Consider Akerlof's market for lemons. Suppose there is asymmetric information in the market for used cars: sellers know the quality of their car, but buyers do not and cannot tell the quality of cars. Buyers assume car quality X is uniformly distributed between 0 and 100. That is, they are equally likely to choose a car j with quality 7 as a car with quality 85 or 71. Given this setup, a buyer's expected value of a car, conditional on price P, is E[Xj |P] = 100+0 2 = 50. Suppose seller's utility is given by Us = [ nj=1 Xj+M, where M is utility from all other goods. Buyer's utility is given by Ub = [nj=1 axj + M. a. In general, when would a buyer buy a car in the Akerlof model with asymmetric information? You may want to write a general equation. b. What is the utility to buyers of the average car? c. What is the maximum price, Pmax, that at least some cars will sell, in terms of a. Note: your answer must include a.