Exercise 3.6 (A Three-Period Open Economy ) Consider a three-period small open endowment economy populated by a large number of households with preferences given by the lifetime utility function In C1 + In C2 + In C3, where C1, C2, and C3 denote, respectively, consumption in periods 1, 2, and 3. Suppose that households receive exogenous endowments of goods given by Q1, Q2, and Q3 in periods 1, 2, and 3, respectively. Every household entersperiod 1 with an asset position, including interest, equal to (1 + rg)B, where m denotes the interest rate prevailing in period 0. Finally, suppose that the country enjoys free capital mobility and that the world interest rate is constant over time and equal to r". 1. Write the household's budget constraint in periods 1, 2, and 3. 2. Write the nchonzi game constraint. 3. Derive the intertemporal budget constraint. 4. Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1, 2, and 3. 5. Assume that in period 1 the economy receives a temporary increase in the endowment equal to AQ > 0, that is, assume that Q1 increases by AQ and that Q2 and Q3 remain unchanged. Calculate the changes in consumption, the trade balance, and the current account in period 1, denoted AC], ATBI, and A021], respectively. 6. Now assume that the endowment shock is permanent, that is, the en dowments in periods 1, 2, and 3 all increase by AQ > 0. Calculate the changes in consumption, the trade balance, and the current account in period 1. 7. Compare your answers to the ones obtained in the two period economy. 8. Answer questions 5 and 6 in the general case of a Tperiod economy, where T is any integer larger than 2