In New Crankshaft, Pennsylvania, there are 200 used cars for sale; 50% of these

Question

In New Crankshaft, Pennsylvania, there are 200 used cars for sale; 50% of these cars are good and 50% of them are lemons.

Owners of lemons are willing to sell them for $500. Owners of good used cars are willing to sell them for prices above $1,500 but will keep them if the price is lower than $1,500.

There is a large number of potential buyers who are willing to pay $600 for a lemon and $2,300 for a good car.

Buyers are aware of the proportion of lemons offered for sale, but cannot tell good cars from bad.

A. There will be an equilibrium in which all used cars sell for more than $1,300.

B. There will be an equilibrium in which lemons sell for $600 and good used cars sell for $2,300.

C. There will be an equilibrium in which all used cars sell for less than $1,300.

D. The only equilibrium is one in which all used cars on the market are lemons and

they sell for $600.

E. There will be an equilibrium in which lemons sell for $500 and good used cars sell for $1,300.

Answer should be D.

Explanation / Answer

Solution:-

There are 100 good cars and 100 lemons. The selling price of lemons is minimum $500 and for good used cars, the selling price is minimum $1500.

Buyers are willing to pay $600 for a lemon and $2300 for a good car.

Buyers can’t tell good cars from bad so they place an expected price over a certain car which is 0.5*600 + 0.5*2300 = $1450.

Now when buyers are willing to pay $1450, both types of sellers are willing to sell their cars and so all cars will be sold at this price.

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