Exercise 5.4 (An Open Economy With Investment) Consider a two- period model of a small open economy with a single good each period. Let preferences of the representative household be described by the utility func- tion In C1 + In C2, where C and C2 denote consumption in periods 1 and 2, respectively. In pe- riods 1 and 2, the household receives profits from the firms it owns, denoted II, and II2, respectively. Households and firms have access to financial mar- kets where they can borrow or lend at the interest rate ri. The production technologies in periods 1 and 2 are given by Q1 = A110 and Q2 = A211, where Q1 and Q2 denote output in periods 1 and 2, Io and I1 denote the capital stock in periods 1 and 2, A1 and A2 denote the productivity factors in periods 1 and 2, and a is a parameter. Assume that Io = 16, A1 = 3}, A2 = 3.2, and a = . At the beginning of period 1 households have B) = 8 bonds. The interest rate on bonds held from period 0 to period 1 is ro 0.25. In period 1, firms borrow the amount Df to purchase investment goods that become productive capital in period 2, 11. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is 20 percent. 1. Compute output and profits in period 1. 2. Compute the optimal levels of investment in period 1 and output and profits in period 2. 3. Solve for the optimal levels of consumption in periods 1 and 2. 4. Find the country's net foreign asset position at the end of period 1, de- noted B*, saving, S1, the trade balance, TB1, and the current account, CA1. 5. Now consider an interest-rate hike in period 1. Specifically, assume that as a result of turmoil in international financial markets, the world interest rate increases from 20 percent to 50 percent in period 1. Find the equilibrium levels of saving, investment, the trade balance, the current account, and the country's net foreign asset position in period 1. Provide intuition. 6. Suppose that the interest rate is 20 percent, and that Aj increases to 4. Calculate the equilibrium values of consumption, saving, investment, and the current account in period 1. Explain. 7. Suppose that the interest rate is 20 percent, that A1 = 3], and that A2 increases from 3.2 to 4. Calculate the equilibrium values of con- sumption, saving, investment, and the current account in period 1. Explain. Exercise 5.4 (An Open Economy With Investment) Consider a two- period model of a small open economy with a single good each period. Let preferences of the representative household be described by the utility func- tion In C1 + In C2, where C and C2 denote consumption in periods 1 and 2, respectively. In pe- riods 1 and 2, the household receives profits from the firms it owns, denoted II, and II2, respectively. Households and firms have access to financial mar- kets where they can borrow or lend at the interest rate ri. The production technologies in periods 1 and 2 are given by Q1 = A110 and Q2 = A211, where Q1 and Q2 denote output in periods 1 and 2, Io and I1 denote the capital stock in periods 1 and 2, A1 and A2 denote the productivity factors in periods 1 and 2, and a is a parameter. Assume that Io = 16, A1 = 3}, A2 = 3.2, and a = . At the beginning of period 1 households have B) = 8 bonds. The interest rate on bonds held from period 0 to period 1 is ro 0.25. In period 1, firms borrow the amount Df to purchase investment goods that become productive capital in period 2, 11. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is 20 percent. 1. Compute output and profits in period 1. 2. Compute the optimal levels of investment in period 1 and output and profits in period 2. 3. Solve for the optimal levels of consumption in periods 1 and 2. 4. Find the country's net foreign asset position at the end of period 1, de- noted B*, saving, S1, the trade balance, TB1, and the current account, CA1. 5. Now consider an interest-rate hike in period 1. Specifically, assume that as a result of turmoil in international financial markets, the world interest rate increases from 20 percent to 50 percent in period 1. Find the equilibrium levels of saving, investment, the trade balance, the current account, and the country's net foreign asset position in period 1. Provide intuition. 6. Suppose that the interest rate is 20 percent, and that Aj increases to 4. Calculate the equilibrium values of consumption, saving, investment, and the current account in period 1. Explain. 7. Suppose that the interest rate is 20 percent, that A1 = 3], and that A2 increases from 3.2 to 4. Calculate the equilibrium values of con- sumption, saving, investment, and the current account in period 1. Explain
