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 C, 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) = Co + 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 2 on the long term consumption growth rate. ([04 pts])

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