Gerald is considering buying a used Ford Focus. From reading car magazines, Gerald knows that half of all Ford Focuses up for sale have mechanical problems (they’re lemons), and the other half run just fine (they’re plums). Gerald is willing to pay $10,000 for a plum, but only $4,000 for a lemon. People who own plums are willing to sell them for any price at or above $8,000, and people own lemons are willing to sell them for any price at or above $2,000.
(A) If everyone knows whether a used car is a lemon or a plum, is Gerald likely to purchase a car?
(B) Now suppose Gerald cannot tell whether a used car is a lemon or a plum. Instead, sellers have private information about the quality of their cars. If half of all used Ford Focuses for sale are lemons and half are all plums, then if Gerald is risk-neutral, what's the most he would be willing to pay for a used Ford Focus?
If Gerald offered to pay the owner of used a Ford Focus this amount, would he be likely to be buying a lemon or a plum?