Consider a two-period, small open economy populated by identical households with preferences given by

lnC1 +lnC2,

where C1 and C2 denote consumption in periods 1 and 2, respectively. Households are endowed with Q1 = 5 units of goods in period 1 and Q2 = 10 units in period 2. In period 1, households can borrow or lend at the interest rate i. Let D1 denote the amount of debt of the household in period 1. Assume that the initial level of debt is zero, D0 = 0. The world interest rate, denoted i, is 10 percent.

1. Calculate the equilibrium current account in period1 under free capital mobility.

2. Now assume that the government introduces capital controls in period 1. Specifically, the government charges foreign lenders a proportional tax on the amount of debt extended to domestic residents. So foreign lenders pay D1 to the government in period 1. Suppose that the tax rate is 10 percent. In period 1, the government transfers all of these revenues to households via a lump-sum transfer denoted T . The government does not intervene in the economy in period 2.

1. (a) Calculate the interest rate differential.

2. (b) Calculate the equilibrium current account balance in period 1. Compare this situation to what happens under free capital mo- bility and provide intuition.

3. (c) Suppose now that instead of setting it at 10 percent, the gov- ernment sets to a level consistent with a 50 percent reduction in the current account relative to the level prevailing under free capital mobility (i.e., when = 0). Calculate the equilibrium capital control tax rate. Calculate the new interest rate differen- tial. Discuss your results.