Consider the two-period, small open economy model with investment and capital accu- mulation. There is a single household in the country who gets utility from consumption of a nal good in two periods. The household has h = 125 units of time which it devotes completely to working (because it does not care about leisure). There is no government in the model. Household preferences over consumption of the nal good in each period is given by the following utility function. U(C1, C2) = 111(C1) +41n(C2 + 1) The nal good is produced in each period using labour and capital with the following production technologies: 2 1 3 1 Y1 =21NfKi' Y2 =ZzNKS where the values for 21 and 22 are given below for different cases. The capital stock in period one is exogenous and is equal to K1 2 K = 1000. Capital completely depreciates between period one and two so rst period investment equals the second period capital stock: K2 = I. If the country trades with the rest of the world it can do so at a real interest rate equal to R. A) (30 points) Assume initially that 21 = 4 and 22 = 12. Assume the country can trade with the rest of the world. Derive the investment demand function, I D (R, 12) as a function of R. Graph this function for values of R between 1.0 and 3.0. Now assume that 21 = 4 and 22 = 15. Graph the new investment demand function, I D (R, 15) on the same graph as the previous one and use economic intuition to explain the position of the new function relative to the original one. B) (40 points) Assume the gross real interest rate is R = 1. 2. Complete Table 1 below. C) (15 points) Use your results in columns 12 in Table 1 to answer this question. Provide economic intuition for the direction of the change in investment, household savings, the trade balance, and utility when the country moves from autarky to trade. D) (15 points) Use your results in columns 14 in Table 1 to answer this question. In response to an increase in the productivity parameter in period one, provide eco- nomic intuition to explain why the direction of the investment responses and the trade balance responses are different between autarky and trade but the direction of the savings responses are the same. Table 1: Equilibrium Variables Open Econ- Open Econ- omy 21:10:2212 21:1022212 1428.39 1071.61 Autarky 2500.00 3378.60 39.48 39.73