1. (5pts) Compute the firm’s optimal levels of period-1 investment (I1).

2. (5pts) Solve for the optimal levels of consumption in periods 1 and 2 (C1 and C2).

3. (5pts) Find the current account in periods 1 and 2 (CA1 and CA2).

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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 C₁ and C2 denote consumption in periods 1 and 2, respectively. 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. (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 = Q2 = ln (11) 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 (i.e., r* = ro = 1 = = 0.1). Finally, assume that the economy's initial net foreign asset position is zero (B* = 0). 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 C₁ and C2 denote consumption in periods 1 and 2, respectively. 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. (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 = Q2 = ln (11) 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 (i.e., r* = ro = 1 = = 0.1). Finally, assume that the economy's initial net foreign asset position is zero (B* = 0).