1. [15 points] Consider a three period small open endowment economy populated by a large number of households with preferences given by the lifetime utility function In Cl +1an 4-1an where C1, 02 and 03 denote consumption in periods 1, 2 and 3. Each household receives exogenous endowment of goods equal to Q1, Q2 and Q3. Every household enters period 1 with an asset position, including interest, equal to (1 + To) 36', where To is the interest rate prevailing in period U. Finally suppose that the country enjoys free capital mobility and that the world interest rate is constant over time and equal to w\". a. 13. U}! 11. write the household's flow budget constraints in each period 1, 2 and 3. Discuss the transversality condition that applies in the three period model. [Hint: apply the same arguments use in the two period model] Derive the interternporal budget constraint. Compute the equilibrium levels of consumption. Assuming an initial net international investment position of zero. caculate the trade balance in periods 1, 2 and 3 and verify that the present discounted value of this sequence is equal to zero. . Assume that in period 1 the economy receives a temporary increase in the endowment equal to A in period 1, while the remaining endowments are unchanged. Calculate the changes in consumption, the trade balance, and the current account in period 1. Now assume that the endowment shock is permanent, so that endowment rises by A in periods 1, 2 and 3. Calculate the change in consumption, trade balance and current account in period 1. Compare your results to the two period model developed in class. Are the results robust to the additional period. What are the general insights on the effects of temporary and permanent shocks for the behavior of the current account. Answer 0. and f. in the general case of a T period economy where T :> 3