Consider two countries, A and B. In the last 30 years, the average annual growth rate of the real per capita GDP of country A is 1.5% and country B is 2.0 %. In the current year, the real per capita GDP of country A is $10,000, and the real per capita GDP of country B is $X. Based on the current real per capita GDP of the two countries and the average annual growth rate of the real per capita GDP of the two countries in the last 30 years, we find that 25 years from now, the two countries will have the same real per capita GDP.

a) Solve for the real per capita GDP of country B in the current year, $X.

b) According to the rule of 70, how many years will it take for country A to double its per capita real GDP?

c) Suppose that the production function of country A satisfies the assumption that the marginal product of capital is positive but diminishing and that the growth of the real per capita GDP in country A is driven purely by capital accumulation. Then, would your answer in (b) tend to over-estimate or under-estimate the length of time that it takes the country to double its real per capita GDP? Explain.