There are two second-hand car dealer. First, dealer A, which always sells high-quality cars that is carefully inspects, it costs deal A $8000 to buy each car that it sells. The second dealership, dealer B, always sells lower-quality cars. On average, it costs dealer B only $5000 for each car that it sells. If consumers knew the quality of the second-hand car that they are buying, they would gladly pay $10000 on average for dealer A, but only $7000 on average for dealer B. Without more information, consumers do not know the quality of each dealer's cars. In this case, consumers would figure that they have a 50% chance of ending up with high-quality car, and are thus willing to pay $8500 for a car. Therefore, dealer A has an idea: He will offer a bumper-to-bumper warranty for all cars he sells. He knows that a warranty lasting X years will cost $500X on average, and he also knows that if dealer B tries to offer the same warranty, it will cost dealer B $1000X on average.

a. Suppose dealer A offers a 1-year warranty on all cars it sells.

a1. What is dealer B's profit if it does not offer a 1-year warranty? What if it does offer a 1-year warranty?

a2. What is dealer A's profit if dealer B does not offer a 1-year warranty? What if it does offer a 1-year warranty?

a3. Will dealer B match dealer A 1-year warranty? Explain your answer. a4. It is good idea for dealer A to offer a 1-year warranty? Explain your answer.

b. What if dealer A offers a 2-years warranty? Will this generate a credible signal of quality? How about 3-years warranty?

c. If you were advising dealer A, how long a warranty would you advise him to offer? Explain why.