microeconomics book solution 15

A this is a prisoners dilemma situation whatever air

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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 air- lines 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 pay- offs 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. Low price Low price Untied Ai r “R” Us High price High price \$ 20 profit \$ 20 profit \$ 50 profit \$ 0 profit \$ 0 profit \$ 50 profit \$ 40 profit \$ 40 profit S-216 C H A P T E R 1 5 O L I G O P O LY S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-216

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Solution 8. Suppose that Coke and Pepsi are the only two producers of cola drinks, making them duopolists. Both companies have zero marginal cost and a fixed cost of \$100,000. a. Assume first that consumers regard Coke and Pepsi as perfect substitutes. Currently both are sold for \$0.20 per can, and at that price each company sells 4 million cans per day. i. How large is Pepsi’s profit? ii. If Pepsi were to raise its price to \$0.30 cents per can, and Coke does not respond, what would happen to Pepsi’s profit? b. Now suppose that each company advertises to differentiate its product from the other company’s. As a result of advertising, Pepsi realizes that if it raises or lowers its price, it will sell less or more of its product, as shown by the demand schedule in the accompanying table. If Pepsi now were to raise its price to \$0.30 per can, what would happen to its profit? c. Comparing your answer to part a(i) and to part b, what is the maximum amount Pepsi would be willing to spend on advertising? 8. a. i. Pepsi sells 4 million cans at \$0.20 for total revenue of \$0.20 × 4 million = \$800,000. Its only cost is the fixed cost of \$100,000, so its profit is \$800,000 \$100,000 = \$700,000. ii. If Pepsi were to raise its price, it would lose all its customers. This is because customers regard Coke and Pepsi as identical products and so will buy none of the product that is more expensive. So Pepsi loses money, its fixed cost: its loss will be \$100,000. b. If Pepsi now raises its price to \$0.30, it will lose some customers but not all cus- tomers. It will sell 3 million cans at a price of \$0.30 per can and so have total rev- enue of \$0.30 × 3 million = \$900,000. Since its only cost is the fixed cost, Pepsi’s profit is \$900,000 \$100,000 = \$800,000.
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