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 oneyear
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.