There are many potential buyers for used cars. All of them are willing for pay $1000 for a lemon and $2000 for a good used car. There are 1000 owners of lemon and 1000 owners of good used car.
The reservation price of owners of lemon is $750. Among the 1000 owners of good used cars, 600 of them have reservation price at $1250, and 400 has reservation price at $1750.

a) Suppose by running CARFAX the buyers of used cars can identify which car is a lemon and which car is of good quality. With the sellers having a stronger bargaining power, how much a lemon and a good car will be sold for? And how many of them will be sold?

b) With no CARFAX, the buyers do not know which car is a lemon and which car is of good quality. They only know there are 1000 lemons and 1000 good cars. They assess that with probability 1/2 a car is a lemon and with probability 1/2 a car is of good quality, how much are they willing to pay for a car?