A population of 1000 is hoping to sell their used cars. The value of a car V, ranges from $0 and $3000. The distribution of car values is such that the number of used cars worth less than $V is V/3. The value of a car to a buyer is the car's expected value. An owner can have the car inspected for $300 which will allow the car to sell at the true value.

Note: for part a ignore the market price for the used car and instead find the customer's willingness to pay for the car

4. A population of 1,000 is hoping to sell their used cars. The value of a car, V, ranges between $0 and $3,000. The distribution of car values is such that the number of used cars worth less V than SV is -. The value of a car to a buyer is the car's expected value. An owner can have 3 the car inspected for $300, which will allow the car to sell at the true value. (a) Suppose no cars are inspected. What would be the market price for used cars? (b) Suppose every car worth more than some value, $900, gets inspected (but not cars worth less than $900). What would be the market price for cars as a function of 900? (c) Suppose every car worth more than some value, SX, gets inspected (but not cars worth less than $X). What would be the market price for cars as a function of X? (d) In equilibrium, the owner of a car worth X is indifferent between getting the inspection and not. What is the equilibrium value of X