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Consider a two-period model of a small open economy with a single good each period. Let preferences of the representative household be described by the utility functionln(C1) + ln(C2),where C1 and C2 denote consumption in periods 1 and 2, respectively, and ln denotes the natural logarithm. In period 1, the household receives an endowment of Q1 = 5. In period 2, the household receives profits, denoted by ?2, from the firms it owns. Households and firms have access to financial markets where they can borrow or lend at the interest rate r1. (r1 is the interest rate on assets held between periods 1 and 2.).Representative firm borrows D1f in period 1 to make investment I1 that enable the firm to produce goods in period 2. The production technology in period 2 is given byQ2 = ?(I1),where Q2 and I1 denote, respectively, output in period 2 and investment in period 1.Assume that there exists free international capital mobility and that the world interest rate, r*, is 10% per period (i.e., r* = 0.1). Finally, assume that the economy’s initial net foreign asset position is zero (B0* = 0)c) Find the country’s net foreign asset position at the end of period 1, the trade balance in periods 1 and 2, and the current account in periods 1 and 2.d) Now consider an investment surge. Specifically, assume that as a result of a technological improvement, the production technology becomes Q2 = 2?(I1). Find the profit maximizing level of investment made in period-1 and the level of profit for period-2. Find the equilibrium levels of saving, the trade balance, the current account, and the country’s net foreign asset position in period 1.
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