Exercise 5.4 (An Open Economy With Investment) 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 func- tion In Cl + In 02, . Find the country's net foreign asset position at the end of period 1, de noted Bf, saving, 81, the trade balance, T31, and the current account, CA1. . Now consider an interest-rate hike in period 1. Specically, assume that as a result of turmoil in international nancial markets, the world interest rate increases from 20 percent to 50 percent in period 1. Find the equilibrium levels of saving, investment, the trade balance, the current account, and the country's net foreign asset position in period 1. Provide intuition. . Suppose that the interest rate is 20 percent, and that Al increases to 4. Calculate the equilibrium values of consumption, saving, investment, and the current account in period 1. Explain. . Suppose that the interest rate is 20 percent, that A1 = 31, and that A2 increases from 3.2 to 4. Calculate the equilibrium values of con sumption, saving, investment, and the current account in period 1. Explain. . Answer questions 2- 4 and 6-7 under the assumption that the economy is closed, and that B; = 0 and IO = 16. First use a graphical approach to analyze the qualitative differences relative to the open economy for each case. Then nd the numerical solution. Discuss the extend to which your numerical solutions conforms (or does not conform) with the qualitative solution given in table 5.1. Where 0'1 and Cg denote consumption in periods 1 and 2, respectively. In pe- riods 1 and 2, the household receives prots from the rms it owns, denoted H1 and H2, respectively. Households and rms have access to nancial mar kets Where they can borrow or lend at the interest rate n. The production technologies in periods 1 and 2 are given by Q1 = A113 Q2 =A21i', Where Q1 and Q2 denote output in periods 1 and 2, Io and 11 denote the capital stock in periods 1 and 2, A1 and A2 denote the productivity factors in periods 1 and 2, and a is a parameter. Assume that Io = 16, A1 = 3%, A2 = 3.2, and a = %. At the beginning of period 1 households have Bf; = 8 bonds. The interest rate on bonds held from period 0 to period 1 is To = 0.25. In period 1, rms borrow the amount Dir to purchase investment goods that become productive capital in period 2, II. Assume that there exists free international capital mobility and that the world interest rate, denoted r\