Exercise 1 Consider a small, open economy where there is one good and one representative individual who lives for two periods. In this simplified economy, there is neither government nor 22 More precisely, the return from financial assets is the same between countries. Given that in the model there is no exchange rate, an equal return translates into the same interest rate. Reread Section 3.3 for more details on the meaning of equal return between financial assets when there are different currencies and the exchange rate between them that can change over time. 23 This explanation for global imbalances is explored by Caballero et al. (2008) and Mendoza et al. (2009).

Chapter 4 • What Is the Optimum Current-Account Level? 93 production. Each period the individual receives an endowment of the good, Yt, and chooses how much to consume, Ct, so as to maximize its utility U1, represented by U1 5 lnðC1Þ 1 β lnðC2Þ;

where β is the intertemporal discount rate.

In the first period, the difference between what they consume and their endowment is their savings or debt, which in the second period will either be redeemed or paid, depending on the case. As such, the consumer should satisfy the following budget constraint:

C1 1 C2 1 1 r 5 Y1 1 Y2 1 1 r

;

where r is the real interest rate. Assume that β 5 1=ð1 1 rÞ 5 0:75.

a. Assume that Y1 5 Y2 5 100. Calculate the value of consumption and the value of the current account for each period.

b. Assume there is a negative product shock in the first period, so that the endowment becomes Y1 5 80 and Y2 5 100. What are the new values of consumption? What is the new current account in the two periods? Interpret the results.

c. Now suppose that the negative product shock affects both periods, i.e., Y1 5 Y2 5 80.

What are the quantities consumed and the current account in this case? Interpret the results.