Consider a twoperiod model ot a small open economy with a single. perishable goodLet preferences of the representative household be described by the utility function. in (:1 + in (:2? where C1 and (32 denote consumption in periods 1 and 2, respectively. Each period t = 1, 2, the household receives profifits l'lt from the represenative firm it owns. The production technologies in periods 1 and 2 are given by Q1 = 3543?] Q2 = 4' film: We have detected text content Use text instead where Q1 and Q2 denote output in periods 1 and 2, respectively. In = 39.0625 is exoge- nously given and represbnts the investment from \"period 0\" and I1 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 El\" and in period 1), as in the lecture. Assume that there exists 'ee international capital mobility and that the world interest rate, r*, is 5% each period [i.e.. m = r1 = r* = 0.05, where r: is the interest rate on assets held between periods t and t+1). Finally. assume that the household's initial net asset position is BE = 1C|. a} Compute the initial net toreign asset position of the economy. bl Compute the fitirm's output Q1 and profifit H1 in period 1. t t (c) lCompute the fifirm's optimal level of investment in period 1 and its profifit in period 2. (d) Derive the optimal levels of consumption in periodsl and 2. t e) Find the country's net foreign asset position at the end of period 1 and, for each of the periods 1 and 2. the countly's savings. trade balance and current account balance. We have detected text content Use text instead Now suppose that the government at the beginning of period 1 publicly announces an investment subsidy. Specifically, for each unit of investment that the firm makes in period I, the government promises to pay the firm a subsidy of $2 6 (0, 1 + r1 ) units of the good in period 2. The government finances 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. ONLY QUESTION f-kl (f) Write down the government's budget constraint in period 2. (g)Write down a formula for the fifirm's profifit in period 2. Derive the optimal investment condition and calculate the optimal investment as a function of $2. Using a MPK-MCK-graph, illustrate in a fifigure how the optimal investment and the fifirm's period-2 profifit n2 change after the subsidy is introduced (h)Write down the household's period 1 and period 2 budget constraints. Derive the household's intertemporal budget constraint. (i) Derive the economy's resource constraint. Compare it to resource constraint that holds without the subsidy. Provide intuition for your comparison. (j) Assume that $2 = 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, C2 and CA1 of introducing the subsidy and intuition for your results. Is the household better off after the subsidy was introduced? (k) 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