Consider a two-period, two-country endowment economy. Let one of the countries be the United States and the other Europe. Households in the United States have preferences described by the utility function ln(C1U ) + ln(C2U ), where C1U and C2U denote consumption of U.S. households in periods 1 and 2, respectively. Europeans have identical preferences, given by ln(C1E ) + ln(C2E ), where C1E and C2E denote consumption of European households in periods 1 and 2, respectively. Let QU1 and QU2 denote the U.S. endowments of goods in periods 1 and 2, respectively. Similarly, let QE1 and QE2 denote the European endowments of goods in periods 1 and 2, respectively. Assume further that the endowments are nonstorable, that the U.S. and Europe are of equal size, and that there is free capital mobility between the two economies. The United States starts period 1 with a zero net foreign asset position carried over from period 0.
(a) Symmetric Equilibrium Suppose that QU1 = QU2 = QE1 = QE2 = 10. Calculate the equilibrium world interest rate, and the current accounts in the United States and Europe in period.