There are 1,000 individuals in the city of Lincoln wishing to sell their used cars. The value of a car, V, ranges between $0 and $3000. The distribution of values is such that the number of used cars is worth less than $V is V/3. The true value of the car is known only to the owner. Potential buyers are risk neutral and value a car at its expected value. An owner may choose to have his car inspected for a fee of $300, and will then be able to sell his car for the true value.
(a) Suppose nobody has his car inspected. What would the market price for used cars be?
(b) Now suppose every car worth more than $X gets inspected, whereas every car worth less than $X does not get inspected. What would be the market price of uninspected used cars be, as a function of X?
(c) In equilibrium, the owner of a car worth $X is indifferent between getting an inspection and not getting an inspection. What is the equilibrium value of X?
(d) How many cars will not get inspected? How much will each car sell for?