Question

Suppose there are two types of cars, good and bad cars. The qualities of cars are not observable but are known to the sellers. Now suppose that sellers value a good care at 4500 and a bad car at 2500 and the quality is not observed by the buyers. What is the highest price that a risk-neutral buyer will offer for a used car if they recognize adverse selection?

Answer 1

Risk neutral buyers & sellers have their own valuation of good & bad cars as follows:

Type of cars	Buyer’s valuation	Seller’s valuation
Good (50% probability)	5000	4500
Bad (50% probability)	3000	2500

• Buyers & sellers are separately able to identify good & bad cars.
• Two different prices are established for two separate goods.
• Price will be bid up to opportunity cost of the buyer – all cars will be sold if the value for the buyer > value for seller for both the types of goods.
• Price will be based on expected frequency of good cars in the population: assume 50/50 in this case.
• Results in efficiency – all cars are sold if the expected value for the buyer is > expected value of the seller.