Consider an economy with total population of 400. Let these 400 workers be equally divided between two groups: the rich and the poor. The poor have less human capital per person than the rich do.

I. Within each group, individuals do not differ by their skill level. Each individual in this economy accumulates human capital.

II. Each period, a person has one unit of time to split between work and human capital accumulation.

III. There is no savings in this economy

IV. Each person devotes u=0.8 units of time to working in each period.

V. Suppose that b is equal to 15 and 12 for the rich and poor respectively.

VI. In the economy, output is produced using the efficiency units of labor. That is output in period t is given by Yt=zu(200Rt+200Pt), where Rt and Pt are the human capital of a rich and poor person, respectively, at the beginning of period t. Let z=1, R0 =10 and P0 =5.

a) What is economy-wide human capital growth rate between periods 0 and 1?

b) What is economy-wide human capital growth rate between periods 1 and 2? Explain why in this economy the human capital growth rate could be different across time.

c) Argue that in this economy income inequality increases over time.