Answer the following questions

Consider the human capital growth model with the representative consumer. The efficiency pa- rameter of human capital accumulation technology is b. The total productivity factor is given by z = 1. Denote by H, the human capital accumulated in period t, and by u the time spent working in period t. Assume the initial human capital is Ho = 1. 1. Compute the consumer consumption Cf 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 func- tion, F(u) = Co+ In(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])