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. ([02.00 pts]) Assume there are only two periods and the consumer is willing to maximize his utility function, F(u) = C0 + ln(C1)/1 + r

2.Find the optimal value of u.

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 is your estimate of b?

4. After how many years will the consumption double?

5. Quantity the implication of a 10% increase in z on the long term consumption growth rate.