台大經研99碩班考題 - 經濟

來源:99年台大經研個經

科目:個經

問題:
A worker has the utility function U=(1-L)^(2/3) * (X-2)^(1/3)
where L is work measured as the proportion of total available time and X is
a basket of consumption goods.
The worker receives a wage w and receives non-labour income 2.5
Suppose the worker wishes to supply a positive amount of labour if
and only if w>w*

(A)w*=0
(B)0<w*<=0.6
(C) 0.6<w*<=1.2
(D)w*>=1.2


我的想法:
先把U改成(z)^(2/3) * (Y)^(1/3)
z=1-L即休閒；Y=X-2
原限制式為a+w=wz+X => 2.5+w=wz+Y+2
MRS(z,Y)=2Y/z=w 把wz以Y換掉帶入限制式首先得到Y=(1/3)w+1/6
再得到z=2/3+1/(3w)
題目要求正的勞到供給
因此1>z>0
求出的答案卻非常怪...
且完全沒跟答案選項契合的地方...


懇請指點迷津








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