1.9. Two used car dealerships compete side by side on a main road. The first, Harry’s Cars, always sells high-quality cars that it carefully inspects and, if necessary, services. On average, it costs Harry’s $8000 to buy and service each car that it sells. The second dealership, Lew’s Motors, always sells lower-quality cars. On average, it costs Lew’s only $5000 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would pay $10,000 on average for Harry’s cars and only $7000 on average for Lew’s cars.

Without more information, consumers do not know the quality of each dealership’s cars. In this case, they would figure that they have a 50–50 chance of ending up with a high-quality car and are thus willing to pay $8500 for a car.

Harry has an idea: He will offer a bumper-to-bumper warranty for all cars that he sells. He knows that a warranty lasting Y years will cost $500Y on average, and he also knows that if Lew tries to offer the same warranty, it will cost Lew $1000Y on average.

a. Suppose Harry offers a one-year warranty on all of the cars he sells.

i. What is Lew’s profit if he does not offer a one-year warranty? If he does offer a one-year warranty?

ii. What is Harry’s profit if Lew does not offer a one-year warranty? If he does offer a one-year warranty?

iii. Will Lew’s match Harry’s one-year warranty?

iv. Is it a good idea for Harry to offer a one-year warranty?

b. What if Harry offers a two-year warranty? Will this offer generate a credible signal of quality? What about a three-year warranty?

c. If you were advising Harry, how long a warranty would you urge him to offer? Explain why.