All used cars are lemons or peaches. Owners know whether or not their car is a lemon, but buyers do not; that is, the quality of a car is private information. There are many more buyers than sellers

Question

Buyers value a peach at $4,000 and a lemon at $200; owners value a peach at $3,000 and a lemon at $100 . Owners can have their cars inspected for $100 . If they do have their car inspected, they will receive a certificate that shows whether the car is a lemon or a peach. Show that owners of peaches will have their cars inspected and will sell those cars for $4,000 . Show also that the owners of lemons will not obtain a certificate and will sell their cars for $200 .

Answer 1

If the owners of peaches obtain a certificate stating that their cars are not lemons, they will be able to sell their cars to buyers for $4,000, thus gaining from trade. Those who own lemons will not obtain a certificate since the certificate would not help them convince buyers their cars are peaches. Buyers will therefore conclude that any owner who is selling a car without a certificate must own a lemon. This is an application of Michael Spence's theory of signaling. In a market with asymmetric information and adverse selection, individuals could choose costly signals in order to reveal their private information. Since buyers cannot distinguish between lemons and peaches, there is asymmetric information in the used car market. With the certificate, sellers are sending a signal to buyers about the true quality of their car.
See Michael Spence, "Job Market Signaling," Quarterly Journal of Economics August 1973, pp 355–374