產經的問題 - 經濟

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！！

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