Holly's utility function is U(c 1 , c 2 )  c 1/2 1  0.87c 1/2 2 , where c 1 is her consumption in period 1 and c 2 is her consumption in period 2.In period 2, her income is twice as large as her income in period 1.At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.)A) 0.30B) 0.08C) 0.23D) 0E) 0.15

Question

Holly's utility function is U(c 1 , c 2 )    c 1/2 1     0.87c 1/2 2 , where c 1  is her consumption in period 1 and c 2  is her consumption in period 2.In period 2, her income is twice as large as her income in period 1.At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.)A) 0.30B) 0.08C) 0.23D) 0E) 0.15

Jeriberi Niyongabo · Accepted Answer

Final Answer : E, Explanation :  Given that Holly's income in period 2 is twice as large as in period 1, for her to choose to consume the same amount in both periods, the interest rate must be such that the present value of her future income (period 2 income) is equal to her current income (period 1 income) when discounted back to period 1. This scenario implies a consumption-smoothing behavior, where the interest rate plays a crucial role in determining the present value of future income. An interest rate of 0.15 (15%) closely achieves this balance, allowing for equal consumption across both periods given the doubling of income in the second period.

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