A prospective used car buyer has $3,200 value for a car. A used car seller, whos value for a car is $2,700, has two types of cars Lemons (L) and Plums (M). The expected repair costs on a Lemon is $1,700 and for a Plum is only $200. Given these values and repair costs, the following table shows the net value (i.e. value after deducting repair cost) of a used car of each type to the buyer and the seller.

	Plum	Lemon
Net Value to Buyer	$3,000	$1,500
Net Value to Seller	$2,500	$1,000

a. Suppose the buyer could distinguish between a Lemon and Plum, would a Plum be traded between the buyer and seller at some price? What about a Lemon? If yes, what is the range of prices that the seller could charge for the trade to occur?

Suppose the buyer cannot tell a Lemon from a Plum, but she knows that half the cars in the dealership are Lemons and the remaining half are Plums. Thus, the prior probabilities are =Pr []=1/2 , 1- =Pr []=1/2.

b. What is the buyers updated belief conditional on the seller offering a car for sale? c. Given the buyers updated beliefs, what is the highest price that the buyer will be willing to pay for a car? d. Given the highest price that the buyer is willing to pay (determined in part c), is a best response for the seller to offer both types of cars up for sale? e. Based on your answers to a) to d), is there a pooling PBE (perfect bayesian equilibrium) where both types of cars are sold? f. Show that there is a separating equilibrium that is a PBE (perfect bayesian equilibrium) where only Lemons are traded, while Plums are not. (Adverse Selection). Describe the PBE (perfect bayesian equilibrium) completely as a pair of strategies chosen by the seller and buyer and the buyers conditional belief about the car type, g. Show that there cannot be a separating equilibrium where only Plums are traded, while Lemons are not.

PLEASE EXPLAIN AND SHOW WORK AND ESPECIALLY ANSWER THE LAST 2 PARTS