A second-hand car dealer is doing a promotion of a certain model of used truck. Due to differences in the care with which the owners used their cars, there are four possible quality levels (q1 > q2 > q3 > q4) of the trucks on sale. Suppose that the dealer knows the car’s quality (quite obvious), but buyers only know that cars for sale can be of quality q1, q2, q3 or q4. Faced with a given car, the buyers cannot identify its precise quality. However, they believe that there is a probability 0.2 that the quality is q1, a probability 0.3 that it is q2, and a probability 0.3 that it is q3. The respective values of the cars to the buyers are $20,000 for the q1 quality, $15,000 for q2, $10,000 for q3 and $5,000 for q4.
Assume that all agents (including the buyers) are risk neutral (only care about “return”) in the sense that a buyer does not want to pay more for a car than its expected worth and the car owner (the car dealer) does not wish to sell at less than what the car is worth.
a) Define adverse selection in general and in the current context.
b) If all four types of used truck are offered for sale, what is the highest price a buyer would be willing to pay for a used truck? At this price, what type(s) of truck will be offered for sale?
c) Now suppose the $20,000 trucks are no longer offered for sale but other types are (and is known to the buyers). What is the maximum price a buyer is willing to pay for a used truck? At this price, what type(s) of truck will be offered for sale? [Hint: What are the respective probabilities of the types of cars that will be offered for sale?]
d) Explain how adverse selection causes this market to a partial market breakdown (i.e., only the worst used trucks (q4 type) are traded in the market).