Elmer's utility function is U(x, y)  minx, y².If the price of x is $20, the price of y is $20, and Elmer chooses to consume 8 units of y, what must Elmer's income be?

A) $2,880
B) $320
C) $1,540
D) $1,440
E) There is not enough information to tell.

Question

Lorella Restivo · Accepted Answer

Final Answer : D, Explanation :  To solve the problem, we need to use the budget constraint:P_x * x + P_y * y = Iwhere P_x is the price of x, P_y is the price of y, y is the amount of y consumed, and I is Elmer's income. Plug in the given values:20x + 20(8) = I20x + 160 = IThen, we need to find x that maximizes Elmer's utility function U(x, y). Since Elmer is consuming 8 units of y, we can simply convert the utility function into a function of x only:U(x) = U(x, 8) = 10 min {x, 8} - 20xTo maximize U(x), we take the derivative and set it to zero:dU(x)/dx = 10 - 20 = 0Solving for x, we get x = 0.5. Plugging this value into the budget constraint, we can solve for I:20(0.5) + 20(8) = II = $1,440Therefore, the answer is D.

Elmer's utility function is U(x, y)  minx, y².If the price of x is $20, the price of y is $20, and Elmer chooses to consume 8 units of y, what must Elmer's income be?

A) $2,880
B) $320
C) $1,540
D) $1,440
E) There is not enough information to tell.

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Learning Objectives

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Elmer's utility function is U(x, y)  minx, y2.If the price of x is $20, the price of y is $20, and Elmer chooses to consume 8 units of y, what must Elmer's income be?A) $2,880B) $320C) $1,540D) $1,440E) There is not enough information to tell.

Definitions

Learning Objectives

Learning Objectives

Related questions

Elmer's utility function is U(x, y)  minx, y².If the price of x is $20, the price of y is $20, and Elmer chooses to consume 8 units of y, what must Elmer's income be?

A) $2,880
B) $320
C) $1,540
D) $1,440
E) There is not enough information to tell.