2 of 4 Exercise 2. Consider a two-period model of a small open economy with a...

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2 of 4 Exercise 2. 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 function In C + In C2, where C1 and C2 denote consumption in periods 1 and 2, respectively. In periods 1 and 2, the household receives profits from the firms it owns, denoted and , respectively. Households and firms have access to financial markets where they can borrow or lend at the interest rate r. The production technologies in periods 1 and 2 are given by and Q = AIo Q2 = A21, 4' where Q1 and Q2 denote output in periods 1 and 2, I and I 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 I = 16, A = 3, A = 3.2, and a A2 = 3. 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 D to purchase investment goods that become productive capital in period 2, I. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is 20 percent. Clarification: ro refers to the interest rate on assets/debt purchased in period 0 to period 2 of 4 10 712 4 g 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 D to purchase investment goods that become productive capital in period 2, I. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is 20 percent. Clarification: ro refers to the interest rate on assets/debt purchased in period 0 to period 1, whereas r* refers to the interest rate on assets/debt purchased in period 1 that pay out in period 2. 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, denoted B, saving, S, the trade balance, TB, and the current account, CA. 2 2 of 4 Exercise 2. 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 function In C + In C2, where C1 and C2 denote consumption in periods 1 and 2, respectively. In periods 1 and 2, the household receives profits from the firms it owns, denoted and , respectively. Households and firms have access to financial markets where they can borrow or lend at the interest rate r. The production technologies in periods 1 and 2 are given by and Q = AIo Q2 = A21, 4' where Q1 and Q2 denote output in periods 1 and 2, I and I 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 I = 16, A = 3, A = 3.2, and a A2 = 3. 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 D to purchase investment goods that become productive capital in period 2, I. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is 20 percent. Clarification: ro refers to the interest rate on assets/debt purchased in period 0 to period 2 of 4 10 712 4 g 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 D to purchase investment goods that become productive capital in period 2, I. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is 20 percent. Clarification: ro refers to the interest rate on assets/debt purchased in period 0 to period 1, whereas r* refers to the interest rate on assets/debt purchased in period 1 that pay out in period 2. 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, denoted B, saving, S, the trade balance, TB, and the current account, CA. 2