Question

Suppose, for simplicity, that there are two kinds of used cars in the market. Exactly 50% of the cars are good cars worth $10,000, and 50% are bad cars (lemons) worth only $5,000. Also suppose that only the car owner truly knows the type of car that it is.

A.If both kinds of cars are sold, what is your expected value from buying a used car?

B.Now suppose that current owners of good cars (i.e., the sellers) have a reservation value of $8,500 (i.e., they’d rather keep a good quality car than sell it for less than $8,500). The sellers of bad cars value their cars at only $4,500. You know the reservation prices exist; however, you cannot distinguish the good sellers from the bad ones. If someone offers you a car at $6,500, do you buy it? Why or why not? C

C.What problem of asymmetric information is this exercise related to (be specific)?

Answer 1

(A)

The worth of good cars is $10,000. The probability of car being good is 50% or 0.50.

The worth of bad cars is $5,000. The probability of car being bad is also 50% or 0.50.

Calculate the expected value from buying a used car -

Expected value = [Worth of good cars * Probability of car being good] + [Worth of bad cars * Probability of car being bad]

Expected value = [$10,000 * 0.50] + [$5,000 * 0.50] = $5,000 + $2,500 = $7,500

Thus,

The expected value from buying a used car is $7,500.

(B)

Now, the reservation price for good cars is $8,500 and the reservation price of bad cars is $4,500. The probability of getting a good car or bad car is 50%.

Calculate the expected reservation price for used car -

Expected reservation price for used car = [Reservation price of good cars * Probability of car being good] + [Reservation price of bad cars * Probability of car being bad]

Expected reservation price for used car = [$8,500 * 0.50] + [$4,500 * 0.50] = $4,250 + $2,250 = $6,500

Thus,

The expected reservation price for used car is $6,500.

This means we would be willing to pay $6,500 for a used car.

Now, someone offers the used car for $6,500.

The price offerred is equal to the price that we are willing to pay.

So,

We will buy the car.

(c)

In this case, the sellers of car has more information about the car than the buyers.

When seller have more information than buyers in an exchange then problem of adverse selection tends to exist.

Thus,

This excercise is related to adverse selection problem of asymmetric information.