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."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 value, 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 How much will used cars end up costing if all the good cars are withdrawn?

Answer 1

A) the average value of a used car = ($13,000 + $5,000) / 2 = $18,000 / 2 = $9,000

B) the average value is $4,000 higher than the value of a bad used car. A good used car exceeds the average value by $4,000.

C) No, because he/she knows that his good used car is worth much more.

D) If the seller accepts the average value, it is more likely that his car is a bad car.

E) The majority of used cars should be bad or lemon, since good used cars will be sold quickly. If all good used cars were removed, then the price of used cars would drop to $5,000 (the value of a lemon car).