Patience has a utility function U(c₁, c₂)= c^1/2₁ + .083c^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)0.10 B)0 C)1 D)0.20 E)0.30

Question

Quizplus · Accepted Answer

To consume the same amount in both periods, the marginal rate of substitution (MRS) must equal the interest rate. Given the utility function, the MRS is 0.083. Since her income in period 1 is 5 times that of period 2, the interest rate that equates the MRS to the income ratio is 0.20.

Patience Has a Utility Function U(c1, C2)= C1/21

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