Suppose there are two countries. In the rich country, the representative consumer has Hr units of human capital and total factor productivity is z_r. In the poor country, the representative consumer has Hp units of human capital and total factor productivity is zp. Assume that b and u are the same in the rich and poor countries, that H_r > H_p, and that z_r > z_p.

a. How do the levels of income per capita, the growth rates of income per capita, and real wages compare between the rich and poor countries?

b. If consumers could choose their country of residence, where would they want to live?

c. If each country could determine immigration policy, what should they do to maximize the welfare of the current residents? 

d. What is the immigration policy that maximizes the welfare of the citizens of both countries?

e. Explain your results. Do you think this is a good model for analyzing the effects of immigration? Why or why not?