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

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Consider a two-period lived household, whose preferences
for
consumption are described by the lifetime utility function
−(C_1)^−1 −(C_2)^-1 ,
where C1 and C2 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 + r0)B0, whereB0 is an inherited stock of bonds and r0
is the interest rate on assets held between periods 0and 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 interestrate 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.
3. Find the responses of consumption in period 1, ∆C1, the trade
balance in period 1, ∆T B1, andthe 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, ∆T B1, and the current account in period 1,
∆CA1, to a permanent increase in the endowment,
∆Q1 = ∆Q2 > 0.