(b) Suppose that there are 3 types of used cars in the market: good, mediocre and bad. Their values to buyers and sellers are summarized in the table belovw Value of car to buyers Value to car to sellers Types of used cars Good Mediocre Bad 18,000 15,000 8,000 17,000 4,000 6,000 Assume that 20% of used cars are good, 60% of them are mediocre, and the remaining 20% are bad Suppose that only the sellers know the quality of their cars. The buyers know the proportion of each type of car in the market, but they do not know the exact quality of each car. Assume that the buyers are risk- neutral and also so numerous that in the market all the surplus is captured by the sellers, i.e. buyers offer a price equal to their valuation of the car (i) Compute the expected value of a used car to buyers. (3 points) (ii) If a buyer offers a price that equals the answer in part (i), what kind of sellers will be willing to sell their cars? (2 points) (iii) What is the buyer's expected value of a used car in the market conditional on the sellers' response in part (ii)? (3 points)