4. (20 points) Consider a variation of Akerlofs market for the lemons model. Seller utility is the sum of all their used car qualities, Xjs, and amount of other good M, that is, US = Xj + M. Assume buyers value used cars 60% more than sellers. So their utility is given by UB = 1.6Xj + M. Also assume use car quality follows a uniform distribution from 0 to 100. a. Consider an offer of $80 by a buyer to a seller for a potential used car. What used cars will sellers offer in this case? Would the change in buyer expected utility be positive or negative in this case? Explain.

b. What does your result in part a imply about the current and future viability of the used car markets? Explain.

c. Would reduce the prospective offer down to $40 help with the situation? Explain.

d. Suppose a quality price floor is now instituted in the used car market. It is not legal, nor permitted, to sell any used car worth 10 or less. Are there now any prices that result in used cars selling to buyers? Does this help with the survival of the used car market? Explain.