Problem2. 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 {[0102} where G1 and 02 denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of 01 = 10. In period 2, the household receives profits, denoted by 112, from the rms it owns. In period 1, households and firms have access to nancial markets where they can borrow or lend at the interest rate r1. Firms borrow in period 1 to invest in physical capital. They are subject to a collateral constraint of the form D1f5 K1 where DJdenotes the amount of debt assumed by the firm in period 1 and H1 denotes the value of the filTTI'S collateral. Suppose that H1 equals 4. In turn, firms use the physical capital purchased in period 1 to produce nal goods in period 2. The production technology in period 2 is given by 02 = 51"11Jr3 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. Finally, assume that the economy's initial net foreign asset position is zero {80* = D}. a) Compute the firm's optimal levels of period-1 investment and period-2 profits. Is the collateral constraint binding in period 1? Explain