3. Consider a world in which used cars can be either good or bad. The seller of a car knows its type but buyers can't verify the quality of the car before buying it. If there were a way to tell the types of car apart, the market-clearing price for good cars would be $10,000 and the market-clearing price for bad cars would be $3,000. Say that sellers can offer a warranty: if a warranty is offered then if the car ends up breaking down the buyer can get their money back. Good cars break down x% of the time and bad cars break down y% of the time. For the seller the expected profit on a car is the sales price minus the expected warranty cost (if one is offered). We are interested in seeing if it could be the case that buyers could be confident that if they see a warranty then the car is good. a) Say that buyers expect only good cars to have a warranty, so that they are willing to pay $10,000 if a warranty is offered but only $3,000 if no warranty is offered. Write an equation that says when it is incentive compatible for the good seller to offer a warranty and an equation that says when it is incentive compatible bad seller not to offer a warranty. b) Using your answer from a), for what values of x and y can the warranty serve as a credible signal of good quality in this market? Explain your answerin general terms, what makes it so that a signal can separate good quality from bad? 3. Consider a world in which used cars can be either good or bad. The seller of a car knows its type but buyers can't verify the quality of the car before buying it. If there were a way to tell the types of car apart, the market-clearing price for good cars would be $10,000 and the market-clearing price for bad cars would be $3,000. Say that sellers can offer a warranty: if a warranty is offered then if the car ends up breaking down the buyer can get their money back. Good cars break down x% of the time and bad cars break down y% of the time. For the seller the expected profit on a car is the sales price minus the expected warranty cost (if one is offered). We are interested in seeing if it could be the case that buyers could be confident that if they see a warranty then the car is good. a) Say that buyers expect only good cars to have a warranty, so that they are willing to pay $10,000 if a warranty is offered but only $3,000 if no warranty is offered. Write an equation that says when it is incentive compatible for the good seller to offer a warranty and an equation that says when it is incentive compatible bad seller not to offer a warranty. b) Using your answer from a), for what values of x and y can the warranty serve as a credible signal of good quality in this market? Explain your answerin general terms, what makes it so that a signal can separate good quality from bad