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Question 1: Consider a two-period two-country endowment economy. Households have preferences described by the utility function ln CU1 + ln CU2 where CU1 and CU2 denote the consumption in period 1 and period 2. Suppose that households receive exogenous endowments of goods given by QU1 =10, QU2 = 15 in periods 1 and 2, respectively. Europeans have identical preferences, given by ln CE1 + ln CE2 where CE1 and CE2 denote the consumption in period 1 and period 2. Suppose that households receive exogenous endowments of goods given by QE1 =10, QE2 = 15 in periods 1 and 2, respectively. Assume further that the endowments are nonstorable, that the U.S. and Europe are of equal size, and that there is free capital mobility between the two economies. The United States starts period 1 with a zero net foreign asset position.
1. Compute the equilibrium levels of world interest rate, consumption, the trade balance, and the current account in periods 1 and 2 in the U.S.
2. Suppose that a contraction originates in the United States. The U.S. endowment falls from 10 to 8 in the first period and is expected to continue to fall to 6 in the second period. The endowments in Europe remain unchanged each period. Calculate again the equilibrium interest rate and current accounts in the U.S. and Europe in period 1.
3. Now instead suppose that the Europe experience a favorable shock that temporarily increases the Europe endowment from 10 to 15 in the first period. The second period is still 15. There is no change in the U.S. endowment (QU1 =10, QU2 = 15). Calculate again the equilibrium interest rate and the two current accounts in period 1.
4. Show on a current account-world interest rate plot qualitatively how a domestic shock can increase the current deficit for the U.S. How a external shock can increase the current account deficit for the U.S.. Point out the difference in the equilibrium world interest rates.
Question 2: Consider a two-period consumption-savings model, augmented with a government sector. Each consumer has preferences described by the utility function:
u(c1, c2)= lnc1 + lnc2
where c1 is consumption in period one, and c2 is consumption in period two.
Suppose that both households and the government start with zero initial assets (i.e., a =0 and b =0), and that the real interest rate is always 10 percent. Assume that government purchases in the first period are one (g1 = 9) and in the second period are 1 (g2 = 11). Finally, the real incomes of the consumer in the two periods are y1 = 20 and y2 =33.
1. In the first period, the government levies lump-sum taxes of 6 (t1 = 6). What are lump-sum taxes in period two (t2), given the above information? Compute the consumption and national savings in period one.
2. Consider in the first period the tax is reduced from 6 to 5 unit, with government purchases left unchanged. Will the consumption, national saving, and current account in period one change? Does this result satisfy the Ricardian equivalence or not?
3. Suppose that in period 1 the government increases spending from 9 to 10 units of goods. What is the effect of this policy change on the optimal consumption, fiscal balance, national saving, and current account in period 1?
Question 3. Consider a two-period small open economy model. There is no government. The households receive endowment in both periods. The world interest rate is r*.
1. Draw the optimal consumption decision for the two periods from the households’ problem. Please draw the case where the households are borrowing in the first period. Carefully label the slope and endowment point on the budget constraint line, mark the optimal consumption and the amount of borrowing in the first period.
2. Now suppose there is capital control so no borrowing is allowed. Please show the consumption decision for the households. How does the capital control affect the country’s welfare?
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