寡占市場的問題...(急) - 經濟

※ 引述《SsimpleLlove ( ilobimd)》之銘言：
: 下下禮拜要參加研究所考試了，這邊有一個問題困擾我
: 懇請各位能幫幫我。。。
: －－－－－－－－－－－－－－－－－－－－－－－－－－
: Two firms compete by choosing price. their demand functions are
: Q1=20-P1+P2 and Q2=20+P1-P2
: where P1 and P2 are the price charged by each firm respectively and
: Q1 and Q2 are the resulting demands. Note that the demand for each good
: depends only on the difference in price; if the two firms
: colluded and set the same price, they could make that price as
: high as they want, and earn infinite profits. Marginal costs are zero.
: 1. Suppose the two firms set their prices at the same time. Find the
: resulting Nash equilibrium. What price will each firm charge,
: how much will it sell, and what will its profit be?
: 2. Suppose Firm 1 sets its price first and then Firm 2 sets its price.
: What price will each firm charge, how much will it sell,
: and what will its profit be?
: 這是在講秦柏霖勾結是嗎??? 怎麼算啊????
這個都是在說Bertrand價格競爭

第一題有點類似Cournot競爭 第二題類似Stockelberg競爭

一樣都是先算兩家的利潤=TR-TC

然後再分別對兩家的利潤用P微分(第一家用P1 第二家用P2)

可以得到兩家的反應函數 類似P1=a+bP2這樣的函數

第一題是用兩個反應函數解聯立就可以得到

第二題因為說第一家先第二家後，所以第一家在做決策的時候要把第二家的決策

考慮進去，簡單說就是把第二家的反應函數P2=a+bP1帶進去第一家的利潤裡面的P2

然後對再對第一家的利潤用P1微分，就解出來了~

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