Assignment Problem: Adverse selection
In the market for used cars there are good cars and bad cars.
The good cars comprise a fraction G of all the cars that may be potentially up for sale, where 0
Buyers cannot distinguish a good car from a bad car, whereas each seller knows the type of car she has.
The valuation of good and bad cars by buyers and sellers are given in the accompanying table.
|
|
Good
|
Bad
|
|
Buyers
|
50
|
20
|
|
Sellers
|
30
|
10
|
All buyers are risk neutral.
(a) Assuming that all cars are put up for sale, calculate the expected price that a buyer would be willing to pay.
(b) Suppose buyers pay this price. What is the minimum value of G for which both types of cars will be offered on the market? Show the reasoning.
(c) Suppose that G=8/10. What is the maximum price buyers are willing to pay for a car? Will both types of cars be offered for sale in the market at this price?
(d) Continue to assume that G=8/10
There is an agency that can assess each car and certify it as "good" or "bad".
If certified as good, the seller can negotiate a price of 45 with the buyer.
If uncertified cars are selling for the price you found in (c), what is the maximum that a seller of a good car will be willing to pay to get his car assessed?
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