1. (Endowment shocks) Consider a two-period lived household, whose preferences for consumption are described by the lifetime utility function lnC1 + lnC2 where C1 and C2 denote consumption in periods 1 and 2, respectively, and is the subjective discount factor.

(a) Do these preferences give rise to indifference curves that are downward sloping and convex? Show your work.

(b) Suppose that the household starts period 1 with financial wealth equal to (1 + r0)B0, where B0 is an inherited stock of bonds and r0 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 Q2 in periods 1 and 2, respectively. In period 1, the household can borrow or lend at the interest rate r1 > 0 via a bond denoted B1. Find the optimal levels of consumption in periods 1 and 2 as functions of the household's lifetime wealth, Y = (1 + r0)B0 + Q1 + Q2/(1 + r1) and the interest rate r1.

(c) Find the responses of consumption in period 1, C1, the trade balance in period 1, T B1, and the current account in period 1, CA1, to a temporary increase in the endowment, Q1 > 0 and Q2 = 0. Provide intuition.

(d) Find the responses of consumption in period 1, C1, the trade balance in period 1, T B1, and the current account in period 1, CA1, to a permanent increase in the endowment, Q1 = Q2 >0. Provide intuition.

(e) Suppose Q2 increases, Q2 > 0, while Q1 is unchanged, Q1 = 0. Find the responses of consumption in period 1, C1, the trade balance in period 1, T B1, and the current account in period 1, CA1. Provide intuition.