homework5F2011 - Econ3014 Fall 2011 Instructor Yan YU...

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Econ3014 Fall, 2011 Instructor: Yan YU Problem Set #5 (due Nov. 24 th Thursday 5pm in room 2394) 1. (8. 7) Compute the Nash equilibrium in randomized strategy for the following game. Bob Left Right Top (3, 6) (4, 5) Ann Bottom (6, 4) (2, 6) 2. (7.2, 6.1, 8.4) Consider a duopolistic market with two firms, A and B, facing a market demand curve of P=122-q A –q B for the same product. Assume that each firm has access to the same technology and the cost of production is C A =2q A for firm A and C B =2q B for firm B. (1) How many units does each firm produce in the Nash equilibrium (this is Cournot model)? What is each firm’s profit? (2) If the two firms form a cartel and restrict supply to maximize joint profit, what is the optimal output level for each firm if they split the product equally? What is each firm’s profit? (3) Denote the optimal output level in part (2) Q 0 . Suppose firm A follows the quota Q 0 , what is firm B’s strategy (in terms of output level) to maximize his own
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