are100b-hwk2

are100b-hwk2 - ARE[0 Spring 2008 M.Whitney Intermediate...

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Unformatted text preview: ARE [0% Spring 2008 ' M.Whitney Intermediate Microeconomic Theory Homework 2 Due Thursday, Ma} 81'”, at start of class 1. (18) Suppose each firm in an industry has the following cost function: TCr= f +g*qj “1*ch where f, g and h are positive constants. a. In terms of f, g, and h, what quantity minimizes average total cost? (Hint: take the derivative of ATC) b. Under perfect competition in the long run, marginal cost equals average total cost. Explain why this is true. Now solve for long-run firm output, qi *, in terms of f, g, and h. How does your answer compare to the answer in part a? c. Now let each firm’s cost function be TCi= 40,000 + 100"'qi + qi 2 Under competition in the long run, how much will each firm produce, and at what price? If market demand for this good is Qd = 3000 - 2P, how many units are sold, and what is the long—run equilibrium number of firms? What is consumer surplus in this market? And what is the profit or loss per firm? d. Suppose that the firms’ cost functions and market demand are the same as in part c, and the number of firms is equal to that in part c. However, the firms are monopolistically competitive. Find each firm’s optimal output; market price and quantity; marginal cost and average cost per unit, and consumer surplus. What is the profit or loss per firm? Will additional firms enter or exit this market? 2. (l6) Demand for home theater systems is Q = 1800 - P. The two firms that produce these systems have the following cost functions: Tc,= 100,000 + 300*ql + .5 ql 2 TC2 = 50,000 + 200*q2 + q2 2 For each market structure below, find (i) output of each firm; (ii) market quantity; (iii) market price; (iv) profit for each firm; (v) producer surplus and consumer surplus. (Hint: remember producer surplus for an industry equals total industry profits, plus fixed costs) a). The firms are Coumot oligopolists b) The firms are Bertrand oligopolists. c) Firm 1 is a Stackelberg leader, and Firm 2 is a follower. d) The two firms form a cartel. 3. (4) Four identical Coumot oligopolists each have total cost functions of : TCi = 30 + 5*qi + .1in Inverse market demand for their product is: P = 100 - 2Q a. What quantity should each firm produce? What is the market quantity and price? What is each firm's profit or loss? b. The managers of these firms collude to form a cartel. Now, what is the equilibrium market quantity? What is the equilibrium price? How much is sold by each firm, and what is each firm's profit or loss? 4. (4) Collegetown Hardware and Big Barn Supply are two rival home improvement stores. Each is considering expanding by additing one or two new stores to the existing locations. The expected impact on profits of these proposals are shown below. — m- m a. Does either player have a dominant strategy? Why or why not? b. If each store adopts a maximin approach, what strategy will it choose first? What are the payoffs? Is this solution a Nash equilibrium? If not, what will happen next? c. If the 2 stores cooperated, what strategy would be optimal? Is this a Nash equilibrium point? 5.(4) The payoff matrix belowshows outcomes for a zero-sum game: If each store adopts a maximin approach, what strategy will it choose first? What are the payoffs? Is this solution a Nash equilibrium? If not, what will happen next? 6. (4) Three oligopolists produce breakfast cereal. Each is considering whether to introduce a new “healthy” cereal, or a “sweet” cereal. The a 011' matrix below shows the 0 c ssible outcomes of their decisions: a. If each firm adopts a maximin approach, what strategy will it choose first, and what are the payoffs? Is this outcome 3 Nash equilibrium? b. What set of strategies would provide the best cooperative outcome for the industry? Is this solution a Nash I equilibrium? ...
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This note was uploaded on 05/03/2008 for the course ARE 100B taught by Professor Whitney during the Spring '08 term at UC Davis.

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are100b-hwk2 - ARE[0 Spring 2008 M.Whitney Intermediate...

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