1.u = R^{\frac{1}{3}}C^{\frac{2}{3}} , T = 1000(零用錢) , 一天有24小時 

    請問勞動供給Ls = ?

2.u^A = R^{\frac{1}{3}}C^{\frac{2}{3}}

   u^B = R^{\frac{1}{2}}C^{\frac{1}{2}}

   \omega = [150,200]

   請問契約線函數 = ?

3. 同2.但是WA = [50,100] , WB = [100,100]

    求均衡{\frac{P_1}{P_2}} = ?

ANS:

1.R = {\frac{{\frac{1}{3}}(24W+1000)}{W}}

      = 8 + {\frac{1000}{3W}}

    L = 24 - 8 - {\frac{1000}{3W}}

       = 16 - {\frac{1000}{3W}}

2.MRS_{12}^A = {\frac{\frac{1}{3}}{\frac{2}{3}}}{\frac{X_2^A}{X_1^A}}={\frac{1}{2}}{\frac{X_2^A}{X_1^A}}

   MRS_{12}^B = {\frac{\frac{1}{2}}{\frac{1}{2}}}{\frac{X_2^B}{X_1^B}}={\frac{200-{X_2^A}}{150-{X_1^B}}}

   {\frac{1}{2}}{\frac{X_2^A}{X_1^A}}={\frac{200-{X_2^A}}{150-{X_1^B}}}

    X_2^A(150-X_1^A) = 2X_1^A(200-X_2^A)

    150X_2^A - X_1^A X_2^A = 400 X_1^A - 2 X_1^A X_2^A

   X_2 = {\frac{400X_1}{150 + X_1}}

3.  X_1^A = {\frac{{\frac{1}{3}}(50P_1+100P_2)}{P_1}}

    X_1^B = {\frac{{\frac{1}{2}}(100P_1+100P_2)}{P_1}}

    X_1 = X_1^A+X_1^B = ({\frac{50}{3}}+{\frac{100}{2}})+({\frac{100}{3}}+{\frac{100}{2}}){\frac{P_2}{P_1}}=150

   {\frac{400}{6}}+{\frac{500}{6}}{\frac{P_2}{P_1}} = {\frac{900}{6}}

    {\frac{P_2}{P_1}} = 1
開始日期: 2008年 12月 15日(一.) 09:10
截止日期: 2008年 12月 15日(一.) 09:30