6. Consider the market for used cars in which there are two types of vehicles, namely, good and bad. A good car is valued by buyers at 2,000 and valued by the sellers at 1,600. A bad car is valued by buyers at 1,000 and by sellers at 200. Sellers have complete information on the type of car they own. However, assume that potential buyers have no way of knowing whether a car is a good type or a bad type but know that the fraction of good cars in the population is one half. Both buyers and sellers are risk neutral. (a) Explain what price buyers would be willing to pay for a car of unknown quality. Discuss the consequences for the market for used cars in this case. [5%] (b) Explain the minimum value of the fraction of good cars in the population required to ensure that the market for good cars does not collapse. [5%] (c) If this minimum value is just satisfied in part (b), at what price do used cars trade? Calculate the payoffs for buyers and sellers of good and bad cars at this market price and interpret your results. [5%]