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can make more money by first setting high prices and then reducing them over time, thereby discriminating and capturing consumer surplus. 412 PART 3 • Market Structure and Competitive Strategy marginal cost of printing an additional copy, whether hardcover or paperback, is quite low, perhaps a dollar or so. The paperback version is sold for much less not because it is much cheaper to print but because high-demand consumers have already purchased the hardbound edition. The remaining consumers— paperback buyers—generally have more elastic demands. Peak-Load Pricing Peak-load pricing also involves charging different prices at different points in time. Rather than capturing consumer surplus, however, the objective is to increase economic efficiency by charging consumers prices that are close to marginal cost. For some goods and services, demand peaks at particular times—for roads and tunnels during commuter rush hours, for electricity during late summer afternoons, and for ski resorts and amusement parks on weekends. Marginal cost is also high during these peak periods because of capacity constraints. Prices should thus be higher during peak periods. This is illustrated in Figure 11.8, where D1 is the demand curve for the peak period and D2 the demand curve for the nonpeak period. The firm sets marginal revenue equal to marginal cost for each period, obtaining the high price P1 for the peak period and the lower price P2 for the nonpeak period, selling corresponding quantities Q1 and Q2. This strategy increases the firm’s profit above what it would be if it charged one price for all periods. It is also more efficient: The sum of producer and consumer surplus is greater because prices are closer to marginal cost. The efficiency gain from peak-load pricing is important. If the firm were a regulated monopolist (e.g., an electric utility), the regulatory agency should set the prices P1 and P2 at the points where the demand curves, D1 and D2, intersect the marginal cost curve, rather than where the marginal revenue curves intersect marginal cost. In that case, consumers realize the entire efficiency gain. Note that peak-load pricing is different from third-degree price discrimination. With third-degree price discrimination, marginal revenue must be equal for In §9.2, we explain that economic efficiency means that aggregate consumer and producer surplus is maximized. $/Q P1 P2 FIGURE 11.8 PEAK-LOAD PRICING Demands for some goods and services increase sharply during particular times of the day or year. Charging a higher price P1 during the peak periods
is more profitable for the firm than charging a single price at all times. It is also more efficient because marginal cost is higher during peak periods. MC D1 AR1 MR1 D2 AR2 MR2 Q 2 Q1 Quantity CHAPTER 11 • Pricing with Market Power 413 each group of consumers and equal to marginal cost. Why? Because the costs of serving the different groups are not independent. For example, with unrestricted versus discounted air fares, increasing the number of seats sold at discounted fares affects the cost of selling unrestricted tickets—marginal cost rises rapidly as the airplane fills up. But this is not so with peak-load pricing (or for that matter, with most instances of intertemporal price discrimination). Selling more tickets for ski lifts or amusement parks on a weekday does not significantly raise the cost of selling tickets on the weekend. Similarly, selling more electricity during offpeak periods will not significantly increase the cost of selling electricity during peak periods. As a result, price and sales in each period can be determined independently by setting marginal cost equal to marginal revenue for each period. Movie theaters, which charge more for evening shows than for matinees, are another example. For most movie theaters, the marginal cost of serving customers during the matinee is independent of marginal cost during the evening. The owner of a movie theater can determine the optimal prices for the evening and matinee shows independently, using estimates of demand and marginal cost in each period. EXAM PLE 11.3 HOW TO PRICE A BEST-SELLING NOVEL Publishing both hardbound and paperback editions of a book allows publishers to price discriminate. As they do with most goods, consumers differ considerably in their willingness to pay for books. For example, some consumers want to buy a new bestseller as soon as it is released, even if the price is $25. Other consumers, however, will wait a year until the book is available in paperback for $10. But how does a publisher decide that $25 is the right price for the new hardbound edition and $10 is the right price for the paperback edition? And how long should it wait before bringing out the paperback edition? The key is to divide consumers into two groups, so that those who are willing to pay a high price do so and only those unwilling to pay a high price wait and buy the paperback. This means that significant time must be allowed to pass before the paperback is released. If consumers know that the paperback will be available within a few months, they will have little incentive to
buy the hardbound edition.10 On the other hand, if the publisher waits too long to bring out the paperback edition, interest will wane and the market will dry up. As a result, publishers typically wait 12 to 18 months before releasing paperback editions. What about price? Setting the price of the hardbound edition is difficult: Except for a few authors whose books always seem to sell, publishers have little data with which to estimate demand for a book that is about to be published. Often, they can judge only from the past sales of similar books. But usually only aggregate data are available for each category of book. Most new novels, therefore, are released at similar prices. It is clear, however, that those consumers willing to wait for the paperback edition have demands that are far more elastic than those of bibliophiles. It is not surprising, then, that paperback editions sell for so much less than hardbacks.11 10Some consumers will buy the hardbound edition even if the paperback is already available because it is more durable and more attractive on a bookshelf. This must be taken into account when setting prices, but it is of secondary importance compared with intertemporal price discrimination. 11Hardbound and paperback editions are often published by different companies. The author’s agent auctions the rights to the two editions, but the contract for the paperback specifies a delay to protect the sales of the hardbound edition. The principle still applies, however. The length of the delay and the prices of the two editions are chosen to price discriminate intertemporally. 414 PART 3 • Market Structure and Competitive Strategy 11.4 The Two-Part Tariff • two-part tariff Form of pricing in which consumers are charged both an entry and a usage fee. The two-part tariff is related to price discrimination and provides another means of extracting consumer surplus. It requires consumers to pay a fee up front for the right to buy a product. Consumers then pay an additional fee for each unit of the product they wish to consume. The classic example of this strategy is an amusement park.12 You pay an admission fee to enter, and you also pay a certain amount for each ride. The owner of the park must decide whether to charge a high entrance fee and a low price for the rides or, alternatively, to admit people for free but charge high prices for the rides. The two-part tariff has been applied in many settings: tennis and golf clubs (you pay an annual membership fee plus a fee for each use of a
court or round of golf); the rental of large mainframe computers (a flat monthly fee plus a fee for each unit of processing time consumed); telephone service (a monthly hook-up fee plus a fee for minutes of usage). The strategy also applies to the sale of products like safety razors (you pay for the razor, which lets you consume the blades that fit that brand of razor). The problem for the firm is how to set the entry fee (which we denote by T) versus the usage fee (which we denote by P). Assuming that the firm has some market power, should it set a high entry fee and low usage fee, or vice versa? To solve this problem, we need to understand the basic principles involved. SINGLE CONSUMER Let’s begin with the artificial but simple case illustrated in Figure 11.9. Suppose there is only one consumer in the market (or many consumers with identical demand curves). Suppose also that the firm knows this consumer’s demand curve. Now, remember that the firm wants to capture as much consumer surplus as possible. In this case, the solution is straightforward: Set the usage fee P equal to marginal cost and the entry fee T equal to the total consumer surplus for each consumer. Thus, the consumer pays T* (or a bit less) to use the product, and P* MC per unit consumed. With the fees set in this way, the firm captures all the consumer surplus as its profit. T* $/Q P* FIGURE 11.9 TWO-PART TARIFF WITH A SINGLE CONSUMER The consumer has demand curve D. The firm maximizes profit by setting usage fee P equal to marginal cost and entry fee T* equal to the entire surplus of the consumer. MC D Quantity 12This pricing strategy was first analyzed by Walter Oi, “A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly,” Quarterly Journal of Economics (February 1971): 77–96. $/Q A P* B T* C CHAPTER 11 • Pricing with Market Power 415 FIGURE 11.10 TWO-PART TARIFF WITH TWO CONSUMERS The profit-maximizing usage fee P* will exceed marginal cost. The entry fee T* is equal to the surplus of the consumer with the smaller demand. The resulting profit is 2T* (P* − MC)(Q1 Q2). Note that this profit is larger than twice the area of triangle ABC. MC
D1 D2 Q2 Q1 Quantity TWO CONSUMERS Now suppose that there are two different consumers (or two groups of identical consumers). The firm, however, can set only one entry fee and one usage fee. It would thus no longer want to set the usage fee equal to marginal cost. If it did, it could make the entry fee no larger than the consumer surplus of the consumer with the smaller demand (or else it would lose that consumer), and this would not yield a maximum profit. Instead, the firm should set the usage fee above marginal cost and then set the entry fee equal to the remaining consumer surplus of the consumer with the smaller demand. Figure 11.10 illustrates this. With the optimal usage fee at P* greater than MC, the firm’s profit is 2T* (P* − MC)(Q1 Q2). (There are two consumers, and each pays T.) You can verify that this profit is more than twice the area of triangle ABC, the consumer surplus of the consumer with the smaller demand when P MC. To determine the exact values of P and T*, the firm would need to know (in addition to its marginal cost) the demand curves D1 and D2. It would then write down its profit as a function of P and T and choose the two prices that maximize this function. (See Exercise 10 for an example of how to do this.) MANY CONSUMERS Most firms, however, face a variety of consumers with different demands. Unfortunately, there is no simple formula to calculate the optimal two-part tariff in this case, and some trial-and-error experiments might be required. But there is always a trade-off: A lower entry fee means more entrants and thus more profit from sales of the item. On the other hand, as the entry fee becomes smaller and the number of entrants larger, the profit derived from the entry fee will fall. The problem, then, is to pick an entry fee that results in the optimum number of entrants—that is, the fee that allows for maximum profit. In principle, we can do this by starting with a price for sales of the item P, finding the optimum entry fee T, and then estimating the resulting profit. The price P is then changed, and the corresponding entry fee calculated, along with the new profit level. By iterating this way, we can approach the optimal two-part tariff. 416 PART 3 • Market Structure and Competitive Strategy Profit FIGURE 11.11 TWO-PART T
ARIFF WITH MANY DIFFERENT CONSUMERS Total profit p is the sum of the profit from the entry fee p a and p a and the profit from sales p s depend on T, the entry fee. Therefore s. Both (T)T + (P - MC)Q(n) where n is the number of entrants, which depends on the entry fee T, and Q is the rate of sales, which is greater the larger is n. Here T* is the profit-maximizing entry fee, given P. To calculate optimum values for P and T, we can start with a number for P, find the optimum T, and then estimate the resulting profit. P is then changed and the corresponding T recalculated, along with the new profit level. Total a s T* T Figure 11.11 illustrates this principle. The firm’s profit p is divided into two components, each of which is plotted as a function of the entry fee T, assuming a fixed sales price P. The first component, p a, is the profit from the entry fee and is equal to the revenue n(T)T, where n(T) is the number of entrants. (Note that a high T implies a small n.) Initially, as T is increased from zero, revenue n(T)T rises. Eventually, however, further increases in T will make n so small that n(T)T falls. The second component, p s, is the profit from sales of the item itself at price P and is equal to (P − MC)Q, where Q is the rate at which entrants purchase the item. The larger the number of entrants n, the larger Q will be. Thus p s falls when T is increased because a higher T reduces n. Starting with a number for P, we determine the optimal (profit-maximizing) T. We then change P, find a new T, and determine whether profit is now higher or lower. This procedure is repeated until profit has been maximized. Obviously, more data are needed to design an optimal two-part tariff than to choose a single price. Knowing marginal cost and the aggregate demand curve is not enough. It is impossible (in most cases) to determine the demand curve of every consumer, but one would at least like to know by how much individual demands differ from one another. If consumers’ demands for your product are fairly similar, you would want to charge a price P that is close to marginal cost and make
the entry fee T large. This is the ideal situation from the firm’s point of view because most of the consumer surplus could then be captured. On the other hand, if consumers have different demands for your product, you would probably want to set P well above marginal cost and charge a lower entry fee T. In that case, however, the two-part tariff is a less effective means of capturing consumer surplus; setting a single price may do almost as well. At Disneyland in California and Walt Disney World in Florida, the strategy is to charge a high entry fee and charge nothing for the rides. This policy makes sense because consumers have reasonably similar demands for Disney vacations. Most people visiting the parks plan daily budgets (including expenditures for food and beverages) that, for most consumers, do not differ very much. CHAPTER 11 • Pricing with Market Power 417 Firms are perpetually searching for innovative pricing strategies, and a few have devised and introduced a two-part tariff with a “twist”—the entry fee T entitles the customer to a certain number of free units. For example, if you buy a Gillette razor, several blades are usually included in the package. The monthly lease fee for a mainframe computer usually includes some free usage before usage is charged. This twist lets the firm set a higher entry fee T without losing as many small customers. Because these small customers might pay little or nothing for usage under this scheme, the higher entry fee will capture their surplus without driving them out of the market, while also capturing more of the surplus of the large customers. EXAM PLE 11.4 PRICING CELLULAR PHONE SERVICE Most telephone service is priced using a two-part tariff: a monthly access fee, which may include some free minutes, plus a per-minute charge for additional minutes. This is also true for cellular phone service, which has grown explosively, both in the United States and around the world. In the case of cellular service, providers have taken the two-part tariff and turned it into an art form. In most parts of the United States, consumers can choose among four national network providers— Verizon, T-Mobile, AT&T, and Sprint. These providers compete among themselves for customers, but each has some market power. This market power arises in part from oligopolistic pricing and output decisions, as we will explain in Chapters 12 and 13. Market power also arises because consumers face switching costs: When they sign up for a cellular plan, they must typically
make a commitment to stay for at least one year, and breaking the contract is quite expensive. Most service providers impose a penalty upwards of $200 for early termination. Because providers have market power, they must think carefully about profit-maximizing pricing strategies. The two-part tariff provides an ideal means by which cellular providers can capture consumer surplus and turn it into profit. Table 11.3 shows cellular rate plans (for 2011) offered by Verizon Wireless, Sprint, and AT&T, as well as Orange (a subsidiary of France Telecom that operates in several countries) and China Mobile. Note that all of these cellular providers give consumers a choice of alternative two-part tariffs, and the plans are structured in similar ways. Let’s focus on the Verizon plans. The least expensive Verizon plan has a monthly access charge of $39.99 and includes 450 “anytime” minutes (i.e., 450 minutes of talk time per month that can be used at any hour of the day). The plan also includes an unlimited amount of talk time during nights and weekends (periods when demand is generally lower). A subscriber who uses more than the 450 “anytime” minutes is charged $0.45 for each additional minute. A customer who uses her cell phone more frequently could sign up for a more expensive plan, e.g., one that costs $59.99 per month but includes 900 “anytime” minutes and a charge of $0.40 for additional minutes. And if you, the reader, use your cell phone constantly (and thus have time for little else), you could sign up for a plan that includes unlimited “anytime” minutes, at a monthly cost of $69.99. Why do cellular phone providers offer several different types of plans and options within each? Why don’t they simply offer a single two-part tariff with a monthly access charge and a per-minute usage charge? Offering several different plans and options allows companies to combine thirddegree price discrimination with the two-part tariff. The plans are structured so that consumers sort themselves into groups based on their plan choices. A different two-part tariff is then applied to each group. 418 PART 3 • Market Structure and Competitive Strategy TABLE 11.3 CELLULAR RATE PLANS (2011) ANYTIME MINUTES MONTHLY ACCESS CHARGES NIGHT & WEEKEND MINUTES PER-MINUTE RATE AFTER ALLOWANCE A. VERIZON: AMERICA’
S CHOICE BASIC 450 900 Unlimited $39.99 $59.99 $69.99 Unlimited Unlimited Unlimited 200 450 900 450 900 Unlimited 100 200 300 None 100 400 150 450 800 1200 1800 B. SPRINT: BASIC TALK PLANS $29.99 $39.99 $59.99 Unlimited Unlimited Unlimited C. AT&T INDIVIDUAL PLANS $39.99 $59.99 $69.99 £10.00 £15.00 £20.00 28.00 NIS 38.00 NIS 61.90 NIS 58 RMB 158 RMB 258 RMB 358 RMB 458 RMB 5000 Unlimited Unlimited D. ORANGE (UK) None None None E. ORANGE (ISRAEL) None None None F. CHINA MOBILE None None None None None $0.45 $0.40 Included $0.45 $0.45 $0.40 $0.45 $0.40 Included 25 pence 25 pence 25 pence 0.59 NIS 0.59 NIS 0.59 NIS 0.40 RMB 0.35 RMB 0.32 RMB 0.30 RMB 0.25 RMB To convert the international prices to U.S. dollars (as of August 2011), use the following conversion factors: 1£ $1.60, 1 NIS $0.30, and 1 RMB $0.13. Data from various cellular providers. To see how this sorting works, consider the plan choices of different types of consumers. People who use a cell phone only occasionally will want to spend as little as possible on the service and will choose the least expensive plan (with the fewest “anytime” minutes). The most expensive plans are best suited to very heavy users (perhaps a salesperson who travels extensively and makes call throughout the day), who will want to minimize their per-minute cost. Other plans are better suited to consumers with moderate calling needs. Consumers will choose a plan that best matches their needs. Thus they will sort themselves into CHAPTER 11 • Pricing with Market Power 419 groups, and the consumers in each group will be relatively homogeneous in terms of demands for cellular service. Remember that the two-part tariff works best when consumers have identical or very similar demands. (Recall from Figure 11.9 that with identical consumers, the two-part tariff can be used to capture all consumer surplus.) Creating a situation in which consumers sort themselves into groups in this way makes
best use of the two-part tariff. • bundling Practice of selling two or more products as a package. *11.5 Bundling You have probably seen the 1939 film Gone with the Wind. It is a classic that is nearly as popular now as it was then.13 Yet we would guess that you have not seen Getting Gertie’s Garter, a flop that the same company (MGM, a division of Loews) also distributed. And we would also guess that you did not know that these two films were priced in what was then an unusual and innovative way.14 Movie theaters that leased Gone with the Wind also had to lease Getting Gertie’s Garter. (Movie theaters pay the film companies or their distributors a daily or weekly fee for the films they lease.) In other words, these two films were bundled—i.e., sold as a package.15 Why would the film company do this? You might think that the answer is obvious: Gone with the Wind was a great film and Gertie was a lousy film, so bundling the two forced movie theaters to lease Gertie. But this answer doesn’t make economic sense. Suppose a theater’s reservation price (the maximum price it will pay) for Gone with the Wind is $12,000 per week, and its reservation price for Gertie is $3000 per week. Then the most it would pay for both films is $15,000, whether it takes the films individually or as a package. Bundling makes sense when customers have heterogeneous demands and when the firm cannot price discriminate. With films, different movie theaters serve different groups of patrons and therefore different theaters may face different demands for films. For example, different theaters might appeal to different age groups, who in turn have different relative film preferences. To see how a film company can use customer heterogeneity to its advantage, suppose that there are two movie theaters and that their reservation prices for our two films are as follows: GONE WITH THE WIND GETTING GERTIE’S GARTER Theater A Theater B $12,000 $10,000 $3000 $4000 13Adjusted for inflation, Gone with the Wind was also the largest grossing film of all time. Titanic, released in 1997, made $601 million. Gone with the Wind grossed $81.5 million in 1939 dollars, which is equivalent to $941 million in 1997 dollars. 14For those readers who claim to know all this
, our final trivia question is: Who played the role of Gertie in Getting Gertie’s Garter? 15The major Hollywood studios were forced to stop bundling their films in 1948, when the Supreme Court decided that the studios were acting in violation of antitrust laws by forcing theaters to buy their films on an all-or-nothing basis. In addition, the studios were forced to sell their theater chains, ending decades of monopolistic vertical integration that had made the studios economic powerhouses. 420 PART 3 • Market Structure and Competitive Strategy If the films are rented separately, the maximum price that could be charged for Wind is $10,000 because charging more would exclude Theater B. Similarly, the maximum price that could be charged for Gertie is $3000. Charging these two prices would yield $13,000 from each theater, for a total of $26,000 in revenue. But suppose the films are bundled. Theater A values the pair of films at $15,000 ($12,000 $3000), and Theater B values the pair at $14,000 ($10,000 $4000). Therefore, we can charge each theater $14,000 for the pair of films and earn a total revenue of $28,000. Clearly, we can earn more revenue ($2000 more) by bundling the films. Relative Valuations Why is bundling more profitable than selling the films separately? Because (in this example) the relative valuations of the two films are reversed. In other words, although both theaters would pay much more for Wind than for Gertie, Theater A would pay more than Theater B for Wind ($12,000 vs. $10,000), while Theater B would pay more than Theater A for Gertie ($4000 vs. $3000). In technical terms, we say that the demands are negatively correlated—the customer willing to pay the most for Wind is willing to pay the least for Gertie. To see why this is critical, suppose demands were positively correlated—that is, Theater A would pay more for both films: GONE WITH THE WIND GETTING GERTIE’S GARTER Theater A Theater B $12,000 $10,000 $4000 $3000 The most that Theater A would pay for the pair of films is now $16,000, but the most that Theater B would pay is only $13,000. Thus if we bundled the films, the maximum price that could be charged for the package is $13,000,
yielding a total revenue of $26,000, the same as by renting the films separately. Now, suppose a firm is selling two different goods to many consumers. To analyze the possible advantages of bundling, we will use a simple diagram to describe the preferences of the consumers in terms of their reservation prices and their consumption decisions given the prices charged. In Figure 11.12 the horizontal axis is r1, which is the reservation price of a consumer for good 1, and FIGURE 11.12 RESERVATION PRICES Reservation prices r1 and r2 for two goods are shown for three consumers, labeled A, B, and C. Consumer A is willing to pay up to $3.25 for good 1 and up to $6 for good 2. r2 $10 $6 $5 $3.25 C A B $3.25 $5 $8.25 $10 r1 r2 P2 II I Consumers buy only good 2 Consumers buy both goods III IV Consumers buy neither good Consumers buy only good 1 P1 r1 CHAPTER 11 • Pricing with Market Power 421 FIGURE 11.13 CONSUMPTION DECISIONS WHEN PRODUCTS ARE SOLD SEPARATELY The reservation prices of consumers in region I exceed the prices P1 and P2 for the two goods, so these consumers buy both goods. Consumers in regions II and IV buy only one of the goods, and consumers in region III buy neither good. the vertical axis is r2, which is the reservation price for good 2. The figure shows the reservation prices for three consumers. Consumer A is willing to pay up to $3.25 for good 1 and up to $6 for good 2; consumer B is willing to pay up to $8.25 for good 1 and up to $3.25 for good 2; and consumer C is willing to pay up to $10 for each of the goods. In general, the reservation prices for any number of consumers can be plotted this way. Suppose that there are many consumers and that the products are sold separately, at prices P1 and P2, respectively. Figure 11.13 shows how consumers can be divided into groups. Consumers in region I of the graph have reservation prices that are above the prices being charged for each of the goods, so they will buy both goods. Consumers in region II have a reservation price for good 2 that is above P2, but a reservation price for good 1 that is below P1; they will buy only good 2. Similarly,
consumers in region IV will buy only good 1. Finally, consumers in region III have reservation prices below the prices charged for each of the goods, and so will buy neither. Now suppose the goods are sold only as a bundle, for a total price of PB. We can then divide the graph into two regions, as in Figure 11.14. Any given r2 PB I Consumers buy bundle r2 = PB – r1 II Consumers do not buy bundle PB r1 FIGURE 11.14 CONSUMPTION DECISIONS WHEN PRODUCTS ARE BUNDLED Consumers compare the sum of their reservation prices r1 + r2, with the price of the bundle PB. They buy the bundle only if r1 + r2 is at least as large as PB. 422 PART 3 • Market Structure and Competitive Strategy consumer will buy the bundle only if its price is less than or equal to the sum of that consumer’s reservation prices for the two goods. The dividing line is therefore the equation PB r1 r2 or, equivalently, r2 PB − r1. Consumers in region I have reservation prices that add up to more than PB, so they will buy the bundle. Consumers in region II, who have reservation prices that add up to less than PB, will not buy the bundle. Depending on the prices, some of the consumers in region II of Figure 11.14 might have bought one of the goods if they had been sold separately. These consumers are lost to the firm, however, when it sells the goods only as a bundle. The firm, then, must determine whether it can do better by bundling. In general, the effectiveness of bundling depends on the extent to which demands are negatively correlated. In other words, it works best when consumers who have a high reservation price for good 1 have a low reservation price for good 2, and vice versa. Figure 11.15 shows two extremes. In part (a), each point represents the two reservation prices of a consumer. Note that the demands for the two goods are perfectly positively correlated—consumers with a high reservation price for good 1 also have a high reservation price for good 2. If the firm bundles and charges a price PB P1 P2, it will make the same profit that it would make by selling the goods separately at prices P1 and P2. In part (b), on the other hand, demands are perfectly negatively correlated—a higher reservation price for good 2 implies a proportionately lower one for good 1. In this case
, bundling is the ideal strategy. By charging the price PB the firm can capture all the consumer surplus. Figure 11.16, which shows the movie example that we introduced at the beginning of this section, illustrates how the demands of the two movie theaters are negatively correlated. (Theater A will pay relatively more for Gone with the r2 PB r2 P2 P1 (a) r1 PB r1 (b) FIGURE 11.15 RESERVATION PRICES In (a), because demands are perfectly positively correlated, the firm does not gain by bundling: It would earn the same profit by selling the goods separately. In (b), demands are perfectly negatively correlated. Bundling is the ideal strategy—all the consumer surplus can be extracted. (Gertie) r2 $10,000 5000 4000 3000 CHAPTER 11 • Pricing with Market Power 423 FIGURE 11.16 MOVIE EXAMPLE Consumers A and B are two movie theaters. The diagram shows their reservation prices for the films Gone with the Wind and Getting Gertie’s Garter. Because the demands are negatively correlated, bundling pays. B A $5000 10,000 12,000 14,000 r1 (Wind) Wind, but Theater B will pay relatively more for Getting Gertie’s Garter.) This makes it more profitable to rent the films as a bundle priced at $14,000. Mixed Bundling So far, we have assumed that the firm has two options: to sell the goods either separately or as a bundle. But there is a third option, called mixed bundling. As the name suggests, the firm offers its products both separately and as a bundle, with a package price below the sum of the individual prices. (We use the term pure bundling to refer to the strategy of selling the products only as a bundle.) Mixed bundling is often the ideal strategy when demands are only somewhat negatively correlated and/or when marginal production costs are significant. (Thus far, we have assumed that marginal production costs are zero.) In Figure 11.17, mixed bundling is the most profitable strategy. Although demands are perfectly negatively correlated, there are significant marginal costs. (The marginal cost of producing good 1 is $20, and the marginal cost of producing good 2 is $30.) We have four consumers, labeled A through D. Now, let’s compare three strategies: 1. Selling the goods separately at prices P1 $50 and P2 $90 2. Selling the
goods only as a bundle at a price of $100 3. Mixed bundling, whereby the goods are offered separately at prices P1 P2 $89.95, or as a bundle at a price of $100. Table 11.4 shows these three strategies and the resulting profits. (You can try other prices for P1, P2, and PB to verify that those given in the table maximize profit for each strategy.) When the goods are sold separately, only consumers B, C, and D buy good 1, and only consumer A buys good 2; total profit is 3($50 − $20) 1($90 − $30) $150. With pure bundling, all four consumers buy the bundle for $100, so that total profit is 4($100 − $20 − $30) $200. As we should expect, pure bundling is better than selling the goods separately because consumers’ demands are negatively correlated. But what about mixed bundling? • mixed bundling Selling two or more goods both as a package and individually. • pure bundling Selling products only as a package. 424 PART 3 • Market Structure and Competitive Strategy c1 $20 A FIGURE 11.17 MIXED VERSUS PURE BUNDLING With positive marginal costs, mixed bundling may be more profitable than pure bundling. Consumer A has a reservation price for good 1 that is below marginal cost c1, and consumer D has a reservation price for good 2 that is below marginal cost c2. With mixed bundling, consumer A is induced to buy only good 2, and consumer D is induced to buy only good 1, thus reducing the firm’s cost. r2 $100 90 80 70 60 50 40 30 20 10 B C c2 $30 D $10 20 30 40 50 60 70 80 90 100 r1 Consumer D buys only good 1 for $89.95, consumer A buys only good 2 for $89.95, and consumers B and C buy the bundle for $100. Total profit is now ($89.95 − $20) ($89.95 − $30) 2($100 − $20 − $30) $229.90.16 In this case, mixed bundling is the most profitable strategy, even though demands are perfectly negatively correlated (i.e., all four consumers have reservation prices on the line r2 100 − r1). Why? For each good, marginal production cost exceeds the reservation price of one consumer. For example, consumer A has
a reservation price of $90 for good 2 but a reservation price of only $10 for good 1. Because the cost of producing a unit of good 1 is $20, the firm would prefer that consumer A buy only good 2, not the bundle. It can achieve this goal by offering good 2 separately for a price just below consumer A’s reservation price, while also offering the bundle at a price acceptable to consumers B and C. Mixed bundling would not be the preferred strategy in this example if marginal costs were zero: In that case, there would be no benefit in excluding TABLE 11.4 BUNDLING EXAMPLE Sold separately Pure bundling P1 $50 — P2 $90 — Mixed bundling $89.95 $89.95 PB — $100 $100 PROFIT $150 $200 $229.90 16Note that in the mixed bundling strategy, goods 1 and 2 are priced at $89.95 rather than at $90. If they were priced at $90, consumers A and D would be indifferent between buying a single good and buying the bundle, and if they buy the bundle, total profit will be lower. r2 $120 100 90 80 60 40 20 10 A B C D CHAPTER 11 • Pricing with Market Power 425 FIGURE 11.18 MIXED BUNDLING WITH ZERO MARGINAL COSTS If marginal costs are zero, and if consumers’ demands are not perfectly negatively correlated, mixed bundling is still more profitable than pure bundling. In this example, consumers B and C are willing to pay $20 more for the bundle than are consumers A and D. With pure bundling, the price of the bundle is $100. With mixed bundling, the price of the bundle can be increased to $120 and consumers A and D can still be charged $90 for a single good. $10 20 40 60 80 90 100 120 r1 consumer A from buying good 1 and consumer D from buying good 2. We leave it to you to demonstrate this (see Exercise 12).17 If marginal costs are zero, mixed bundling can still be more profitable than pure bundling if consumers’ demands are not perfectly negatively correlated. (Recall that in Figure 11.17, the reservation prices of the four consumers are perfectly negatively correlated.) This is illustrated by Figure 11.18, in which we have modified the example of Figure 11.17. In Figure 11.18, marginal costs are zero, but the reservation
prices for consumers B and C are now higher. Once again, let’s compare three strategies: selling the two goods separately, pure bundling, and mixed bundling. Table 11.5 shows the optimal prices and the resulting profits for each strategy. (Once again, you should try other prices for P1, P2, and PB to verify that those given in the table maximize profit for each strategy.) When the goods are sold separately, only consumers C and D buy good 1, and only consumers A and B buy good 2; total profit is thus $320. With pure bundling, all four TABLE 11.5 MIXED BUNDLING WITH ZERO MARGINAL COSTS Sell separately Pure bundling Mixed bundling P1 $80 — $90 P2 $80 — $90 PB — $100 $120 PROFIT $320 $400 $420 17Sometimes a firm with monopoly power will find it profitable to bundle its product with the product of another firm; see Richard L. Schmalensee, “Commodity Bundling by Single-Product Monopolies,” Journal of Law and Economics 25 (April 1982): 67–71. Bundling can also be profitable when the products are substitutes or complements. See Arthur Lewbel, “Bundling of Substitutes or Complements,” International Journal of Industrial Organization 3 (1985): 101–7. 426 PART 3 • Market Structure and Competitive Strategy consumers buy the bundle for $100, so that total profit is $400. As expected, pure bundling is better than selling the goods separately because consumers’ demands are negatively correlated. But mixed bundling is better still. With mixed bundling, consumer A buys only good 2, consumer D buys only good 1, and consumers B and C buy the bundle at a price of $120. Total profit is now $420. Why does mixed bundling give higher profits than pure bundling even though marginal costs are zero? The reason is that demands are not perfectly negatively correlated: The two consumers who have high demands for both goods (B and C) are willing to pay more for the bundle than are consumers A and D. With mixed bundling, therefore, we can increase the price of the bundle (from $100 to $120), sell this bundle to two consumers, and charge the remaining consumers $90 for a single good. Bundling in Practice Bundling is a widely used pricing strategy. When you buy a new car, for example
, you can purchase such options as power windows, power seats, or a sunroof separately, or you can purchase a “luxury package” in which these options are bundled. Manufacturers of luxury cars (such as Lexus, BMW, or Infiniti) tend to include such “options” as standard equipment; this practice is pure bundling. For more moderately priced cars, however, these items are optional, but are usually offered as part of a bundle. Automobile companies must decide which items to include in such bundles and how to price them. Another example is vacation travel. If you plan a vacation to Europe, you might make your own hotel reservations, buy an airplane ticket, and order a rental car. Alternatively, you might buy a vacation package in which airfare, land arrangements, hotels, and even meals are all bundled together. Still another example is cable television. Cable operators typically offer a basic service for a low monthly fee, plus individual “premium” channels, such as Cinemax, Home Box Office, and the Disney Channel, on an individual basis for additional monthly fees. However, they also offer packages in which two or more premium channels are sold as a bundle. Bundling cable channels is profitable because demands are negatively correlated. How do we know that? Given that there are only 24 hours in a day, the time that a consumer spends watching HBO is time that cannot be spent watching the Disney Channel. Thus consumers with high reservation prices for some channels will have relatively low reservation prices for others. How can a company decide whether to bundle its products, and determine the profit-maximizing prices? Most companies do not know their customers’ reservation prices. However, by conducting market surveys, they may be able to estimate the distribution of reservation prices, and then use this information to design a pricing strategy. This is illustrated in Figure 11.19. The dots are estimates of reservation prices or a representative sample of consumers (obtained, say, from a market survey). The company might first choose a price for the bundle, PB, such that a diagonal line connecting these prices passes roughly midway through the dots in the figure. It could then try individual prices P1 and P2. Given P1, P2, and PB, we can separate consumers into four regions, as shown in the figure. Consumers in Region I buy nothing (because r1 < P1, r2 < P2, and r1 r2 < PB). Consumers in Region II buy
the bundle (because r1 r2> PB). Consumers in Region III buy only good 2 (because r2> P2 but r1 < PB − P2). Likewise, consumers in Region IV buy only good 1. Given this distribution, we can calculate the resulting profits. We III—Buy Only Good 2 r2 PB P2 I—Buy Nothing CHAPTER 11 • Pricing with Market Power 427 FIGURE 11.19 MIXED BUNDLING IN PRACTICE The dots in this figure are estimates of reservation prices for a representative sample of consumers. A company could first choose a price for the bundle, PB, such that a diagonal line connecting these prices passes roughly midway through the dots. The company could then try individual prices P1 and P2. Given P1, P2, and PB, profits can be calculated for this sample of consumers. Managers can then raise or lower P1, P2, and PB and see whether the new pricing leads to higher profits. This procedure is repeated until total profit is roughly maximized. II—Buy Bundle IV—Buy Only Good 1 P1 PB r1 can then raise or lower P1, P2, and PB and see whether doing so leads to higher profits. This can be done repeatedly (on a computer) until prices are found that roughly maximize total profit. EXAM PLE 11.5 THE COMPLETE DINNER VERSUS À LA CARTE: A RESTAURANT’S PRICING PROBLEM Many restaurants offer both complete dinners and à la carte menus. Why? Most customers go out to eat knowing roughly how much they are willing to spend for dinner (and choose the restaurant accordingly). Diners, however, have different preferences. For example, some value appetizers highly but could happily skip dessert. Others attach little value to the appetizer but regard dessert as essential. And some customers attach moderate values to both appetizers and desserts. What pricing strategy lets the restaurant capture as much consumer surplus as possible from these heterogeneous customers? The answer, of course, is mixed bundling. For a restaurant, mixed bundling means offering both complete dinners (the appetizer, main course, and dessert come as a package) and an à la carte menu (the customer buys the appetizer, main course, and dessert separately). This strategy allows the à la carte menu to be priced to capture consumer surplus from customers who value some dishes much more highly than others. (Such customers would correspond to
consumers A and D in Figure 11.17 (page 424).) At the same time, the complete dinner retains those customers who have lower variations in their reservation prices for different dishes (e.g., customers who attach moderate values to both appetizers and desserts). For example, if the restaurant expects to attract customers willing to spend about $20 for dinner, it might charge about $5 for appetizers, $14 for a typical main dish, and $4 for dessert. It could also offer a complete dinner, which includes an appetizer, 428 PART 3 • Market Structure and Competitive Strategy main course, and dessert, for $20. Then, the customer who loves dessert but couldn’t care less about an appetizer will order only the main dish and dessert, and spend $18 (saving the restaurant the cost of preparing an appetizer). At the same time, another customer who attaches a moderate value (say, $3 or $3.50) to both the appetizer and dessert will buy the complete dinner. You don’t have to go an expensive French restaurant to experience mixed bundling. Table 11.6 shows the prices of some individual items at McDonald’s, as well as the prices of “super meals” that include meat or fish items along with a large order of French fries and a large soda. Note that you can buy a Big Mac, a large fries, and a large soda separately for a total of $9.27, or you can buy them as a bundle for $6.99. You say you don’t care for fries? Then just buy the Big Mac and large soda separately, for a total of $6.68, which is $0.31 less than the price of the bundle. Unfortunately for consumers, perhaps, creative pricing is sometimes more important than creative cooking for the financial success of a restaurant. Successful restaurateurs know their customers’ demand characteristics and use that knowledge to design a pricing strategy that extracts as much consumer surplus as possible. TABLE 11.6 MIXED BUNDLING AT MCDONALD’S (2011) INDIVIDUAL ITEM Chicken Sandwich Filet-O-Fish Big Mac Quarter Pounder Double Quarter Pounder 10-piece Chicken McNuggets Large French Fries Large Soda PRICE $5.49 $4.39 $4.69 $4.69 $6.09 $5.19 $2.59 $1.99 Data from McDonald’s restaurant menu
. MEAL (INCLUDES SODA AND FRIES) UNBUNDLED PRICE PRICE OF BUNDLE SAVINGS Chicken Sandwich Filet-O-Fish Big Mac Quarter Pounder Double Quarter Pounder 10-piece Chicken McNuggets $10.07 $8.97 $9.27 $9.27 $10.67 $9.77 $7.89 $6.79 $6.99 $7.19 $8.39 $7.59 $2.18 $2.18 $2.28 $2.08 $2.28 $2.18 • tying Practice of requiring a customer to purchase one good in order to purchase another. Tying Tying is a general term that refers to any requirement that products be bought or sold in some combination. Pure bundling is a common form of tying, but tying can also take other forms. For example, suppose a firm sells a product (such as a copying machine) that requires the consumption of a secondary product (such as paper). The consumer who buys the first product is also required to buy the secondary product from the same company. This requirement is usually imposed through a contract. Note that this is different from the examples of bundling discussed earlier. In those examples, the consumer might have been happy to buy just one of the products. In this case, however, the first product is useless without access to the secondary product. Why might firms use this kind of pricing practice? One of the main benefits of tying is that it often allows a firm to meter demand and thereby practice price discrimination more effectively. During the 1950s, for example, when Xerox had a monopoly on copying machines but not on paper, customers who leased Xerox CHAPTER 11 • Pricing with Market Power 429 copiers also had to buy Xerox paper. This allowed Xerox to meter consumption (customers who used a machine intensively bought more paper), and thereby apply a two-part tariff to the pricing of its machines. Also during the 1950s, IBM required customers who leased its mainframe computers to use paper computer cards made only by IBM. By pricing cards well above marginal cost, IBM was effectively charging higher prices for computer usage to customers with larger demands.18 Tying can also be used to extend a firm’s market power. As we discussed in Example 10.8 (page 394), in 1998 the Department of Justice brought suit against Microsoft, claiming that the company had tied its Internet Explorer Web browser to its
Windows 98 operating system in order to maintain its monopoly power in the market for PC operating systems. Tying can have other uses. An important one is to protect customer goodwill connected with a brand name. This is why franchises are often required to purchase inputs from the franchiser. For example, Mobil Oil requires its service stations to sell only Mobil motor oil, Mobil batteries, and so on. Similarly, until recently, a McDonald’s franchisee had to purchase all materials and supplies— from the hamburgers to the paper cups—from McDonald’s, thus ensuring product uniformity and protecting the brand name.19 *11.6 Advertising We have seen how firms can utilize their market power when making pricing decisions. Pricing is important for a firm, but most firms with market power have another important decision to make: how much to advertise. In this section, we will see how firms with market power can make profit-maximizing advertising decisions, and how those decisions depend on the characteristics of demand for the firm’s product.20 For simplicity, we will assume that the firm sets only one price for its product. We will also assume that having done sufficient market research, it knows how its quantity demanded depends on both its price P and its advertising expenditures in dollars A; that is, it knows Q(P, A). Figure 11.20 shows the firm’s demand and cost curves with and without advertising. AR and MR are the firm’s average and marginal revenue curves when it does not advertise, and AC and MC are its average and marginal cost curves. It produces a quantity Q0, where MR MC, and receives a price P0. Its profit per unit is the difference between P0 and average cost, so its total profit p 0 is given by the gray-shaded rectangle. Now suppose the firm advertises. This causes its demand curve to shift out and to the right; the new average and marginal revenue curves are given by AR and MR. Advertising is a fixed cost, so the firm’s average cost curve rises (to AC). Marginal cost, however, remains the same. With advertising, the firm produces Q1 (where MR MC) and receives a price P1. Its total profit p 1, given by the purple-shaded rectangle, is now much larger. 18Antitrust actions ultimately forced IBM to discontinue this pricing practice. 19In some cases, the courts have ruled that tying is not necessary to protect customer goodwill and is anticomp
etitive. Today, a McDonald’s franchisee can buy supplies from any McDonald’s-approved source. For a discussion of some of the antitrust issues involved in franchise tying, see Benjamin Klein and Lester F. Saft, “The Law and Economics of Franchise Tying Contracts,” Journal of Law and Economics 28 (May 1985): 345–61. 20A perfectly competitive firm has little reason to advertise: By definition it can sell as much as it produces at a market price that it takes as given. That is why it would be unusual to see a producer of corn or soybeans advertise. In §7.1, marginal cost—the increase in cost that results from producing one extra unit of output—is distinguished from average cost— the cost per unit of output. 430 PART 3 • Market Structure and Competitive Strategy $/Q P1 P0 π 0 π 1 MC AR′ AC ′ AC MR ′ AR MR Q0 Q1 Quantity FIGURE 11.20 EFFECTS OF ADVERTISING AR and MR are average and marginal revenue when the firm doesn’t advertise, and AC and MC are average and marginal cost. The firm produces Q0 and receives a price P0. Its total profit p 0 is given by the gray-shaded rectangle. If the firm advertises, its average and marginal revenue curves shift to the right. Average cost rises (to AC) but marginal cost remains the same. The firm now produces Q1 (where MR = MC), and receives a price P1. Its total profit, p 1, is now larger. Although the firm in Figure 11.20 is clearly better off when it advertises, the figure does not help us determine how much advertising it should do. It must choose its price P and advertising expenditure A to maximize profit, which is now given by: p = PQ(P, A) - C(Q) - A Given a price, more advertising will result in more sales and thus more revenue. But what is the firm’s profit-maximizing advertising expenditure? You might be tempted to say that the firm should increase its advertising expenditures until the last dollar of advertising just brings forth an additional dollar of revenue—that is, until the marginal revenue from advertising, (PQ)/A, is just equal to 1. But as Figure 11.20 shows, this reasoning omits an important element. Remember that advertising leads to increased output (in the figure, output increased from Q0 to
Q1). But increased output in turn means increased production costs, and this must be taken into account when comparing the costs and benefits of an extra dollar of advertising. The correct decision is to increase advertising until the marginal revenue from an additional dollar of advertising, MRAds, just equals the full marginal CHAPTER 11 • Pricing with Market Power 431 cost of that advertising. That full marginal cost is the sum of the dollar spent directly on the advertising and the marginal production cost resulting from the increased sales that advertising brings about. Thus the firm should advertise up to the point that MRAds = P Q A = 1 + MC Q A (11.3) = full marginal cost of advertising This rule is often ignored by managers, who justify advertising budgets by comparing the expected benefits (i.e., added sales) only with the cost of the advertising. But additional sales mean increased production costs that must also be taken into account.21 A Rule of Thumb for Advertising Like the rule MR = MC, equation (11.3) is sometimes difficult to apply in practice. In Chapter 10, we saw that MR MC implies the following rule of thumb for pricing: (P − MC)/P −1/ED, where ED is the firm’s price elasticity of demand. We can combine this rule of thumb for pricing with equation (11.3) to obtain a rule of thumb for advertising. First, rewrite equation (11.3) as follows: (P - MC) Q A = 1 Now multiply both sides of this equation by A/PQ, the advertising-to-sales ratio: P - MC P c A Q Q A d = A PQ In equation (10.1), we offer a rule of thumb for pricing for a profit-maximizing firm—the markup over marginal cost as a percentage of price should equal minus the inverse of the price elasticity of demand. • advertising-to-sales ratio Ratio of a firm’s advertising expenditures to its sales. The term in brackets, (A/Q)(Q/A), is the advertising elasticity of demand, the percentage change in the quantity demanded that results from a 1-percent increase in advertising expenditures. We will denote this elasticity by EA. Because (P − MC)/P must equal −1/EP, we can rewrite this equation as follows: • advertising elasticity of demand Percentage change in quantity demanded resulting from a 1-percent increase in advertising expenditures. A/PQ = -(EA
/EP) (11.4) Equation (11.4) is a rule of thumb for advertising. It says that to maximize profit, the firm’s advertising-to-sales ratio should be equal to minus the ratio of 21To derive this result using calculus, differentiate p(Q,A) with respect to A, and set the derivative equal to zero: 0p/0A = P(0Q/0A) - MC(0Q/0A) - 1 = 0 Rearranging gives equation (11.3). 432 PART 3 • Market Structure and Competitive Strategy the advertising and price elasticities of demand. Given information (from, say, market research studies) on these two elasticities, the firm can use this rule to check that its advertising budget is not too small or too large. To put this rule into perspective, assume that a firm is generating sales revenue of $1 million per year while allocating only $10,000 (1 percent of its revenues) to advertising. The firm knows that its advertising elasticity of demand is.2, so that a doubling of its advertising budget from $10,000 to $20,000 should increase sales by 20 percent. The firm also knows that the price elasticity of demand for its product is −4. Should it increase its advertising budget, knowing that with a price elasticity of demand of −4, its markup of price over marginal cost is substantial? The answer is yes; equation (11.4) tells us that the firm’s advertising-to-sales ratio should be −(.2/−4) = 5 percent, so the firm should increase its advertising budget from $10,000 to $50,000. This rule makes intuitive sense. It says firms should advertise a lot if (i) demand is very sensitive to advertising (EA is large), or if (ii) demand is not very price elastic (EP is small). Although (i) is obvious, why should firms advertise more when the price elasticity of demand is small? A small elasticity of demand implies a large markup of price over marginal cost. Therefore, the marginal profit from each extra unit sold is high. In this case, if advertising can help sell a few more units, it will be worth its cost.22 E XAM PLE 11.6 ADVERTISING IN PRACTICE In Example 10.2 (page 370), we looked at the use of markup pricing by supermarkets, convenience stores, and
makers of designer jeans. We saw in each case how the markup of price over marginal cost depended on the firm’s price elasticity of demand. Now let’s see why these firms, as well as producers of other goods, advertise as much (or as little) as they do. First, supermarkets. We said that the price elasticity of demand for a typical supermarket is around −10. To determine the advertising-to-sales ratio, we also need to know the advertising elasticity of demand. This number can vary considerably depending on what part of the country the supermarket is located in and whether it is in a city, suburb, or rural area. A reasonable range, however, would be 0.1 to 0.3. Substituting these numbers into equation (11.4), we find that the manager of a typical supermarket should have an advertising budget of around 1 to 3 percent of sales—which is indeed what many supermarkets spend on advertising. Convenience stores have lower price elasticities of demand (around −5), but their advertising-to-sales ratios are usually less than those for supermarkets (and are often zero). Why? Because convenience stores mostly serve customers who live nearby; they may need a few items late at night or may simply not want to drive to the supermarket. These customers already know about the convenience store and are unlikely to change their buying habits if the store 22Advertising often affects the price elasticity of demand, and this fact must be taken into account. For some products, advertising broadens the market by attracting a large range of customers, or by creating a bandwagon effect. This is likely to make demand more price elastic than it would have been otherwise. (But EA is likely to be large, so that advertising will still be worthwhile.) Sometimes advertising is used to differentiate a product from others (by creating an image, allure, or brand identification), making the product’s demand less price elastic than it would otherwise be. CHAPTER 11 • Pricing with Market Power 433 advertises. Thus EA is very small, and advertising is not worthwhile. Advertising is quite important for makers of designer jeans, who will have advertising-to-sales ratios as high as 10 or 20 percent. Advertising helps to make consumers aware of the label and gives it an aura and image. We said that price elasticities of demand in the range of −3 to −4 are typical for the major labels, and advertising elasticities of demand can range from.3 to as high
as 1. So, these levels of advertising would seem to make sense. Laundry detergents have among the highest advertising-to-sales ratios of all products, sometimes exceeding 30 percent, even though demand for any one brand is at least as price elastic as it is for designer jeans. What justifies all the advertising? A very large advertising elasticity. The demand for any one brand of laundry detergent depends crucially on advertising; without it, consumers would have little basis for selecting that particular brand.23 Finally, Table 11.7 shows sales, advertising expenditures, and the ratio of the two for leading brands of over-the-counter drugs. Observe that overall, the ratios are quite high. As with laundry detergents, the advertising elasticity for name-brand drugs is very high. Alka-Seltzer, Mylanta, and Tums, for instance, are all antacids that do much the same thing. Sales depend on consumer identification with a particular brand, which requires advertising. TABLE 11.7 SALES AND ADVERTISING EXPENDITURES FOR LEADING BRANDS OF OVER-THE-COUNTER DRUGS (IN MILLIONS OF DOLLARS) SALES ADVERTISING RATIO (%) Pain Medications Tylenol Advil Bayer Excedrin Antacids Alka-Seltzer Mylanta Tums 855 360 170 130 160 135 135 Cold Remedies (decongestants) Benadryl Sudafed Cough Medicine Vicks Robitussin Halls 130 115 350 205 130 143.8 91.7 43.8 26.7 52.2 32.8 27.6 30.9 28.6 26.6 37.7 17.4 17 26 26 21 33 24 20 24 25 8 19 13 Data from Milt Freudenheim, “Rearranging Drugstore Shelves,” THE NEW YORK TIMES, September 27, 1994. 23For an overview of statistical approaches to estimating the advertising elasticity of demand, see Ernst R. Berndt, The Practice of Econometrics (Reading, MA: Addison-Wesley, 1991), ch. 8. 434 PART 3 • Market Structure and Competitive Strategy SUMMARY 1. Firms with market power are in an enviable position because they have the potential to earn large profits. Realizing that potential, however, may depend critically on pricing strategy. Even if the firm sets a single price
, it needs an estimate of the elasticity of demand for its output. More complicated strategies, which can involve setting several different prices, require even more information about demand. 2. A pricing strategy aims to enlarge the customer base that the firm can sell to and capture as much consumer surplus as possible. There are a number of ways to do this, and they usually involve setting more than a single price. 3. Ideally, the firm would like to price discriminate perfectly—i.e., to charge each customer his or her reservation price. In practice, this is almost always impossible. On the other hand, various forms of imperfect price discrimination are often used to increase profits. 4. The two-part tariff is another means of capturing consumer surplus. Customers must pay an “entry” fee that allows them to buy the good at a per-unit price. The two-part tariff is most effective when customer demands are relatively homogeneous. 5. When demands are heterogeneous and negatively correlated, bundling can increase profits. With pure bundling, two or more different goods are sold only as a package. With mixed bundling, the customer can buy the goods individually or as a package. Mixed bundling can be more profitable than pure bundling if marginal costs are significant or if demands are not perfectly negatively correlated. 6. Bundling is a special case of tying, a requirement that products be bought or sold in some combination. Tying can be used to meter demand or to protect customer goodwill associated with a brand name. 7. Advertising can further increase profits. The profit-maximizing advertising-to-sales ratio is equal in magnitude to the ratio of the advertising and price elasticities of demand. QUESTIONS FOR REVIEW 1. Suppose a firm can practice perfect, first-degree price discrimination. What is the lowest price it will charge, and what will its total output be? 2. How does a car salesperson practice price discrimination? How does the ability to discriminate correctly affect his or her earnings? 3. Electric utilities often practice second-degree price discrimination. Why might this improve consumer welfare? 4. Give some examples of third-degree price discrimination. Can third-degree price discrimination be effective if the different groups of consumers have different levels of demand but the same price elasticities? 5. Show why optimal, third-degree price discrimination requires that marginal revenue for each group of consumers equals marginal cost. Use this condition to explain how a firm should change its prices and total output if the demand curve for one group
of consumers shifts outward, causing marginal revenue for that group to increase. 6. When pricing automobiles, American car companies typically charge a much higher percentage markup over cost for “luxury option” items (such as leather trim, etc.) than for the car itself or for more “basic” options such as power steering and automatic transmission. Explain why. 7. How is peak-load pricing a form of price discrimination? Can it make consumers better off? Give an example. 8. How can a firm determine an optimal two-part tariff if it has two customers with different demand curves? (Assume that it knows the demand curves.) 9. Why is the pricing of a Gillette safety razor a form of two-part tariff? Must Gillette be a monopoly producer of its blades as well as its razors? Suppose you were advising Gillette on how to determine the two parts of the tariff. What procedure would you suggest? 10. In the town of Woodland, California, there are many dentists but only one eye doctor. Are senior citizens more likely to be offered discount prices for dental exams or for eye exams? Why? 11. Why did MGM bundle Gone with the Wind and Getting Gertie’s Garter? What characteristic of demands is needed for bundling to increase profits? 12. How does mixed bundling differ from pure bundling? Under what conditions is mixed bundling preferable to pure bundling? Why do many restaurants practice mixed bundling (by offering a complete dinner as well as an à la carte menu) instead of pure bundling? 13. How does tying differ from bundling? Why might a firm want to practice tying? 14. Why is it incorrect to advertise up to the point that the last dollar of advertising expenditures generates another dollar of sales? What is the correct rule for the marginal advertising dollar? 15. How can a firm check that its advertising-to-sales ratio is not too high or too low? What information does it need? EXERCISES 1. Price discrimination requires the ability to sort customers and the ability to prevent arbitrage. Explain how the following can function as price discrimination schemes and discuss both sorting and arbitrage: a. Requiring airline travelers to spend at least one Saturday night away from home to qualify for a low fare. b. Insisting on delivering cement to buyers and basing prices on buyers’ locations. c. Selling food processors along with coupons that can be sent to the manufacturer for a $
10 rebate. d. Offering temporary price cuts on bathroom tissue. e. Charging high-income patients more than low- income patients for plastic surgery. 2. If the demand for drive-in movies is more elastic for couples than for single individuals, it will be optimal for theaters to charge one admission fee for the driver of the car and an extra fee for passengers. True or false? Explain. 3. In Example 11.1 (page 408), we saw how producers of processed foods and related consumer goods use coupons as a means of price discrimination. Although coupons are widely used in the United States, that is not the case in other countries. In Germany, coupons are illegal. a. Does prohibiting the use of coupons in Germany make German consumers better off or worse off? b. Does prohibiting the use of coupons make German producers better off or worse off? 4. Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $20,000 and a fixed cost of $10 billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States. The demand for BMWs in each market is given by and QE = 4,000,000 - 100PE QU = 1,000,000 - 20PU where the subscript E denotes Europe, the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be? b. If BMW were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company’s profit? 5. A monopolist is deciding how to allocate output between two geographically separated markets (East CHAPTER 11 • Pricing with Market Power 435 Coast and Midwest). Demand and marginal revenue for the two markets are P1 P2 = 15 - Q1 MR1 = 25 - 2Q2 MR2 = 15 - 2Q1 = 25 - 4Q2 The monopolist’s total cost is C 5 3(Q1 Q2). What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions? *6. Elizabeth Airlines (EA) flies only one route: Chicago–
Honolulu. The demand for each flight is Q 500 − P. EA’s cost of running each flight is $30,000 plus $100 per passenger. a. What is the profit-maximizing price that EA will charge? How many people will be on each flight? What is EA’s profit for each flight? b. EA learns that the fixed costs per flight are in fact $41,000 instead of $30,000. Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA’s average cost curve when fixed costs are $30,000, and EA’s average cost curve when fixed costs are $41,000. c. Wait! EA finds out that two different types of people fly to Honolulu. Type A consists of business people with a demand of QA 260 − 0.4P. Type B consists of students whose total demand is QB 240 − 0.6P. Because the students are easy to spot, EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight? d. What would EA’s profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus? e. Before EA started price discriminating, how much consumer surplus was the Type A demand getting from air travel to Honolulu? Type B? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged? 7. Many retail video stores offer two alternative plans for renting films: • A two-part tariff: Pay an annual membership fee (e.g., $40) and then pay a small fee for the daily rental of each film (e.g., $2 per film per day). • A straight rental fee: Pay no membership fee, but pay a higher daily rental fee (e.g., $4 per film per day). 436 PART 3 • Market Structure and Competitive Strategy What is the logic behind the two-part tariff in this case? Why offer the customer a choice of two plans rather than simply a two-part tariff? 8. Sal’s satellite company broadcasts TV to subscribers in Los Angeles and New York. The demand functions for each of these two groups are profits? Explain why price would not be equal to marginal cost.
10. As the owner of the only tennis club in an isolated wealthy community, you must decide on membership dues and fees for court time. There are two types of tennis players. “Serious” players have demand QNY QLA = 60 - 0.25PNY = 100 - 0.50PLA where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by C = 1000 + 40Q where Q QNY QLA. a. What are the profit-maximizing prices and quantities for the New York and Los Angeles markets? b. As a consequence of a new satellite that the Pentagon recently deployed, people in Los Angeles receive Sal’s New York broadcasts and people in New York receive Sal’s Los Angeles broadcasts. As a result, anyone in New York or Los Angeles can receive Sal’s broadcasts by subscribing in either city. Thus Sal can charge only a single price. What price should he charge, and what quantities will he sell in New York and Los Angeles? c. In which of the above situations, (a) or (b), is Sal better off? In terms of consumer surplus, which situation do people in New York prefer and which do people in Los Angeles prefer? Why? *9. You are an executive for Super Computer, Inc. (SC), which rents out super computers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of P cents per second. SC has two types of potential customers of equal number—10 businesses and 10 academic institutions. Each business customer has the demand function Q 10 − P, where Q is in millions of seconds per month; each academic institution has the demand Q 8 − P. The marginal cost to SC of additional computing is 2 cents per second, regardless of volume. a. Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What would be your profits? b. Suppose you were unable to keep the two types of customers separate and charged a zero rental fee. What usage fee would maximize your profits? What would be your profits? c. Suppose you set up one two-part tariff—that is, you set one rental and one usage fee that both business and academic customers pay. What usage and rental fees would you set? What would be your Q1 = 10 - P where Q1 is court hours per week and P is the
fee per hour for each individual player. There are also “occasional” players with demand Q2 = 4 - 0.25P Assume that there are 1000 players of each type. Because you have plenty of courts, the marginal cost of court time is zero. You have fixed costs of $10,000 per week. Serious and occasional players look alike, so you must charge them the same prices. a. Suppose that to maintain a “professional” atmosphere, you want to limit membership to serious players. How should you set the annual membership dues and court fees (assume 52 weeks per year) to maximize profits, keeping in mind the constraint that only serious players choose to join? What would profits be (per week)? b. A friend tells you that you could make greater profits by encouraging both types of players to join. Is your friend right? What annual dues and court fees would maximize weekly profits? What would these profits be? c. Suppose that over the years, young, upwardly mobile professionals move to your community, all of whom are serious players. You believe there are now 3000 serious players and 1000 occasional players. Would it still be profitable to cater to the occasional player? What would be the profit- maximizing annual dues and court fees? What would profits be per week? 11. Look again at Figure 11.12 (p. 420), which shows the reservation prices of three consumers for two goods. Assuming that marginal production cost is zero for both goods, can the producer make the most money by selling the goods separately, by using pure bundling, or by using mixed bundling? What prices should be charged? 12. Look again at Figure 11.17 (p. 424). Suppose that the marginal costs c1 and c2 were zero. Show that in this case, pure bundling, not mixed bundling, is the most profitable pricing strategy. What price should be charged for the bundle? What will the firm’s profit be? 13. Some years ago, an article appeared in the New York Times about IBM’s pricing policy. The previous day, IBM had announced major price cuts on most of its small and medium-sized computers. The article said: IBM probably has no choice but to cut prices periodically to get its customers to purchase more and lease less. If they succeed, this could make life more difficult for IBM’s major competitors. Outright purchases of computers are needed for ever larger IBM revenues and profits, says Morgan Stanley’s Ul
ric Weil in his new book, Information Systems in the 80’s. Mr. Weil declares that IBM cannot revert to an emphasis on leasing. a. Provide a brief but clear argument in support of the claim that IBM should try “to get its customers to purchase more and lease less.” b. Provide a brief but clear argument against this claim. c. What factors determine whether leasing or selling is preferable for a company like IBM? Explain briefly. 14. You are selling two goods, 1 and 2, to a market consisting of three consumers with reservation prices as follows: RESERVATION PRICE ($) CONSUMER FOR 1 FOR 2 A B C 20 60 100 100 60 20 The unit cost of each product is $30. a. Compute the optimal prices and profits for (i) selling the goods separately, (ii) pure bundling, and (iii) mixed bundling. b. Which strategy would be most profitable? Why? 15. Your firm produces two products, the demands for which are independent. Both products are produced at zero marginal cost. You face four consumers (or groups of consumers) with the following reservation prices: CHAPTER 11 • Pricing with Market Power 437 b. Now suppose that the production of each good entails a marginal cost of $30. How does this information change your answers to (a)? Why is the optimal strategy now different? 16. A cable TV company offers, in addition to its basic service, two products: a Sports Channel (Product 1) and a Movie Channel (Product 2). Subscribers to the basic service can subscribe to these additional services individually at the monthly prices P1 and P2, respectively, or they can buy the two as a bundle for the price PB, where PB < P1 P2. They can also forgo the additional services and simply buy the basic service. The company’s marginal cost for these additional services is zero. Through market research, the cable company has estimated the reservation prices for these two services for a representative group of consumers in the company’s service area. These reservation prices are plotted (as x’s) in Figure 11.21, as are the prices P1, P2, and PB that the cable company is currently charging. The graph is divided into regions I, II, III, and IV. a. Which products, if any, will be purchased by the consumers in region I? In region II? In region III? In region IV?
Explain briefly. b. Note that as drawn in the figure, the reservation prices for the Sports Channel and the Movie Channel are negatively correlated. Why would you, or why would you not, expect consumers’ reservation prices for cable TV channels to be negatively correlated? c. The company’s vice president has said: “Because the marginal cost of providing an additional channel is zero, mixed bundling offers no advantage over pure bundling. Our profits would be just r1 PB P1 II XX X X X X X X X X IV III X X PB X r2 X P2 CONSUMER GOOD 1($) GOOD 2($) A B C D 25 40 80 100 100 80 40 25 PB–P2 X I a. Consider three alternative pricing strategies: (i) selling the goods separately; (ii) pure bundling; (iii) mixed bundling. For each strategy, determine the optimal prices to be charged and the resulting profits. Which strategy would be best? PB–P1 FIGURE 11.21 FIGURE FOR EXERCISE 16 438 PART 3 • Market Structure and Competitive Strategy as high if we offered the Sports Channel and the Movie Channel together as a bundle, and only as a bundle.” Do you agree or disagree? Explain why. d. Suppose the cable company continues to use mixed bundling to sell these two services. Based on the distribution of reservation prices shown in Figure 11.21, do you think the cable company should alter any of the prices that it is now charging? If so, how? *17. Consider a firm with monopoly power that faces the demand curve P = 100 - 3Q + 4A1/2 and has the total cost function C = 4Q2 + 10Q + A where A is the level of advertising expenditures, and P and Q are price and output. a. Find the values of A, Q, and P that maximize the firm’s profit. b. Calculate the Lerner index, L (P − MC)/P, for this firm at its profit-maximizing levels of A, Q, and P. CHAPTER 11 • Pricing with Market Power 439 • horizontal integration Organizational form in which several plants produce the same or related products for a firm. • vertical integration Organizational form in which a firm contains several divisions, with some producing parts and components that others use to produce finished products. Internal • transfer prices prices at which parts and components from upstream divisions are “sold” to
downstream divisions within a firm. Appendix to Chapter 11 The Vertically Integrated Firm Many firms are integrated—they consist of several divisions, each with its own managers. Some firms are horizontally integrated: There are several divisions that produce the same or closely related products. We saw an example of this when we discussed the multi-plant firm in Section 10.1. Some firms are vertically integrated: They have several divisions, with some divisions producing parts and components which other divisions use to produce the finished product. For example, automobile companies have “upstream” divisions that produce engines, brakes, radiators and other components that the “downstream” divisions use to produce the finished cars. (Some firms are both vertically and horizontally integrated.) This appendix explains the economic issues that arise in a vertically integrated firm. As we will see, vertical integration has important benefits, but it also introduces complex pricing decisions: How should the firm value the parts and components that are transferred from the upstream to the downstream divisions? The firm must determine transfer prices, the internal prices at which the parts and components from upstream divisions are “sold” to downstream divisions. Transfer prices must be chosen correctly because they are the signals that divisional managers use to determine output levels. We will begin by explaining the advantages of vertical integration—advantages to the firm, as well as to the consumers who buy the end products of the firm. Some firms, however, are not vertically integrated; they simply buy parts and components from other independent firms. To understand why, we will explain some of the problems associated with vertical integration. Next, we will explain transfer pricing, and show how a vertically integrated firm should choose its transfer prices in a way that maximizes the firm’s total profit. Why Vertically Integrate? There are a number of advantages to vertical integration. If upstream and downstream divisions are part of the same firm, it might be easier to guarantee that parts and components are produced and delivered on time, and are made to the precise specifications needed by the downstream division. (On the other hand, a carefully written and enforced contract between independent upstream and downstream firms can often achieve the same thing.) The biggest advantage of vertical integration, however, is that it avoids the problem of “double marginalization,” i.e., it avoids a double markup. Market Power and Double Marginalization Often, one or more firms selling to each other along a vertical chain will have market power. For example, United Technologies and General Electric have monopoly power in the
production of jet aircraft engines, which they sell to Boeing and Airbus, which in turn have monopoly power in the market for commercial aircraft. How do firms along a vertical chain exercise such monopoly power, and how are prices and output affected? Would the firms benefit from a vertical merger that integrates an upstream and a related downstream business? Would consumers? 440 PART 3 • Market Structure and Competitive Strategy To answer these questions, consider the following example. Suppose an engine manufacturer has monopoly power in the market for engines, and an automobile manufacturer that buys these engines has monopoly power in the market for its cars. Would this market power cause these two firms to benefit in any way if they were to merge? Would consumers of the final product—automobiles—be better or worse off if the two companies merged? Many people (who haven’t read this book) would answer “maybe” to the first question, and “worse off” to the second question. It turns out, however, that when there is market power of this sort, a vertical merger can be beneficial to the two firms, and also beneficial to consumers. SEPARATE FIRMS To see this, consider the following simple example. Suppose a monopolist producer of specialty engines produces those engines at a constant marginal cost cE, and sells the engines at a price PE. The engines are bought by a monopolist producer of sports cars, which sells the cars at the price P. Demand for the cars is given by Q = A - P (A11.1) with the constant A > cE. To keep this example as simple as possible, we will assume that the automobile manufacturer has no additional costs other than the cost of the engine. (As an exercise, you can repeat this example assuming that there is an additional constant marginal cost cA to assemble the cars.) If the two companies are independent of each other, the automobile manufacturer will take the price of engines as given, and choose a price for its cars to maximize its profits: p A = (P - PE)(A - P) (A11.2) You can check that given PE, the profit maximizing price of cars is:1 P* = 1 2 (A + PE) (A11.3) Then the number of cars sold and the automobile company’s profit are:2 and A - PE) (A11.4) (A - PE)2 (A11.5) 1Take the derivative of p A with respect to P and set
it equal to zero. 2Substitute expression (A11.3) for P* into equations (A11.1) for Q and (A11.2) for p A. What about the engine manufacturer? It chooses the price of engines, PE, to maximize its profit: CHAPTER 11 • Pricing with Market Power 441 p E = (PE - cE)Q(PE) = (PE - cE) 1 2 (A - PE) You can confirm that the profit-maximizing price of engines is:3 PE* = 1 2 (A + cE) The profit to the engine manufacturer is then equal to: E* = 1 p 8 (A - cE)2 (A11.6) (A11.7) (A11.8) Now go back to Equation (A11.5) for the profit to the automobile manufacturer, and substitute in Equation (A11.7) for the price of engines. You will see that the automobile company’s profit is then: A* = 1 p 16 (A - cE)2 Hence the total profit for the two companies is: p TOT* = p A* + p E* = 3 16 (A - cE)2 Also, the price of cars paid by consumers is: P* = 1 4 (3A + cE) (A11.9) (A11.10) (A11.11) VERTICAL INTEGRATION Now suppose that the engine company and the automobile company merge to form a vertically integrated firm. The management of this firm would choose a price of automobiles to maximize the firm’s profit: p = (P - cE)(A - P) (A11.12) The profit-maximizing price of cars is now: P* = (A + cE)/2 (A11.13) which yields a profit of: p* = 1 4 (A - cE)2 (A11.14) 3Now take the derivative of p E with respect to PE and set it equal to zero. 442 PART 3 • Market Structure and Competitive Strategy • double marginalization When each firm in a vertical chain marks up its price above its marginal cost, thereby increasing the price of the final product. Observe that the profit for the integrated firm is greater than the total profit for the two individual firms that operate independently. Furthermore, the price to consumers for automobiles is lower
. (To confirm that this is indeed the case, compare (A11.11) with (A11.13) and remember that A > cE.) Hence, in this case vertical integration benefits not only the merging firms, but also consumers. DOUBLE MARGINALIZATION Why would a vertical merger make both the merging firms and consumers better off? The reason is that vertical integration avoids the problem of double marginalization. When the two firms operate independently, each one exercises its monopoly power by marking up its price above its marginal cost. But to do this, each firm must contract its output. The engine producer contracts its output to mark up its price above its marginal cost, and then the automobile manufacturer does likewise. This “double marginalization” pushes the price above the “single marginalization” or single markup over price of the integrated firm. This example of double marginalization is illustrated graphically in Figure A11.1, which shows the demand curve (average revenue curve) for cars, and the corresponding marginal revenue curve. For the automobile company, the marginal revenue curve for cars is the demand curve for engines (effectively, the net marginal revenue for engines). It describes the number of engines that the auto maker will buy as a function of price. From the point of view of the engine company, it is the average revenue curve for engines (i.e., the demand curve for engines that the engine company faces). Corresponding to that demand curve is the engine company’s marginal revenue curve for engines, labeled MRE in the figure. If the engine company and automobile company are separate entities, the engine company will produce a quantity of engines at the point where its marginal revenue curve intersects its marginal cost curve. That $/Q A ′ PA PA cE FIGURE A11.1 EXAMPLE OF DOUBLE MARGINALIZATION For the automobile company, the marginal revenue curve for cars is the demand curve for engines (the net marginal revenue for engines). Corresponding to that demand curve is the engine company’s marginal revenue curve, MRE. If the engine company and automobile company are separate entities, the engine company will produce a quantity of engines QE at the point where its marginal revenue curve intersects its marginal cost curve. The automobile maker will buy those engines and produce an equal number of cars. Hence, the price of cars will be P’A. But if the firms merge, the integrated company will have the demand curve ARCARS
and marginal revenue curve MRCARS. It produces a number of engines and equal number of cars at the point where MRCARS equals the marginal cost of producing cars, which is MCE. Thus more engines and cars are produced, and the price of cars is lower. MCE ARCARS MRCARS = NMRE Q ′ ′ QE = QA QE = QA MRE CHAPTER 11 • Pricing with Market Power 443 • quantity forcing Use of a sales quota or other incentives to make downstream firms sell as much as possible. quantity of engines is labeled Q’E. The automobile maker will buy those engines and produce an equal number of cars. Hence, the price of cars will be P’A. What happens if the two companies merge? The integrated company will have the demand curve ARCARS and the corresponding marginal revenue curve MRCARS. It will produce a number of engines and equal number of cars at the point where the marginal revenue curve for cars intersects the marginal cost of producing cars, which in this example is simply the marginal cost of engines. As shown in the figure, there will be a larger quantity of engines and cars produced at a correspondingly lower price. ALTERNATIVES TO VERTICAL INTEGRATION What can firms do to reduce the problem of double marginalization if a vertical merger is not an option? One solution is for the upstream firm to try to make the downstream market as competitive as possible, thereby reducing any double marginalization. Thus, Intel, which has monopoly power in processors, would like to do everything it can to make sure that the market for personal computers remains highly competitive, and might even help computer firms that are in danger of going out of business. A second method of dealing with double marginalization is called quantity forcing. The idea is to impose a sales quota or other restriction on downstream firms so that they cannot reduce their output in an attempt to marginalize. For example, automobile companies will create financial incentives to push dealerships (which have some monopoly power) to sell as many cars as possible. Transfer Pricing in the Integrated Firm We now turn to the profit-maximizing vertically integrated firm and see how it should choose its transfer prices and divisional output levels. We begin with the simplest case: There is no outside market for the output of the upstream division; i.e., the upstream division produces a good that is neither produced nor used by any other firm. Later we will consider what happens when there is an outside market for
the upstream division’s output. Transfer Pricing When There Is No Outside Market Look again at Figure A11.1. We saw that if the firm is integrated, the profit- maximizing number of engines and cars it will produce is QE QA, at the point where MRCARS equals the marginal cost of producing cars, which is MCE. Now suppose the downstream automobile division had to “pay” the upstream engine division a transfer price for each engine it used. What should that transfer price be? It should equal the marginal cost of producing engines, i.e., MCE. Why? Because then the automobile division will have a marginal cost of producing cars equal to MCE, so that even if it is left to maximize its own divisional profit, it will produce the correct number of cars. Another way to see this is in terms of opportunity cost. What is the opportunity cost to the integrated firm of utilizing one more engine (to produce one more car)? It is the marginal cost of engines. Thus we have a simple rule: Set the transfer price of any upstream parts and components equal to the marginal cost of producing those parts and components. You might argue that the example illustrated in Figure A11.1 is oversimplified because the only cost of producing a car is the cost of an engine. So now consider a firm with three divisions: Two upstream divisions produce inputs to 444 PART 3 • Market Structure and Competitive Strategy In §10.1, we explain that a firm maximizes its profit at the output at which marginal revenue is equal to marginal cost. a downstream processing division. The two upstream divisions produce quantities Q1 and Q2 and have total costs C1(Q1) and C2(Q2). The downstream division produces a quantity Q using the production function Q = f(K, L, Q1, Q2) where K and L are capital and labor inputs, and Q1 and Q2 are the intermediate inputs from the upstream divisions. Excluding the costs of the inputs Q1 and Q2, the downstream division has a total production cost Cd(Q). Total revenue from sales of the final product is R(Q). We assume there are no outside markets for the intermediate inputs Q1and Q2; they can be used only by the downstream division. Then the firm has two problems: 1. What quantities Q1, Q2, and Q will maximize its profit? 2. Is there an incentive scheme that will decentralize the firm’s management?
In particular, is there a set of transfer prices P1 and P2, so that if each division maximizes its own divisional profit, the profit of the overall firm will also be maximized? To solve these problems, we note that the firm’s total profit is p(Q) = R(Q) - Cd(Q) - C1(Q1) - C2(Q2) (A11.15) What is the level of Q1 that maximizes this profit? It is the level at which the cost of the last unit of Q1 is just equal to the additional revenue it brings to the firm. The cost of producing one extra unit of Q1 is the marginal cost C1/Q1 MC1. How much extra revenue results from that one extra unit? An extra unit of Q1 allows the firm to produce more final output Q of an amount Q/Q1 MP1, the marginal product of Q1. An extra unit of final output results in additional revenue R/Q MR, but it also results in additional cost to the downstream division of an amount Cd/Q MCd. Thus the net marginal revenue NMR1 that the firm earns from an extra unit of Q1 is (MR − MCd)MP1. Setting this equal to the marginal cost of the unit, we obtain the following rule for profit maximization4: NMR1 = (MR - MCd)MP1 = MC1 (A11.16) Going through the same steps for the second intermediate input gives NMR2 = (MR - MCd)MP2 = MC2 (A11.17) Note from equations (A11.16) and (A11.17) that it is incorrect to determine the firm’s final output level Q by setting marginal revenue equal to marginal cost for the downstream division—i.e., by setting MR MCd. Doing so ignores the cost of producing the intermediate input. (MR exceeds MCd because this cost is positive.) Also, note that equations (A11.16) and (A11.17) are standard 4Using calculus, we can obtain this rule by differentiating equation (A11.15) with respect to Q1: dp/dQ1 = (dR/dQ)(0Q/0Q1) - (dCd/dQ)(0Q/0Q1) - dC1/dQ1 = (MR - MCd)
MP1 - MC1 Setting dp/dQ 0 to maximize profit gives equation (A11.4). conditions of marginal analysis: The output of each upstream division should be such that its marginal cost is equal to its marginal contribution to the profit of the overall firm. CHAPTER 11 • Pricing with Market Power 445 Now, what transfer prices P1 and P2 should be “charged” to the downstream division for its use of the intermediate inputs? Remember that if each of the three divisions uses these transfer prices to maximize its own divisional profit, the profit of the overall firm should be maximized. The two upstream divisions will maximize their divisional profits, p 2, which are given by 1 and p and p 1 = P1Q1 - C1(Q1) p 2 = P2Q2 - C2(Q2) Because the upstream divisions take P1 and P2 as given, they will choose Q1 and Q2 so that P1 MC1 and P2 MC2. Similarly, the downstream division will maximize p(Q) = R(Q) - Cd(Q) - P1Q1 - P2Q2 Because the downstream division also takes P1 and P2 as given, it will choose Q1 and Q2 so that (MR - MCd)MP1 = NMR1 = P1 (A11.18) and (MR - MCd)MP2 = NMR2 = P2 (A11.19) Note that by setting the transfer prices equal to the respective marginal costs (P1 MC1 and P2 MC2), the profit-maximizing conditions given by equations (A11.16) and (A11.17) will be satisfied. We therefore have a simple solution to the transfer pricing problem: Set each transfer price equal to the marginal cost of the respective upstream division. Then when each division is required to maximize its own profit, the quantities Q1 and Q2 that the upstream divisions will want to produce will be the same quantities that the downstream division will want to “buy,” and they will maximize the firm’s total profit. To illustrate this graphically, suppose Race Car Motors, Inc., has two divisions. The upstream Engine Division produces engines, and the downstream Assembly Division puts together automobiles, using one engine (and a few other parts) in each car. In Figure A11.2, the average revenue curve AR is Race Car Motors’ demand curve for
cars. (Note that the firm has monopoly power in the automobile market.) MCA is the marginal cost of assembling automobiles, given the engines (i.e., it does not include the cost of the engines). Because the car requires one engine, the marginal product of the engines is one. Thus the curve labeled MR − MCA is also the net marginal revenue curve for engines: NMRE = (MR - MCA)MPE = MR - MCA The profit-maximizing number of engines (and number of cars) is given by the intersection of the net marginal revenue curve NMRE with the marginal cost curve for engines MCE. Having determined the number of cars that it will produce, and knowing its divisional cost functions, the management of Race Car 446 PART 3 • Market Structure and Competitive Strategy $/Q PA PE FIGURE A11.2 RACE CAR MOTORS, INC. The firm’s upstream division should produce a quantity of engines QE that equates its marginal cost of engine production MCE with the downstream division’s net marginal revenue of engines NMRE. Because the firm uses one engine in every car, NMRE is the difference between the marginal revenue from selling cars and the marginal cost of assembling them, i.e., MR − MCA. The optimal transfer price for engines PE equals the marginal cost of producing them. Finished cars are sold at price PA. MCE AR MCA MR Quantity Q A = Q E NMRE = (MR – MCA) Motors can now set the transfer price PE that correctly values the engines used to produce its cars. This is the transfer price that should be used to calculate divisional profit (and year-end bonuses for divisional managers). Transfer Pricing with a Competitive Outside Market Now suppose there is a competitive outside market for the intermediate good produced by an upstream division. Because the outside market is competitive, there is a single market price at which one can buy or sell the good. Therefore, the marginal cost of the intermediate good is simply the market price. Because the optimal transfer price must equal marginal cost, it must also equal the competitive market price. To see this, suppose there is a competitive market for the engines that Race Car Motors produces. If the market price is low, Race Car Motors may want to buy some or all of its engines in the market; if it is high, it may want to sell engines in the market. Figure A11.3 illustrates the first case. For quantities below QE,1, the
upstream division’s marginal cost of producing engines MCE is below the market price PE,M; for quantities above QE,1, it is above the market price. The * firm should obtain engines at the least cost, so the marginal cost of engines MCE will be the upstream division’s marginal cost for quantities up to QE,1 and the market price for quantities above QE,1. Note that Race Car Motors uses more engines and produces more cars than it would have had there been no outside engine market. The downstream division now buys QE,2 engines and produces an equal number of automobiles. However, it “buys” only QE,1 of these engines from the upstream division and the rest on the open market. It might seem strange that Race Car Motors must go into the open market to buy engines that it can make itself. If it made all of its own engines, however, its marginal cost of producing them would exceed the competitive market price. Although the profit of the upstream division would be higher, the total profit of the firm would be lower. $/Q PA PE,M CHAPTER 11 • Pricing with Market Power 447 MCE AR MC* E MCA MR FIGURE A11.3 BUYING ENGINES IN A COMPETITIVE OUTSIDE MARKET Race Car Motors’ marginal cost of engines * is the upstream division’s marginal cost MCE for quantities up to QE,1 and the market price PE,M for quantities above QE,1. The downstream division should use a total of QE,2 engines to produce an equal number of cars; in that case, the marginal cost of engines equals net marginal revenue. QE,2 − QE,1 of these engines are bought in the outside market. The downstream division “pays” the upstream division the transfer price PE,M for the remaining QE,1 engines. QE,1 Q E,2 QE Quantity NMRE = (MR MCA) Figure A11.4 shows the case where Race Car Motors sells engines in the outside market. Now the competitive market price PE,M is above the transfer price that the firm would have set had there been no outside market. In this case, although the upstream Engine Division produces QE,1 engines, only QE,2 engines $/Q PA PE,M MCE AR MC*E MCA MR FIGURE A11.4 SELLING ENGINES
IN A COMPETITIVE OUTSIDE MARKET The optimal transfer price for Race Car Motors is again the market price PE,M. This price is above the point at which MCE intersects NMRE, so the upstream division sells some of its engines in the outside market. The upstream division produces QE,1 engines, the quantity at which MCE equals PE,M. The downstream division uses only QE,2 of these engines, the quantity at which NMRE equals PE,M. Compared with Figure A11.2, in which there is no outside market, more engines but fewer cars are produced. Q E,2 QA QE,1 NMRE = (MR Quantity MCA) 448 PART 3 • Market Structure and Competitive Strategy are used by the downstream division to produce automobiles. The rest are sold in the outside market at the price PE,M. Note that compared with a situation in which there is no outside engine market, Race Car Motors is producing more engines but fewer cars. Why not produce this larger number of engines but use all of them to produce more cars? Because the engines are too valuable. On the margin, the net revenue that can be earned from selling them in the outside market is higher than the net revenue from using them to build additional cars. Transfer Pricing with a Noncompetitive Outside Market Now suppose there is an outside market for the output of the upstream division, but that market is not competitive. Suppose that the engines produced by the upstream Engine Division is a special one that only Race Car Motors can make, so that Race Car Motors can be a monopoly supplier to that outside market while also producing engines for its own use. We will not work through the details of this case, but you should be able to see that the transfer price paid to the Engine Division will be below the price at which engines are bought in the outside market. Why “pay” the Engine Division a price that is lower than that paid in the outside market? The reason is that the opportunity cost of utilizing an engine internally is just the marginal cost of producing the engine, whereas the opportunity cost of selling it outside is higher, because it includes a monopoly markup. Sometimes a vertically integrated firm can buy components in an outside market in which it has monopsony power. Suppose, for example, that Race Car Motors is the only company that uses the engines produced by its upstream Engine Division, but other companies also make that engine. Thus Race Car Motors can obtain its engines from its upstream Engine Division, or can purchase
them as a monopsonist in the outside market. You should be able to see that in this case, the transfer price paid to the Engine Division will be above the price at which engines are bought in the outside market. Why “pay” the upstream division a price that is higher than that paid in the outside market? With monopsony power, purchasing one additional engine in the outside market incurs a marginal expenditure that is greater than the actual price paid in that market. (The marginal expenditure is higher because purchasing an additional unit raises the average expenditure paid for all units bought in the outside market.) The marginal expenditure is the opportunity cost of buying an engine outside, and therefore should equal the transfer price paid to the Engine Division, so the transfer price will be greater than the price paid outside. Taxes and Transfer Pricing So far we have ignored taxes in our discussion of transfer pricing. But in fact taxes can play an important role in determining transfer prices when the objective is to maximize the after-tax profits of the integrated firm. This is especially the case when the upstream and downstream divisions of the firm operate in different countries. To see this, suppose that the upstream Engine Division of Race Car Motors happens to be located in an Asian country with a low corporate profits tax rate, while the downstream Assembly Division is located in the United States, with a higher tax rate. Suppose that in the absence of taxes, the marginal cost and thus the optimal transfer price for an engine is $5000. How would this transfer price be affected by taxes? CHAPTER 11 • Pricing with Market Power 449 In our example, the difference in tax rates will cause the opportunity cost of using an engine downstream to exceed $5000. Why? Because the downstream profit generated by the use of the engine will be taxed at a relatively high rate. Thus, taking taxes into account, the firm will want to set a higher transfer price, perhaps $7000. This will reduce the downstream profits in the United States (so that the firm will pay less in taxes) and increase the profits of the upstream division, which faces a lower tax rate. In §10.5, we explain that when a buyer has monopsony power, its marginal expenditure curve lies above its average expenditure curve because the decision to buy an extra unit of the good raises the price that must be paid on all units. A Numerical Example Suppose Race Car Motors has the following demand for its automobiles: Its marginal revenue is thus P = 20,000 - Q MR = 20,000 -
2Q The downstream division’s cost of assembling cars is CA(Q) = 8000Q so that the division’s marginal cost is MCA 8000. The upstream division’s cost of producing engines is CE(QE) = 2QE 2 The division’s marginal cost is thus MCE(QE) 4QE. First, suppose there is no outside market for the engines. How many engines and cars should the firm produce? What should be the transfer price for engines? To solve this problem, we set the net marginal revenue for engines equal to the marginal cost of producing engines. Because each car has one engine, QE Q. The net marginal revenue of engines is thus NMRE = MR - MCA = 12,000 - 2QE Now set NMRE equal to MCE: 12,000 - 2QE = 4QE Thus 6QE 12,000 and QE 2000. The firm should therefore produce 2000 engines and 2000 cars. The optimal transfer price is the marginal cost of these 2000 engines: PE = 4QE = $8000 Second, suppose that engines can be bought or sold for $6000 in an outside competitive market. This is below the $8000 transfer price that is optimal when there is no outside market, so the firm should buy some engines outside. Its marginal cost of engines, and the optimal transfer price, is now $6000. Set this $6000 marginal cost equal to the net marginal revenue of engines: 6000 = NMRE = 12,000 - 2QE 450 PART 3 • Market Structure and Competitive Strategy Thus the total quantity of engines and cars is now 3000. The company now produces more cars (and sells them at a lower price) because its cost of engines is lower. Also, since the transfer price for the engines is now $6000, the upstream Engine Division supplies only 1500 engines (because MCE(1500) $6000). The remaining 1500 engines are bought in the outside market. EXERCISES 1. Suppose Boeing faces the following demand curve for the monthly sales of its 787 aircraft: Q = 120 - 0.5p Where Q is airplanes sold per month and P is the price in millions of dollars. The airplane uses a set of engines made by General Electric, and Boeing pays GE a price PE (in millions of dollars) for each set of engines. The marginal cost to GE of producing a set of engines is 20 (million dollars). In addition to paying for engines, Boeing incurs a marginal cost
of 100 (million dollars) per plane. a. What is Boeing’s profit-maximizing price of airplanes, given a price PE for the engines? What is the profit-maximizing price that GE will charge for each set of engines? Given that price of engines, what price will Boeing charge for its airplanes? b. Suppose Boeing were to acquire GE’s engine division, so that now the engines and airplanes are made by a single company. Now what price will the company charge for its airplanes? 2. Review the numerical example about Race Car Motors. Calculate the profit earned by the upstream division, the downstream division, and the firm as a whole in each of the three cases examined: (a) there is no outside market for engines; (b) there is a competitive market for engines in which the market price is $6000; and (c) the firm is a monopoly supplier of engines to an outside market. In which case does Race Car Motors earn the most profit? In which case does the upstream division earn the most? The downstream division? 3. Ajax Computer makes a computer for climate control in office buildings. The company uses a microprocessor produced by its upstream division, along with other parts bought in outside competitive markets. The microprocessor is produced at a constant marginal cost of $500, and the marginal cost of assembling the computer (including the cost of the other parts) by the downstream division is a constant $700. The firm has been selling the computer for $2000, and until now there has been no outside market for the microprocessor. a. Suppose an outside market for the microprocessor develops and that Ajax has monopoly power in that market, selling microprocessors for $1000 each. Assuming that demand for the microprocessor is unrelated to the demand for the Ajax computer, what transfer price should Ajax apply to the microprocessor for its use by the downstream computer division? Should production of computers be increased, decreased, or left unchanged? Explain briefly. b. How would your answer to (a) change if the demands for the computer and the microprocessors were competitive; i.e., if some of the people who buy the microprocessors use them to make climate control systems of their own? 4. Reebok produces and sells running shoes. It faces a market demand schedule P 11 − 1.5Qs, where Qs is the number of pairs of shoes sold and P is the price in dollars per pair of shoes. Production of each pair of shoes requires
1 square yard of leather. The leather is shaped and cut by the Form Division of Reebok. The cost function for leather is TCL = 1 + QL + 0.5QL 2 where QL is the quantity of leather (in square yards) produced. Excluding leather, the cost function for running shoes is TCs = 2Qs a. What is the optimal transfer price? b. Leather can be bought and sold in a competitive market at the price of PF 1.5. In this case, how much leather should the Form Division supply internally? How much should it supply to the outside market? Will Reebok buy any leather in the outside market? Find the optimal transfer price. c. Now suppose the leather is unique and of extremely high quality. Therefore, the Form Division may act as a monopoly supplier to the outside market as well as a supplier to the downstream division. Suppose the outside demand for leather is given by P 32 − QL. What is the optimal transfer price for the use of leather by the downstream division? At what price, if any, should leather be sold to the outside market? What quantity, if any, will be sold to the outside market? C H A P T E R 12 Monopolistic Competition and Oligopoly In the last two chapters, we saw how firms with monopoly power can choose prices and output levels to maximize profit. We also saw that monopoly power does not require a firm to be a pure monopolist. In many industries, even though several firms compete with each other, each firm has at least some monopoly power: It has control over price and can profitably charge a price that exceeds marginal cost. In this chapter, we examine market structures other than pure monopoly that can give rise to monopoly power. We begin with what might seem like an oxymoron: monopolistic competition. A monopolistically competitive market is similar to a perfectly competitive market in two key respects: There are many firms, and entry by new firms is not restricted. But it differs from perfect competition in that the product is differentiated: Each firm sells a brand or version of the product that differs in quality, appearance, or reputation, and each firm is the sole producer of its own brand. The amount of monopoly power wielded by a firm depends on its success in differentiating its product from those of other firms. Examples of monopolistically competitive industries abound: Toothpaste, laundry detergent, and packaged coffee are a few. The second form of market structure we will examine is oligopoly:
a market in which only a few firms compete with one another, and entry by new firms is impeded. The product that the firms produce might be differentiated, as with automobiles, or it might not be, as with steel. Monopoly power and profitability in oligopolistic industries depend in part on how the firms interact. For example, if the interaction is more cooperative than competitive, firms could charge prices well above marginal cost and earn large profits. In some oligopolistic industries, firms do cooperate, but in others, they compete aggressively, even though this means lower profits. To see why, we need to consider how oligopolistic firms decide on output and prices. These decisions are complicated because each firm must operate strategically—when making a decision, it must weigh the probable reactions of its competitors. To understand oligopolistic markets, we must therefore introduce some basic concepts of gaming and strategy. We develop these concepts more fully in Chapter 13. The third form of market structure that we examine is a cartel. In a cartelized market, some or all firms explicitly collude: They coordinate prices and output levels to maximize joint profits. Cartels can arise in markets that would otherwise be competitive, as with the OPEC oil cartel, or oligopolistic, as with the international bauxite cartel 12.1 Monopolistic Competition 452 12.2 Oligopoly 456 12.3 Price Competition 464 12.4 Competition versus Collusion: The Prisoners’ Dilemma 469 12.5 Implications of the Prisoners’ Dilemma for Oligopolistic Pricing 472 12.6 Cartels 477 12.1 Monopolistic Competition in the Markets for Colas and Coffee 455 12.2 A Pricing Problem for Procter & Gamble 467 12.3 Procter & Gamble in a Prisoners’ Dilemma 471 12.4 Price Leadership and Price Rigidity in Commercial Banking 475 12.5 The Prices of College Textbooks 476 12.6 The Cartelization of Intercollegiate Athletics 480 12.7 The Milk Cartel 481 451 452 PART 3 • Market Structure and Competitive Strategy • monopolistic competition Market in which firms can enter freely, each producing its own brand or version of a differentiated product. • oligopoly Market in which only a few firms compete with one another, and entry by new firms is impeded. • cartel Market in which some or all firms explicitly collude, coordinating prices and output levels to maximize joint profits. In
§10.2, we explain that a seller of a product has some monopoly power if it can profitably charge a price greater than marginal cost. At first glance, a cartel may seem like a pure monopoly. After all, the firms in a cartel appear to operate as though they were parts of one big company. But a cartel differs from a monopoly in two important respects. First, because cartels rarely control the entire market, they must consider how their pricing decisions will affect noncartel production levels. Second, because the members of a cartel are not part of one big company, they may be tempted to “cheat” their partners by undercutting prices and grabbing bigger shares of the market. As a result, many cartels tend to be unstable and short-lived. 12.1 Monopolistic Competition In many industries, the products are differentiated. For one reason or another, consumers view each firm’s brand as different from other brands. Crest toothpaste, for example, is perceived to be different from Colgate, Aim, and other toothpastes. The difference is partly flavor, partly consistency, and partly reputation—the consumer’s image (correct or incorrect) of the relative decay-preventing efficacy of Crest. As a result, some consumers (but not all) will pay more for Crest. Because Procter & Gamble is the sole producer of Crest, it has monopoly power. But its monopoly power is limited because consumers can easily substitute other brands if the price of Crest rises. Although consumers who prefer Crest will pay more for it, most of them will not pay much more. The typical Crest user might pay 25 or 50 cents a tube more, but probably not one or two dollars more. For most consumers, toothpaste is toothpaste, and the differences among brands are small. Therefore, the demand curve for Crest toothpaste, though downward sloping, is fairly elastic. (A reasonable estimate of the elasticity of demand for Crest is −5.) Because of its limited monopoly power, Procter & Gamble will charge a price that is higher, but not much higher, than marginal cost. The situation is similar for Tide detergent or Scott paper towels. The Makings of Monopolistic Competition A monopolistically competitive market has two key characteristics: 1. Firms compete by selling differentiated products that are highly substitutable for one another but not perfect substitutes. In other words, the crossprice elasticities of demand are large but not infinite. 2. There is free entry and exit:
It is relatively easy for new firms to enter the market with their own brands and for existing firms to leave if their products become unprofitable. To see why free entry is an important requirement, let’s compare the markets for toothpaste and automobiles. The toothpaste market is monopolistically competitive, but the automobile market is better characterized as an oligopoly. It is relatively easy for other firms to introduce new brands of toothpaste, and this limits the profitability of producing Crest or Colgate. If the profits were large, other firms would spend the necessary money (for development, production, advertising, and promotion) to introduce new brands of their own, which would reduce the market shares and profitability of Crest and Colgate. The automobile market is also characterized by product differentiation. However, the large-scale economies involved in production make entry by new firms difficult. Thus, until the mid-1970s, when Japanese producers became important competitors, the three major U.S. automakers had the market largely to themselves. CHAPTER 12 • Monopolistic Competition and Oligopoly 453 There are many other examples of monopolistic competition besides toothpaste. Soap, shampoo, deodorants, shaving cream, cold remedies, and many other items found in a drugstore are sold in monopolistically competitive markets. The markets for many sporting goods are likewise monopolistically competitive. So is most retail trade, because goods are sold in many different stores that compete with one another by differentiating their services according to location, availability and expertise of salespeople, credit terms, etc. Entry is relatively easy, so if profits are high in a neighborhood because there are only a few stores, new stores will enter. Equilibrium in the Short Run and the Long Run As with monopoly, in monopolistic competition firms face downward-sloping demand curves. Therefore, they have some monopoly power. But this does not mean that monopolistically competitive firms are likely to earn large profits. Monopolistic competition is also similar to perfect competition: Because there is free entry, the potential to earn profits will attract new firms with competing brands, driving economic profits down to zero. To make this clear, let’s examine the equilibrium price and output level for a monopolistically competitive firm in the short and long run. Figure 12.1(a) shows the short-run equilibrium. Because the firm’s product differs from its competitors’, its demand curve DSR is downward sloping. (This is the firm’s demand curve, not the market
demand curve, which is more steeply sloped.) The profitmaximizing quantity QSR is found at the intersection of the marginal revenue $/Q PSR $/Q PLR AC DSR MC MRSR AC DLR MC MRLR QSR (a) Quantity QLR (b) Quantity FIGURE 12.1 A MONOPOLISTICALLY COMPETITIVE FIRM IN THE SHORT AND LONG RUN Because the firm is the only producer of its brand, it faces a downward-sloping demand curve. Price exceeds marginal cost and the firm has monopoly power. In the short run, described in part (a), price also exceeds average cost, and the firm earns profits shown by the yellow-shaded rectangle. In the long run, these profits attract new firms with competing brands. The firm’s market share falls, and its demand curve shifts downward. In long-run equilibrium, described in part (b), price equals average cost, so the firm earns zero profit even though it has monopoly power. 454 PART 3 • Market Structure and Competitive Strategy In §10.1, we explain that a monopolist maximizes profit by choosing an output at which marginal revenue is equal to marginal cost. Recall from §8.7 that with the possibility of entry and exit, firms will earn zero economic profit in long-run equilibrium. In §9.2, we explain that competitive markets are efficient because they maximize the sum of consumers’ and producers’ surplus. In §10.4, we discuss the deadweight loss from monopoly power. and marginal cost curves. Because the corresponding price PSR exceeds average cost, the firm earns a profit, as shown by the shaded rectangle in the figure. In the long run, this profit will induce entry by other firms. As they introduce competing brands, our firm will lose market share and sales; its demand curve will shift down, as in Figure 12.1(b). (In the long run, the average and marginal cost curves may also shift. We have assumed for simplicity that costs do not change.) The long-run demand curve DLR will be just tangent to the firm’s average cost curve. Here, profit maximization implies the quantity QLR and the price PLR. It also implies zero profit because price is equal to average cost. Our firm still has monopoly power: Its long-run demand curve is downward sloping because its particular brand is still unique. But the entry and competition of other firms
have driven its profit to zero. More generally, firms may have different costs, and some brands will be more distinctive than others. In this case, firms may charge slightly different prices, and some will earn small profits. Monopolistic Competition and Economic Efficiency Perfectly competitive markets are desirable because they are economically efficient: As long as there are no externalities and nothing impedes the workings of the market, the total surplus of consumers and producers is as large as possible. Monopolistic competition is similar to competition in some respects, but is it an efficient market structure? To answer this question, let’s compare the long-run equilibrium of a monopolistically competitive industry to the long-run equilibrium of a perfectly competitive industry. Figure 12.2 shows that there are two sources of inefficiency in a monopolisti- cally competitive industry: 1. Unlike perfect competition, with monopolistic competition the equilibrium price exceeds marginal cost. This means that the value to consumers of additional units of output exceeds the cost of producing those units. If output were expanded to the point where the demand curve intersects the marginal cost curve, total surplus could be increased by an amount equal to the yellow-shaded area in Figure 12.2(b). This should not be surprising. We saw in Chapter 10 that monopoly power creates a deadweight loss, and monopoly power exists in monopolistically competitive markets. 2. Note in Figure 12.2(b) that for the monopolistically competitive firm, output is below that which minimizes average cost. Entry of new firms drives profits to zero in both perfectly competitive and monopolistically competitive markets. In a perfectly competitive market, each firm faces a horizontal demand curve, so the zero-profit point occurs at minimum average cost, as Figure 12.2(a) shows. In a monopolistically competitive market, however, the demand curve is downward sloping, so the zero-profit point is to the left of minimum average cost. Excess capacity is inefficient because average cost would be lower with fewer firms. These inefficiencies make consumers worse off. Is monopolistic competition then a socially undesirable market structure that should be regulated? The answer—for two reasons—is probably no: 1. In most monopolistically competitive markets, monopoly power is small. Usually enough firms compete, with brands that are sufficiently substitutable, so that no single firm has much monopoly power. Any resulting deadweight CHAPTER 12 • Monopolistic Competition and Oligopoly 455 Pc MC AC PMC D MR Qc (
a) Quantity QMC MC AC D Quantity MR Qc (b) FIGURE 12.2 COMPARISON OF MONOPOLISTICALLY COMPETITIVE EQUILIBRIUM AND PERFECTLY COMPETITIVE EQUILIBRIUM Under perfect competition, as in (a), price equals marginal cost, but under monopolistic competition, price exceeds marginal cost. Thus there is a deadweight loss, as shown by the yellow-shaded area in (b). In both types of markets, entry occurs until profits are driven to zero. Under perfect competition, the demand curve facing the firm is horizontal, so the zero-profit point occurs at the point of minimum average cost. Under monopolistic competition the demand curve is downward-sloping, so the zero-profit point is to the left of the point of minimum average cost. In evaluating monopolistic competition, these inefficiencies must be balanced against the gains to consumers from product diversity. loss will therefore be small. And because firms’ demand curves will be fairly elastic, average cost will be close to the minimum. 2. Any inefficiency must be balanced against an important benefit from monopolistic competition: product diversity. Most consumers value the ability to choose among a wide variety of competing products and brands that differ in various ways. The gains from product diversity can be large and may easily outweigh the inefficiency costs resulting from downwardsloping demand curves. EXAM PLE 12.1 MONOPOLISTIC COMPETITION IN THE MARKETS FOR COLAS AND COFFEE The markets for soft drinks and coffee illustrate the characteristics of monopolistic competition. Each market has a variety of brands that differ slightly but are close substitutes for one another. Each brand of cola, for example, tastes a little different from the next. (Can you tell the difference between Coke and Pepsi? Between Coke and RC Cola?) And each brand of ground coffee has a slightly different flavor, fragrance, and caffeine content. Most consumers develop their own preferences; you might prefer Maxwell House coffee to 456 PART 3 • Market Structure and Competitive Strategy other brands and buy it regularly. Brand loyalties, however, are usually limited. If the price of Maxwell House were to rise substantially above those of other brands, you and most other consumers who had been buying it would probably switch brands. Just how much monopoly power does General Foods, the producer of Maxwell House, have with this brand? In other words, how elastic is the demand for Maxwell House? Most large companies carefully study
product demands as part of their market research. Company estimates are usually proprietary, but two published studies of the demands for various brands of colas and ground coffees used simulated shopping experiments to determine how market shares for each brand would change in response to specific changes in price. Table 12.1 summarizes the results by showing the elasticities of demand for several brands.1 First, note that among colas, RC Cola is much less price elastic than Coke. Although it has a small share of the cola market, its taste is more distinctive than that of Coke, Pepsi, and other brands, so consumers who buy it have stronger brand loyalty. But even though RC Cola has more monopoly power than Coke, it is not necessarily more profitable. Profits depend on fixed costs and volume, as well as price. Even if its average profit is smaller, Coke will generate more profit because it has a much larger share of the market. Second, note that coffees as a group are more price elastic than colas. There is less brand loyalty among coffee buyers than among cola buyers because the differences among coffees are less perceptible than the differences among colas. Note that the demand for Chock Full o’ Nuts is less price elastic than its competitors. Why? Because Chock Full o’ Nuts, like RC Cola, has a more distinctive taste than Folgers or Maxwell House, and so consumers who buy it tend to remain loyal. Fewer consumers notice or care about the taste differences between Folgers and Maxwell House. With the exception of RC Cola and Chock Full o’ Nuts, all the colas and coffees are quite price elastic. With elasticities on the order of −4 to −8, each brand has only limited monopoly power. This is typical of monopolistic competition. TABLE 12.1 ELASTICITIES OF DEMAND FOR BRANDS OF COLAS AND COFFEE BRAND ELASTICITY OF DEMAND Colas Ground coffee RC Cola Coke Folgers Maxwell House Chock Full o’Nuts −2.4 −5.2 to −5.7 −6.4 −8.2 −3.6 12.2 Oligopoly In oligopolistic markets, the products may or may not be differentiated. What matters is that only a few firms account for most or all of total production. In some oligopolistic markets, some or all firms earn substantial profits over the long run because barriers to entry make it difficult or
impossible for new firms to enter. Oligopoly is a prevalent form of market structure. Examples of 1The elasticity estimates in Table 12.1 are from John R. Nevin, “Laboratory Experiments for Estimating Consumer Demand: A Validation Study,” Journal of Marketing Research 11 (August 1974): 261–68; and Lakshman Krishnamurthi and S. P. Raj, “A Model of Brand Choice and Purchase Quantity Price Sensitivities,” Marketing Science (1991). In typical simulated shopping experiments, consumers are asked to choose the brands that they prefer from a variety of prepriced brands. This trial is repeated several times, with different prices each time. CHAPTER 12 • Monopolistic Competition and Oligopoly 457 oligopolistic industries include automobiles, steel, aluminum, petrochemicals, electrical equipment, and computers. Why might barriers to entry arise? We discussed some of the reasons in Chapter 10. Scale economies may make it unprofitable for more than a few firms to coexist in the market; patents or access to a technology may exclude potential competitors; and the need to spend money for name recognition and market reputation may discourage entry by new firms. These are “natural” entry barriers—they are basic to the structure of the particular market. In addition, incumbent firms may take strategic actions to deter entry. For example, they might threaten to flood the market and drive prices down if entry occurs, and to make the threat credible, they can construct excess production capacity. Managing an oligopolistic firm is complicated because pricing, output, advertising, and investment decisions involve important strategic considerations. Because only a few firms are competing, each firm must carefully consider how its actions will affect its rivals, and how its rivals are likely to react. Suppose that because of sluggish car sales, Ford is considering a 10-percent price cut to stimulate demand. It must think carefully about how competing auto companies will react. They might not react at all, or they might cut their prices only slightly, in which case Ford could enjoy a substantial increase in sales, largely at the expense of its competitors. Or they might match Ford’s price cut, in which case all of the firms will sell more cars, but might make much lower profits because of the lower prices. Another possibility is that some firms will cut their prices by even more than Ford to punish Ford for rocking the boat, and this in turn might lead to a price war and to a drastic fall in profits for
the entire industry. Ford must carefully weigh all these possibilities. In fact, for almost any major economic decision that a firm makes—setting price, determining production levels, undertaking a major promotion campaign, or investing in new production capacity—it must try to determine the most likely response of its competitors. These strategic considerations can be complex. When making decisions, each firm must weigh its competitors’ reactions, knowing that these competitors will also weigh its reactions to their decisions. Furthermore, decisions, reactions, reactions to reactions, and so forth are dynamic, evolving over time. When the managers of a firm evaluate the potential consequences of their decisions, they must assume that their competitors are as rational and intelligent as they are. Then, they must put themselves in their competitors’ place and consider how they would react. Equilibrium in an Oligopolistic Market When we study a market, we usually want to determine the price and quantity that will prevail in equilibrium. For example, we saw that in a perfectly competitive market, the equilibrium price equates the quantity supplied with the quantity demanded. Then we saw that for a monopoly, an equilibrium occurs when marginal revenue equals marginal cost. Finally, when we studied monopolistic competition, we saw how a long-run equilibrium results as the entry of new firms drives profits to zero. In these markets, each firm could take price or market demand as given and largely ignore its competitors. In an oligopolistic market, however, a firm sets price or output based partly on strategic considerations regarding the behavior of its competitors. At the same time, competitors’ decisions depend on the first firm’s decision. How, then, can we figure out what the market price and output will be in equilibrium—or whether there will even be an equilibrium? To answer 458 PART 3 • Market Structure and Competitive Strategy In §8.7, we explain that in a competitive market, longrun equilibrium occurs when no firm has an incentive to enter or exit because firms are earning zero economic profit and the quantity demanded is equal to the quantity supplied. • Nash equilibrium Set of strategies or actions in which each firm does the best it can given its competitors’ actions. • duopoly Market in which two firms compete with each other. Recall from §8.8 that when firms produce homogeneous or identical goods, consumers consider only price when making their purchasing decisions. • Cournot model Oligopoly model in which firms produce a homogeneous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how
much to produce. these questions, we need an underlying principle to describe an equilibrium when firms make decisions that explicitly take each other’s behavior into account. Remember how we described an equilibrium in competitive and monopolistic markets: When a market is in equilibrium, firms are doing the best they can and have no reason to change their price or output. Thus a competitive market is in equilibrium when the quantity supplied equals the quantity demanded: Each firm is doing the best it can—it is selling all that it produces and is maximizing its profit. Likewise, a monopolist is in equilibrium when marginal revenue equals marginal cost because it, too, is doing the best it can and is maximizing its profit. NASH EQUILIBRIUM With some modification, we can apply this same principle to an oligopolistic market. Now, however, each firm will want to do the best it can given what its competitors are doing. And what should the firm assume that its competitors are doing? Because the firm will do the best it can given what its competitors are doing, it is natural to assume that these competitors will do the best they can given what that firm is doing. Each firm, then, takes its competitors into account, and assumes that its competitors are doing likewise. This may seem a bit abstract at first, but it is logical, and as we will see, it gives us a basis for determining an equilibrium in an oligopolistic market. The concept was first explained clearly by the mathematician John Nash in 1951, so we call the equilibrium it describes a Nash equilibrium. It is an important concept that we will use repeatedly: Nash Equilibrium: Each firm is doing the best it can given what its competitors are doing. We discuss this equilibrium concept in more detail in Chapter 13, where we show how it can be applied to a broad range of strategic problems. In this chapter, we will apply it to the analysis of oligopolistic markets. To keep things as uncomplicated as possible, this chapter will focus largely on markets in which two firms are competing with each other. We call such a market a duopoly. Thus each firm has just one competitor to take into account in making its decisions. Although we focus on duopolies, our basic results will also apply to markets with more than two firms. The Cournot Model We will begin with a simple model of duopoly first introduced by the French economist Augustin Cournot in 1838. Suppose the firms produce a homogeneous good and know the market demand curve. Each firm must decide how
much to produce, and the two firms make their decisions at the same time. When making its production decision, each firm takes its competitor into account. It knows that its competitor is also deciding how much to produce, and the market price will depend on the total output of both firms. The essence of the Cournot model is that each firm treats the output level of its competitor as fixed when deciding how much to produce. To see how this works, let’s consider the output decision of Firm 1. Suppose Firm 1 thinks that Firm 2 will produce nothing. In that case, Firm 1’s demand curve is the market demand curve. In Figure 12.3 this is shown as D1(0), which means the demand curve for Firm 1, assuming Firm 2 produces zero. Figure 12.3 also shows the corresponding marginal revenue curve MR1(0). We have assumed that Firm 1’s marginal P1 D1(0) MR1(0) CHAPTER 12 • Monopolistic Competition and Oligopoly 459 FIGURE 12.3 FIRM 1’S OUTPUT DECISION Firm 1’s profit-maximizing output depends on how much it thinks that Firm 2 will produce. If it thinks Firm 2 will produce nothing, its demand curve, labeled D1(0), is the market demand curve. The corresponding marginal revenue curve, labeled MR1(0), intersects Firm 1’s marginal cost curve MC1 at an output of 50 units. If Firm 1 thinks that Firm 2 will produce 50 units, its demand curve, D1(50), is shifted to the left by this amount. Profit maximization now implies an output of 25 units. Finally, if Firm 1 thinks that Firm 2 will produce 75 units, Firm 1 will produce only 12.5 units. MC1 MR1(75) MR1(50) D1(75) D1(50) 12.5 25 50 75 Q1 cost MC1 is constant. As shown in the figure, Firm 1’s profit-maximizing output is 50 units, the point where MR1(0) intersects MC1. So if Firm 2 produces zero, Firm 1 should produce 50. Suppose, instead, that Firm 1 thinks Firm 2 will produce 50 units. Then Firm 1’s demand curve is the market demand curve shifted to the left by 50. In Figure 12.3, this curve is labeled D1(50), and the corresponding marginal revenue curve is labeled
MR1(50). Firm 1’s profit-maximizing output is now 25 units, the point where MR1(50) = MC1. Now, suppose Firm 1 thinks that Firm 2 will produce 75 units. Then Firm 1’s demand curve is the market demand curve shifted to the left by 75. It is labeled D1(75) in Figure 12.3, and the corresponding marginal revenue curve is labeled MR1(75). Firm 1’s profit-maximizing output is now 12.5 units, the point where MR1(75) = MC1. Finally, suppose Firm 1 thinks that Firm 2 will produce 100 units. Then Firm 1’s demand and marginal revenue curves (which are not shown in the figure) would intersect its marginal cost curve on the vertical axis; if Firm 1 thinks that Firm 2 will produce 100 units or more, it should produce nothing. REACTION CURVES To summarize: If Firm 1 thinks that Firm 2 will produce nothing, it will produce 50; if it thinks Firm 2 will produce 50, it will produce 25; if it thinks Firm 2 will produce 75, it will produce 12.5; and if it thinks Firm 2 will produce 100, then it will produce nothing. Firm 1’s profit-maximizing output is thus a decreasing schedule of how much it thinks Firm 2 will produce. We call this schedule Firm 1’s reaction curve and denote it by Q*1(Q2). This curve is plotted in Figure 12.4, where each of the four output combinations that we found above is shown as an x. • reaction curve Relationship between a firm’s profitmaximizing output and the amount it thinks its competitor will produce. 460 PART 3 • Market Structure and Competitive Strategy FIGURE 12.4 REACTION CURVES AND COURNOT EQUILIBRIUM Firm 1’s reaction curve shows how much it will produce as a function of how much it thinks Firm 2 will produce. (The xs at Q2 = 0, 50, and 75 correspond to the examples shown in Figure 12.3.) Firm 2’s reaction curve shows its output as a function of how much it thinks Firm 1 will produce. In Cournot equilibrium, each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits. Therefore, neither firm will move from this equilibrium. Q1 100 75 50 x 25 12.5 Firm 2’s Reaction
Curve Q2(Q1) x Firm 1’s Reaction Curve Q1(Q2) 25 50 Cournot Equilibrium x 75 100 Q2 • Cournot equilibrium Equilibrium in the Cournot model in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly. We can go through the same kind of analysis for Firm 2; that is, we can determine Firm 2’s profit-maximizing quantity given various assumptions about how much Firm 1 will produce. The result will be a reaction curve for Firm *(Q1) that relates its output to the output that it thinks Firm 2—i.e., a schedule Q 2 1 will produce. If Firm 2’s marginal revenue or marginal cost curve is different from that of Firm 1, its reaction curve will also differ in form. For example, Firm 2’s reaction curve might look like the one drawn in Figure 12.4. COURNOT EQUILIBRIUM How much will each firm produce? Each firm’s reaction curve tells it how much to produce, given the output of its competitor. In equilibrium, each firm sets output according to its own reaction curve; the equilibrium output levels are therefore found at the intersection of the two reaction curves. We call the resulting set of output levels a Cournot equilibrium. In this equilibrium, each firm correctly assumes how much its competitor will produce, and it maximizes its profit accordingly. Note that this Cournot equilibrium is an example of a Nash equilibrium (and thus it is sometimes called a Cournot-Nash equilibrium). Remember that in a Nash equilibrium, each firm is doing the best it can given what its competitors are doing. As a result, no firm would individually want to change its behavior. In the Cournot equilibrium, each firm is producing an amount that maximizes its profit given what its competitor is producing, so neither would want to change its output. Suppose the two firms are initially producing output levels that differ from the Cournot equilibrium. Will they adjust their outputs until the Cournot equilibrium is reached? Unfortunately, the Cournot model says nothing about the dynamics of the adjustment process. In fact, during any adjustment process, the model’s central assumption that each firm can assume that its competitor’s output is fixed will not hold. Because both firms would be adjusting their outputs, neither output would be fixed. We need different models to understand dynamic adjustment, and we will examine some in Chapter 13. When is it rational for
each firm to assume that its competitor’s output is fixed? It is rational if the two firms are choosing their outputs only once because CHAPTER 12 • Monopolistic Competition and Oligopoly 461 then their outputs cannot change. It is also rational once they are in Cournot equilibrium because then neither firm will have any incentive to change its output. When using the Cournot model, we must therefore confine ourselves to the behavior of firms in equilibrium. The Linear Demand Curve—An Example Let’s work through an example—two identical firms facing a linear market demand curve. This will help clarify the meaning of a Cournot equilibrium and let us compare it with the competitive equilibrium and the equilibrium that results if the firms collude and choose their output levels cooperatively. Suppose our duopolists face the following market demand curve: P = 30 - Q where Q is the total production of both firms (i.e., Q = Q1 + Q2). Also, suppose that both firms have zero marginal cost: MC 1 = MC 2 = 0 We can determine the reaction curve for Firm 1 as follows. To maximize profit, it sets marginal revenue equal to marginal cost. Its total revenue R1 is given by R1 = PQ1 = 30Q1 = 30Q1 = (30 - Q)Q1 - (Q1 - Q 1 + Q2)Q1 2 - Q2Q1 Its marginal revenue MR1 is just the incremental revenue R1 resulting from an incremental change in output Q1: MR1 = R1/Q1 = 30 - 2Q1 - Q2 Now, setting MR1 equal to zero (the firm’s marginal cost) and solving for Q1, we find = Firm 1 s reaction curve: Q1 = 15 - The same calculation applies to Firm 2: = Firm 2 s reaction curve: Q2 = 15 - 1 2 Q2 1 2 Q1 (12.1) (12.2) The equilibrium output levels are the values for Q1 and Q2 at the intersection of the two reaction curves—i.e., the levels that solve equations (12.1) and (12.2). By replacing Q2 in equation (12.1) with the expression on the righthand side of (12.2), you can verify that the equilibrium output levels are Cournot equilibrium: Q1 = Q2 = 10 462 PART 3 • Market Structure and Competitive Strategy FIGURE 12.5 DUOPOLY EXAM
PLE The demand curve is P = 30 − Q, and both firms have zero marginal cost. In Cournot equilibrium, each firm produces 10. The collusion curve shows combinations of Q1 and Q2 that maximize total profits. If the firms collude and share profits equally, each will produce 7.5. Also shown is the competitive equilibrium, in which price equals marginal cost and profit is zero. Q1 30 15 10 7.5 Collusion Curve Firm 2’s Reaction Curve Competitive Equilibrium Cournot Equilibrium Collusive Equilibrium Firm 1’s Reaction Curve 7.5 10 15 30 Q2 The total quantity produced is therefore Q = Q1 + Q2 = 20, so the equilibrium market price is P = 30 − Q = 10, and each firm earns a profit of 100. Figure 12.5 shows the firms’ reaction curves and this Cournot equilibrium. Note that Firm 1’s reaction curve shows its output Q1 in terms of Firm 2’s output Q2. Likewise, Firm 2’s reaction curve shows Q2 in terms of Q1. (Because the firms are identical, the two reaction curves have the same form. They look different because one gives Q1 in terms of Q2 and the other gives Q2 in terms of Q1.) The Cournot equilibrium is at the intersection of the two curves. At this point, each firm is maximizing its own profit, given its competitor’s output. We have assumed that the two firms compete with each other. Suppose, instead, that the antitrust laws were relaxed and the two firms could collude. They would set their outputs to maximize total profit, and presumably they would split that profit evenly. Total profit is maximized by choosing total output Q so that marginal revenue equals marginal cost, which in this example is zero. Total revenue for the two firms is R = PQ = (30 - Q)Q = 30Q - Q 2 Marginal revenue is therefore MR = R/Q = 30 - 2Q Setting MR equal to zero, we see that total profit is maximized when Q = 15. Any combination of outputs Q1 and Q2 that add up to 15 maximizes total profit. The curve Q1 + Q2 = 15, called the collusion curve, therefore gives all pairs of outputs Q1 and Q2 that maximize total profit. This curve is also shown in CHAPTER 12 • Monopolistic Competition and Oligopoly 463 Figure 12.5. If the firms agree to share
profits equally, each will produce half of the total output: Q1 = Q2 = 7.5 As you would expect, both firms now produce less—and earn higher profits (112.50)—than in the Cournot equilibrium. Figure 12.5 shows this collusive equilibrium and the competitive output levels found by setting price equal to marginal cost. (You can verify that they are Q1 = Q2 = 15, which implies that each firm makes zero profit.) Note that the Cournot outcome is much better (for the firms) than perfect competition, but not as good as the outcome from collusion. First Mover Advantage—The Stackelberg Model We have assumed that our two duopolists make their output decisions at the same time. Now let’s see what happens if one of the firms can set its output first. There are two questions of interest. First, is it advantageous to go first? Second, how much will each firm produce? Continuing with our example, we assume that both firms have zero marginal cost, and that market demand is given by P = 30 − Q, where Q is total output. Suppose Firm 1 sets its output first and then Firm 2, after observing Firm 1’s output, makes its output decision. In setting output, Firm 1 must therefore consider how Firm 2 will react. This Stackelberg model of duopoly is different from the Cournot model, in which neither firm has any opportunity to react. Let’s begin with Firm 2. Because it makes its output decision after Firm 1, it takes Firm 1’s output as fixed. Therefore, Firm 2’s profit-maximizing output is given by its Cournot reaction curve, which we derived above as equation (12.2): = Firm 2 s reaction curve: Q2 = 15 - 1 2 Q1 (12.2) What about Firm 1? To maximize profit, it chooses Q1 so that its marginal rev- enue equals its marginal cost of zero. Recall that Firm 1’s revenue is R1 = PQ1 = 30Q1 - Q 1 2 - Q2Q1 (12.3) Because R1 depends on Q2, Firm 1 must anticipate how much Firm 2 will produce. Firm 1 knows, however, that Firm 2 will choose Q2 according to the reaction curve (12.2). Substituting equation (12.2) for Q2 into equation (12.3), we find that Firm 1’
s revenue is R1 = 30Q1 - Q1 2 - Q1 a 15 - 1 2 b Q1 = 15Q1 - 1 2 2 Q1 Its marginal revenue is therefore MR1 = R1/Q1 = 15 - Q1 (12.4) • Stackelberg model Oligopoly model in which one firm sets its output before other firms do. 464 PART 3 • Market Structure and Competitive Strategy Setting MR1 = 0 gives Q1 = 15. And from Firm 2’s reaction curve (12.2), we find that Q2 = 7.5. Firm 1 produces twice as much as Firm 2 and makes twice as much profit. Going first gives Firm 1 an advantage. This may appear counterintuitive: It seems disadvantageous to announce your output first. Why, then, is going first a strategic advantage? The reason is that announcing first creates a fait accompli: No matter what your competitor does, your output will be large. To maximize profit, your competitor must take your large output level as given and set a low level of output for itself. If your competitor produced a large level of output, it would drive price down and you would both lose money. So unless your competitor views “getting even” as more important than making money, it would be irrational for it to produce a large amount. As we will see in Chapter 13, this kind of “firstmover advantage” occurs in many strategic situations. The Cournot and Stackelberg models are alternative representations of oligopolistic behavior. Which model is the more appropriate depends on the industry. For an industry composed of roughly similar firms, none of which has a strong operating advantage or leadership position, the Cournot model is probably the more appropriate. On the other hand, some industries are dominated by a large firm that usually takes the lead in introducing new products or setting price; the mainframe computer market is an example, with IBM the leader. Then the Stackelberg model may be more realistic. 12.3 Price Competition We have assumed that our oligopolistic firms compete by setting quantities. In many oligopolistic industries, however, competition occurs along price dimensions. For example, automobile companies view price as a key strategic variable, and each one chooses its price with its competitors in mind. In this section, we use the Nash equilibrium concept to study price competition, first in an industry that produces a homogeneous good and then in an industry with some degree of product differentiation. Price
Competition with Homogeneous Products—The Bertrand Model The Bertrand model was developed in 1883 by another French economist, Joseph Bertrand. Like the Cournot model, it applies to firms that produce the same homogeneous good and make their decisions at the same time. In this case, however, the firms choose prices instead of quantities. As we will see, this change can dramatically affect the market outcome. Let’s return to the duopoly example of the last section, in which the market demand curve is P = 30 - Q where Q = Q1 + Q2 is again total production of a homogeneous good. This time, however, we will assume that both firms have a marginal cost of $3: MC 1 = MC 2 = $3 As an exercise, you can show that the Cournot equilibrium for this duopoly, which results when both firms choose output simultaneously, is Q1 = Q2 = 9. You • Bertrand model Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge. CHAPTER 12 • Monopolistic Competition and Oligopoly 465 can also check that in this Cournot equilibrium, the market price is $12, so that each firm makes a profit of $81. Now suppose that these two duopolists compete by simultaneously choosing a price instead of a quantity. What price will each firm choose, and how much profit will each earn? To answer these questions, note that because the good is homogeneous, consumers will purchase only from the lowest-price seller. Thus, if the two firms charge different prices, the lower-price firm will supply the entire market and the higher-price firm will sell nothing. If both firms charge the same price, consumers will be indifferent as to which firm they buy from and each firm will supply half the market. What is the Nash equilibrium in this case? If you think about this problem a little, you will see that because of the incentive to cut prices, the Nash equilibrium is the competitive outcome—i.e., both firms set price equal to marginal cost: P1 = P2 = $3. Then industry output is 27 units, of which each firm produces 13.5 units. And because price equals marginal cost, both firms earn zero profit. To check that this outcome is a Nash equilibrium, ask whether either firm would have any incentive to change its price. Suppose Firm 1 raised its price. It would then
lose all of its sales to Firm 2 and therefore be no better off. If, instead, it lowered its price, it would capture the entire market but would lose money on every unit it produced; again, it would be worse off. Therefore, Firm 1 (and likewise Firm 2) has no incentive to deviate: It is doing the best it can to maximize profit, given what its competitor is doing. Why couldn’t there be a Nash equilibrium in which the firms charged the same price, but a higher one (say, $5), so that each made some profit? Because if either firm lowered its price just a little, it could capture the entire market and nearly double its profit. Thus each firm would want to undercut its competitor. Such undercutting would continue until the price dropped to $3. By changing the strategic choice variable from output to price, we get a dramatically different outcome. In the Cournot model, because each firm produces only 9 units, the market price is $12. Now the market price is $3. In the Cournot model, each firm made a profit; in the Bertrand model, the firms price at marginal cost and make no profit. The Bertrand model has been criticized on several counts. First, when firms produce a homogeneous good, it is more natural to compete by setting quantities rather than prices. Second, even if firms do set prices and choose the same price (as the model predicts), what share of total sales will go to each one? We assumed that sales would be divided equally among the firms, but there is no reason why this must be the case. Despite these shortcomings, the Bertrand model is useful because it shows how the equilibrium outcome in an oligopoly can depend crucially on the firms’ choice of strategic variable.2 Price Competition with Differentiated Products Oligopolistic markets often have at least some degree of product differentiation.3 Market shares are determined not just by prices, but also by differences in the design, performance, and durability of each firm’s product. In such cases, it is natural for firms to compete by choosing prices rather than quantities. 2Also, it has been shown that if firms produce a homogeneous good and compete by first setting output capacities and then setting price, the Cournot equilibrium in quantities again results. See David Kreps and Jose Scheinkman, “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes,” Bell Journal of Economics 14 (1983): 326–38.
3Product differentiation can exist even for a seemingly homogeneous product. Consider gasoline, for example. Although gasoline itself is a homogeneous good, service stations differ in terms of location and services provided. As a result, gasoline prices may differ from one service station to another. 466 PART 3 • Market Structure and Competitive Strategy To see how price competition with differentiated products can work, let’s go through the following simple example. Suppose each of two duopolists has fixed costs of $20 but zero variable costs, and that they face the same demand curves: = = Firm 1 Firm 2 s demand: Q1 s demand: Q2 = 12 - 2P1 = 12 - 2P2 + P2 + P1 (12.5a) (12.5b) where P1 and P2 are the prices that Firms 1 and 2 charge, respectively, and Q1 and Q2 are the resulting quantities that they sell. Note that the quantity that each firm can sell decreases when it raises its own price but increases when its competitor charges a higher price. CHOOSING PRICES We will assume that both firms set their prices at the same time and that each firm takes its competitor’s price as fixed. We can therefore use the Nash equilibrium concept to determine the resulting prices. Let’s begin with Firm 1. Its profit p 1 is its revenue P1Q1 less its fixed cost of $20. Substituting for Q1 from the demand curve of equation (12.5a), we have p 1 = P1Q1 - 20 = 12P1 - 2P1 2 + P1P2 - 20 At what price P1 is this profit maximized? The answer depends on P2, which Firm 1 assumes to be fixed. However, whatever price Firm 2 is charging, Firm 1’s profit is maximized when the incremental profit from a very small increase in its own price is just zero. Taking P2 as fixed, Firm 1’s profit-maximizing price is therefore given by p 1/P1 = 12 - 4P1 + P2 = 0 This equation can be rewritten to give the following pricing rule, or reaction curve, for Firm 1: = Firm 1 s reaction curve: P1 = 3 + 1 4 P2 This equation tells Firm 1 what price to set, given the price P2 that Firm 2 is setting. We can similarly find the following pricing rule for Firm 2: = Firm 2 s reaction curve:
P2 = 3 + 1 4 P1 These reaction curves are drawn in Figure 12.6. The Nash equilibrium is at the point where the two reaction curves cross; you can verify that each firm is then charging a price of $4 and earning a profit of $12. At this point, because each firm is doing the best it can given the price its competitor has set, neither firm has an incentive to change its price. Now suppose the two firms collude: Instead of choosing their prices independently, they both decide to charge the same price—namely, the price that maximizes both of their profits. You can verify that the firms would then charge $6, and that they would be better off colluding because each would now earn a profit of $16.4 Figure 12.6 shows this collusive equilibrium. Firm 2’s reaction curve P1 $6 $4 CHAPTER 12 • Monopolistic Competition and Oligopoly 467 Collusive equilibrium Firm 1’s reaction curve Nash equilibrium FIGURE 12.6 NASH EQUILIBRIUM IN PRICES Here two firms sell a differentiated product, and each firm’s demand depends both on its own price and on its competitor’s price. The two firms choose their prices at the same time, each taking its competitor’s price as given. Firm 1’s reaction curve gives its profit-maximizing price as a function of the price that Firm 2 sets, and similarly for Firm 2. The Nash equilibrium is at the intersection of the two reaction curves: When each firm charges a price of $4, it is doing the best it can given its competitor’s price and has no incentive to change price. Also shown is the collusive equilibrium: If the firms cooperatively set price, they will choose $6. $4 $6 P2 Finally, suppose Firm 1 sets its price first and that, after observing Firm 1’s decision, Firm 2 makes its pricing decision. Unlike the Stackelberg model in which the firms set their quantities, in this case Firm 1 would be at a distinct disadvantage by moving first. (To see this, calculate Firm 1’s profit-maximizing price, taking Firm 2’s reaction curve into account.) Why is moving first now a disadvantage? Because it gives the firm that moves second an opportunity to undercut slightly and thereby capture a larger market share. (See Exercise 11 at the end of the chapter.) EXAM PLE 12.
2 A PRICING PROBLEM FOR PROCTER & GAMBLE When Procter & Gamble (P&G) planned to enter the Japanese market for Gypsy Moth Tape, it knew its production costs and understood the market demand curve but found it hard to determine the right price to charge because two other firms—Kao, Ltd., and Unilever, Ltd.—were also planning to enter the market. All three firms would be choosing their prices at about the same time, and P&G had to take this into account when setting its own price.5 4The firms have the same costs, so they will charge the same price P. Total profit is given by p T = p + p 2 1 = 24P - 4P2 + 2P2 - 40 = 24P - 2P2 - 40. This is maximized when p P = $6. Each firm’s profit is therefore T/P = 0. p T/P = 24 − 4P, so the joint profit-maximizing price is p 1 = p 2 = 12P - P2 - 20 = 72 - 36 - 20 = $16 5This example is based on classroom material developed by Professor John Hauser of MIT. To protect P&G’s proprietary interests, some of the facts about the product and the market have been altered. The fundamental description of P&G’s problem, however, is accurate. 468 PART 3 • Market Structure and Competitive Strategy Because all three firms were using the same technology for producing Gypsy Moth Tape, they had the same production costs. Each firm faced a fixed cost of $480,000 per month and a variable cost of $1 per unit. From market research, P&G ascertained that its demand curve for monthly sales was Q = 3375P -3.5(PU).25(PK).25 where Q is monthly sales in thousands of units, and P, PU, and PK are P&G’s, Unilever’s, and Kao’s prices, respectively. Now, put yourself in P&G’s position. Assuming that Unilever and Kao face the same demand conditions, with what price should you enter the market, and how much profit should you expect to earn? You might begin by calculating the profit you would earn as a function of the price you charge, under alternative assumptions about the prices that Unilever and Kao will charge.
Using the demand curve and cost numbers given above, we have done these calculations and tabulated the results in Table 12.2. Each entry shows your profit, in thousands of dollars per month, for a particular combination of prices (while assuming in each case that Unilever and Kao set the same price). For example, if you charge $1.30 and Unilever and Kao both charge $1.50, you will earn a profit of $15,000 per month. But remember that in all likelihood, the managers of Unilever and Kao are making the same calculations that you are and probably have their own versions of Table 12.2. Now suppose your competitors charge $1.50 or more. As the table shows, you would want to charge only $1.40, because that price gives you the highest profit. (For example, if they charged $1.50, you would make $29,000 per month by charging $1.40 but only $20,000 by charging $1.50, and $15,000 by charging $1.30.) Consequently, you would not want to charge $1.50 (or more). Assuming that your competitors have followed the same reasoning, you should not expect them to charge $1.50 (or more) either. What if your competitors charge $1.30? In that case, you will lose money, but you will lose the least amount of money ($6000 per month) by charging TABLE 12.2 P&G’S PROFIT (IN THOUSANDS OF DOLLARS PER MONTH) COMPETITOR’S (EQUAL) PRICES ($) P&G’S PRICE ($) 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 −226 −106 −56 −44 −52 −70 −93 −215 −204 −194 −183 −174 −165 −155 −89 −37 −25 −32 −51 −76 −73 −19 −6 −15 −34 −59 −87 −58 −43 −28 −15 2 12 3 −18 −44 −72 15 29 20 −1 −28 −57 31 46 36 14 −13 −44 47 62 52 30 1 −2 62 78 68 44 15 −118 −102 −30 −17 CH
APTER 12 • Monopolistic Competition and Oligopoly 469 $1.40. Your competitors would therefore not expect you to charge $1.30, and by the same reasoning, you should not expect them to charge a price this low. What price lets you do the best you can, given your competitors’ prices? It is $1.40. This is also the price at which your competitors are doing the best they can, so it is a Nash equilibrium.6 As the table shows, in this equilibrium you and your competitors each make a profit of $12,000 per month. If you could collude with your competitors, you could make a larger profit. You would all agree to charge $1.50, and each of you would earn $20,000. But this collusive agreement might be hard to enforce: You could increase your profit further at your competitor’s expense by dropping your price below theirs, and of course your competitors could do the same thing to you. 12.4 Competition versus Collusion: The Prisoners’ Dilemma A Nash equilibrium is a noncooperative equilibrium: Each firm makes the decisions that give it the highest possible profit, given the actions of its competitors. As we have seen, the resulting profit earned by each firm is higher than it would be under perfect competition but lower than if the firms colluded. Collusion, however, is illegal, and most managers prefer to stay out of jail. But if cooperation can lead to higher profits, why don’t firms cooperate without explicitly colluding? In particular, if you and your competitor can both figure out the profit-maximizing price you would agree to charge if you were to collude, why not just set that price and hope your competitor will do the same? If your competitor does do the same, you will both make more money. The problem is that your competitor probably won’t choose to set price at the collusive level. Why not? Because your competitor would do better by choosing a lower price, even if it knew that you were going to set price at the collusive level. To understand this, let’s go back to our example of price competition from the last section. The firms in that example each have a fixed cost of $20, have zero variable cost, and face the following demand curves: = = Firm 1 Firm 2 s demand: Q1 s demand: Q2 = 12 - 2P1 = 12 - 2P2 + P2
+ P1 We found that in the Nash equilibrium each firm will charge a price of $4 and earn a profit of $12, whereas if the firms collude, they will charge a price of $6 and earn a profit of $16. Now suppose that the firms do not collude, but that Firm 1 charges the $6 collusive price, hoping that Firm 2 will do the same. If Firm 2 does do the same, it will earn a profit of $16. But what if it charges the $4 price instead? In that case, Firm 2 would earn a profit of p 2 = P2Q2 - 20 = (4)[12 - (2)(4) + 6] - 20 = $20 6This Nash equilibrium can also be derived algebraically from the demand curve and cost data above. We leave this to you as an exercise. 470 PART 3 • Market Structure and Competitive Strategy • noncooperative game Game in which negotiation and enforcement of binding contracts are not possible. • payoff matrix Table showing profit (or payoff) to each firm given its decision and the decision of its competitor. • prisoners’ dilemma Game theory example in which two prisoners must decide separately whether to confess to a crime; if a prisoner confesses, he will receive a lighter sentence and his accomplice will receive a heavier one, but if neither confesses, sentences will be lighter than if both confess. Firm 1, on the other hand, will earn a profit of only p 1 = P1Q1 - 20 = (6)[12 - (2)(6) + 4] - 20 = $4 So if Firm 1 charges $6 but Firm 2 charges only $4, Firm 2’s profit will increase to $20. And it will do so at the expense of Firm 1’s profit, which will fall to $4. Clearly, Firm 2 does best by charging only $4. Similarly, Firm 1 does best by charging only $4. If Firm 2 charges $6 and Firm 1 charges $4, Firm 1 will earn a $20 profit and Firm 2 only $4. PAYOFF MATRIX Table 12.3 summarizes the results of these different possibilities. In deciding what price to set, the two firms are playing a noncooperative game: Each firm independently does the best it can, taking its competitor into account. Table 12.3 is called the payoff matrix for this game because it shows the profit (or payoff) to each firm given its decision and the decision of its
competitor. For example, the upper left-hand corner of the payoff matrix tells us that if both firms charge $4, each will make a $12 profit. The upper right-hand corner tells us that if Firm 1 charges $4 and Firm 2 charges $6, Firm 1 will make $20 and Firm 2 $4. This payoff matrix can clarify the answer to our original question: Why don’t firms behave cooperatively, and thereby earn higher profits, even if they can’t collude? In this case, cooperating means both firms charging $6 instead of $4 and thereby earning $16 instead of $12. The problem is that each firm always makes more money by charging $4, no matter what its competitor does. As the payoff matrix shows, if Firm 2 charges $4, Firm 1 does best by charging $4. And if Firm 2 charges $6, Firm 1 still does best by charging $4. Similarly, Firm 2 always does best by charging $4, no matter what Firm 1 does. As a result, unless the two firms can sign an enforceable agreement to charge $6, neither firm can expect its competitor to charge $6, and both will charge $4. THE PRISONERS’ DILEMMA A classic example in game theory, called the prisoners’ dilemma, illustrates the problem faced by oligopolistic firms. It goes as follows: Two prisoners have been accused of collaborating in a crime. They are in separate jail cells and cannot communicate with each other. Each has been asked to confess. If both prisoners confess, each will receive a prison term of five years. If neither confesses, the prosecution’s case will be difficult to make, so the prisoners can expect to plea bargain and receive terms of two years. On the other hand, if one prisoner confesses and the other does not, the one who confesses will receive a term of only one year, while the other will go to prison for 10 years. If you were one of these prisoners, what would you do—confess or not confess? The payoff matrix in Table 12.4 summarizes the possible outcomes. (Note that the “payoffs” are negative; the entry in the lower right-hand corner means a TABLE 12.3 PAYOFF MATRIX FOR PRICING GAME FIRM 2 CHARGE $4 CHARGE $6 Firm 1 Charge $4 Charge $6 $12, $12 $20, $4 $4, $20 $
16, $16 CHAPTER 12 • Monopolistic Competition and Oligopoly 471 TABLE 12.4 PAYOFF MATRIX FOR PRISONERS’ DILEMMA PRISONER B CONFESS DON’T CONFESS Prisoner A Confess Don’t confess −5, −5 −10, −1 −1, −10 −2, −2 two-year sentence for each prisoner.) As the table shows, our prisoners face a dilemma. If they could both agree not to confess (in a way that would be binding), then each would go to jail for only two years. But they can’t talk to each other, and even if they could, can they trust each other? If Prisoner A does not confess, he risks being taken advantage of by his former accomplice. After all, no matter what Prisoner A does, Prisoner B comes out ahead by confessing. Likewise, Prisoner A always comes out ahead by confessing, so Prisoner B must worry that by not confessing, she will be taken advantage of. Therefore, both prisoners will probably confess and go to jail for five years. Oligopolistic firms often find themselves in a prisoners’ dilemma. They must decide whether to compete aggressively, attempting to capture a larger share of the market at their competitor’s expense, or to “cooperate” and compete more passively, coexisting with their competitors and settling for their current market share, and perhaps even implicitly colluding. If the firms compete passively, setting high prices and limiting output, they will make higher profits than if they compete aggressively. Like our prisoners, however, each firm has an incentive to “fink” and undercut its competitors, and each knows that its competitors have the same incentive. As desirable as cooperation is, each firm worries—with good reason—that if it competes passively, its competitor might decide to compete aggressively and seize the lion’s share of the market. In the pricing problem illustrated in Table 12.3, both firms do better by “cooperating” and charging a high price. But the firms are in a prisoners’ dilemma, where neither can trust its competitor to set a high price. EXAM PLE 12.3 PROCTER & GAMBLE IN A PRISONERS’ DILEMMA In Example 12.2, we examined the problem that arose when P&G, Unilever, and Kao
Soap all planned to enter the Japanese market for Gypsy Moth Tape at the same time. They all faced the same cost and demand conditions, and each firm had to decide on a price that took its competitors into account. In Table 12.2, (page 468) we tabulated the profits to P&G corresponding to alternative prices that the firm and its competitors might charge. We argued that P&G should expect its competitors to charge a price of $1.40 and should do the same.7 P&G would be better off if it and its competitors all charged a price of $1.50. This is clear from the payoff matrix in Table 12.5. This payoff matrix is the portion of Table 12.2 corresponding to prices of $1.40 and $1.50, with the payoffs to P&G’s competitors also tabulated.8 If all the firms charge $1.50, each will make a profit of $20,000 per month, 7As in Example 12.2, some of the facts about the product and the market have been altered to protect P&G’s proprietary interests. 472 PART 3 • Market Structure and Competitive Strategy TABLE 12.5 PAYOFF MATRIX FOR PRICING PROBLEM UNILEVER AND Kao CHARGE $1.40 CHARGE $1.50 P&G Charge $1.40 Charge $1.50 $12, $12 $3, $21 $29, $11 $20, $20 instead of the $12,000 per month they make by charging $1.40. So why don’t they charge $1.50? Because these firms are in a prisoners’ dilemma. No matter what Unilever and Kao do, P&G makes more money by charging $1.40. For example, if Unilever and Kao charge $1.50, P&G can make $29,000 per month by charging $1.40, versus $20,000 by charging $1.50. Unilever and Kao are in the same boat. For example, if P&G charges $1.50 and Unilever and Kao both charge $1.40, P&G’s competitors will each make $21,000, instead of $20,000.9 As a result, P&G knows that if it sets a price of $1.50, its competitors will
have a strong incentive to undercut and charge $1.40. P&G will then have only a small share of the market and make only $3000 per month profit. Should P&G make a leap of faith and charge $1.50? If you were faced with this dilemma, what would you do? 12.5 Implications of the Prisoners’ Dilemma for Oligopolistic Pricing Does the prisoners’ dilemma doom oligopolistic firms to aggressive competition and low profits? Not necessarily. Although our imaginary prisoners have only one opportunity to confess, most firms set output and price over and over again, continually observing their competitors’ behavior and adjusting their own accordingly. This allows firms to develop reputations from which trust can arise. As a result, oligopolistic coordination and cooperation can sometimes prevail. Take, for example, an industry made up of three or four firms that have coexisted for a long time. Over the years, the managers of those firms might grow tired of losing money because of price wars, and an implicit understanding might arise by which all the firms maintain high prices and no firm tries to take market share from its competitors. Although each firm might be tempted to undercut its competitors, its managers know that the resulting gains will be short lived: Competitors will retaliate, and the result will be renewed warfare and lower profits over the long run. This resolution of the prisoners’ dilemma occurs in some industries, but not in others. Sometimes managers are not content with the moderately high profits resulting from implicit collusion and prefer to compete aggressively in order to increase market share. Sometimes implicit understandings are difficult to reach. For example, firms with different costs and different assessments of market demand might disagree about the “correct” collusive price. Firm A might think 8This payoff matrix assumes that Unilever and Kao both charge the same price. Entries represent profits in thousands of dollars per month. 9If P&G and Kao both charged $1.50 and only Unilever undercut and charged $1.40, Unilever would make $29,000 per month. It is especially profitable to be the only firm charging the low price. CHAPTER 12 • Monopolistic Competition and Oligopoly 473 the “correct” price is $10, while Firm B thinks it is $9. When it sets a $9 price, Firm A might view this as an attempt to undercut and retaliate by lowering its price to $8. The result is a
price war. In many industries, therefore, implicit collusion is short lived. There is often a fundamental layer of mistrust, so warfare erupts as soon as one firm is perceived by its competitors to be “rocking the boat” by changing its price or increasing advertising. Price Rigidity Because implicit collusion tends to be fragile, oligopolistic firms often have a strong desire for price stability. This is why price rigidity can be a characteristic of oligopolistic industries. Even if costs or demand change, firms are reluctant to change price. If costs fall or market demand declines, they fear that lower prices might send the wrong message to their competitors and set off a price war. And if costs or demand rises, they are reluctant to raise prices because they are afraid that their competitors may not raise theirs. Price rigidity is the basis of the kinked demand curve model of oligopoly. According to this model, each firm faces a demand curve kinked at the currently prevailing price P. (See Figure 12.7.) At prices above P, the demand curve is very elastic. The reason is that the firm believes that if it raises its price above P, other firms will not follow suit, and it will therefore lose sales and much of its market share. On the other hand, the firm believes that if it lowers its price below P, other firms will follow suit because they will not want to lose their shares of the market. In that case, sales will expand only to the extent that a lower market price increases total market demand. Because the firm’s demand curve is kinked, its marginal revenue curve is discontinuous. (The bottom part of the marginal revenue curve corresponds to the less elastic part of the demand curve, as shown by the solid portions of each curve.) As a result, the firm’s costs can change without resulting in a change in • price rigidity Characteristic of oligopolistic markets by which firms are reluctant to change prices even if costs or demands change. • kinked demand curve model Oligopoly model in which each firm faces a demand curve kinked at the currently prevailing price: at higher prices demand is very elastic, whereas at lower prices it is inelastic. $/Q P* MC′ MC D FIGURE 12.7 THE KINKED DEMAND CURVE Each firm believes that if it raises its price above the current price P*, none of its competitors will follow suit, so it will lose most of its sales. Each firm
also believes that if it lowers price, everyone will follow suit, and its sales will increase only to the extent that market demand increases. As a result, the firm’s demand curve D is kinked at price P, and its marginal revenue curve MR is discontinuous at that point. If marginal cost increases from MC to MC’, the firm will still produce the same output level Q and charge the same price P. Q Quantity MR 474 PART 3 • Market Structure and Competitive Strategy • price signaling Form of implicit collusion in which a firm announces a price increase in the hope that other firms will follow suit. • price leadership Pattern of pricing in which one firm regularly announces price changes that other firms then match. price. As shown in Figure 12.7, marginal cost could increase but still equal marginal revenue at the same output level, so that price stays the same. Although the kinked demand curve model is attractively simple, it does not really explain oligopolistic pricing. It says nothing about how firms arrived at price P* in the first place, and why they didn’t arrive at some different price. It is useful mainly as a description of price rigidity rather than as an explanation of it. The explanation for price rigidity comes from the prisoners’ dilemma and from firms’ desires to avoid mutually destructive price competition. Price Signaling and Price Leadership A big impediment to implicitly collusive pricing is the fact that it is difficult for firms to agree (without talking to each other) on what the price should be. Coordination is particularly difficult when cost and demand conditions—and thus the “correct” price—are changing. Price signaling is a form of implicit collusion that sometimes gets around this problem. For example, a firm might announce that it has raised its price (perhaps through a press release) and hope that its competitors will take this announcement as a signal that they should also raise prices. If competitors follow suit, all of the firms will earn higher profits. Sometimes a pattern is established whereby one firm regularly announces price changes and other firms in the industry follow suit. This pattern is called price leadership: One firm is implicitly recognized as the “leader,” while the other firms, the “price followers,” match its prices. This behavior solves the problem of coordinating price: Everyone charges what the leader is charging. Suppose, for example, that three oligopolistic firms are currently charging $10 for their product. (If they all know the market
demand curve, this might be the Nash equilibrium price.) Suppose that by colluding, they could all set a price of $20 and greatly increase their profits. Meeting and agreeing to set a price of $20 is illegal. But suppose instead that Firm A raises its price to $15, and announces to the business press that it is doing so because higher prices are needed to restore economic vitality to the industry. Firms B and C might view this as a clear message—namely, that Firm A is seeking their cooperation in raising prices. They might then raise their own prices to $15. Firm A might then increase price further—say, to $18—and Firms B and C might raise their prices as well. Whether or not the profit-maximizing price of $20 is reached (or surpassed), a pattern of coordination has been established that, from the firm’s point of view, may be nearly as effective as meeting and formally agreeing on a price.10 This example of signaling and price leadership is extreme and might lead to an antitrust lawsuit. But in some industries, a large firm might naturally emerge as a leader, with the other firms deciding that they are best off just matching the leader’s prices, rather than trying to undercut the leader or each other. An example is the U.S. automobile industry, where General Motors has traditionally been the price leader. Price leadership can also serve as a way for oligopolistic firms to deal with the reluctance to change prices, a reluctance that arises out of the fear of being undercut or “rocking the boat.” As cost and demand conditions change, firms may find it increasingly necessary to change prices that have remained rigid for some time. In that case, they might look to a price leader to signal when and by how much price should change. Sometimes a large firm will naturally act as leader; sometimes different firms will act as leader from time to time. The example that follows illustrates this. 10For a formal model of how such price leadership can facilitate collusion, see Julio J. Rotemberg and Garth Saloner, “Collusive Price Leadership,” Journal of Industrial Economics, 1990; 93–111. CHAPTER 12 • Monopolistic Competition and Oligopoly 475 EXAM PLE 12.4 PRICE LEADERSHIP AND PRICE RIGIDITY IN COMMERCIAL BANKING Commercial banks borrow money from individuals and companies who deposit funds in checking accounts, savings accounts, and
certificates of deposit. They then use this money to make loans to household and corporate borrowers. By lending at an interest rate higher than the rate that they pay on their deposits, they earn a profit. The largest commercial banks in the United States compete with each other to make loans to large corporate clients. The main form of competition is over price—in this case, the interest rates they charge. If competition becomes aggressive, the interest rates fall, and so do profits. The incentive to avoid aggressive competition leads to price rigidity, and to a form of price leadership. The interest rate that banks charge large corporate clients is called the prime rate. Because it is widely known, it is a convenient focal point for price leadership. Most large banks charge the same or nearly the same prime rate; they avoid making frequent changes in the rate that might be destabilizing and lead to competitive warfare. The prime rate changes only when money market conditions cause other interest rates to rise or fall substantially. When that happens, one of the major banks announces a change in its rate and other banks quickly follow suit. Different banks act as leader from time to time, but when one bank announces a change, the others follow within two or three days. Figure 12.8 compares the prime rate with the interest rate on high-grade (AAA) corporate bonds. Observe that although the corporate bond rate fluctuated continuously, there were extended periods during which the prime rate did the change. This is an example of price rigidity—banks are reluctant to change their lending rate for fear of being undercut and losing business to their competitors. 10 Prime Rate AAA Corporate Bond Yield 3 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 FIGURE 12.8 PRIME RATE VERSUS CORPORATE BOND RATE The prime rate is the rate that major banks charge large corporate customers for short-term loans. It changes only infrequently because banks are reluctant to undercut one another. When a change does occur, it begins with one bank, and other banks quickly follow suit. The corporate bond rate is the return on long-term corporate bonds. Because these bonds are widely traded, this rate fluctuates with market conditions. 476 PART 3 • Market Structure and Competitive Strategy E XAM PLE 12.5 THE PRICES OF COLLEGE TEXTBOOKS If you bought this book new at a college bookstore in the United States, you probably paid something close to $200 for it. Now, there’s no doubt about
it—this is a fantastic book! But $200? Why so much?11 These publishers have an incentive to avoid a price war that could drive prices down. The best way to avoid a price war is to avoid discounting and to increase prices in lockstep on a regular basis. A quick visit to the bookstore will prove that the price of this book is not at all unusual. Most textbooks sold in the United States have retail prices in the $200 range. In fact even other microeconomics textbooks—which are clearly inferior to this one—sell for around $200. Publishing companies set the prices of their textbooks, so should we expect competition among publishers to drive down prices? Partly because of mergers and acquisitions over the last decade or so, college textbook publishing is an oligopoly. (Pearson, the publisher of this book, is the largest college textbook publisher, followed by Cengage Learning and McGraw-Hill.) The retail bookstore industry is also highly concentrated, and the retail markup on textbooks is around 30 percent. Thus a $200 retail price implies that the publisher is receiving a net (wholesale) price of about $150. The elasticity of demand is low, because the instructor chooses the textbook, often disregarding the price. On the other hand, if the price is too high, some students will buy a used book or decide not to buy the book at all. In fact, it might be the case that publishers could earn more money by lowering textbook prices. So why don’t they do that? First, that might lead to a dreaded price war. Second, publishers might not have read this book! • dominant firm Firm with a large share of total sales that sets price to maximize profits, taking into account the supply response of smaller firms. The Dominant Firm Model In some oligopolistic markets, one large firm has a major share of total sales while a group of smaller firms supplies the remainder of the market. The large firm might then act as a dominant firm, setting a price that maximizes its own profits. The other firms, which individually could have little influence over price, would then act as perfect competitors: They take the price set by the dominant firm as given and produce accordingly. But what price should the dominant firm set? To maximize profit, it must take into account how the output of the other firms depends on the price it sets. Figure 12.9 shows how a dominant firm sets its price. Here, D is the market demand curve, and SF is
the supply curve (i.e., the aggregate marginal cost curve) of the smaller fringe firms. The dominant firm must determine its demand curve DD. As the figure shows, this curve is just the difference between market demand and the supply of fringe firms. For example, at price P1, the supply of fringe firms is just equal to market demand; thus the dominant firm can sell nothing at this price. At a price P2 or less, fringe firms will not supply any of the good, so the dominant firm faces the market demand curve. At prices between P1 and P2, the dominant firm faces the demand curve DD. 11You might have saved some money by buying the book via the Internet. If you bought the book used, or if you rented an electronic edition, you probably paid about half the U.S. retail price. And if you bought the International Student Edition of the book, which is paperback and only sold outside the U.S., you probably paid much less. For an updated list of the prices of intermediate microeconomics textbooks, go to http://theory.economics.utoronto.ca/poet/. CHAPTER 12 • Monopolistic Competition and Oligopoly 477 Price D P1 P* P2 SF MCD DD FIGURE 12.9 PRICE SETTING BY A DOMINANT FIRM The dominant firm sets price, and the other firms sell all they want at that price. The dominant firm’s demand curve, DD, is the difference between market demand D and the supply of fringe firms SF. The dominant firm produces a quantity QD at the point where its marginal revenue MRD is equal to its marginal cost MCD. The corresponding price is P. At this price, fringe firms sell QF, so that total sales equal QT. QF QD QT Quantity MRD Corresponding to DD is the dominant firm’s marginal revenue curve MRD. MCD is the dominant firm’s marginal cost curve. To maximize its profit, the dominant firm produces quantity QD at the intersection of MRD and MCD. From the demand curve DD, we find price P. At this price, fringe firms sell a quantity QF; thus the total quantity sold is QT = QD + QF. 12.6 Cartels Producers in a cartel explicitly agree to cooperate in setting prices and output levels. Not all the producers in an industry need to join the cartel, and most cartels involve only a subset of producers
. But if enough producers adhere to the cartel’s agreements, and if market demand is sufficiently inelastic, the cartel may drive prices well above competitive levels. Cartels are often international. While U.S. antitrust laws prohibit American companies from colluding, those of other countries are much weaker and are sometimes poorly enforced. Furthermore, nothing prevents countries, or companies owned or controlled by foreign governments, from forming cartels. For example, the OPEC cartel is an international agreement among oil-producing countries which has succeeded in raising world oil prices above competitive levels. Other international cartels have also succeeded in raising prices. During the mid-1970s, for example, the International Bauxite Association (IBA) quadrupled bauxite prices, and a secretive international uranium cartel pushed up uranium prices. Some cartels had longer successes: From 1928 through the early 1970s, 478 PART 3 • Market Structure and Competitive Strategy Recall from §10.2 that monopoly power refers to market power on the part of a seller—the ability of a firm to price its product above its marginal cost of production. a cartel called Mercurio Europeo kept the price of mercury close to monopoly levels, and an international cartel monopolized the iodine market from 1878 through 1939. However, most cartels have failed to raise prices. An international copper cartel operates to this day, but it has never had a significant impact on copper prices. Cartel attempts to drive up the prices of tin, coffee, tea, and cocoa have also failed.12 CONDITIONS FOR CARTEL SUCCESS Why do some cartels succeed while others fail? There are two conditions for cartel success. First, a stable cartel organization must be formed whose members agree on price and production levels and then adhere to that agreement. Unlike our prisoners in the prisoners’ dilemma, cartel members can talk to each other to formalize an agreement. This does not mean, however, that agreeing is easy. Different members may have different costs, different assessments of market demand, and even different objectives, and they may therefore want to set price at different levels. Furthermore, each member of the cartel will be tempted to “cheat” by lowering its price slightly to capture a larger market share than it was allotted. Most often, only the threat of a long-term return to competitive prices deters cheating of this sort. But if the profits from cartelization are large enough, that threat may be sufficient. The second condition is the potential for monopoly power. Even if a cartel can
solve its organizational problems, there will be little room to raise price if it faces a highly elastic demand curve. Potential monopoly power may be the most important condition for success; if the potential gains from cooperation are large, cartel members will have more incentive to solve their organizational problems. Analysis of Cartel Pricing Only rarely do all the producers of a good combine to form a cartel. A cartel usually accounts for only a portion of total production and must take into account the supply response of competitive (noncartel) producers when it sets price. Cartel pricing can thus be analyzed by using the dominant firm model discussed earlier. We will apply this model to two cartels, the OPEC oil cartel and the CIPEC copper cartel.13 This will help us understand why OPEC was successful in raising price while CIPEC was not. ANALYZING OPEC Figure 12.10 illustrates the case of OPEC. Total demand TD is the total world demand curve for crude oil, and Sc is the competitive (non-OPEC) supply curve. The demand for OPEC oil DOPEC is the difference between total demand and competitive supply, and MROPEC is the corresponding marginal revenue curve. MCOPEC is OPEC’s marginal cost curve; as you can see, OPEC has much lower production costs than do non-OPEC producers. OPEC’s marginal revenue and marginal cost are equal at quantity QOPEC, which is the quantity that OPEC will produce. We see from OPEC’s demand curve that the price will be P*, at which competitive supply is Qc. Suppose petroleum-exporting countries had not formed a cartel but had instead produced competitively. Price would then have equaled marginal cost. We can therefore determine the competitive price from the point where OPEC’s 12See Jeffrey K. MacKie-Mason and Robert S. Pindyck, “Cartel Theory and Cartel Experience in International Minerals Markets,” in Energy: Markets and Regulation (Cambridge, MA: MIT Press, 1986). 13CIPEC is the French acronym for International Council of Copper Exporting Countries. CHAPTER 12 • Monopolistic Competition and Oligopoly 479 Price TD Sc FIGURE 12.10 THE OPEC OIL CARTEL TD is the total world demand curve for oil, and Sc is the competitive (non-OPEC) supply curve. OPEC’s demand DOPEC is the difference between the two. Because both total demand and competitive supply are inelastic, OPEC
’s demand is inelastic. OPEC’s profit-maximizing quantity QOPEC is found at the intersection of its marginal revenue and marginal cost curves; at this quantity, OPEC charges price P. If OPEC producers had not cartelized, price would be Pc, where OPEC’s demand and marginal cost curves intersect. DOPEC MC OPEC P ′ Pc MR OPEC Qc QOPEC QT Quantity demand curve intersects its marginal cost curve. That price, labeled Pc, is much lower than the cartel price P. Because both total demand and non-OPEC supply are inelastic, the demand for OPEC oil is also fairly inelastic. Thus the cartel has substantial monopoly power, and it has used that power to drive prices well above competitive levels. In Chapter 2, we stressed the importance of distinguishing between short-run and long-run supply and demand. That distinction is important here. The total demand and non-OPEC supply curves in Figure 12.10 apply to a short- or intermediate-run analysis. In the long run, both demand and supply will be much more elastic, which means that OPEC’s demand curve will also be much more elastic. We would thus expect that in the long run OPEC would be unable to maintain a price that is so much above the competitive level. Indeed, during 1982–1989, oil prices fell in real terms, largely because of the long-run adjustment of demand and non-OPEC supply. ANALYZING CIPEC Figure 12.11 provides a similar analysis of CIPEC, which consists of four copper-producing countries: Chile, Peru, Zambia, and Congo (formerly Zaire), that collectively account for less than half of world copper production. In these countries, production costs are lower than those of non-CIPEC producers, but except for Chile, not much lower. In Figure 12.11, CIPEC’s marginal cost curve is therefore drawn only a little below the non-CIPEC supply curve. CIPEC’s demand curve DCIPEC is the difference between total demand TD and non-CIPEC supply Sc. CIPEC’s marginal cost and marginal revenue curves intersect at quantity QCIPEC, with the corresponding price P. Again, the competitive price Pc is found at the point where CIPEC’s demand curve intersects its marginal cost curve. Note that this price is very close to the
cartel price P. Why can’t CIPEC increase copper prices much? As Figure 12.11 shows, the total demand for copper is more elastic than that for oil. (Other materials, such 480 PART 3 • Market Structure and Competitive Strategy Price TD FIGURE 12.11 THE CIPEC COPPER CARTEL TD is the total demand for copper and Sc is the competitive (non-CIPEC) supply. CIPEC’s demand DCIPEC is the difference between the two. Both total demand and competitive supply are relatively elastic, so CIPEC’s demand curve is elastic, and CIPEC has very little monopoly power. Note that CIPEC’s optimal price P is close to the competitive price Pc. P* Pc Sc MCCIPEC DCIPEC MR CIPEC QCIPEC Qc QT Quantity as aluminum, can easily be substituted for copper.) Also, competitive supply is much more elastic. Even in the short run, non-CIPEC producers can easily expand supply if prices should rise (in part because of the availability of supply from scrap metal). Thus CIPEC’s potential monopoly power is small. As the examples of OPEC and CIPEC illustrate, successful cartelization requires two things. First, the total demand for the good must not be very price elastic. Second, either the cartel must control nearly all the world’s supply or, if it does not, the supply of noncartel producers must not be price elastic. Most international commodity cartels have failed because few world markets meet both conditions. E XAM PLE 12.6 THE CARTELIZATION OF INTERCOLLEGIATE ATHLETICS Many people think of intercollegiate athletics as an extracurricular activity for college students and a diversion for fans. They assume that universities support athletics because it not only gives amateur athletes a chance to develop their skills and play football or basketball before large audiences but also provides entertainment and promotes school spirit and alumni support. Although it does these things, intercollegiate athletics is also a big—and an extremely profitable—industry. Like any industry, intercollegiate athletics has firms and consumers. The “firms” are the universities that support and finance teams. The inputs to production are the coaches, student athletes, and capital in the form of stadiums and playing fields. The consumers, many of whom are current or former college students, are the fans who buy
tickets to games and the TV and radio networks that pay to broadcast them. There are many firms and consumers, which suggests that the industry is competitive. But the persistently high level of profits in this industry is inconsistent with competition—a large state university can regularly earn more than $6 million a year in profits from football games CHAPTER 12 • Monopolistic Competition and Oligopoly 481 alone.14 This profitability is the result of monopoly power, obtained via cartelization. The cartel organization is the National Collegiate Athletic Association (NCAA). The NCAA restricts competition in a number of important ways. To reduce bargaining power by student athletes, the NCAA creates and enforces rules regarding eligibility and terms of compensation. To reduce competition by universities, it limits the number of games that can be played each season and the number of teams that can participate in each division. And to limit price competition, the NCAA positioned itself as the sole negotiator of all football television contracts, thereby monopolizing one of the main sources of industry revenues. The NCAA was forced to end this practice in 1984. Has the NCAA been a successful cartel? Like most cartels, its members have occasionally broken its rules and regulations. But until 1984, it was successful in increasing the monopoly power of the college basketball industry well above what it would have been otherwise. In 1984, however, the Supreme Court ruled that the NCAA’s monopolization of football television contracts was illegal, allowing individual universities to negotiate their own contracts. The ensuing competition led to an increase in the amount of college football shown on television, but a drop in the contract fees paid to schools, which has resulted in a decrease in the total revenues to schools. All in all, although the Supreme Court’s ruling reduced the NCAA’s monopoly power, it did not eliminate it. The NCAA still negotiates fees for other televised collegiate sports; in 2010, CBS and Turner Broadcasting signed a $10.8 billion deal with the NCAA to cover the Division I Men’s Basketball Championship for 14 years. At the same time, the Association continued a 2001 deal with ESPN to allow coverage of 11 nonrevenue sports (including the Division I Women’s Basketball Championship, soccer, men’s ice hockey, and the College World Series). The original deal called for ESPN to pay the NCAA $200 million over 11 years. The NCAA’s anticompetitive practices have come under numerous attacks. In 2005, the National Invitation Tournament (NIT), a college basketball tournament operated by the
Metropolitan Intercollegiate Basketball Committee, challenged the NCAA’s rule that effectively forced schools invited to its tournament to boycott the NIT. The NIT claimed that this practice was anticompetitive and an illegal use of the NCAA’s powers. The parties ultimately settled the lawsuit for nearly $60 million. In 2007, the NCAA was sued by 11,500 Division I football and basketball players claiming that it illegally fixed the price of an athletic scholarship below the cost of a college education. According to the players, the NCAA shortchanged them, on average, $2,500 a year because of its arbitrary limit on scholarships. EX AM PLE 12.7 THE MILK CARTEL The U.S. government has supported the price of milk since the Great Depression and continues to do so today. The government, however, scaled back price supports during the 1990s, and as a result, wholesale prices of milk have fluctuated more widely. Not surprisingly, farmers have been complaining. In response to these complaints, in 1996 the federal government allowed milk producers in the six New England states to cartelize. The cartel—called the Northeast Interstate Dairy Compact—set minimum wholesale prices for milk, and was exempt from the antitrust laws. The result was that consumers in New England paid more for a gallon of milk than consumers elsewhere in the nation. In 1999, Congress responded to the lobbying efforts of farmers in other states by attempting to expand the milk cartel. introduced Legislation was that would have allowed dairy farmers in New York, New Jersey, Maryland, Delaware, and Pennsylvania to join the New England states and thereby form a cartel covering most of the northeast United States.15 Not wanting to be left out, dairy 14See “In Big-Time College Athletics, the Real Score Is in Dollars,” New York Times, March 1, 1987. 482 PART 3 • Market Structure and Competitive Strategy farmers in the South also lobbied Congress for higher milk prices. As a result, the 1999 legislation also authorized 16 southern states, including Texas, Florida, and Georgia, to create their own regional cartel. Studies have suggested that the original cartel (covering only the New England states) has caused retail prices of milk to rise by only a few cents a gallon. Why so little? The reason is that the New England cartel is surrounded by a fringe of noncartel producers—namely, dairy farmers in New York, New Jersey, and other states. Expanding the cartel, however, would have shrunk the competitive fringe, thereby giving the
cartel a greater influence over milk prices. Recognizing the political headaches and regional conflict caused by these attempts at cartelization, Congress ended the Northeast Interstate Dairy Compact in October 2001. Although proponents of the Compact attempted to revive the cartel, opposition in Congress has been strong and, as of 2011, the cartel has not been re-authorized. Nonetheless, milk production continues to benefit from federal price supports. SUMMARY 1. In a monopolistically competitive market, firms compete by selling differentiated products, which are highly substitutable. New firms can enter or exit easily. Firms have only a small amount of monopoly power. In the long run, entry will occur until profits are driven to zero. Firms then produce with excess capacity (i.e., at output levels below those that minimize average cost). 2. In an oligopolistic market, only a few firms account for most or all of production. Barriers to entry allow some firms to earn substantial profits, even over the long run. Economic decisions involve strategic considerations—each firm must consider how its actions will affect its rivals, and how they are likely to react. 3. In the Cournot model of oligopoly, firms make their output decisions at the same time, each taking the other’s output as fixed. In equilibrium, each firm is maximizing its profit, given the output of its competitor, so no firm has an incentive to change its output. The firms are therefore in a Nash equilibrium. Each firm’s profit is higher than it would be under perfect competition but less than what it would earn by colluding. 4. In the Stackelberg model, one firm sets its output first. That firm has a strategic advantage and earns a higher profit. It knows that it can choose a large output and QUESTIONS FOR REVIEW that its competitors will have to choose smaller outputs if they want to maximize profits. 5. The Nash equilibrium concept can also be applied to markets in which firms produce substitute goods and compete by setting price. In equilibrium, each firm maximizes its profit, given the prices of its competitors, and so has no incentive to change price. 6. Firms would earn higher profits by collusively agreeing to raise prices, but the antitrust laws usually prohibit this. They might all set high prices without colluding, each hoping its competitors will do the same, but they are in a prisoners’ dilemma, which makes this unlikely. Each firm has an incentive to cheat by lowering its price and capturing sales from competitors. 7. The prisoners�
� dilemma creates price rigidity in oligopolistic markets. Firms are reluctant to change prices for fear of setting off price warfare. 8. Price leadership is a form of implicit collusion that sometimes gets around the prisoners’ dilemma. One firm sets price and other firms follow suit. 9. In a cartel, producers explicitly collude in setting prices and output levels. Successful cartelization requires that the total demand not be very price elastic, and that either the cartel control most supply or else the supply of noncartel producers be inelastic. 1. What are the characteristics of a monopolistically competitive market? What happens to the equilibrium price and quantity in such a market if one firm introduces a new, improved product? 2. Why is the firm’s demand curve flatter than the total market demand curve in monopolistic competition? Suppose a monopolistically competitive firm is making a profit in the short run. What will happen to its demand curve in the long run? 3. Some experts have argued that too many brands of breakfast cereal are on the market. Give an argument to support this view. Give an argument against it. 15“Congress Weighs an Expanded Milk Cartel That Would Aid Farmers by Raising Prices,” New York Times, May 2, 1999. For an update, go to the following Web site: www.dairycompact.org. CHAPTER 12 • Monopolistic Competition and Oligopoly 483 4. Why is the Cournot equilibrium stable? (i.e., Why don’t firms have any incentive to change their output levels once in equilibrium?) Even if they can’t collude, why don’t firms set their outputs at the joint profitmaximizing levels (i.e., the levels they would have chosen had they colluded)? 5. In the Stackelberg model, the firm that sets output first has an advantage. Explain why. 6. What do the Cournot and Bertrand models have in common? What is different about the two models? 7. Explain the meaning of a Nash equilibrium when firms are competing with respect to price. Why is the equilibrium stable? Why don’t the firms raise prices to the level that maximizes joint profits? EXERCISES 1. Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain. 2. Consider two firms facing the demand curve
P = 50 − 5Q, where Q = Q1 + Q2. The firms’ cost functions are C1(Q1) = 20 + 10 Q1 and C2(Q2) = 10 + 12 Q2. a. Suppose both firms have entered the industry. What is the joint profit-maximizing level of output? How much will each firm produce? How would your answer change if the firms have not yet entered the industry? b. What is each firm’s equilibrium output and profit if they behave noncooperatively? Use the Cournot model. Draw the firms’ reaction curves and show the equilibrium. c. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but a takeover is not? 3. A monopolist can produce at a constant average (and marginal) cost of AC = MC = $5. It faces a market demand curve given by Q = 53 − P. a. Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. b. Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1 + Q2 = 53 - P 8. The kinked demand curve describes price rigidity. Explain how the model works. What are its limitations? Why does price rigidity occur in oligopolistic markets? 9. Why does price leadership sometimes evolve in oligopolistic markets? Explain how the price leader determines a profit-maximizing price. 10. Why has the OPEC oil cartel succeeded in raising prices substantially while the CIPEC copper cartel has not? What conditions are necessary for successful cartelization? What organizational problems must a cartel overcome? d. Calculate the Cournot equilibrium (i.e., the values of Q1 and Q2 for which each firm is doing as well as it can given its competitor’s output). What are the resulting market price and profits of each firm? *e. Suppose there are N firms in the industry, all with the same constant marginal cost, MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as N becomes large, the market price approaches the price that would prevail under perfect competition. 4. This exercise is a continuation of Exercise 3. We return to two
firms with the same constant average and marginal cost, AC = MC = 5, facing the market demand curve Q1 + Q2 = 53 − P. Now we will use the Stackelberg model to analyze what will happen if one of the firms makes its output decision before the other. a. Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2). Find the reaction curves that tell each firm how much to produce in terms of the output of its competitor. b. How much will each firm produce, and what will its profit be? 5. Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of Q1 and Q2. c. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of output on the assumption that its competitor’s output is fixed. Find each firm’s “reaction curve” (i.e., the rule that gives its desired output in terms of its competitor’s output). where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level. 6. Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs 484 PART 3 • Market Structure and Competitive Strategy are given by C1 = 60Q1 and C2 = 60Q2, where Q1 is the output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve: of lights, Everglow and Dimlit. They have identical cost functions: P = 300 - Q Ci = 10Qi + 1 2 Q = QE 2(i = E, D) Q i + QD where Q = Q1 + Q2. a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit. c. Suppose Firm 1 were the only
firm in the industry. How would market output and Firm 1’s profit differ from that found in part (b) above? d. Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm’s profits? 7. Suppose that two competing firms, A and B, produce a homogeneous good. Both firms have a marginal cost of MC = $50. Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium, and (iii) Bertrand equilibrium. a. Because Firm A must increase wages, its MC increases to $80. b. The marginal cost of both firms increases. c. The demand curve shifts to the right. 8. Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) = 40q. Assume that the demand curve for the industry is given by P = 100 − Q and that each firm expects the other to behave as a Cournot competitor. a. Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes its profits when taking its rival’s output as given. What are the profits of each firm? b. What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $25 and American had constant marginal and average costs of $40? c. Assuming that both firms have the original cost function, C(q) = 40q, how much should Texas Air be willing to invest to lower its marginal cost from 40 to 25, assuming that American will not follow suit? How much should American be willing to spend to reduce its marginal cost to 25, assuming that Texas Air will have marginal costs of 25 regardless of American’s actions? *9. Demand for light bulbs can be characterized by Q = 100 − P, where Q is in millions of boxes of lights sold and P is the price per box. There are two producers a. Unable to recognize the potential for collusion, the two firms act as short-run perfect competitors. What are the equilibrium values of QE, QD, and P? What are each firm’s profits? b. Top management in both firms is replaced. Each new manager independently recognizes the oligopolistic
nature of the light bulb industry and plays Cournot. What are the equilibrium values of QE, QD, and P? What are each firm’s profits? c. Suppose the Everglow manager guesses correctly that Dimlit is playing Cournot, so Everglow plays Stackelberg. What are the equilibrium values of QE, QD, and P? What are each firm’s profits? d. If the managers of the two companies collude, what are the equilibrium values of QE, QD, and P? What are each firm’s profits? 10. Two firms produce luxury sheepskin auto seat covers: Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by C(q) = 30q + 1.5q 2 The market demand for these seat covers is represented by the inverse demand equation P = 300 - 3Q where Q = q1 + q2, total output. a. If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm? b. It occurs to the managers of WW and BBBS that they could do a lot better by colluding. If the two firms collude, what will be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case? c. The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. To aid in making the decision, the manager of WW constructs a payoff CHAPTER 12 • Monopolistic Competition and Oligopoly 485 matrix like the one below. Fill in each box with the profit of WW and the profit of BBBS. Given this payoff matrix, what output strategy is each firm likely to pursue? PROFIT PAYOFF MATRIX BBBS (WW PROFIT, BBBS PROFIT) PRODUCE COURNOT q PRODUCE CARTEL q WW Produce Cournot q Produce Cartel q d. Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much will BBBS produce?
What is the market price, and what is the profit for each firm? Is WW better off by choosing its output first? Explain why or why not. 11. Two firms compete by choosing price. Their demand functions are and Q1 = 20 - P1 + P2 Q2 = 20 + P1 - P2 where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why. 12. The dominant firm model can help us understand the behavior of some cartels. Let’s apply this model to the OPEC oil cartel. We will use isoelastic curves to describe world demand W and noncartel (competitive) supply S. Reasonable numbers for the price elasticities of world demand and noncartel supply are −1/2 and 1/2, respectively. Then, expressing W and S in millions of barrels per day (mb/d), we could write and W = 160P -1/2 S = (3 1 3 )P1/2 Note that OPEC’s net demand is D = W − S. a. Draw the world demand curve W, the non-OPEC supply curve S, OPEC’s net demand curve D, and OPEC’s marginal revenue curve. For purposes of approximation, assume OPEC’s production cost is zero. Indicate OPEC’s optimal price, OPEC’s optimal production, and non-OPEC production
on the diagram. Now, show on the diagram how the various curves will shift and how OPEC’s optimal price will change if non-OPEC supply becomes more expensive because reserves of oil start running out. b. Calculate OPEC’s optimal (profit-maximizing) price. (Hint: Because OPEC’s cost is zero, just write the expression for OPEC revenue and find the price that maximizes it.) c. Suppose the oil-consuming countries were to unite and form a “buyers’ cartel” to gain monopsony power. What can we say, and what can’t we say, about the impact this action would have on price? 13. Suppose the market for tennis shoes has one dominant firm and five fringe firms. The market demand is Q = 400 − 2 P. The dominant firm has a constant marginal cost of 20. The fringe firms each have a marginal cost of MC = 20 + 5q. a. Verify that the total supply curve for the five fringe firms is Qf = P − 20. b. Find the dominant firm’s demand curve. c. Find the profit-maximizing quantity produced and price charged by the dominant firm, and the quantity produced and price charged by each of the fringe firms. d. Suppose there are 10 fringe firms instead of five. How does this change your results? e. Suppose there continue to be five fringe firms but that each manages to reduce its marginal cost to MC = 20 + 2q. How does this change your results? 486 PART 3 • Market Structure and Competitive Strategy *14. A lemon-growing cartel consists of four orchards. Their total cost functions are TC 1 TC 2 TC 3 TC 4 = 20 + 5Q 1 2 = 25 + 3Q 2 2 = 15 + 4Q 3 2 = 20 + 6Q 4 2 TC is in hundreds of dollars, and Q is in cartons per month picked and shipped. a. Tabulate total, average, and marginal costs for each firm for output levels between 1 and 5 cartons per month (i.e., for 1, 2, 3, 4, and 5 cartons). b. If the cartel decided to ship 10 cartons per month and set a price of $25 per carton, how should output be allocated among the firms? c. At this shipping level, which firm has the most incentive to cheat? Does any firm not have an incentive to cheat? C H A P T
E R 13 Game Theory and Competitive Strategy In Chapter 12, we began to explore some of the strategic output and pricing decisions that firms must often make. We saw how a firm can take into account the likely responses of its competitors when it makes these decisions. However, there are many questions about market structure and firm behavior that we have not yet addressed. For example, why do firms tend to collude in some markets and to compete aggressively in others? How do some firms manage to deter entry by potential competitors? And how should firms make pricing decisions when demand or cost conditions are changing or new competitors are entering the market? To answer these questions, we will use game theory to extend our analysis of strategic decision making. The application of game theory has been an important development in microeconomics. This chapter explains some key aspects of this theory and shows how it can be used to understand how markets evolve and operate, and how managers should think about the strategic decisions they continually face. We will see, for example, what happens when oligopolistic firms must set and adjust prices strategically over time, so that the prisoners’ dilemma, which we discussed in Chapter 12, is repeated over and over. We will show how firms can make strategic moves that give them advantages over competitors or an edge in bargaining situations, and how they can use threats, promises, or more concrete actions to deter entry. Finally, we will turn to auctions and see how game theory can be applied to auction design and bidding strategies. 13.1 Gaming and Strategic Decisions First, we should clarify what gaming and strategic decision making are all about. A game is any situation in which players (the participants) make strategic decisions—i.e., decisions that take into account each other’s actions and responses. Examples of games include firms competing with each other by setting prices, or a group of consumers bidding against each other at an auction for a work of art. Strategic decisions result in payoffs to the players: outcomes that generate rewards or benefits. For the price-setting firms, the payoffs are profits 13.1 Gaming and Strategic Decisions 487 13.2 Dominant Strategies 490 13.3 The Nash Equilibrium Revisited 492 13.4 Repeated Games 498 13.5 Sequential Games 502 13.6 Threats, Commitments, and Credibility 505 13.7 Entry Deterrence 510 *13.8 Auctions 516 13.1 Acquiring a Company 490 13.2 Oligopolistic Cooperation in the Water Meter Industry

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