3. Consider a small open economy which is perfectly integrated with the rest of world in capital market, where the world interest rate is 1'. Let preference be 10 1 l' c U= 2 10'+1+T10' Agents are endowed with Q in period 1 and 262 in period 2. (:1) Write down the two-period budget constraints for the agent, and derive the in- tertemporal budget constraints. (b) Solve for the optimal consumption path. (c) Compute the current account and show how it is related to r. Interpret your result. 4. Consider a two-period small open endowment economy populated by a large number of households with preferences given by the lifetime utility function V 01021 where Cl and 02 denote consumption of food in periods 1 and 2, respectively. Suppose that households receive exogenous endowments of copper given by Q1 = Q2 = 10 in periods 1 and 2, respectively. The terms of trade in periods 1 and 2 are TT; = T T; = 1. Every household enters period 1 with no assets or liabilities inherited from the past, 35 = 0. Finally, suppose that the country enjoys free capital mobility and that the world interest rate on assets held between periods 1 and 2, denoted r', is 5 percent. (a) Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1 and 2. (b) Assume now that the terms of trade in period 2 are expected to increase by 50 percent. Calculate the effect of this anticipated terms of trade improvement on consumption, the trade balance, and the current account in periods 1 and 2. Provide intuition. (c) Relate your ndings to those discussed in the case study of the copper price ap- preciation experience by Chile in the early 20005 presented in the lecture. In particular, explain why the results obtained in items (a) and (b) make the be- havior of the Chilean current account in the period 2003-2007 puzzling under the naive view that in the early 20005 Chileans had perfect foresight about the future path of the price of copper