Suppose that there are two types of cars, good and bad. The qualities of cars are not observable but are known to the sellers. Risk-neutral buyers and sellers have their own valuation of these two types of cars as follows: Now suppose that sellers value a good car at $4,500 and a bad car at $2,500, and quality is not observed by the buyers. What is the highest price that risk-neutral buyers will offer for a used car if they recognize adverse selection?

Question

Suppose that there are two types of cars, good and bad. The qualities of cars are not observable but are known to the sellers. Risk-neutral buyers and sellers have their own valuation of these two types of cars as follows:  Now suppose that sellers value a good car at $4,500 and a bad car at $2,500, and quality is not observed by the buyers. What is the highest price that risk-neutral buyers will offer for a used car if they recognize adverse selection?

Quizplus · Accepted Answer

Since buyers recognize adverse selection, they know that there is a higher likelihood of getting a bad car. Therefore, they will only offer a price that reflects the expected value of getting a bad car, which is $2,500. Any higher offer would result in a negative expected value for the buyer, which they would want to avoid as risk-neutral individuals. The highest price they will offer is the second-best option they have, which is buying a bad car and paying $2,500 for it. Thus, the highest price that risk-neutral buyers will offer for a used car if they recognize adverse selection is $3,000 (the expected value weighted by the probability of getting a good car: $4,500 x 0.5 + $2,500 x 0.5 = $3,500, but buyers will discount this to account for adverse selection).

Suppose That There Are Two Types of Cars, Good and Bad