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Unformatted text preview: Problem Set 6
Econ 115b November 6, 2007 1. Define (a) Oligopoly (b) Nash Equilibrium (c) Differentiated Products (d) Collusion 2. Explain why p = mc in the Bertrand model. 3. Consider a Cournot duopoly with firms that have differing marginal costs mc1 and mc2 . Show how the Cournot equilibrium would change if the marginal cost of firm 1 declined. 4. Consider a demand function for a differentiated duopolist of q1 = a - bp1 + dp2 , (1) where q1 is demand of firm one, p1 is price of firm 1, p2 is price of firm two and where a, b and d are constants. (a) If firm 1 raises price by a small amount, how much does it's revenue change (holding p2 fixed)? (b) If firm 1's marginal cost is constant at c1 , what is the reaction function of firm 1? (c) Suppose that the demand curve for firm 2 is q2 = a - bp2 + dp1 . Graph the Nash price equilibrium for the two firms. 1 ...
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