假定消费者的效用函数为U=x1^3/8+

假定消费者的效用函数为U=x1^3/8+

首先这是柯布-道格拉斯类型的效用函数题目中应该是这样的x代表1的数量,y...2...我给你一个公式推导U=(x^α)·(y^β)α+β=1要满足消费者要用最大化有(1)MUx/MUy=Px/Py(2)Px·X+Py·Y=MMUx=aU/aX=αX^(α-1)YMUy=aU/a...

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 = 250100 = 10k

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