Question

Consider a used-car market with asymmetric information. The owners of used cars know what their vehicles are worth but have no way of credibly demonstrating those values to potential buyers. Thus, potential buyers must always worry that the used car they are being offered may be a low-quality "lemon." 

Instructions: Enter your answers as whole numbers. 

a. Suppose that there are equal numbers of good and bad used cars in the market and that good used cars are worth $13,000 while bad used cars are worth $5,000. What is the average value of a used car? 

b. By how much does the average value exceed the value of a bad used car? By how much does the value of a good used car exceed the average value? 

c. Would a potential seller of a good used car be willing to accept the average value as payment for her vehicle?

d. If a buyer negotiates with a seller to purchase the seller's used car for a price equal to the average, is the car more likely to be good or bad?

e. Will the used-car market come to feature mostly-if not exclusively-lemons? How much will each used car end up costing if all the good cars are withdrawn?

Answer 1

a) Solution: $9,000

Working: Because there are an equal number of good and bad used cars in the market thus likelihood of both the type is 0.50 (i.e. 50% good and 50% bad)). It means the average value of a used car equals $9000 (=0.5 * $13,000 + 0.5 * $5,000).

b) i) Solution: $4,000

Working: $9,000- $5,000

ii) Solution: $4,000

Working: $13,000- $9,000

c) Solution: No

Working: No, a potential seller of a good used car would not be willing to accept the average value as payment for her vehicle as there is a 50 percent chance that they are not getting the full value of the car

d) Solution: Bad

Working: When a buyer negotiates with a seller to purchase the seller’s used car for a price equal to the average, the car will be likely to be bad. The seller of a good used car would not be willing to accept $9,000 (i.e. average value) for a car whose worth equals $13,000 (i.e. value of a good used car)

e) i) Yes, the market will come to feature mostly - if not exclusively- lemons.

ii) Solution: $5,000

Working: When all the good cars are withdrawn, the remaining bad cars must go for what they are worth i.e. the amount of $5,000 each.