作者reluctant (reluctant)
看板EconStudy
标题Re: [问题]算消费者均衡的问题
时间Thu Jan 13 21:32:15 2011
※ 引述《suxxx (无聊新鲜人)》之铭言：
: 效用涵数为U(X，Y)=X平方+Y平方，Px=10 Py=20 M=1000 求消费者均衡?
: 要用Lagrange求 我真的不会 请各位帮帮忙
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
预算限制式为：
B = Px*X + Py*Y -M = 0
所以Lagrange式为：
L(X,Y,Lampda) = U + Lampda*B
对X微分：dL/dX = 0.5X^-0.5 + Lampda*Px = 0
对Y微分：dL/dY = 0.5X^-0.5 + Lampda*Py = 0
对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
把题目给你的东西带进去，
Lampda = (3/80000)^0.5
X = 200/3
Y = 50/3
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◆ From: 61.228.41.88
1F：推 alianlin:U不是等於X平方+Y平方吗? 01/21 19:57
2F：→ reluctant:对喔....我好像搞错了XD 01/21 23:00
3F：推 joseph1124:x与y的数量为2:1的关系，这样就？ 01/21 23:46
4F：推 joseph1124:不满足凸性假设,还可以用L解吗? 01/25 22:22
5F：推 IamMaster:此题角解X=100 U=10000 01/30 22:58