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### Homework5

Course: MATH 201, Spring 2011
School: Hawaii
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Word Count: 698

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1: Table Separating the Market McGraw Hall Microeconomics Macroeconomics Microeconomics 5,5 10,10 Prentice Hill Macroeconomics 10,10 5,5 Table 2: Pursuing Macro Market McGraw Hall Microeconomics Macroeconomics Microeconomics 10,10 5,15 Prentice Hill Macroeconomics 15,5 8,8 Homework #5 Due Date: Friday, April 29th Note: Only one randomly selected question will be graded. Question 1 There are two textbook...

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1: Table Separating the Market McGraw Hall Microeconomics Macroeconomics Microeconomics 5,5 10,10 Prentice Hill Macroeconomics 10,10 5,5 Table 2: Pursuing Macro Market McGraw Hall Microeconomics Macroeconomics Microeconomics 10,10 5,15 Prentice Hill Macroeconomics 15,5 8,8 Homework #5 Due Date: Friday, April 29th Note: Only one randomly selected question will be graded. Question 1 There are two textbook publishers, Prentice Hill and McGraw Hall. They can make only one kind of textbook among Microeconomics or Macroeconomics. They should make a decision without knowing the opponents decision. Consider the Table 1. The rst gure is a payo for Prentice Hill and the second gure is for McGraw Hall in each cell. (a) List the strategies of Prentice Hill. (b) What is the best response of McGraw Hall when Prentice Hill chooses Microeconomics? (c) Find all possible Nash equilibrium. A Nash equilibrium is written like (Prentice Hills strategy, McGraw Halls strategy). Now, Macroeconomics becomes very popular, but it needs a pre-requisite Microeconomics class. That is, if a publisher makes Microeconomics textbook, then Macroeconomics textbook becomes very popular. Although students can take Macroeconomics without taking Microeconomics, the popularity is not high enough without Microeconomics class. The Table 2 shows payos for both publishers. (d) What is the best response of McGraw Hall when Prentice Hill chooses Microeconomics? (e) Find all possible Nash equilibrium. Can we reach to (10,10) payo combination 1 Table 3: Repeated Game McGraw Hall Microeconomics Macroeconomics Microeconomics 10,10 8,8 Prentice Hill Macroeconomics 8,8 8,8 at the equilibria? (f) Does Prentice Hill have a dominant strategy? If yes, what is a dominant strategy for Prentice Hill? Does McGraw Hall have a dominant strategy? If yes, what is a dominant strategy for McGraw Hall? Now, the publishers take this game every year. That is, they have a repeated game. Consider the Table 3. (g) What is the best response of McGraw Hall when Prentice Hill chooses Microeconomics? (h) Find all possible Nash equilibrium. Can we reach to (10,10) payo combination at the equilibria? (i) Does Prentice Hill have a dominant strategy? yes, If what is a dominant strategy for Prentice Hill? Does McGraw Hall have a dominant strategy? If yes, what is a dominant strategy for McGraw Hall? Question 2 Apple decides the price of iPhone. Apples possible choice is a high price or a low price. If Apple makes a high price, then Apple can get a high prot, but it may attract Samsungs entry in the smart phone market. If Apple makes a low price, it can deter Samsungs entry, although it gives a low prot to Apple. Consider the Figure 1. Each branch represents each players actions. And upper number of payo implies Apples prot and lower number of payo implies Samsungs prot. (a) List the actions and strategies of Samsung. (b) What is the best response of Samsung when Apple takes \$400? (c) Find all possible (subgame perfect) Nash equilibrium. A Nash equilibrium is written like (Apples strategy, Samsungs strategy). (d) Samsung announced that they will enter the market, regardless of Apples pricing policy. An economist argued that this is a just empty threat. Explain why the 2 Figure 1: Entry Deterrence Game APPLE \$600 \$400 SAMSUNG Enter 20M 20M SAMSUNG Not 40M 0M Enter Not 10M -10M 30M 0M economist can argue like that. Question 3 Jacob dug wells and began to sell water. In the neighborhood, Jacob was the only seller. Jacobs marginal cost function is M C = 5 + 0.01Q. The inverse demand function of the neighborhood is P = 10 0.02Q. Then, the total revenue of Jacob is T R = P Q = (10 0.02Q)Q = 10Q 0.02Q2 . The marginal revenue curve is M R = T R (Q) = 10 0.04Q. (a) Draw the demand curve, the marginal cost curve, and the marginal revenue curve in (Q, P ) plane. (b) Calculate the prot maximizing Q, denoting Q . (c) At Q , calculate the equilibrium price, denoting P . (d) What is the consumer surplus and producer surplus? (e) Assume that this market is perfectly competitive and the total supply function is same with Jacobs marginal cost function. Then, what is the equilibrium quantity, denoting QP and the equilibrium price, denoting P P ? (f) Calculate the consumer and producer surplus at the perfectly competitive market. 3 (g) Calculate the deadweight loss induced by the monopolist, Jacob. 4
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