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 = ln ( C 1 ) + ln ( C 2 ) where C1 and C2 denote consumption in periods 1 and 2, respectively. In periods 1 and 2, the household receives profits from the firms it owns, denoted 1 and 2, respectively. Households and firms have access to financial markets where they can borrow or lend at the interest rate r1. The production technologies in periods 1 and 2 are given by Q i = A i I i 1 where Qi denotes output in period i={1,2}, Ii denotes the capital stock in period i, Ai denotes the productivity factor in period i, and is a parameter. Assume that I0 = 16, A1 = 10/3, A2 = 16/5, and =0.75. At the beginning of period 1 households have B h o = 8 bonds. The interest rate on bonds held from period 0 to period 1 is r0 = 0.25. In period 1, firms borrow the amount D 1 f to purchase investment goods that become productive capital in period 2, I1. Assume that there exists free international capital mobility and that the world interest rate, denoted r*, is equal to 20 percent (r*=0.2). Assume =1. For this problem, do not forget to include your step-by-step calculations/derivations and formulas to get full credits and to explain in detail the economic intuition behind your results.

3.a) (8 points) Compute output and profits in period 1 (Q1, 1).

3.b) (10 points) Compute the optimal level of investment in period 1 (I1), and output and profits in period 2 (Q2, 2).

3.c) (10 points) Compute the optimal levels of consumption in periods 1 and 2 (C1 and C2) .

3.d) (12 points) Find the country's net foreign asset position at the end of period 1, denoted B 1 * , saving (S1), the trade balance, (TB1), and the current account (CA1).