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 Ht the human capital accumulated in period t, and by u the time spent working in period t. Assume the initial human capital is H0 = 3.

1. Compute C0, C1 as functions of u. [05 pts]
2. Assume the consumer is willing to maximize the lifetime utility function,

LU = ln(C0) + ln(C1)/ 1+r

where r = 0.1 is the real interest rate. Give the optimal value of u? [10 pts]

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]