Consider the following example of a previously owned car market under asymmetric information. The quality of the used cars that are offered on this market is drawn from a uniform distribution on [1, 10], that is q U [1, 10]. Current owners' utility from owning a car of quality q is equal to q, prospective buyers have a gross utility 1.6q if they buy a car of quality level q. If a buyer gets a car of quality q for a price p, their utility is 1.6q p, otherwise, it is zero.

(a) Suppose the buyers know the quality of the car (full information). For which values of q will there be a trade?

(b) Suppose buyers do not have information about the quality of the car they are purchasing. Will there be a trade? If so, what quality of cars will be traded in this market? How much are buyers willing to pay for such cars?

(c) Is the market outcome efficient or inefficient? Explain