Using production function and MPK diagrams, answer the following questions. For simplicity, assume there are two countries: a poor country (with low living standards) and a rich country (with high living standards).

a. Assuming that poor and rich countries have the same production function, illustrate how the poor country will converge with the rich country. Describe how this mechanism works.

b. In the data, countries with low living standards have capital-to-worker ratios that are too high to be consistent with the model used in (a). Describe and illustrate how we can modify the model used in (a) to be consistent with the data.

c. Given your assumptions from (b), what does this suggest about the ability of poor countries to converge with rich countries? What do we expect to happen to the gap between rich and poor countries over time? Explain. Using the model from (b), explain and illustrate how convergence works in the following cases.

d. The poor country has a marginal product of capital that is higher than that of the rich country.

e. The marginal products in each country are equal. Then, the poor country experiences an increase in human capital through government funding of education.

f. The marginal products in each country are equal. Then, the poor country experiences political instability such that investors require a risk premium to invest in the poor country.