Exercise 3.2 (Endowment Shocks) Consider a two-period lived house- hold, whose preferences for consumption are described by the lifetime utility function where C, and Co denote consumption in periods 1 and 2, respectively. 1. Do these preferences give rise to indifference curves that are downward sloping and convex? Show your work.2. Suppose that the household starts period 1 with financial wealth equal to (1 + ro)Bj, where Bj is an inherited stock of bonds and ro is the interest rate on assets held between periods 0 and 1. In addition, the household receives endowments of goods in the amounts Q1 and (2 in periods 1 and 2, respectively. In period 1, the household can borrow or lend at the interest rate > > 0 via a bond denoted Bj. Find the optimal levels of consumption in periods 1 and 2 as functions of the household's lifetime wealth, F = (1 + ro) Bj + Q1 + Q2/(1 + ) and the interest rate rj. 3. Find the responses of consumption in period 1, ACi, the trade balance in period 1, ATBi, and the current account in period 1, ACAj, to a temporary increase in the endowment, AQ, > 0 and AQ, = 0. 4. Find the responses of consumption in period 1, ACi, the trade balance in period 1, ATBj, and the current account in period 1, ACA , to a permanent increase in the endowment, AQ1 = AQ, 30. 5. Compare your findings to those obtained under log-preferences as pre- sented in section 3.9