Consider the human capital growth model with the representative consumer. The efficiency parameter of human capital accumulation technology is b. The total productivity factor is given by z = 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.

1. Compute the consumer consumption Ct for periods 0 and 1 as a function of u.

2. Assume there are only two periods and the consumer is willing to maximize the discounted value of her consumptions over the two periods, C0 + C1 1 + r , where r = 0.05 is the real interest rate. Give the optimal value of u as a function of b ?

3. Empirically, it has been observed that the annual growth rate of the country consumption per capita has been close to 2.5% historically. Taking this as granted, what are your estimates of u and b.