ps11_09 - Cornell University Economics 3130 Problem Set 11...

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Cornell University Economics 3130 Problem Set 11 Due 5/1/09 1. In a given market, there are two firms i = { 1 , 2 } that face the demand curve Q D = 16 - p for p 16 and Q D = 0 for p > 16. As usual, Q D is the aggregate quantity demanded. The firms have no fixed cost. Each has a marginal cost of production of c i > 0. The firms compete by simultaneously choosing an amount of (identical) goods x i to produce (fractions are allowed), and the amount each produces must be less than or equal to some high number ¯ x . For parts (a)-(e), assume that c 1 = c 2 = 4. (a) What is the cost function for firm i ? (b) What are the possible actions for firm i ? (c) What is firm i ’s best response function? (d) Which actions for firm i are strictly dominated? Can this game be solved through iterated elimination of strictly dominated strategies/actions. If so, solve it. If not, explain why not. (e) What are the pure strategy Nash equilibria? What are the profits of each firm in each equilibrium?
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