Exercise 9 The world economy is formed by two countries, foreign and home, which exist for two periods. Each individual in each country receives an exogenous, perishable endowment of goods for each period, Yc t , with tAf1; 2g and c 5 fH; Fg. Superscript H denotes variables associated with the domestic economy, while superscript F denotes variables associated with the foreign economy. This is an endowment economy where there is neither production nor capital accumulation. The net exports for each economy in period t is given by NXc t , and where, in equilibrium, the net exports of one country should correspond to the net imports of the other, i.e., NX H t 1 NXF t 5 0 should be true.

The utility function for consumers in each economy is given by Uc 1 5 lnðCc 1Þ 1 β lnðCc 2Þ;

where Cc t represents consumption of country c in period t and βAð0; 1Þ represents the intertemporal discount rate. Let Bc t represent the net international investment position for each economy and assume that BH 1 5 BH 3 5 BF 1 5 BF 3 5 0.

a. Compute the interest rate equilibrium under autarky for each of the countries, denoted by rA;H and rA;F .

b. Find the international interest rate when there is the free trade of goods and services between the countries, denoted by r, and show that it remains between the values of autarky interest rates rA;H and rA;F .

c. Show that the country with an autarky interest rate lower than the world interest rates will have a surplus in current account in period 1, while the country with interest rates above the international rate will run a deficit.

d. How does an increase in YF 2 affect the utility of the representative consumer in the domestic economy? What conclusions can you draw?