Suppose a consumer's utility function is U(F₀,F₁)= F₀^0.6F₁^0.4,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 0.6 × (F₁/F₀)^0.4 and the marginal utility of food consumed next year is 0.4 × (F₀/F₁)^0.6.Which of the following expressions gives the consumer's marginal rate of substitution for food this year with food next year (MRS₀₁)? A) MRS₀₁ = F₁/F₀ B) MRS₀₁ = (2/3) × (F₀/F₁) C) MRS₀₁ = (2/3) × (F₁/F₀) D) MRS₀₁ = (3/2) × (F₁/F₀)

Question

Quizplus · Accepted Answer

The marginal rate of substitution (MRS) is the ratio of the marginal utility of food consumed this year to the marginal utility of food consumed next year. Therefore, MRS₀₁ = (0.6 × (F₁/F₀)^0.4) / (0.4 × (F₀/F₁)^0.6) = (0.6/0.4) × (F₁/F₀) = (3/2) × (F₁/F₀). However, the correct expression in the options is (2/3) × (F₁/F₀), which is option C.

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

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