6. Consider the model of the market for lemons. Suppose that there are two types of used cars, good ones and lemons, and that sellers know which type of car they have. Buyers do not know which type of car a seller has. The fraction of used cars that are good cars is g and buyers know this fraction. Let’s suppose that a seller who has a good car values it at $10,000 and that a seller with a lemon values the lemon at $4,000. A seller is willing to sell his car for any price greater than or equal to his value for the car; the seller is not willing to sell the car at a price below the value of the car. Buyers values for good cars and lemons are, $12,000 and $5,000, respectively. As in Chapter 22 we will assume that buyers are risk neutral; that is, they are willing to pay their expected value of a car.

(a) Suppose that you observe that used cars sell for a price of $10,000. What can you say about the fraction of used cars that are lemons?

(b) Suppose, instead that the fraction of used cars that are lemons is g = 0.5. What is the maximum selling price for used cars?