Macroeconomics Question: Please answer parts a-d in the image form.

1. [Endowment Shocks] Consider a twoperiod lived household, whose preferences for consumption are described by the lifetime utility function where 01 and 02 denote consumption in periods 1 and 2, respectively. (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 nancial wealth equal to (1 + r033, where B 3 is an inherited stock of bonds and To 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 B I Find the optimal levels of consumption in periods 1 and 2 as functions of the household's lifetime wealth, Y E (1 + r0 )3?) + Q1 + Q2/(1 + T1) and the interest rate 7'1. (c) Find the responses of consumption in period 1, A01, the trade balance in period 1, ATBl, and the current account in period 1, ACA1, to a temporary increase in the endowment, AQi > 0 and AQZ = 0. (d) Find the responses of consumption in period 1, A01, the trade balance in period 1, ATB 1, and the current account in period 1, ACAl, to a permanent increase in the endowment, AQl : A622 > 0