Question

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).

Answer 1

a. Adverse selection is a situation in which in a given market, the seller has the information that the buyers does not have the full information about the product being sold. Under such situations, the buyers take wrong decisions as there is a possibility that the prices and the quantity the buyers buy may not be worth enough to buy that is the buyers could end up paying more than supposed to. In the given case, as the buyer is not sure of the quality of the truck so he may pay a higher value for the worst of the quality of truck traded.

b. Being risk neutral, the buyer would value the truck at 0.2*20000+.3*15000+.3*10000+.2*5000 which is 12500. The buyer would be willing to pay $12500 for the truck. At this price, the trucks of q3 and q4 quality would be offered for sale.

c. Now the maximum price will be (3/8)*15000+(3/8)*10000+(2/8)*5000 or $10625. The truck which would now be offered will be of quality q3 and q4.

d. As can be seen from the above calculations, due to adverse selection, in both the cases, only the worst of the two are being traded in the market.