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！！
--
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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