There are two types of used cars on the market: Lemons and Cherries. Lemons are worth $200 to sellers and $600 to buyers. Cherries are worth $800 to sellers and $1200 to buyers. Buyers know how many cars of each type are available for sale, but they cannot tell Lemons apart from Cherries. If a seller does not receive at least the amount the car is worth, he/she will take that car off the market. Buyers will anticipate this and adjust their offered prices accordingly.
a) What is the minimum proportion of cars that need to be Cherries in order for all cars to be traded?
b) Suppose that there are 20 Cherries and 30 Lemons available for sale. What is the total surplus generated from the sale of used cars?
c) Suppose that there are 10 Cherries and 30 Lemons available for sale. A car mechanic offers to inspect cars for a fee, and provide an accurate certificate of the car’s quality. What is the maximum revenue that the mechanic can earn from such a program, assuming that he optimally sets his price taking into account the rational response by car sellers?