+ 1-O 1. (Parts a to f 10 points, g 20 points) Consider an endowment economy with two goods (A and B) and with two periods. Households earn y, and Yc+1 as endowment income. They can save, Swith an interest rate of (1+r) and consume goods A and B. Consumption levels for goods A and B at time t are given by CA and CB, respectively. The lifetime B utility of the household is given by: (C) (c) (CA) + B6 1-o 1-a 1- (a) Write the flow budget constraints of the household. Give economic intuition. (b) Using the flow budget constraints, derive the household's intertemporal budget constraint. What is the economic meaning of this constraint? (e) Write down the household's problem and derive optimality conditions. Interpret each condition economically. Derive the relationship between current consumption levels A and B and their relationship with their respective future consumption levels. (d) Derive the intertemporal elasticity of substitution (IES) for goods A and B. Give economie intuition for the IES. Now define, aggregate consumption level in the economy, G, as the sum of consumption levels for goods A and B at timet (similarly for + 1). Derive the IES for aggregate consumption level. (e) Derive the consumption function for goods A and B