Re: [問題]算消費者均衡的問題

看板EconStudy作者reluctant (reluctant)時間13年前 (2011/01/13 21:32)推噓4(4推 0噓 1→)

留言5則, 4人參與討論串2/2 (看更多)

※ 引述《suxxx (無聊新鮮人)》之銘言： : 效用涵數為U(X，Y)=X平方+Y平方，Px=10 Py=20 M=1000 求消費者均衡? : 要用Lagrange求我真的不會請各位幫幫忙我今天就好人做到底吧平常不上B，一上就PO一堆文XD U = X^0.5 + Y^0.5 預算限制式為： B = Px*X + Py*Y -M = 0 所以Lagrange式為： L(X,Y,Lampda) = U + Lampda*B 對X微分：dL/dX = 0.5X^-0.5 + Lampda*Px = 0 對Y微分：dL/dY = 0.5X^-0.5 + Lampda*Py = 0 對Lampda微分：dL/dLampda = B = 0 所以 X = (2*Lampda*Px)^-2 Y = (2*Lampda*Py)^-2 Lampda = 0.5*(M^-0.5)*(Px^-1+Py^-1)^0.5 把題目給你的東西帶進去， Lampda = (3/80000)^0.5 X = 200/3 Y = 50/3 -- Nobody ever saw a dog make a fair and deliberate exchange of one bone for another with another dog. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.41.88

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alianlin

01/21 19:57, , 1^F

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reluctant

01/21 23:00, , 2^F

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joseph1124

01/21 23:46, , 3^F

01/21 23:46, 3^F