Exercise 7 Consider a small, open economy, with a single good and a representative individual who lives for two periods. In this economy, there is a government that has a balanced budget.

There is no production and the individual receives an endowment of goods, Yt. They choose how much to consume each period in such a way as to maximize its utility, represented by U1 5 Cα

1 1 βC12α 2 ;

where Ct represents consumption by the individual in period t; βAð0; 1Þ and αAð0; 1Þ. In the first period, the difference between their available income and endowment is their savings or debt, which will either be redeemed or paid in the second period, depending on the case.

Therefore, the consumer must satisfy a budget constraint at the time they make their choices to consume. The assets or debts in this economy are remunerated by the real interest rate r, which we assume to be constant over time and is equal to the international interest rate.

Moreover, assume that β 5 ð1=1 1 rÞ.

Chapter 4 • What Is the Optimum Current-Account Level? 97

a. Based on the national accounts identities, show the intertemporal budget constraint this individual faces. Interpret the equation.

b. Compute the amount consumed and the level of the current account each period. Under what assumptions should the individual save during the first period? In what situation should they borrow?

c. Assume that Y1 5 Y2. What is the value of the current account in each period? How does this compare with the autarky equilibrium? Interpret the results.

d. Now assume that the representative agent in this economy has become more patient, giving more value to future consumption, so that β0 5 2β is the new intertemporal discount rate. How does this new equilibrium compare with the previous exercise?

Interpret the result.

e. Assume that there has been an exogenous increase in international interest rates, so that r0 5 2r, where r0 is the value of international interest rates and that the intertemporal discount rate remains as before, β. What are the new values for consumption and current account? Interpret the result.