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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 \(\$ 500 Y\) on average, and he also knows that if Lew tries to offer the same warranty, it will cost Lew \(\$ 1000 Y\) 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.