In an isolated town, there are two distinct markets for cars. Buyers will pay up to $12,000 for a high-quality car or $8,000 for a low-quality car. There are 100 high-quality cars for sale, and the sellers have a minimum acceptable price of $11,000. There are also 100 low-quality cars for sale at a minimum acceptable price of $5,000. The supply of automobiles is perfectly inelastic above the reservation price.
a. If there is perfect information, how many high-quality and how many low-quality cars will be sold?
b. Suppose that the quality of a car is known to the seller, but not to the buyer. What price will prevail in the marketplace if buyers correctly estimate the chance of acquiring a low-quality car at 50%? What happens to the number of high-quality cars for sale at that price?
c. After sellers make all adjustments, what will the equilibrium price of cars be? What proportion of those cars will be high-quality cars?
d. What happens to your answers to (a), (b), and (c) if sellers of high-quality cars have a reservation price of $9,500 instead of $11,000?