[考試] 產經的問題

看板Economics (經濟學)作者miaolicity (.....)時間19年前 (2007/05/01 18:53)推噓0(0推 0噓 0→)

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來源: 期中考題目科目:產經問題: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: 假設是stackelberg價格競爭，followers是價格接受者，所以先求出在P=MC的情況下的followers的反應函數。 P=MC=0.5q →q=2P 設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) 請問這樣的邏輯正確嗎？不正確的話要如何解這一題？謝謝！！ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.217.94.252