Suppose in the market for used cars, buyers would be willing to pay $9,000 for a car in good condition, while buyers would have to incur a cost of $3,500 to repair a car in poor condition.If the probability of a car being in bad condition is 0.35, what price would a risk-neutral buyer be willing to pay?
A)$3,925
B)$1,925
C)$7,775
D)$5,850

Question

Quizplus · Accepted Answer

A risk-neutral buyer would be willing to pay the expected value of the car, which takes into account the probability of it being in good or poor condition. Let x be the price a buyer is willing to pay for the car in unknown condition. Then, using probabilities, we can set up the equation:
($9,000 x probability of good condition) + (($9,000 - $3,500) x probability of bad condition) = x
($9,000 x 0.65) + ($5,500 x 0.35) = x
$5,850 + $1,925 = x
$7,775 = x

Therefore, a risk-neutral buyer would be willing to pay $7,775 for the car.

Suppose in the Market for Used Cars, Buyers Would Be