Answer following questions

Question 6 [20 pts] Consider the human capital growth model with the representative consumer who lives in two periods (0, 1}. The eiciency parameter of human capital accumulation technology is b = 4.5. The total productivity factor is given by z = 3 in period D and z = 1.5 in period 1. Denote by H; the human capital accumulated in period t, and by n the time spent working in period t. Assume the initial human capital is Ha = 3. 1. Compute Cu, 01 as functions of u. [05 pts] 2. Assume the consumer is willing to maximise the lifetime utility function, MCI) l +r where r = 0.1 is the real interest rate. Give the optimal value of n? [10 pts] Remark: You are NOT allowed to use an online solver when answering this question. LU = 111(qu + 3. Assume some massive investment in the education system made by the gwermnent increases b to 5. How will this policy a'ect the optimal u of the consumer? Quantify the implication of this policy for the long-term consumption growth. [05pm]