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.”

1. Suppose that there are equal numbers of good and bad used cars in the market. Good used cars are worth \(13,000, and bad used cars are worth \)5,000. What is the average value of a used car?
2. 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?
3. Would a potential seller of a good used car be willing to accept the average value as payment for the vehicle?
4. 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?
5. Will the used-car market come to feature mostly—if not exclusively—lemons? Explain. How much will used cars end up costing if all the good cars are withdrawn from the market?

Short answer

1. The average value of a car is $9000.
2. The average value exceeds a bad used car value by $4000, and the average value of a car is $4000 less than the value of a good used car.
3. No, the seller will not accept the payment..
4. The car is more likely to be bad.
5. It will be filled with lemons due to a lower acceptable price for good used-car owners. The used cars will cost $5000 if the good cars are withdrawn.

Step-by-step solution

Step 1. The explanation for part (a)

The average value in the used-car market is determined to reduce the risk of asymmetric information, which can lead to adverse selection. It is calculated by adding up the product of the probability of choosing a good with the value of a good car and the probability of choosing a bad car with the value of a bad car.

Thus, the average value of the used car given that there is an equal number of good cars worth $13,000 and bad cars worth $5,000 is given below:

$$\begin{gathered} AverageValue=P_g\times W_g+P_b\times W_b \\ =\frac{1}{2}\times 13000+\frac{1}{2}\times 5000 \\ =9000 \end{gathered}$$

Step 2. The explanation for part (b)

The value of the bad car is $4000 less than the average value of a car in the used-car market (=$9000-$5000). Thus, the average value exceeds the bad car value by $4000. The value of a good car is $4000 more than the average value of a car in a used-car market (=$13000-$9000).

Step 3. The explanation for part (c)

The seller of a good used car knows the car’s worth and thus, would be unwilling to accept a lower payment value. Since the average value of a car in the used-car market is $4000 less than the true value of the good used car. The seller will not engage in any transaction.

Step 4. The explanation for part (d)

If a buyer is able to negotiate and convince a seller to sell his/her car at a price equal to the average value of the car ($9000), then the car is a bad used car. A well-used car owner will find the lower payment (compared to $13000) unacceptable, whereas a badly used car owner will be happy to get a higher price (compared to $5000).

Step 5. The explanation for part (e)

Since most good used-car owners will be unwilling to accept lower prices for their good cars, the market will be filled with lemons (bad used cars). The badly used car owners will be more than happy to sell their cars at the average value.

The withdrawal of good used cars will reduce the average value to $5000, which is the true value of a bad used car.