In Town X, there are two used car dealerships that compete fiercely with each other. The first dealership, Janet's Motors, always sells high-quality cars that it carefully inspects and, if necessary, services. On average, it costs Janet $16,000 to buy and service each car that it sells. The second dealership, Bruce's Cars, always sells lower-quality cars. On average, it costs Bruce only $10,000 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would gladly pay $20,000 on average for Janet's cars, but only $14,000 on average for Bruce's cars.

Lacking more information, consumers do not know the quality of each dealership's cars. In this case, consumers would assume that they have a 50/50 chance of ending up with a high-quality car, and are thus willing to pay a price that reflects the average value of the car.

(a) Calculate the profits of Janet's Motors and Bruce's Cars.

To deal with the (asymmetric) information problem, Janet has come up with an idea: She will offer a "complete" warranty for all cars he sells. She knows that a warranty lasting Y years will cost $500Y on average, and she also knows that if Bruce tries to offer the same warranty, it will cost him $1,000Y on average.

(b) Suppose Janet's Motors offers a one-year warranty on all cars it sells.

i) What will Bruce's profit be if it does not offer a one-year warranty? What if it offers a one-year warranty?

ii) What will Janet's profit be if Bruce's does not offer a one-year warranty? What if Bruce's does offer a one-year warranty?

iii) Will Bruce's "match" Janet's one-year warranty? Explain your answer.

iv) Is it a good idea for Janet's to offer a one-year warranty? Explain your answer.

(c) What if Janet offers a two-year warranty? Will this generate a "credible" signal of quality (i.e., a signal that Bruce's will NOT follow/match so that the warranty will be able to convince the potential buyers that Janet's cars are of higher quality)?