Exercise 4.2 (An Economy With Investment) Consider a two-period model of a small open economy with a single good each period. Let prefer- ences of the representative household be described by the utility function In(C1) + In(C2), where Ci and C2 denote consumption in periods 1 and 2, respectively, and In denotes the natural logarithm. In period 1, the household receives an endowment of Q1 = 10. In period 2, the household receives profits, denoted by II2, from the firms it owns. Households and firms have access to financial markets where they can borrow or lend at the interest rate r1. (r is the interest rate on assets held between periods 1 and 2.) Firms invest in period 1 to be able to produce goods in period 2. The production technology in period 2 is given by Q2 = VII, 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 theworld 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 (B; = 0). 1. Compute the firm's optimal levels of period-1 investment and period-2 profits. 2. State the maximization problem of the representative household and solve for the optimal levels of consumption in periods 1 and 2. 3. 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. 4. Now consider an investment surge. Specifically, assume that as a re- sult of a technological improvement, the production technology becomes Q2 = 2VI1. Find the equilibrium levels of savings, investment, the trade balance, the current account, and the country's net foreign asset position in period 1. Compare your results with those obtained in items 1.-3. providing interpretation and intuition