2 Problem Consider the following variation of the model of the market for used cars that we studied in class. Used cars oomeiuthreedifFereutqualities: =,l'= 1f2or=L Theowuerofausedcarof quality I? gets utility El from keeping the car, and gets utility 1:: if she sells the car at price p. A potential buyer of a used car gets utility g9 p from buying a used car of quality ii at price p1 and gets utility zero if she doesn't buy a used car. Assume that sellers know the quality of their used car, but buyers cannot observe this quality. Buyers only know that there is a fraction ly'3 of used carsofead1quality3=1,l=1f2andl5l=ll. {i} Suppose rst that the price for used cars is p L: 1. What will be the average quality of the cars or sale at this price? What is the expected payoff of a buyer who buys a car at this price? Can there be an equilibrium in which the price of used cars is p 3:1? {ii} Suppose next that p E [I'M1 1}. 1What will be the average quality of the cars for sale at this price? What is the expected payoff of a buyer who buys a car at this price? Can there he an equilibrium in which the price of used cars is p E[1y"21 1]? {iii} Suppose next that p E [3,1f2}. 1What will be the average quality of the cars for sale at this price? What is the expected payoff of a buyer who buys a car at this price? Can there he an equilibrium in which the price of used cars is p E[D,1f]? {iv} Consider a different market in which the fraction of cars of quality ti = l is 31:01, and the fraction of cars of qualities I? = If? and H = I] is US each. Buyers and sellers in this market have the same utility as above. Can there be an equilibrium in this market in which all types ofused cars aresoldatpricep=1