Question: Consider an economy with total population of 200. Let these 200 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. Each person devotes u = 0.9 units of time to working in each period.

iv. Suppose that b is equal to 14 and 12 for the rich and poor respectively.

v. In the economy, output is produced using the efficiency units of labor. That is output in period t is given by Y_t = zu (100 R_t + 100P_t), 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 average labor income in period 0?

b. What is economy-wide human capital growth rate between periods 0 and 1?

c. 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.