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Unformatted text preview: ECN 712 Fall 2009 Problem Set XI, Due 24 November 1. MWG, Exercise 10.C.3. (The Herfindahl index is often used to measure market concentra tion.) 2. Consider a Bertrand duopoly game with identical goods. Firm i s cost function given by c i ( q i ) = kq i + F if q i > 0 and c i (0) = 0 for i = 1 , 2, where ( k,F ) 0. The market inverse demand p ( · ) is strictly decreasing and crosses each firm’s average cost function exactly twice (so a monopolist in this market would earn positive profit). Let ˆ q denote largest output for which p ( q ) = k + F/q , and let ˆ p = p (ˆ q ). The rules are similiar to the Bertrand game discussed in the lecture: if the firms set different prices, the firm with the lowest price gets the entire market demand; but if they name the same price, then one firm is picked at random to serve the entire market demand. (a) Identify one purestrategy Nash equilibrium of this game. Argue that all purestrategy Nash equilibria yield the same social welfare. (b) Suppose a planner wants to maximize welfare, subject to the constraint that any active firms make nonnegative profit. The planner can control the output of each firm, butfirms make nonnegative profit....
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 Spring '10
 schlee
 Microeconomics, Game Theory, SPNE

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