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, C as functions of u. [05 pts] 2. Assume the consumer is willing to maximize the lifetime utility function, LU=In(Co) + In(C) 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]