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 U(C_1,C_2)=\ln C_1+\ln C_2 where $C_1$ and $C_2$ denote consumption in periods 1 and 2. In both periods, the household receives profits from the firm it owns, denoted $\Pi_1$ and $\Pi_2$. Households and firms have access to financial markets where they can borrow or lend at the interest rate $r_1$. The production technologies in periods 1 and 2 are given by

Q_1=A_1I_0^{\alpha}

and

Q_2=A_2I_1^{\alpha}

where $Q_1$ and $Q_2$ denote output in periods 1 and 2, $I_0$ and $I_1$ denote the capital stock in periods 1 and 2, $A_1$ and $A_2$ denote the productivity factors in periods 1 and 2, and $\alpha$ is a parameter. Assume that $I_0=16$, $A_1=3\frac{1}{3}$, $A_2=3.2$, and $\alpha=\frac{3}{4}$. At the beginning of period 1 households have $B_0^h=8$ bonds. The interest rate on bonds held from period 0 to period 1 is $r_0=0.25$. In period 1, firms borrow the amount $D_1^f$ to purchase investment goods that become productive capital in period 2, $I_1$. Assume that there exists free international capital mobility and that the world interest rate, denoted $r^*$, is 20 percent.\\

a. Compute output and profits in period 1.\\

b. Compute the optimal levels of investment in period 1 and output and profits in period 2.\\

c. Solve for the optimal levels of consumption in periods 1 and 2.\\

d. Find the country's net foreign asset position at the end of period 1, denoted $B_1^*$, saving, $S_1$, trade balance, $TB_1$, and current account, $CA_1$.