Suppose that in Sydemere Kentucky the quality distribution o

Suppose that in Sydemere, Kentucky, the quality distribution of the 6,000 used cars on the market is such that the number of used cars of value less than V is V/2 .

Original owners must sell their used cars.

Original owners know what their cars are worth, but buyers can’t determine a car’squality until they buy it.

An owner can either take his car to an appraiser and pay the appraiser $400 to appraise the car (accurately and credibly) or sell the car unappraised.

In equilibrium, car owners will have their cars appraised if and only if the car’s value is at least

A. $1,200.

B. $3,000.

C. $400.

D. $800.

E. $1,600.

Answer should be D.

Solution

Solution:-

According to the question, the value of the cars below $X follows a uniform distribution on [0, X].

Likewise, the expected value of used car = X/2

If I get appraisal then my proceeds = X – 400

In equilibrium, the expected value of the unapprised car = value of the appraised car

X/2 = X – 400

X/2 = 400

X = 800

I.e. If X is at least $800 then the owner will get it appraised.

For e.g. suppose the value of car = $900 then the one who gets its appraised will get 900 – 400 = $500 but the one who gets unapprised is expected to earn 900/2 = $450