請問若題目的需求函數是general form 該怎麼解啊 ? - 經濟

學校:NTU

教師:黃鴻

科目:貿易政策

題目:

Assume　there are two firms- Home and Foreign, producing a homogeneous product

and exporting all their outputs to a third country. The marginal costs of the

Home and Foreign firms are respectively c and c* and their outputs q and q*.

Moreover, the demand for the product in the third country is: P=a-bQ

where P is the price and Q is the output defined as q+q*.

Use the above setting to answer the following questions.

1. If the two firms play Cournot, derive the equilibrium price and

the outputs of the two firms.

2.3.4.略

5.Instead of the linear demand, let us assume the demand to be implicit

and take the following form: P=f(q+q*). Ditto 1-4.

我的想法:

要求Cournot解是兩個reflection function解聯立方程式

第一題的home firm的 reflection function

home firm的利潤π=Pq-cq
=f(q+q*)q-cq

foreign firm的利潤π*=Pq*-c*q*
=f(q+q*)q*-c*q*

Max π and π*

一階條件 π對q偏微分 = f(q+q*)+f'(q+q*)q-c = o
π*對q*偏微分 = f(q+q*)+f'(q+q*)q*-c = o

二階條件 結果很怪 無法判斷 是否小於零

暫時不理會二階條件
c - f(q+q*)
reflection function RF(q*) = q =-------------
f'(q+q*)

c*- f(q+q*)
RF*(q) = q*=-------------
f'(q+q*)

應該不是這樣吧? 這樣無法解聯立
求不出equilibrium output and price啊......@@

希望有好心人能給我些提示 謝謝!!

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