Overall prompt can be found in screenshot.

3.

Questions 1-3 below refer to a consumer with preferences over consumption when young and old that is given by either of the following utility functions (a = .5). Either representation of preferences gives rise to the marginal rate of substitution function below: C! U(01:62) = CW; U(61,C2) = alog(c1) + (1 a) log(C2) U1 (Cl: C2) 062 M = R5031, 62) U2 (01, C2) (1 (1)61 3. Now imagine that the consumer can work both when young and when old. The wages earned when young are 101 = 10 and when old are 202 = 5. The budget constraints can then be written as either of the two lines indicated below: Cl +02 S 101 and C2 5 w2+a2(1 +T2) Cl +Cg/(1 +T2) S 1111 +102/(1 +T2) a. What are the utility maximizing values for (cl, c2, a2) when the real interest rate r2 = 0? b. Repeat part a. when r2 = 1. c. Graph the consumption choices and budget sets in part ab on a single graph