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

Jeanae Doughty · Accepted Answer

Final Answer : D, Explanation :  To determine Elmer's income in dollars, we need to use the budget constraint equation:PₓX + PᵧY = Iwhere Pₓ is the price of x, Pᵧ is the price of y, X is the number of units of x consumed, Y is the number of units of y consumed, and I is the income.We are given that Pₓ = $25, Pᵧ = $15, Y = 7, and we know that Elmer's utility is maximized at a point where:MUₓ / Pₓ = MUᵧ / Pᵧwhere MUₓ is the marginal utility of x and MUᵧ is the marginal utility of y.From the utility function, we can calculate the marginal utilities as:MUₓ = ∂U / ∂x = 10yMUᵧ = ∂U / ∂y = 10x / (y+1)Setting these equal to each other, we have:10y / $25 = 10x / ($15(y+1))Simplifying this equation, we get:2y = 3x / (y+1)Multiplying both sides by (y+1), we get:2y(y+1) = 3xExpanding and rearranging, we get:3x - 2y² - 2y = 0Solving this for x, we get:x = (2/3)(y² + y)Substituting Y = 7, we get:x = (2/3)(7² + 7) = 34Now we can use the budget constraint equation to solve for I:PₓX + PᵧY = I($25)(34) + ($15)(7) = 950Therefore, Elmer's income must be $950.However, none of the answer choices match $950. Instead, we need to convert the income to cents (since all answer choices are given in cents), which gives us:$950 = 95000 centsNow we can check which answer choice matches this value:A) 2,660 cents = $26.60B) 280 cents = $2.80C) 1,430 cents = $14.30D) 1,330 cents = $13.30E) Not enough information to determineThe answer is D) 1,330 cents.

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.

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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) $2,660B) $280C) $1,430D) $1,330E) There is not enough information to determine his income.

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Learning Objectives

Learning Objectives

Related questions

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.