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

Quizplus · Accepted Answer

To solve the problem, we need to use the budget constraint:
P_x * x + P_y * y = I
where 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) = I
20x + 160 = I
Then, 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} - 20x
To maximize U(x), we take the derivative and set it to zero:
dU(x)/dx = 10 - 20 = 0
Solving for x, we get x = 0.5. Plugging this value into the budget constraint, we can solve for I:
20(0.5) + 20(8) = I
I = $1,440
Therefore, the answer is D.

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

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