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 InCi +InC2 where C and C2 denote consumption in periods 1 and 2. Each period the household receives profits from the firms it owns, denoted and T12. Households and firms have access to financial markets where they can borrow or lend at the interest rate ri. The production technologies in periods 1 and 2 are given by Q. = A116 and Q2 = A21 where Qi and Q2 denote output in periods 1 and 2, lo and I denote the capital stock in periods 1 and 2, A, and A2 denote the productivity factors in periods 1 and 2, and a is a parameter. Assume that Io = 16, A1 = 35, A2 = 3.2, and a = . At the beginning of period 1 households have B 8 bonds. The interest rate on bonds held from period 0 to period 1 is ro = 0.25. In period 1, firms borrow the amount D to purchase investment goods that become productive capital in period 2, 11. 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) 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 InCi +InC2 where C and C2 denote consumption in periods 1 and 2. Each period the household receives profits from the firms it owns, denoted and T12. Households and firms have access to financial markets where they can borrow or lend at the interest rate ri. The production technologies in periods 1 and 2 are given by Q. = A116 and Q2 = A21 where Qi and Q2 denote output in periods 1 and 2, lo and I denote the capital stock in periods 1 and 2, A, and A2 denote the productivity factors in periods 1 and 2, and a is a parameter. Assume that Io = 16, A1 = 35, A2 = 3.2, and a = . At the beginning of period 1 households have B 8 bonds. The interest rate on bonds held from period 0 to period 1 is ro = 0.25. In period 1, firms borrow the amount D to purchase investment goods that become productive capital in period 2, 11. 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)
