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Economics 661

Department of Economics

Spring Semester 2026

Problem set 1

Due: February 15 at 11:59 pm CST

Question 1. Countries A and B are identical in all respects, except that the initial net international asset position  of country A is lower than that of country B. Indicate whether the following statements are true, false, or uncertain and explain why.

1. It must be the case that consumption in country A is lower than consumption in country B.

2. It must be the case that the trade balance in country A in period 1 is higher than in country B.

3. It must be the case that the current account in country A in period 2 is higher than in country B.

4. All of the above statements are true.

Question 2 [anticipated shocks and debt forgiveness].   Consider a small open economy where households live for two periods and have the following preferences

where the subjective discount factor β equals  Suppose that households receive a constant endowment over time equal to 10, Q1 = Q2 = 10. Suppose that households start period 1 with debt including interest equal to  and that r0 = 0.1. Finally, assume that the country enjoys free capital mobility and that the world interest rate is 10 percent, r* = 0.1.

1. Calculate the equilibrium values of consumption, the trade balance, and the current account in period 1.

2. Assume now that the endowment in period 2 is expected to increase from 10 to 15. Calculate the effect of this anticipated output increase on consumption, the trade balance, and the current account in period 1. Provide intuition.

3. Suppose now that foreign lenders decide to forgive all of the country’s initial external debt including interest. Calculate the effect of this external gift on consumption, the trade balance, and the current account in period 1. Provide an intuitive explanation of your findings.

Question 3 [oil shocks].   Consider a small open endowment economy that lasts for two periods. The households receive in every period an endowment of “oil”, Q1 and Q2, and they derive utility from consuming food. We denote by TT1 and TT2 the price of food in terms of oil (units of food that a unit of oil purchases). The utility function of the representative household is

U(C1, C2) = ln C1 + β ln C2

where C1 and C2 are food consumptions in period 1 and period 2, and β ≤ 1. In period 1, the household can borrow and save from the rest of the world at the interest rate r1. Moreover, assume that in period 1 their net foreign asset position equals zero, B0 = 0.

1. Write down the budget constraints for the representative household in each period.

2. Derive the intertemporal budget constraint.

3. Solve for the optimal C1, C2 as a function of r1, TT1, TT2, Q1 and Q2.

4. Suppose now that the world economy experiences an increase in oil prices by ∆ > 0. The increase is perceived to be transitory. That is, the new terms of trade are now  How does this affect the trade balance in period 1?