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 , where r = 0.1 is the real interest rate.

2. Find the optimal value of u. ([08 pts])

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? ([03 pts])

4. After how many years will the consumption double? ([03 pts])

5. Quantity the implication of a 10% increase in z on the long term consumption growth rate. ([04 pts])

Consider the human capital growth model with the representative consumer. The efciency pa- rameter 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 H 0 = l. 1. Compute the consumer consumption Ct for periods 0 and l as a function of H. ([02.00 pts]) Assume there are only two periods and the consumer is willing to maximize his utility func- tion, 111(01) 1 + 'r' ' F(u)=00+ where r = 0.1 is the real interest rate. . Find the optirnal value of u. ([08 pts]) . 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? ([03 pts]) . After how many years will the consumption double? ([03 pts]) . Quantity the implication of a 10% increase in 2 on the long term consumption growth rate. ([04 PtSD