来源: 期中考题目 科目:产经 问题:the stackelberg model may be extended to an industry with more than two firms. assume that the industry has one firm that is the leader and n-1 firms that are follower firms. assume further that the followers are so numerous that they act as competitors producing where price equals marginal cost. now consider the following specific case. industry demand is P=100-0.5Q, where Q is total industry output equal to the sum of the output of the leader firm, qL,and the combined output of the followers,(n-1)qF. marginal cost at each firm is given by MC=0.5q. again,follower firms always produce where marginal cost equals the industry price. a. calculate the leader firm's optimal output strategy taking into account the response of the follower firms. what is the industry price? does the leader's optimal output rise or fall as the number of followers increases? b. what happens to industry output and industry price as the number of follower firms increases? 我的想法: 假设是stackelberg价格竞争，followers是价格接受者，所以先求出在P=MC的 情况下的followers的反应函数。 P=MC=0.5q →q=2P 设q1=Σqf=2(n-1)P qL=Q-2(n-1)P =200-2nP ΠL=P*qL-TC =P*(200-2nP)-TC dΠL/dP=200-4nP-P=0 P=200/(4n+1) qL=200-(400n/(4n+1)) q1=(400(n-1))/(4n+1) qF=400/(4n+1) 请问这样的逻辑正确吗？ 不正确的话要如何解这一题？ 谢谢！！ --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 61.217.94.252