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Question: Consider a two-period small open economy in which the representative agent has the following life...

Show transcribed image text Consider a two-period small open economy in which the representative agent has the following lifetime utility function: U(C_1, C_2) = Squareroot C_1 + Squareroot C_2 Let Q_1 and Q_2 denote the agent's endowments in the first and second period, respectively. Let B_0* denote the initial net foreign asset position, and r* denote the constant world real interest rate which is given exogenously. a. What is the intertemporal budget constraint of this economy in terms of C_1, C_2, Q_1, Q_2, B_0* and r* b. Now suppose that house-holds' endowments are 6 units of goods in period 1 and 12 units of goods in period 2. Households start period I with a zero net asset position (B_0* = 0) and the world interest rate is zero (r* = 0). Find equilibrium consumption in periods 1 and 2, the country's net foreign asset position at the end of period 1, and the trade balance in periods 1 and 2. What is the utility level of the household at the optimum? c. Now assume that the government announces in period 1 that a strong nation is one with a positive net foreign asset position and that therefore the country must save more. In particular, the government enforces that the net foreign asset position at the end of period 1 is positive and equal to 3. That is, the government imposes capital controls of the form B_1* = 3. What is the new consumption point of the households? Is the utility level higher with capital controls compared to before? What happens to the domestic interest rate after capital controls are imposed? Find the new domestic equilibrium interest rate.

Consider a two-period small open economy in which the representative agent has the following lifetime utility function: U(C_1, C_2) = Squareroot C_1 + Squareroot C_2 Let Q_1 and Q_2 denote the agent's endowments in the first and second period, respectively. Let B_0* denote the initial net foreign asset position, and r* denote the constant world real interest rate which is given exogenously. a. What is the intertemporal budget constraint of this economy in terms of C_1, C_2, Q_1, Q_2, B_0* and r* b. Now suppose that house-holds' endowments are 6 units of goods in period 1 and 12 units of goods in period 2. Households start period I with a zero net asset position (B_0* = 0) and the world interest rate is zero (r* = 0). Find equilibrium consumption in periods 1 and 2, the country's net foreign asset position at the end of period 1, and the trade balance in periods 1 and 2. What is the utility level of the household at the optimum? c. Now assume that the government announces in period 1 that a strong nation is one with a positive net foreign asset position and that therefore the country must save more. In particular, the government enforces that the net foreign asset position at the end of period 1 is positive and equal to 3. That is, the government imposes capital controls of the form B_1* = 3. What is the new consumption point of the households? Is the utility level higher with capital controls compared to before? What happens to the domestic interest rate after capital controls are imposed? Find the new domestic equilibrium interest rate.