2.Suppose that the consumer has a wage income when young of w1 = 10

and has no wage income when old.

a. What are the utility maximizing values for (c1, c2, a2) when the real

interest rate r = 0?

[Note: The real interest rate in this case is 0%.]

b. Repeat part a for the case when r = 1.

[Note: The real interest rate in this case is 100%.]

c. Graph the consumption choices and budget sets in part a-b on a single

graph.

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: U(cl, Cg) = cfc?\" U031, 02) = at10g(t91) + (1 01) 10g(02) U1 (01,02) 002 M = = RS(C1' c2) U2(c1, C2) (1 (1)01 1. Calculate the marginal rate of substitution between cl and c2 when (i) (61,62) = (1? 1): (ii) (61162) = (1: 2) and (iii) (61:02) = (211) 2. Suppose that the consumer has a wage income when young of wl = 10 and has no wage income when old. a. What are the utility maximizing values for (c1,C2, (12) when the real interest rate 'r = 0? [Note: The real interest rate in this case is 0%.] b. Repeat part a for the case when r = 1. [Note: The real interest rate in this case is 100%.] c. Graph the consumption choices and budget sets in part ab on a single graph