The world comprises two countries, A and B. There is only one good, whose price is normalized

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Question:

The world comprises two countries, A and B. There is only one good, whose price is normalized to 1; hence nominal and real measures coincide. These two countries differ with respect to their production technology. In particular, MPK_A = 10 - 0.8K_A and MPK_B = 7 - 0.7K_B , where MPK_i denotes the marginal product of capital and K_i the capital stock in country i = ?, ?.The total capital stock in the world is 10 units.

a) The initial allocation of capital is K_A=5 and K_B=5. Find each country’s total income as well as labor and capital income. What is the world income?

b) Next, consider the case where there is free capital mobility. Find the capital allocation between the two countries, each country’s total income, as well as labor and capital income. What happens to world income? Explain your answers.

c) Assume now that, succumbing to domestic pressure, the government of country A imposes a 30% tax on capital income. Show graphically the equilibria before and after taxation. Find the new capital allocation between the two countries, total income, tax revenue, as well as labor and net capital income in each country. Explain your answers.

Note: Round your answers to the second decimal point.