Exercise 11 Consider a small, open economy where there is the accumulation of capital and production.

Production in the domestic economy is given by means of function:

Yt 5 AtKα

t :

There is total depreciation of capital from one period to the next, such that Kt11 5 It, and each individual receives an initial endowment of capital in the first period, K1 . 0, so that production is exogenous at t 5 1. Besides this, assume that B1 5 B3 5 0. The utility function for the representative agent is given by U1 5 lnðC1Þ 1 β lnðC2Þ;

where βAð0; 1Þ represents the intertemporal discount rate and Ct is consumption in period t.

a. Obtain the savings of the domestic economy in period 1, denoted by S1, in function of Y1, Y2, K1, K2, and r.

b. Given interest rate r, determine the optimum level of capital in the second period, K2, consistent with the maximization of the utility of the representative individual, and the respective level of investment. Show that investment in the economy, represented by I1, is a negative function of interest rates.

c. Using the optimum choice of K2 determined in item (b), and the corresponding production Y2, compute domestic savings as a function of interest rates r, i.e., S1ðrÞ. Show that S1ðrÞ is a positive function of interest rates.

100 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS

d. Illustrate the autarky equilibrium in the domestic economy on a graph with savings and investment represented on the vertical axis and interest rates on the horizontal axis.

e. Assume the world is composed of only a domestic economy and a foreign economy, and that all is symmetrical to the domestic economy, with the exception of the intertemporal discount rate. Assume that β . β

, where β is the intertemporal discount rate in the foreign economy. Find the current-account balance for the domestic economy and for the foreign economy.

f. Illustrate on a graph the equilibrium obtained in the previous item.