Suppose a consumer's utility function is U(F₀,F₁)= F₀^0.5F₁^0.5,where F₀ represents food consumed this year and F₁ represents food consumed next year.For that utility function,the marginal utility of food consumed this year is 0.5 × (F₁/F₀)^0.5 and the marginal utility of food consumed next year is 0.5 × (F₀/F₁)^0.5.Suppose the consumer earns $100 this year and nothing in the next,food costs $1 per unit in both years,and the interest rate is 10%.How much does she spend this year,and how much does she save? A) She spends $45 this year and saves $55. B) She spends $50 this year and saves $50. C) She spends $55 this year and saves $45. D) She spends $95 this year and saves $5.

Question

Quizplus · Accepted Answer

Given the utility function and the marginal utilities, the consumer optimizes utility by equalizing the marginal utility per dollar spent on food this year and next year. With an interest rate of 10%, $1 saved this year becomes $1.10 next year. Thus, to maximize utility, the consumer divides spending equally between the two periods, considering the interest rate. Since the consumer earns $100 this year and nothing next year, she needs to allocate her resources to ensure consumption in both periods. By spending $50 this year, she can save $50, which becomes $55 next year due to the interest, allowing for equal consumption across both years.

Suppose a Consumer's Utility Function Is U(F0,F1)= F00

Suppose a Consumer's Utility Function Is U(F₀,F₁)= F₀⁰