Patience has a utility function U(c₁, c₂)=c^1/2₁ + .087c^1/2₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2.Her income in period 1 is 5 times as large as her income in period 2.At what interest rate will she choose to consume the same amount in period 1 as in period 2? A)0.75 B)0 C)0.08 D)0.15 E)0.23

Question

Quizplus · Accepted Answer

To find the interest rate that makes the consumer indifferent between consuming in period 1 and period 2, we need to find the rate that will make the present value of the income in period 1 equal to the present value of the income in period 2. Let P0 be the income in period 2, then the income in period 1 is 5P0.

Therefore, the present value of the income in period 1 is 5P0/(1+r) and the present value of the income in period 2 is P0. Setting these equal to each other and solving for r:

5P0/(1+r) = P0
5 = 1+r
r = 4

So, the consumer is indifferent between consuming in period 1 and period 2 if the interest rate is 0.15 or 15%. Therefore, the answer is D.

Patience Has a Utility Function U(c1, C2)=c1/21

Patience Has a Utility Function U(c₁, C₂)=c^1/2₁