Bonus question Competition à la Cournot with homogenous goods and asymmetric incomplete information. Consider a duopoly that competes à la Cournot (choosing quantities simultane- ously), facing inverse demand function p(Q) = a – Q where Q = q1 + q2, where the cost function for firm 1 is c1(41) = cqı with c > 0 which is common knowledge for both firms. The cost function for firm 2 is not common knowledge and can be c2(92) = CH92 with probability 0 € (0,1) or c2(92) = CL92 with probability 1 – 0, where cL < CH. The notation cL means low cost and cH means high cost. Firm 2 can be a new entrant to the industry, or could have just invented a new technology. Firm 2 knows its marginal cost which means it has private information since it know if it is cz or CH. Firm 1 on the other hand does not know the marginal cost of firm 2 (we don't either) and therefore it has less information than firm 2 and therefore constitutes asymmetric information. Firm 2 may want to choose a different (presumably lower) quantity if its marginal cost is high than if it is low. Firm 1, for its part, should anticipate that firm 2 may tailor its quantity to ist cost in this way. Find the best response of firm 2 to any quantity q1 that firm 1 chooses when it has marginal a. cost cí and cL. (Hint: maximize profits for firm 2 separately when marginal cost is cH and when it is cL)
Bonus question Competition à la Cournot with homogenous goods and asymmetric incomplete information. Consider a duopoly that competes à la Cournot (choosing quantities simultane- ously), facing inverse demand function p(Q) = a – Q where Q = q1 + q2, where the cost function for firm 1 is c1(41) = cqı with c > 0 which is common knowledge for both firms. The cost function for firm 2 is not common knowledge and can be c2(92) = CH92 with probability 0 € (0,1) or c2(92) = CL92 with probability 1 – 0, where cL < CH. The notation cL means low cost and cH means high cost. Firm 2 can be a new entrant to the industry, or could have just invented a new technology. Firm 2 knows its marginal cost which means it has private information since it know if it is cz or CH. Firm 1 on the other hand does not know the marginal cost of firm 2 (we don't either) and therefore it has less information than firm 2 and therefore constitutes asymmetric information. Firm 2 may want to choose a different (presumably lower) quantity if its marginal cost is high than if it is low. Firm 1, for its part, should anticipate that firm 2 may tailor its quantity to ist cost in this way. Find the best response of firm 2 to any quantity q1 that firm 1 chooses when it has marginal a. cost cí and cL. (Hint: maximize profits for firm 2 separately when marginal cost is cH and when it is cL)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter12: Price And Output Determination: Oligopoly
Section: Chapter Questions
Problem 2E
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