Consumers know that some fraction X of all new cars produced and sold in the market are defective.The defective ones cannot be identified except by those who own them.Assume for this problem that cars do not depreciate with use.
Suppose that good used cars are worth $10,000 and lemon used cars are worth $5,000 to their owners.If X = 20%,how much a risk-neutral consumer would be willing to pay for a used car?

Question

Quizplus · Accepted Answer

Since X = 20% of the total cars available in the market are defective, there is a 20% chance that the consumer may end up with a lemon used car, which is worth only $5,000. On the other hand, there is an 80% chance that the consumer may end up with a good used car, which is worth $10,000.

To calculate the expected value of a used car, we take the weighted average of the value of a good used car and the value of a lemon used car:

Expected Value = (0.8)($10,000) + (0.2)($5,000) = $9,000

Therefore, a risk-neutral consumer would be willing to pay $9,000 for a used car.

Consumers Know That Some Fraction X of All New Cars