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PS11(09)

# PS11(09) - ECN 712 Fall 2009 Problem Set XI Due 24 November...

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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 pure-strategy Nash equilibrium of this game. Argue that all pure-strategy 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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PS11(09) - ECN 712 Fall 2009 Problem Set XI Due 24 November...

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