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Problem 3 - Intertemporal elasticity of subsitution Consider the two-period consumption-savings model. Suppose that a (C) = Cl-7/ (1 - 7). Remember from you micro classes that the elasticity of subsitution gives how much the relative consumption of two goods changes as their relative price change. Using the same logis, macroeconomists call dIn (C1/C2) /dIn(1 + r) as the intertemporal elasticity of sub- stitution (IES) where Cj and C2 are the utility maximizing values of consumption. (1) What are the FOCs of this problem? (2) What is IES for this particular utility function? (Hint: Use Euler equation) (3) Suppose Y1 increases by 1 unit. How does the increase in Ci and C2 depend on IES? What is the intuition? (4) Suppose that the consumer cannot borrow in the first period. How would your answer to (3) change? (5) Suppose the consumer can borrow freely. However, she is born in period zero and lives infinitely many periods. Find Cf for t = 0, ...,co. If Yo increases by 1 unit, how much would Cf change? How would this change depend on y? How does this compare to your answer in (3)? Problem 4 - Uncertainty in capital income Consider the two-period consumption savings model with uncertainty. Assume that B =1 and 1 +r = 1 -e with prob. 1/2 1 + e with prob. 1/2 so that E(1 + r) = 1. What are the FOCs of the consumer? Would the consumer save more or less if uncertainty increases?Problem 1 (1) Consider the two-period consumption savings model. Assume that S(1 + r) = 1. Compute the optimal consumption and savings if: (a) Y1 = 4, Y2 = 8, (b) Yi = 8, Y2 =4, (c) How would your answer change if the consumer cannot borrow (impose S>0) (2) Consider a three-period-period consumption savings model. Assume that B(1 +7) = 1. Compute the optimal consumption and savings if: (a) Y1 = 3, Y2 = 6, Y3 = 9. (b) Y1 = 9, Y2 = 0, Y3 = 0. (Note: Assume r=0 to simplify your calculations!) (c) Y1 = 0, Y2 = 9, Ya = 0. Problem 2 Consider the two-period consumption-savings model. Assume that B(1 +r) = 1. Recall public savings = 71 -G1 is the opposite of the gov't deficit. Total savings = public savings + private savings S. (1) Assume Y1 = 8, Y2 = 10. The gov't levies taxes 71 = 4, and 72 = 4. Find the optimal consumption and private savings, public savings, total savings. (2) What is the effect on consumption, public savings, private savings, total savings, if the gov't changes 7, to 2? (and increases 72 as needed to keep the gov't budget constraint satisfied, with no change in Gjor Go)? What if the gov't changes 71 to 6