Question

Consider a market for used cars where each buyer wants to purchase exactly one used
car if at all. In case he does not buy a car, his utility is zero. There are two kinds of
used cars, good quality, called peaches, and bad quality, called lemons. Let there be
100 lemons with valuation 0 for both buyers and sellers, whereas there are 100
peaches with valuations of 100 for the buyers, and 60 for the sellers. There are 500
buyers, who do not know which car is of which type.
a. Explain what type of trade should take place in the efficient outcome.
b. Compute the market equilibrium when the buyers know which car is which
type. Is the outcome efficient? Explain clearly.
c. Now consider the case with asymmetric information: the sellers know the type
of their cars but the buyers do not. Explain the market outcome under
asymmetric information. Explain clearly whether the market outcome will be
efficient.

Answer 1

a.) In an efficient outcome, buyers should buy peach cars and sellers should only sell peach cars as there isn't a market for lemon cars. There is a zero valuation to lemon cars which makes it unnecessary to buy/sell.

b.) For an efficient outcome to take place, both buyers and sellers need to have perfect information about the market. If anyone of the them fails to have all the information, there is a risk of market failure or sub-optimal equilibrium. In our case, let us assume that everyone has perfect knowledge about the quality of the cars in the market. A potential buyer will only buy "peach" car because "lemon" gives him/her zero utility. So there is no market for lemon cars as there are no buyers for it. As for the market for peach cars, buyers are willing to pay $100 for a car and sellers are willing to sell at $60. As the number of buyers(500) exceed the available number of care(100), the price of each car will be $100. This price cannot exceed $100 because then there will not be anyone willing to buy the car.

c.) In this case the buyers have to guess about how much each car is worth. The probability of a car to be lemon or peach is equally likely, that means its 0.5 for both as there are equal number of peach and lemon cars in the market. Using the numbers described above this means that the buyer would be willing to pay :-
0.5*100 + 0.5*0 = $50.
But who would be willing to sell their car at that price? The owners of the lemons certainly would, but the owners of the peaches wouldn’t be willing to sell their cars—by assumption they need at least $60 to part with their cars. The price that the buyers are willing to pay for an “average” car is less than the price that the sellers of the peaches want in order to part with their cars. At a price of $50 only lemons would be offered for sale. But if the buyer was certain that he would get a lemon, then he wouldn’t be willing to pay $50 for it!

In such a situation, no car is sold. It is worthwhile to notice that even though the price at which buyers are willing
to buy peaches exceeds the price at which sellers are willing to sell them, no such transactions will take place. This results in market failure. The problem is that there is an externality between the sellers of good cars and bad
cars; when an individual decides to try to sell a bad car, he affects the purchasers’ perceptions of the quality of the average car on the market. This lowers the price that they are willing to pay for the average car, and thus hurts the people who are trying to sell good cars. It is this externality that creates the market failure.