4. (26 pts) There are ten cars potentially available for a used-car market. Two of these cars are high quality. Seven are medium quality and one is low quality. A high-quality car is worth $5000 to its owner. A medium- quality car is worth $3000 to its owner and a low-quality car is worth $1000 to its owner. Each seller has perfect information about the quality of his or her car. There are a large number of potential buyers. A high-quality car is worth $6500 to a potential buyer. A medium-quality car is worth $4500 to a potential buyer and a low-quality car is worth $2500 to a potential buyer. Competition among the potential buyers will drive price up to the (expected) value of the relevant car(s). The potential buyers cannot directly observe the quality of any specific car, but they do know the proportion of each type of car that is on the market. a. If all three types of cars are on the market, what is the maximum amount the buyer will be willing to pay for a car of unknown quality? Show your work. b. Given the price you found in (a), which types of cars will be available on the market? Briefly demonstrate your logic. c. Is the situation described in (a) and (b) a Nash equilibrium? Clearly demonstrate your logic. d. Describe the equilibrium for this market with asymmetric information. Determine which cars will be on the market and the resulting price. e. Briefly describe three ways in which this adverse selection problem could be resolved