(2) [6 points] Suppose that there are two types of used cars - High quality ones and Low quality ones - and that sellers know which type of car they have. Buyers do not know which type of car 1 a seller has, and sellers of High quality cars have no way of proving what kind of car they have. Buyers know that the fraction of used cars in the total population of used cars that are High quality is 1/2 and the fraction of used cars that are Low quality is 1/2 (but as is typical in these situations, it is not necessarily the case that all the owners of these used cars will choose to sell them). The following table summarizes the values of the different cars for sellers and buyers in thousands of dollars We assume that buyers are risk-neutral; that is, they are willing to pay their expected value of a car. (a) Find all of the self-fulling expectations equilibria in this market. (b) Now some totally worthless cars are introduced into the market. These cars are so bad that their value to either buyers or sellers is 0 . As with the other cars in the market the seller knows the quality of the car, but the buyer does not know the quality of the car. Let the fraction of these cars be p; so the sum of the fractions of High and low quality cars is now 1p. Suppose that everyone knows this fraction p. Is there a critical fraction, p, of worthless cars such that for any p>p there is not a self-fulling expectations equilibrium in the market for used cars in which High quality cars are sold? If so, what is p. If not, explain why not. Show your work. (c) Is there a critical fraction, p, of worthless cars such that for any p>p there is not a self-fulling expectations equilibrium in the market for used cars in which Low quality cars are sold? If so, what is p. If not, explain why not. Show your work