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 2 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 B)0.08 C)0.30 D)0.15 E)0.23

Question

Quizplus · Accepted Answer

To find the interest rate where Patience consumes the same amount in both periods, set the marginal rate of substitution (MRS) equal to the interest rate. The MRS is derived from the utility function and is equal to the ratio of the marginal utilities: (1/2)c₁^-1/2 / (0.087/2)c₂^-1/2. Given her income in period 1 is twice that of period 2, solve for the interest rate that equates consumption in both periods. The correct interest rate is 0.15.

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

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