Problem1. 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 function ln(C1] + ln{Cz}, where Cf and (32 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 prots, denoted by 112, from the rms it owns. Households and rms 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.). Firms invest in period 1 to be able to produce goods in period 2. The production technology in period 2 is given by C12: v'{l1}, where 02 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 {30' = D). a) Compute the firm's optimal levels of period-1 investment and period-2 profits