x_1^*=0 means you don't wanna consume x_1. So the marginal utility U_1(x_1,x _2)|x^* \leq p_1. Now the problem becomes choosing x_2^*, given x_1^* is zero. The lagrange function is U(0,x_2)+\lambda*(M-p_2*x_2) F.O.C L_2=U_2(0,x_2)|x^*-p_2=0 L=M-p_2*x_2 \leq 0 As U_2(0,x_2^*)=p_2>0, the more x_2 the better. You will spend all your money, so L=0. Of course, you can argue that the shadow price \lambda is positive to get L=0.
H*3
9 楼
严格说这个还不能算lawyer吧。lawyer必须已经pass the bar exam & admitted.
N*r
10 楼
Conan
x*8
11 楼
十分感谢!
,x
【在 w****r 的大作中提到】 : x_1^*=0 means you don't wanna consume x_1. So the marginal utility U_1(x_1,x : _2)|x^* \leq p_1. : Now the problem becomes choosing x_2^*, given x_1^* is zero. : The lagrange function is : U(0,x_2)+\lambda*(M-p_2*x_2) : F.O.C : L_2=U_2(0,x_2)|x^*-p_2=0 : L=M-p_2*x_2 \leq 0 : As U_2(0,x_2^*)=p_2>0, the more x_2 the better. You will spend all your : money, so L=0. Of course, you can argue that the shadow price \lambda is