There is a used car market with equal number of good and bad cars. There are two buyers and two sellers. The buyers are willing to pay $12,000 for a good car and $8000 for a bad car. A seller with a good car is willing to sell their car for $11,000. The seller with a bad car is willing to sell their car for $7000. However, the buyers do not know which seller has the good car.

a. Derive the average a buyer is willing to pay for a used car if both sellers sell.

b. Show whether the seller with a good car is willing to sell this car at the price in a.

c. What happens in the market?

d. Show whether the outcome in b. is Pareto Efficient (Allocation).