Consider the human capital growth model with the representative consumer who lives in two periods (0,...

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Consider the human capital growth model with the representative consumer who lives in two periods (0, 1). The efficiency parameter of human capital accumulation technology is b=4.5. The total productivity factor is given by z = 3 in period 0 and z = 1.5 in period 1. Denote by H, the human capital accumulated in period t, and by u the time spent working in period t. Assume the initial human capital is Ho = 3. 1. Compute Co, C₁ as functions of u. [05 pts] 2. Assume the consumer is willing to maximize the lifetime utility function, LU=In(Co) + In(C₁) 1+r where r = 0.1 is the real interest rate. Give the optimal value of u? [10 pts] Remark: You are NOT allowed to use an online solver when answering this question. 3. Assume some massive investment in the education system made by the government increases b to 5. How will this policy affect the optimal u of the consumer? Quantify the implication of this policy for the long-term consumption growth. [05pts] Consider the human capital growth model with the representative consumer who lives in two periods (0, 1). The efficiency parameter of human capital accumulation technology is b=4.5. The total productivity factor is given by z = 3 in period 0 and z = 1.5 in period 1. Denote by H, the human capital accumulated in period t, and by u the time spent working in period t. Assume the initial human capital is Ho = 3. 1. Compute Co, C₁ as functions of u. [05 pts] 2. Assume the consumer is willing to maximize the lifetime utility function, LU=In(Co) + In(C₁) 1+r where r = 0.1 is the real interest rate. Give the optimal value of u? [10 pts] Remark: You are NOT allowed to use an online solver when answering this question. 3. Assume some massive investment in the education system made by the government increases b to 5. How will this policy affect the optimal u of the consumer? Quantify the implication of this policy for the long-term consumption growth. [05pts]

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Using the human capital growth model the consumption in each period is given by Co zH0b u1b C1 zH1b u1b Substituting the given values we get Co 3345 u... View the full answer