Exercise 8 Consider a small economy where the individuals live for two periods and receive an exogenous endowment for each period, Yt. Under autarky, the aggregate offer is equal to the aggregate product for each period, i.e., Yt 5 Ct for all of t, where Ct represents aggregate consumption. Besides this, assume that the utility function for the representative consumer is given by U1 5 C12σ 1 1 2 σ 1 β C12σ 2 1 2 σ ;

where βAð0; 1Þ represents the intertemporal discount rate. Let Bt be the net stock of assets inherited from period t 2 1 and assume that B1 5 B3 5 0.

a. Calculate the equilibrium interest under autarky, denoted by rA, and illustrate the intertemporal budget constraint for the representative agent in a diagram with first period consumption shown on the horizontal axis and consumption in the second period shown on the vertical axis.

b. How do changes in Y1 and Y2 affect the equilibrium interest rates in autarky? What is the effect of a marginal change on intertemporal discount rate β?

c. Use a graph to illustrate the effect of changes in Y1; Y2, and β on the equilibrium interest rates in autarky.

d. Now suppose that this small economy has been open to the international goods and credit market since the beginning of period 1. Under what conditions will the current account for period one be positive?

98 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS