Patience has a utility function U(c₁, c₂)= c^1/2₁ + 0.80c^1/2₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2.Her income in period 1 is twice 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)0.25 C)0.13 D)0.50 E)0.38

Question

Quizplus · Accepted Answer

To ensure Patience consumes the same amount in both periods, her consumption must align with her income pattern, considering the interest rate that allows her to smooth consumption. Given her income in period 1 is twice as large as in period 2, she needs to save half of her period 1 income to consume equally across both periods. The interest rate that enables this without any loss or surplus is 0.25 or 25%, as it perfectly offsets the income disparity over the two periods, allowing for equal consumption.

Patience Has a Utility Function U(c1, C2)= C1/21 + 0

Patience Has a Utility Function U(c₁, C₂)= C^1/2₁ + 0