Question

2. (a) Suppose a “lemons” car is valued at $2500 and a good car is valued at $5000. If you know that there is a 50% chance of getting each, what is the expected value of the car?

(b) What will happen in the market if the price is based on the expected value? Explain.

Answer 1

Question 2

(a)

The value of "lemons" car is $2,500. The probability of getting a "lemons" car is 50% or 0.50.

The value of good car is $5,000. The probability of getting a good car is 50% or 0.50.

Calculate the expected value of the car -

Expected value of the car = [Value of lemon car * Probability of getting a lemon car] + [Value of good car * Probability of getting good car]

Expected value of the car = [$2,500 * 0.50] + [$5,000 * 0.50] = $1,250 + $2,500 = $3,750

The expected value of the car is $3,750.

(b)

The expected value of the car is $3,750.

This expected value of the car is greater than the value of "lemon" car but is lower than the value of good car.

If the price of car in the market is equal to the expected value then in that case owners of lemon cars will find it profitable to sell their car as price is greater than the value of their car. However, owners of good car would find it loss making preposition to sell their car in the market as price is less than the value of their car.

So, all good cars will be withdrawn from the market and the market will consist of "Lemon" cars only, if the price is based on the expected value.