1. (An Open Economy With Investment) 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

lnC1 + lnC2

where C1 and C2 denote consumption in periods 1 and 2. Each period the household receives profits from the firms it owns, denoted 1 and 2. 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

andQ 1 = A 1 I 0 Q 2 = A 2 I 1 where Q1 and Q2 denote output in periods 1 and 2, I0 and I1 denote the capital stock in periods 1 and 2, A1 and A2 denote the productivity factors in periods 1 and 2, and is a parameter. Assume that I0 = 16, A1 = 331, A2 = 3.2, and = 34. At the beginning of period 1 households have B0h = 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 D1f 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 20 percent.

(a) Compute output and profits in period 1. (2 marks)

(b) Compute the optimal levels of investment in period 1 and output and profits in period 2. (3 marks)

(c) Solve for the optimal levels of consumption in periods 1 and 2. (4 marks)

(d) Find the country's net foreign asset position at the end of period 1, denoted B1, saving, S1, the trade balance, TB1, and the current account, CA1. (6 marks)

(e) Now consider an interest-rate hike in period 1. Specifically, assume that as a result of turmoil in international financial markets, the world interest rate increases from 20 percent to 50 percent in pe- riod 1. Find the equilibrium levels of saving, investment, the trade balance, the current account, and the country's net foreign asset position in period 1. Provide intuition. (7 marks)

(f) Suppose that the interest rate is 20 percent, and that A1 increases to 4. Calculate the equilibrium values of output, consumption, saving, investment, and the current account in period 1. Provide an intuitive interpretation of the adjustment to the transitory pro- ductivity shock. (7 marks)

(g) Suppose that the interest rate is 20 percent, that A1 = 313, and that A2 increases from 3.2 to 4. Calculate the equilibrium values of consumption, saving, investment and the current account in period 1. Explain your findings. (6 marks)