Desiree's utility function for BMWs and money is given by 9,000x + y, where x is the number of BMWs she has and y is the amount of money she has.Her income is $22,000.Her reservation price for one BMW is
A)$9,000 - p.
B)$9,000.
C)$13,000.
D)$9,000 - y.
E)$31,000.

Question

Quizplus · Accepted Answer

To find Desiree's reservation price for one BMW, we need to find the maximum amount of money she is willing to give up in exchange for one BMW. This means we need to find the marginal utility of BMWs in terms of money.
Taking the partial derivative of the utility function with respect to x, we get:
MUx = 9,000
This means that Desiree's marginal utility for BMWs is a constant value of 9,000. 
To find her reservation price, we need to find the amount of money she is willing to give up for one BMW such that her overall utility stays the same. This means we set the marginal utility of money equal to the marginal utility of BMWs:
MUy = 9,000
Solving for y, we get:
9,000 = MUy = dU/dy = 9,000F1F1F1S1F1F1F10y
y = $31,000
Therefore, Desiree's reservation price for one BMW is the maximum amount of money she is willing to give up for one BMW, which is $31,000. However, the answer choices do not include this option, so the closest choice is B, which is $9,000, representing her constant marginal utility for BMWs.

Desiree's Utility Function for BMWs and Money Is Given by 9,000x