Exercise 4 Consider a small, open economy with two periods where there is only one consumer good for each period. The representative agent preferences are represented by U1 5 lnðC1Þ 1 β lnðC2Þ;

where Ct represents consumption for period t and intertemporal discount factor β is equal to 0.91. The representative consumer has access to the international financial market, where they can freely lend or borrow at interest rate r 5 10%. The beginning net international investment position is equal to zero, i.e., B1 5 0.

The good consumed is produced using capital as input, according to the following production function:

Yt 5 ffiffiffiffiffi Kt p ;

where Yt represents production for period t and Kt the stock of capital. In the first period, each individual receives an endowment of 10 units of capital. Assume that the capital Chapter 4 • What Is the Optimum Current-Account Level? 95 completely depreciates from one period to the next so that the stock of capital in the second period corresponds to the investment made in the first period: K2 5 I1.

a. Write the maximization problem for the representative consumer and find the optimum consumption levels for both periods.

b. Find the optimum level of savings for the economy, as well as the current-account balance for the first period.

c. Now, consider that an increase in capital productivity occurs. More specifically, assume that, as a result of technological improvement, the production function becomes Yt 5 2 ffiffiffiffiffi Kt p . Find the new equilibrium levels for savings and investment and the current-account balance for the first period. Compare your new results with those obtained in the previous items and provide an economic intuition for the differences discovered.