B3) Suppose there are 150 buyers in the market for used cars. There are two types of cars in the market: the high-quality cars have a 90% chance to work, and the low-quality cars have a 40% chance to work. All buyers value a car that works at $10,000 and a car that does not work at $0. The buyers are risk-neutral. Sellers know the quality of their cars. There are 70 sellers with low- quality cars, and 30 sellers with high-quality cars. The sellers' value of a high-quality car is $8000, and their value of a low-quality car is $5000. a) What is the value of a high-quality car to a buyer? What is the value of a low-quality car to a buyer? [2 marks] b) Suppose the buyers do not know the quality of cars. With all the sellers in the market, what is the maximum price that a buyer is willing to pay for a car? [2 marks] c) If the buyers are only willing to pay the maximum price solved for in part b), are the high-quality car sellers willing to sell? How about the low-quality car sellers? [2 marks] d) Combine your answers in parts b) and c), explain which sellers sell their cars in the market, and what is the range of possible prices in the market. [3 marks] e) Suppose there are 70 sellers with high-quality cars and 30 sellers with low-quality cars. Is it possible that the high-quality car sellers are willing to sell? If yes, explain when they are willing sell. If no, explain why. [3 marks] f) Explain how the percentage of sellers in the market with high-quality cars affects the possibility of high-quality cars being sold. Use no more than four sentences. [2 marks]