Exercise 1) Consider a two period model of a small open economy. The preference of the representative household is given by In(C1) + In(C2) (23) In period 1, the household receives an endowment of Y1 = 10. In period 2, the household receives profits denoted by II2 from the firms it owns. Households and firms have access to international financial markets where they can borrow and lend at the interest rate my = 0.1. Bo = 0. Firms invest in period 1 to be able to produce goods in period 2. The production technology in period 2 is given by Q2 = VI1 (24) , where Q2 and In denote, respectively output in period 2 and investment in period 1. (1) Compute the firm's optimal level of period 1 investment and period 2 profits. (2) State the maximization problem of the representative household and solve for Ci and C2. (3) Find CA1, TB1. (4) Now assume that the level of productivity increases to 2 so that we have Q2 = 2VI1. Find the equilibrium level of savings, investment, and trade-balance. Compare your results with what you have in (2) and (3)