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Suppose that used cars can be of four, equally common, types: 25% are peaches (P), 25% are just fine (F), 25% are classified as meh (M), and 25% are lemons (L). The following table shows what each type is worth to its current owner (a seller), or to a new owner (a buyer). Assume buyers and seller are risk neutral, and that in the case of bargaining, the seller and the buyer settle for a price that is the mid point of the range of possible prices that induce trade. Value to a buyer Value to a seller Fraction of the used cars Type P Type F Type M Type L $25,000 $10,000 $5,000 $0 $16,000 $8,000 $4,000 SO 25% 25% 25% 25% (a) If there is perfect information about the type of each car, which types would be sold and what would be the price of each type? (b) If neither sellers nor buyers would know the type, what would be the price of a used car? (there would be one price) (e) Suppose sellers know the type of their own car, but buyers have no way to distinguish between the types. How many cars would be sold of each type? Are there prices that buyers and sellers can agree upon? (show why this must be the case) (d) Suppose only sellers know the type, whereas buyers can get a free inspection to identify if a vehicle is of type P. The inspection is usually accurate, but not always: 85% of type P vehicles will pass the inspection (15% of type P will fail), while only 5% of types F. M, and L will pass the inspection (95% will fail) What fraction of vehicles of each type will be sold, and for what price? (c) Under the assumptions of part (d), suppose that the inspection costs $1000 instead of free. Sellers who wish to get an inspection must pay $1000 upfront, a fee that is not refundable and can only be paid by the sellers (requires proof of current ownership). Which sellers will opt to perform the inspection? (t) Suppose there are 100,000 cars in the county What is the total welfare (.e. the total value extracted from consumption of the 100,000 cars) in each of the cases (a) through (d) above