Question

经济学关于效用的题目.如下

一个消费者每月400元购买两类食品,如果他的效用函数为U(X,Y)=2XY，肉制品X平均每磅4元，豆制品平均每磅2元。求效用最大化的消费量X与Y。

Answer 1

max u(X,Y)
s.t. XPx + YPy = m
Lagrangian
L(X,Y,t) = u(X,Y) + t(m - XPx - YPy)
FONC
dL/dX = du/dX - tPx = MUx - tPx = 0
dL/dY = du/dY - tPy = MUy - tPy = 0
which implies
MUx/Px = MUy/Py = t, or MUx/MUy = Px/Py

MUx = 2Y, MUy = 2X
MRS = MUx/MUy = Y/X
Px/Py = 2
so we have
Y/X = 2, or Y = 2X
with the other linear restriction: 4X + 2Y = 400
X = 50, Y = 100
U_max = 2*50*100 = 10k

Answer 2

MUX=2Y
MUX=2X

MRS=Y/X
效用最大化条件 ：MRS=Py/Px

则,Y/X=1/2
且 4X+2Y=400

解出X=80,Y=40

追问

http://zhidao.baidu.com/question/273726547.html?quesup1#replyask-8457053
你和他做的为什么不一样?