Exercise 3.2 (Endowrneut Shocks} Consider e. two-period lived house hold, whose preferences for consumption are described by the lifetime utility.r function Hll ._. all: where U1 and U2 denote consumption in periods 1 end 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) By, where By 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 Q, and Q2 in periods 1 and 2, respectively. In period 1, the household can borrow or lend at the interest rate r] > 0 via a bond denoted Bi. Find the optimal levels of consumption in periods 1 and 2 as functions of the household's lifetime wealth, Y = (1 + ro) By + Q1 +Q2/(1+ ri) and the interest rate r1. 3. Find the responses of consumption in period 1, AC], the trade balance in period 1, ATBi, and the current account in period 1, ACA, to a temporary increase in the endowment, AQ1 > 0 and AQ2 = 0. 4. Find the responses of consumption in period 1, AC,, the trade balance in period 1, ATBj, and the current account in period 1, ACA,, to a permanent increase in the endowment, AQ1 = AQ, > 0. 5. Compare your findings to those obtained under log-preferences as pre- sented in section 3.9