B. Analytical Problems 2. Consider the market for used cars discussed by Akerlof. Car sellers have the utility function Us = M + Z axl where M is the amount of money they have, x; is the quality level of the jth car, and 'a' is the coefcient on car quality in the utility function. Buyers have utility function \"3 = M + Z bx: There is a uniform distribution of quality of the cars held by sellers, xi~U[0.2]. Sellers know the quality of the cars, but buyers only know the average quality of the cars on the market. Buyers also know the utility function of sellers. a. [5 points] Let P be the price of used cars put up for sale. What is the average quality of cars put up for sale as a function of P and a