Question

4.5 Susan is certain to live just two periods and receives an income of 10,000 in the first period, and 15,000 in the second. She has no other assets. The real interest rate is 8%.

(a) As she begins the first period, what is the present value of her lifetime resources?

(b) IF she choose to consume the exact same amount in both periods (c1 = c2), what would be her consumption in the first (and second) period? SHOW YOUR WORK.

(c) Bill has the exact same income (and life expectancy) of Susan, but chooses to consume 15,000 in the first period. How much will he consume in the second.

Answer 1

Susan has Y1 = 10,000 and Y2 = 15,000. The real interest rate is 8%. Intertemporal budget constraint is given by

C1 + C2/1 + r = Y1 + Y2/1 + r

(a) The constraint changes to C1 + C2/1.08 = 10000 + 15000/1.08

The present value of her lifetime resources = 10000 + 15000/1.08 = 23,889

(b) For C1 = C2, we have C1 + C1/1.08 = 23,889

C1 = C2 = 23889/1.925926 = $12,404

(c) Bill has C1 =15,000 in the first period. This gives

15000 + C2/1.08 = 23889

C2 = 8889*1.08 = 9600

He consumes 9600 in second period