In Bent Crankshaft, Oregon there are several used car owners, who are interested in selling their used cars. One-third of these used car owners have bad used cars, which they would happily sell to any buyer for any price above $300 (which is what the junkyard would pay for it). One third of them have used cars of medium quality, which they would be willing to sell if and only if they could get a price greater than $900. One third of them have good used cars, which they would be willing to sell if and only if they could get a price greater than $1500. There are a large number of potential buyers of used cars. These buyers would have zero value for a bad used car. 

A medium quality used car would be worth $2100 to these buyers. A good used care would be worth an amount vG to these buyers. Although the current owners of used cars know the quality of the car they have, the potential buyers cannot tell the difference between them. Since buyers can’t tell the difference between used cars, all used cars will sell for the same price. A buyer will be willing to buy a used car if and only if, given her beliefs about which used cars come to market, her expected value from buying a used car is at least as high as the price of used cars. We assume that all buyers have the same beliefs about which used cars come to market, and since there are many more buyers than sellers, the price of a used car will be the expected value to buyers of those used cars that are available at this price. 

A) For what values of vG will there be a perfect Bayes-Nash equilibrium in which all of the used cars are sold? What will be the price when this is the case? Explain your answer.

B) At the values of vG for which there is an equilibrium in which all of the used cars are sold, will there also be a perfect Bayes-Nash equilibrium in which only bad used cars and cars of medium quality are sold? If so, what will be the price of used cars in this equilibrium? 

C) Are there any values of vG for which there is no perfect Bayes-Nash equilibrium in which the good used cars are sold but there is one in which the used cars of medium quality are sold? Explain your answer.