Consider a two-period lived house- hold, whose preferences for consumption are described by the lifetime utility function

-C₁^-1 -C₂^-1

whereC1andC2denote 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 +r₀)B*₀ where B*₀ is an inherited stock of bonds andr₀is the

interest rate on assets held between periods 0 and 1 . In addition, the household receives endowments of goods in the amountsQ₁andQ₂inperiods 1 and 2, respectively. In period 1, the household can borrow or lend at the interest rater₁>0 via a bond denotedB₁^*. Find the optimal levels of consumption in periods 1 and 2 as functions of the household lifetime wealth Y(1 +r₀)B₀^*+Q₁+Q₂/(1 +r₁) and the interest rater₁.

3 Find the responses of consumption in period 1, C₁, the trade balance in period 1, TB₁, and the current account in period 1, CA₁, to a temporary increase in the endowment, Q₁>0 and Q₂= 0.

4 Find the responses of consumption in period 1, C₁, the trade balance in period 1, TB₁, and the current account in period 1, CA₁,, to a permanent increase in the endowment, Q₁= Q₂>0.

5 Compare your findings to those obtained under log-preferences lnC₁+lnC₁