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.

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

Assume there are only two periods and the consumer is willing to maximize his utility function,

F(u) = C0 +(ln(C1)/1 + r)

where r = 0.1 is the real interest rate.

B. Find the optimal value of u.

C. Empirically, it has been observed that the annual growth rate of the country consumption per capita has been close to 2.5%. Taking this as granted, what is your estimate of b?

D. After how many years will the consumption double?

E. Quantify the implication of a 10% increase in z on the long-term consumption growth rate.