Microeconomics

Please write details carefully especially the part b, c and v, vi of part a,

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2) Two used car dealerships compete side by side on a main road. The rst, Harry's Cars, always sells high-quality cars that it careilly inspects and, if necessary, services. On average, it costs Harry's $7,500 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 $5,300 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would pay $12,500 on average for Harry's cars and only $8,000 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 gure that they have a 50-50 chance of ending up with a high-quality car and are thus willing to pay $10,250 for a car. Harry has an idea: He will offer a bumper-to-bumper warranty for all cars he sells. He knows that a warranty lasting Y years will cost $600Y on average, and he also knows that if Lew tries to offer the same warranty, it will cost Lew $1,500Y on average. a) Suppose Harry offers a one-year warranty on all of the cars he sells. i. What is Lew's prot if he does not offer a one-year 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? v. If the choice for each is whether or not to offer a one-year warrantee, is there a Nash equilibrium? Construct a payoff matrix to illustrate. vi. What should Lew's do if Harry's does NOT offer a warrantee? b) What if Harry offers a two-year warranty? Will this offer generate a credible signal of quality? What about a veyear warranty? Use payoff matrices for each case to explain your answers. c) If you were advising Harry, how long a warranty would you urge him to offer? Explain why