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November 16th, 2014, 08:08 AM  #1 
Newbie Joined: Oct 2014 From: Korea Posts: 4 Thanks: 0  Oligopoly problems
Please do help me with these. Thanks. Problem 1: Consider an industry with two firms. Let q1 be the output of rm 1, q2 for firm 2, and Q = q1 + q2. Consumer demand in the industry is PD(Q) = 40  Q. Each firms has a cost function of c(q1) = 3q1 and c(q2) = 5q2, respectively. Assume that firms engage in Stackelberg competition. Firm 1 is the Stackelberg leader, which first sets q1. After seeing firm 1's output, firm 2 sets q2. (1) Find the equilibrium quantity of each rm, the market price, and the profits for both firms. Now, assume that the firms compete in a Cournot fashion. (2) Find the output of each firm and the market price at the equilibrium. (3) Do consumers prefer Cournot competition or Stackelber competition? (4) Compare the social welfare of the market outcomes in Cournot and Stackelberg competitions. Problem 2. Consider a market with demand Q = 256/p2 (squared p). To enter the market a firm must first pay an entry cost ,k, thereafter it can produce at a constant marginal cost of 2 with no other fixed costs. (1) If a government grants a firm an exclusive monopoly in this market, how low must be for the potential monopolistic firm to enter the market? (2) If instead there are two identical potential entrants who will engage in Cournot competition after they both enter, how low must k be for both of them to enter the market? 

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