[商管] [經濟] 效用函數
效用函數為U(X,Y)=X^a+Y^b a,b>=0
1)
preferences are quasilinear and convex, and x is a normal good
Ans:
a=1,0<b<1 不知b=1,0<a<1能嗎? 因為只要a大於0 MUx>0 X就為正常財
2)
preferences are homothetic and convex
因homothetic故a=b
MRSxy = (x/y)^(a-1) -> dy/dx=-(x/y)^(a-1)
dMRSxy/dx = (a-1)(x/y)^(a-2)[(y-x(-x/y)^(a-1))/y^2] < 0
由上知0<a<1 -> 0<a=b<1 這是我的解法 答案跟題庫一樣
但不知算法是否正確
很抱歉式子可能有點難看...感謝
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 125.230.28.53
推
07/08 00:41, , 1F
07/08 00:41, 1F
→
07/08 00:42, , 2F
07/08 00:42, 2F
→
07/08 00:45, , 3F
07/08 00:45, 3F
推
07/08 00:46, , 4F
07/08 00:46, 4F
→
07/08 23:25, , 5F
07/08 23:25, 5F