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 = 2.25. The total productivity factor is given by z = 1.5 in period 0 and z = 0.75 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 = 1.5.

1. Compute C0, C1 as functions of u.

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?

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.