence is likely to be in the long-run financial interest of the firm because it ;nerates good'will for the firm and its products. 8.3 Chapter 8 Profit Maximization and Competitive Supply 255 We nm,,' 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 \ve will describe a rule that any firm-whether in a competitive market or not-can Use to find its profit-max{Inizing output level. Then, we will consider the special case of a firm in a competitive market. We distinguish the demand CUl'\"e 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 mmecessary 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 mvners (Le., the stockholders). As a result, owners cannot monitor the managers' behavior on a regular basis. Manaaers then have some leewav in how they run the firm and can deviate from o J_ profit-maximizing behavior. Manaaers o may _ be more concerned with such aoals 0 as reyenue maximization, revenue growth, or the payment of dividends to satisfy shareholders. They miaht also be overly concerned 'with the firm's short-run profit (perhaps to eam a ;romotion or a large bonus) at the expense of its longer-run profit, even thouah lona-run profit maximization better serves the interests of the stockholdo 0 ers.l (We discuss the implications of differences between the incenti\'es of managers and owners in greater detail in Chapter 17.) . . Even so, managers' freedom to pursue goals other than long-run proflt maXImization is limited. If they do pursue such goals, shareholders or boards of directors can replace them, or the firm can be taken over by new mana~ement. In any case, firms that do not come close to maxirnizing profit are not likely t survive. Firms that do survive in competitive industries make long-run profit maximization one of their highest priorities. . Thus our workina assumption of profit maximization is reasonable. FIrms o , that have been in business for a lona time are likely to care a lot about prall, o . -. that whatever else their managers may appear to be dOIng. For example, a hrm Let's begin by looking at the profit-maximizing output decision for allY firm, whether the finn 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 finn'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, Ti, is the difference between revenue and cost: Ti(q) = R(q) - C(q) (Here we show explicitly that 77, R, and C depend on output. Usually we will omit this reminder.) To maximize profit, the firm selects the output for which the difference between revenue and cost is the greatest. This prir1Ciple is illustrated in Figure 8.1. Revenue R(q) is a curved line, which reflects the fact that the firm can sell a greater le\'el of output only by 10werir1g its price. The slope of this revenue curve Cost, Revenue, Profit (dollars per year) Clq! profit Difference behveen total revenue and total cost 1 To be more exact, maximizing the market \'alue of the firm isa more appropriate goal th~n ~rf~! maximization because market value includes the stream of profIts that the fIrm earns 0\ er tIm . the stream of current and future profits that is of direct interest to the stockholdersc firm chooses output q*, so that profit, the difference AB between revenue R and C, is maximized. At that output, marginal revenue (the slope of the revenue :e) is equal to marginal cost (the slope of the cost curve).
256 Part 2 Producers, Consumers, and Competitive Markets 8 Profit Maximization and Competitive Supply 257 marginal revenue Change in revenue resulting from a one-unit increase in output 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, \vhich mea_ sures the additional cost of producing one additional unit of output, is the firm's IIwrgilUll cost. Note that total cost C(q) is positive vvhen output is zero becaUse there is a fixed cost in the short nm. For the firm illustrated in Figure 8.1, profit is negative at low levels of output, because revenue is insufficient to cover fixed and variable costs. As output increases, revenue rises more rapidly than cost, so that profit e\'entuaUy 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-maxim.izing 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, ,,,'hether competitive or not. This important rule can also be derived algebraically. Profit, 7i = R C, is maximized at the point at which an additional increment to output leaves profit unchanged (Le., t:.7i/i'lq = 0): t:.7i/t:.q = t:.R/tlq t:.C/t:.q = 0 t:.R/t:.q is marginal revenue MR and t:.C/tlq is marginal cost Me Thus we conclude that profit is maximized when MR - MC = 0, so that (dollars per bushel) 54 100 (a) 200 q Output (bushels) (dollars per bushel) d 54 (b) 100 o Q Output (millions of bushels) A competitive finn supplies only a small portion of the total output of all the firms in an induShy. 111erefore the firm takes the market price of the product as given, choosing its output on the assumption that the pri~e will be Lmaffected 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. In §4.1, we explain how the demand curve relates the quantity of a good that a consumer will buy to the price of that good. 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 sales, how /Illlell OlltPllt the firm decides to sell will have /Ill ~ffect 011 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 vvill 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. Often we will want to distinguish between market demand curves and the demand curves that individual firms face. In this chapter we will denote market output and demand by capital letters (Q and 0), and the firm's output and demand by lowercase letters (q and d). Because it is a price taker, the demalld curve d facillg all illdividual competitive firm is givell by a horizOlltallille. In Figure 8.2(a), the farmer's demand curve corresponcls 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 0 in Figure 8.2(b). The market demand curve shows how much wheat all cOllsumers 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 ha\'e almost no effect on the market because the industry output of wheat is 100 million bushels. Price is determined bv the interaction ~f 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 CUlye, it can sell an additional unit of output without lowering price. As a result, when it sells an additional Lmit, the firm's total 1"I.'I'CIlUC increases by an amount equal to the price: one bushel of wheat sold for 54 yields additional reyenue of 54. Thus, marginal re\'erlUe is constant at 54. At the same time, llI'cra
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Daniel l. Rubinfeld

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