Suppose that in New Crankshaft, Pennsylvania, the quality distribution of the 4,

Question

Suppose that in New Crankshaft, Pennsylvania, the quality distribution of the 4,000 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’s value 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 their value is at least... (The question itself is to find out this "at least" amount, which is $800)

The answer is $800

Could you provide a step-by-step solution! Thank you :)

Explanation / Answer

According to the question, the value of the cars below $X follow 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 unappraised car = value of appraised car

X/2 = X – 400

X/2 = 400

X = 800

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

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

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.