Consumers know that some fraction, p, of all new cars produced and sold in the market are defective. The defective ones cannot be identified except by those who own them. Cars do not depreciate with use. Consumers are risk-neutral and value nondefective cars at $8,000. If new cars sell for $6,000 and used cars sell for $2,000, then what is the fraction p?

Question

Quizplus · Accepted Answer

Note that since only people with defective cars will sell their cars on the used market, the market price of a used car will equal the value consumers place on having a defective car. In addition, if consumers are risk-neutral, then the market price of a new car will equal the expected value of a new car. That is, $6,000 = (1- p)× $8,000 + p × $2,000. Solving for p yields 1/3 or 0.33.

Consumers Know That Some Fraction, P, of All New Cars