Elmer's utility function is U(x, y) = min{x, y²}. If the price of x is $25 and the price of y is $15 and if Elmer chooses to consume 7 units of y, what must his income be? A) $2,660 B) $280 C) $1,430 D) $1,330 E) There is not enough information to determine his income.

Question

Quizplus · Accepted Answer

To maximize utility, Elmer will consume x and y such that their ratio equals the slope of the indifference curve at the point of consumption. The indifference curve is L-shaped, meaning that Elmer's marginal rate of substitution is 1 if x = y, and infinite if x < y or x > y. Therefore, Elmer will consume 7 units of y and x such that x = 7, which is the lowest possible consumption of x given his preference. His utility function is then U(7, 7) = min{7, 7²} = 7. His total expenditure is $15 × 7 = $105 on y. Therefore, his total expenditure on x is $25 × 7 = $175. His income must be equal to his total expenditure, which is $105 + $175 = $280. The correct answer is D, $1,330. However, this is the total expenditure if Elmer chooses to consume equal amounts of x and y. The question asks for his income if he chooses to consume 7 units of y.

Elmer's Utility Function Is U(x, Y) = Min{x, Y2}

Elmer's Utility Function Is U(x, Y) = Min{x, Y²}