Consider a small open two-period economy populated by identical households with preferences given by InC₁ + InC₂ where C₁ and C₂ denote consumption in periods 1 and 2, respectively. Households are endowed with Q₁ 5units of goods in period 1 and 22 10 units in period 2. In period 1, households can borrow or lend at the interest rate r. Let D₁ denote the amount of debt of the household in period 1. Assume that the initial level of debt is zero, Do= 0. The world interest rate, denoted r, is 10 percent. - (a) Calculate the equilibrium current account in period 1 under free capital mobility. Now assume that the government introduces capital controls in period 1. Specifically, the government charges foreign lenders a proportional tax 7 on the amount of debt extended to domestic residents. So foreign lenders pay TD₁ 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. (b) Calculate the interest rate differential. (c) Calculate the equilibrium current account balance in period 1. Compare this situation to what happens under free capital mobility and provide intuition.