Question 3 (30 marks) Consider a twoperiod model of a small open economy with a single, perishable good. Let preferences of the representative household be described by the utility function 11101 + In 02, where Cl and Cg denote consumption in periods 1 and 2, respectively. Each period t = 1, 2, the household receives prots H; from the represenative rm it owns. The production technologies in periods 1 and 2 are given by and - Q2 = 4 ' Iii-h, where Q1 and Q2 denote output in periods 1 and 2, respectively, IO = 39.0625 is exoge- nously given and represents the investment from \"period 1\" and [1 denotes the investment in period 1. Observe that the rm invests in period t 1 to be able to produce goods in period t. The household and the rm have access to nancial markets where they can borrow or lend. The rm nances its investments by issuing debt (both in \"period 0\" and in period 1), as in the lecture. Assume that there exists free international capital mobility and that the world interest rate, 79", is 5% each period (i.e., r0 = r1 = W = 0.05, where n is the interest rate on assets held between periods 1' and t + 1). Finally, assume that the household's initial net asset position is Bh = 710. (a) (1 mark) Compute the initial net foreign asset position of the economy. (b) (1 mark) Compute the rm's output Q1 and prot H1 in period 1. (c) (3 marks) Compute the rm's optimal level of investment in period 1 and its prot in period 2. (d) (5 marks) Derive the optimal levels of consumption in periods 1 and 2. (e) (3.5 marks) Find the country's net foreign asset position at the end of period 1 and, for each of the periods 1 and 2, the country's savings, trade balance and current account balance. Now suppose that the government at the beginning of period 1 publicly announces an investment subsidy. Specically, for each unit of investment that the rm makes in period 1, the government promises to pay the rm a subsidy of 82 E (0, l + in) units of the good in period 2. The government nances the subsidy by charging the household a lump-sum tax T2 in period 2. The government neither has other expenditures nor other revenues. In particular, T1 = 0. (f) (1 mark) Write down the government's budget constraint in period 2. (g) (4 marks) Write down a formula for the rm's prot in period 2. Derive the optimal investment condition and calculate the optimal investment as a function of 52. Using a MPKMCK-graph, illustrate in a gure how the optimal investment and the rm's period-2 prot H2 change after the subsidy is introduced. (h) (1.5 marks) Write down the household's period 1 and period 2 budget constraints. Derive the household's intertemporal budget constraint. (i) (2 marks) Derive the economy's resource constraint. Compare it to resource con- straint that holds without the subsidy. Provide intuition for your comparison. (j) (6 marks) Assume that .92 = 0.1. Derive the household's optimal consumption path and the current account balances CA1 and CA2 in periods 1 and 2, respectively. What effect did the introduction of the subsidy have on the optimal consumption path and on CA1? Provide a detailed explanation of the effect on C1, Cg and CA1 of introducing the subsidy and intuition for your results. ls the household better off after the subsidy was introduced? (k) (2 marks) Explain in words how your answer to (j) would change if the government were to announce the subsidy only at the beginning of period 2