Question 4 Markets with Asymmetric Information (20 points) Two used car dealerships compete side by side on a main road. The rst, Harry's Cars, always sells high-quality cars that it carefully inspects and, if necessary, services. On average, it costs Harry $8,000 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 only $5,000 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would gladly pay $10,000 on average for Harry's cars, but only $7,000 on average for Lew's cars. Without more information, consumers do not know the quality of each dealership's cars. In this case, consumers would gure that they have a 50-50 chance of ending up with a high- quality car, and are thus willing to pay $8,500 for a car. Harry has an idea: He will offer a bumper-tobumper warranty for all cars 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) (8 points) Suppose Harry offers a one-year warranty on all cars it sells. i. What is Lew's prot if it does not offer a one-year warranty? If it does offer a one- year warranty? Will Lew match Harry one-year warranty? ii. Is it a good idea for Harry's to offer a one-year warranty? b) (8 points) What if Harry offers a two-year warranty? Will this generate a credible signal of quality? What about a three-year warranty? 0) (4 points) If you were advising Harry, how long a warranty would you urge him to offer? Explain why