Suppose that you own a used car dealership. You want to sell a 2005 Honda Civic LX. You know that this car is of high quality, and it cost you $5000 to acquire it (so you will not sell it at a price below $5000). However, consumers cannot see the quality of the car at the time of purchase. They believe that 25% of the cars in the used car market are high-quality cars and 75% are low-quality cars or "lemons." A typical lemon costs $2000 to acquire (so you will not sell it at a price below $2000).

Consumers are eager to buy and are willing to pay up to $3000 for a lemon and $6000 for a high-quality car.

(i) [4 points] Suppose for a moment that buyers could observe the quality of your car at the time of purchase. At what price would you be able to sell the 2005 Honda Civic Accord LX? If you had a lemon instead, what price would it sell at? (Suppose as a savvy dealer you can induce buyers to pay at their highest willingness to pay. Keep this assumption in all of the following questions.)

From now on, suppose that only you (the seller) know the quality of the cars. (Buyers do not know the quality, but know the proportion of high- and low-quality cars in the market).

(ii) [4 points] Will you be able to sell your 2005 Honda Civic Accord LX? Explain your answer formally.

(iii) [6 points] What sort of asymmetric information is this an example of? What are its consequences for the market outcome?

Suppose that you could offer bumper-to-bumper warranties. You know that offering a warranty on a high-quality car costs, on average, $450 per year of warranty offered, while a warranty on a lemon is very costly and it costs $1600 per year. One of your economist friends suggests that you offer a two-year warranty to signal to consumers that your 2005 Honda Civic Accord LX is indeed a high-quality car. She says that this will enable you to sell.

(iv) [4 points] Suppose that you take her advice. If consumers believe that your car is of high quality on being offered the warranty, what would your profit be?

(v) [6 points] Intuitively, you are offering the warranty because you want the consumer to think "The car must be good - otherwise he wouldn't offer a two-year warranty." Suppose that you had a lemon. Use the information you have to show that if your car were a lemon, you would not offer the two-year warranty. [Hint: You need to compare your profits when you offer warranty with those when you don't.]

(vi) [6 points] Suppose now that, in addition to high- and low-quality cars, there are also medium-quality cars in the market. Consumers do not see the quality of the car at the time of purchase, but believe that half of the cars are of low quality, are of medium quality, and are of high quality. As before, if you own a high-quality car, you are willing to sell it at a price of $5000 or more. You are willing to sell a medium-quality car at $3000 or more, and a lemon at $2000 or more. Consumers are willing to pay up to $6000 for a high-quality car, $4000 for a medium-quality car, and $3000 for a lemon. If you had a medium-quality car, do you expect to be able to sell it? Justify your answer.