# chapter: Solution Oligopoly 1. The accompanying table presents market share data for the U.S. breakfast cereal market

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1 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-209 Oligopoly chapter: The accompanying table presents market share data for the U.S. breakfast cereal market in Company a. Use the data provided to calculate the Herfindahl Hirschman Index (HHI) for the market. b. Based on this HHI, what type of market structure is the U.S. breakfast cereal market? 1. a. The HHI is = = 2,098. b. Since the HHI exceeds 1,800, the industry is an oligopoly. 2. The accompanying table shows the demand schedule for vitamin D. Suppose that the marginal cost of producing vitamin D is zero. Price of vitamin D (per ton) Quantity of vitamin D demanded (tons) \$ Market Share Kellogg 30% General Mills 26 PepsiCo (Quaker Oats) 14 Kraft 13 Private Label 11 Other 6 Source: Advertising Age a. Assume that BASF is the only producer of vitamin D and acts as a monopolist. It currently produces 40 tons of vitamin D at \$4 per ton. If BASF were to produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect? Would BASF have an incentive to produce those 10 additional tons? S-209

3 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-211 CHAPTER 15 OLIGOPOLY S-211 b. Uncle Junior, the head of the Soprano family, breaks the agreement and sells 500 more gallons of olive oil than under the cartel agreement. Assuming the Contraltos maintain the agreement, how does this affect the price for olive oil and the s earned by each family? c. Anthony Contralto, the head of the Contralto family, decides to punish Uncle Junior by increasing his sales by 500 gallons as well. How much does each family earn now? 3. a. The accompanying table shows the total revenue and the marginal revenue for the cartel. Since a cartel acts like a monopolist, it will maximize s by producing up to the point where marginal cost equals marginal revenue. For all gallons up to 2,000 gallons, marginal revenue is greater than marginal cost. Producing any more would mean that marginal revenue is less than marginal cost. So the cartel will produce 2,000 gallons and sell them at \$80 each. Since the two families share the market equally, each family has revenue of 1,000 \$80 = \$80,000. The marginal cost per gallon is constant at \$40, so the total cost (remember there is no fixed cost!) of producing 1,000 gallons is \$40,000. So each family makes a of \$80,000 \$40,000 = \$40,000. Price of olive oil Quantity of olive oil (per gallon) demanded (gallons) Total revenue Marginal revenue \$100 1,000 \$100, , , , , , , , , , , , , , , , , ,500 55,000 b. Now the Sopranos sell 1,500 gallons and the Contraltos sell 1,000 gallons, for a total output of 2,500 gallons. So the price falls to \$70 per gallon. The Sopranos have revenue of 1,500 \$70 = \$105,000 and cost of 1,500 \$40 = \$60,000. So their is \$105,000 \$60,000 = \$45,000. The Contraltos have revenue of 1,000 \$70 = \$70,000 and cost of 1,000 \$40 = \$40,000. So their is \$70,000 \$40,000 = \$30,000. \$

4 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-212 S-212 CHAPTER 15 OLIGOPOLY c. If both the Contraltos and the Sopranos sell 1,500 gallons each, the total output in this duopoly is 3,000 gallons, and the price falls to \$60 per gallon. Each family has revenue of 1,500 \$60 = \$90,000 and cost of 1,500 \$40 = \$60,000. So each family s is \$30, In France, the market for bottled water is controlled by two large firms, Perrier and Evian. Each firm has a fixed cost of 1 and a constant marginal cost of 2 per liter of bottled water ( 1 = 1 euro). The following table gives the market demand schedule for bottled water in France. Price of bottled water (per liter) Quantity of bottled water demanded (s of liters) a. Suppose the two firms form a cartel and act as a monopolist. Calculate marginal revenue for the cartel. What will the monopoly price and output be? Assuming the firms divided the output evenly, how much will each produce and what will each firm s s be? b. Now suppose Perrier decides to increase production by 1 liters. Evian doesn t change its production. What will the new market price and output be? What is Perrier s? What is Evian s? c. What if Perrier increases production by 3 liters? Evian doesn t change its production. What would its output and s be relative to those in part b? d. What do your results tell you about the likelihood of cheating on such agreements?

5 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S a. The accompanying table calculates total revenue and marginal revenue for the cartel. The cartel maximizes by producing whenever marginal revenue is greater than marginal cost (which here is 2). That is, the cartel produces a quantity of 4 liters and sells them at a price of 6 per liter. If the firms divide production equally, each produces 2 liters and has revenue of 2 6 = 12. Since the fixed cost is 1 and each liter s marginal cost is 2, each firm has of 12 1 (2 2) = 7. Price of Quantity of bottled bottled water water demanded Total revenue Marginal revenue (per liter) (s of liters) (s) (s) b. If Perrier increases production by 1 liters, the total produced now is 5 liters and the price is 5. Perrier now produces 3 liters and so has of (3 5) 1 (3 2) = 8. Evian s, however, falls to (2 5) 1 (2 2) = 5. c. If Perrier increases production by 3 liters, the total produced is 7 liters and the price is 3. Perrier produces 5 liters and so has of (5 3) 1 (5 2) = 4. This is lower than in part b. This implies that although Perrier has an incentive to increase production somewhat, it does not have an incentive to increase production dramatically. d. Since each firm can significantly increase its by moderately increasing production, the likelihood of cheating is high. CHAPTER 15 OLIGOPOLY S

6 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-214 S-214 CHAPTER 15 OLIGOPOLY 5. To preserve the North Atlantic fish stocks, it is decided that only two fishing fleets, one from the United States and the other from the European Union (EU), can fish in those waters. The accompanying table shows the market demand schedule per week for fish from these waters. The only costs are fixed costs, so fishing fleets maximize by maximizing revenue. Price of fish (per pound) a. If both fishing fleets collude, what is the revenue-maximizing output for the North Atlantic fishery? What price will a pound of fish sell for? b. If both fishing fleets collude and share the output equally, what is the revenue to the EU fleet? To the U.S. fleet? c. Suppose the EU fleet cheats by expanding its own catch by 100 pounds per week. The U.S. fleet doesn t change its catch. What is the revenue to the U.S. fleet? To the EU fleet? d. In retaliation for the cheating by the EU fleet, the U.S. fleet also expands its catch by 100 pounds per week. What is the revenue to the U.S. fleet? To the EU fleet? Quantity of fish demanded (pounds) \$17 1, , , , , a. The accompanying table calculates the total revenue for the entire North Atlantic fishery for different output quantities. The revenue-maximizing output is 2,000 pounds per week, which will fetch a price of \$16 per pound. Price of fish Quantity of fish (per pound) demanded (pounds) Total revenue \$17 1,800 \$30, ,000 32, ,100 31, ,200 30, ,300 27,600 b. If they share the output equally, the U.S. and the EU fleets will each catch 1,000 pounds per week and have revenue of \$16,000 per week. c. If the EU fleet cheats and catches 100 pounds more, the total caught will be 2,100 pounds, which will cause the price to fall to \$15. The EU fleet s revenue will now be 1,100 \$15 = \$16,500, and the U.S. fleet s revenue will fall to 1,000 \$15 = \$15,000. d. Now the total caught will be 2,200 pounds, which will bring the price down to \$14 per pound. Since each fleet now catches 1,100 pounds, each will have revenue of 1,100 \$14 = \$15,400.

7 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-215 CHAPTER 15 OLIGOPOLY S Suppose that the fisheries agreement in Problem 5 breaks down, so that the fleets behave noncooperatively. Assume that the United States and the EU each can send out either one or two fleets. The more fleets in the area, the more fish they catch in total but the lower the catch of each fleet. The accompanying matrix shows the (in dollars) per week earned by the two sides. EU 1 fleet \$10,000 2 fleets \$12,000 1 fleet U.S. \$10,000 \$4,000 \$4,000 \$7,500 2 fleets \$12,000 \$7,500 a. What is the noncooperative Nash equilibrium? Will each side choose to send out one or two fleets? b. Suppose that the fish stocks are being depleted. Each region considers the future and comes to a tit-for-tat agreement whereby each side will send only one fleet out as long as the other does the same. If either of them breaks the agreement and sends out a second fleet, the other will also send out two and will continue to do so until its competitor sends out only one fleet. If both play this tit-for-tat strategy, how much will each make every week? 6. a. If the European Union has only one fleet, the United States will have a higher if it sends out two fleets (\$12,000 rather than \$10,000). If the EU sends out two fleets, the United States will have a higher if it also sends out two fleets (\$7,500 rather than \$4,000). The same reasoning will persuade the EU that its best strategy is also to send out two fleets whether the United States sends out one or two. Both parties will send out two fleets, each earning only \$7,500 each instead of the \$10,000 they would each have earned if they had each limited themselves to one fleet. b. If both play a tit-for-tat strategy, they each will begin by sending out one fleet. The week after that, each does what the other one did the week before that is, each again sends out one fleet, and so on. As a result, the United States and the EU will each have a of \$10,000 every week.

8 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-216 S-216 CHAPTER 15 OLIGOPOLY 7. Untied and Air R Us are the only two airlines operating flights between Collegeville and Bigtown. That is, they operate in a duopoly. Each airline can charge either a high price or a low price for a ticket. The accompanying matrix shows their payoffs, in s per seat (in dollars), for any choice that the two airlines can make. Air R Us Low price \$20 High price \$0 Untied Low price \$20 \$50 \$50 \$40 High price \$0 \$40 a. Suppose the two airlines play a one-shot game that is, they interact only once and never again. What will be the Nash (noncooperative) equilibrium in this oneshot game? b. Now suppose the two airlines play this game twice. And suppose each airline can play one of two strategies: it can play either always charge the low price or tit for tat that is, it starts off charging the high price in the first period, and then in the second period it does whatever the other airline did in the previous period. Write down the payoffs to Untied from the following four possibilities: i. Untied plays always charge the low price when Air R Us also plays always charge the low price. ii. Untied plays always charge the low price when Air R Us plays tit for tat. iii. Untied plays tit for tat when Air R Us plays always charge the low price. iv. Untied plays tit for tat when Air R Us also plays tit for tat. 7. a. This is a prisoners dilemma situation. Whatever Air R Us does, it is best for Untied to charge the low price; whatever Untied does, it is best for Air R Us to charge the low price. So the Nash (noncooperative) equilibrium is for both airlines to charge the low price. b. These are Untied s payoffs: i. Both airlines charge the low price in both periods, so Untied s payoffs are \$20 in the first period and \$20 in the second period, for a total of \$20 + \$20 = \$40. ii. In the first period, Untied charges the low price and Air R Us charges the high price for a payoff to Untied of \$50. In the second period, Untied and Air R Us both charge the low price for a payoff to Untied of \$20. Untied s payoffs are therefore \$50 + \$20 = \$70. iii. In the first period, Untied charges the high price and Air R Us charges the low price for a payoff to Untied of \$0. In the second period, both airlines charge the low price for a payoff to Untied of \$20. Untied s total payoff is therefore \$0 + \$20 = \$20. iv. Both airlines charge the high price in both periods, so Untied s payoffs are \$40 in both periods, for a total of \$40 + \$40 = \$80.

11 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-219 CHAPTER 15 OLIGOPOLY S-219 c. The development of a hydrogen-powered car would make it more difficult to form or maintain an agreement. Remember that a cartel essentially acts like a monopoly. A cartel s (or a monopoly s) market power is eroded if there is entry of new firms or the development of substitute products. 11. Suppose you are an economist working for the Antitrust Division of the Department of Justice. In each of the following cases you are given the task of determining whether the behavior warrants an antitrust investigation for possible illegal acts or is just an example of undesirable, but not illegal, tacit collusion. Explain your reasoning. a. Two companies dominate the industry for industrial lasers. Several people sit on the boards of directors of both companies. b. Three banks dominate the market for banking in a given state. Their s have been going up recently as they add new fees for customer transactions. Advertising among the banks is fierce, and new branches are springing up in many locations. c. The two oil companies that produce most of the petroleum for the western half of the United States have decided to forgo building their own pipelines and to share a common pipeline, the only means of transporting petroleum products to that market. d. The two major companies that dominate the market for herbal supplements have each created a subsidiary that sells the same product as the parent company in large quantities but with a generic name. e. The two largest credit card companies, Passport and OmniCard, have required all banks and retailers who accept their cards to agree to limit their use of rival credit cards. 11. a. This warrants an antitrust investigation because it is likely that having the same set of people sit on the two boards will facilitate cartel-like behavior. b. This does not warrant an antitrust investigation. The intensity of advertising and competition by location indicates that the banks are engaged in nonprice competition. c. This warrants an antitrust investigation. By using the same pipeline, each company can monitor how much output the other is producing. This facilitates cartellike behavior. d. This does not warrant an antitrust investigation. These two companies are actively competing, albeit by using their subsidiaries. e. This warrants an antitrust investigation. These two companies are acting together to shut out a rival. 12. The industry for small, single-engine airplanes is oligopolistic, and it has achieved tacit collusion. Each firm currently sells 10 airplanes at a price of \$200,000 each. Each firm believes that it will sell 1 fewer airplane if it raises the price by \$5,000. And each firm also believes that it can sell 1 more airplane if it lowers the price by \$10,000. That is, each firm has a kinked demand curve. a. How much additional revenue will a firm generate if it produces 1 more (the 11th) airplane? b. How much revenue will a firm lose if it produces 1 fewer airplane? c. If the marginal cost of producing an airplane is \$120,000, how many airplanes will each firm produce, and at what price? d. If the marginal cost of producing an airplane is \$140,000, how many airplanes will each firm produce, and at what price?

12 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-220 S-220 CHAPTER 15 OLIGOPOLY 12. a. Currently, a firm has revenue of \$200, = \$2,000,000. If it produces 11 airplanes, it has to lower the price for each of its airplanes to \$190,000. If it did so, it would have revenue of \$190, = \$2,090,000. That is, as it produces 1 more (the 11th) airplane, its marginal revenue is \$2,090,000 \$2,000,000 = \$90,000. b. Currently, a firm has revenue of \$200, = \$2,000,000. If it produces 9 airplanes, it raises the price for each of its airplanes to \$205,000. If it did so, it would have revenue of \$205,000 9 = \$1,845,000. As it produces 1 fewer airplane, its revenue decreases by \$2,000,000 \$1,845,000 = \$155,000. The marginal revenue of the 10th airplane is \$155,000. c. Each firm s marginal revenue curve has a break at the 10th airplane, where marginal revenue drops from \$155,000 to \$90,000. If the marginal cost is \$120,000, the firm will produce 10 airplanes at the price of \$200,000 each. This is because producing the 11th airplane would create less additional revenue (\$90,000) than the additional cost of producing the 11th airplane (\$120,000). Similarly, producing 1 fewer airplane would lose the firm more revenue (\$155,000) than it creates in cost savings (\$120,000). d. If the marginal cost is \$140,000, the firm will still produce 10 airplanes at the price of \$200,000 each: producing the 11th airplane would create less additional revenue (\$90,000) than the additional cost of producing the 11th airplane (\$140,000). Similarly, producing 1 fewer airplane would lose the firm more revenue (\$155,000) than it creates in cost savings (\$140,000). In other words, small changes in marginal cost do not influence output and prices.

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