Hivalu Motors Inc. (HMI) sells high-quality used cars (which require only a modest amount of servicing/repairs after purchase); it costs HMI $8,000 to buy, inspect, and repair its cars prior to sale. Soso Usedcar Corp. (SUC) sells lower quality used cars (which require a considerable amount of servicing/repairs after purchase); it costs SUC only $5,000 to buy, inspect, and repair its cars prior to sale. HMI and SUC compete with each other, side-by-side on the main road in Nowheresville. Both companies currently claim that they sell high-quality cars. Neither offers a warranty.

If buyers could correctly judge the quality of cars, the buyers would be willing to pay $10,000 for high-quality cars, but would pay only $7,000 for lower-quality cars. Unfortunately, despite the names on the dealerships, buyers currently can't tell the cars apart until after purchase (and their memories are short, so their experience doesn't help them decide where to buy when they again want to buy a used car). The buyers currently believe, however, that if they buy a car from either dealership they have a 50% chance of ending up with a high-quality car and a 50% chance of ending up with a lower-quality car. Consequently, so long as the buyers cannot distinguish quality directly or figure out who sells high-quality cars, they are willing to pay their average value -- $8,500 -- for any car that they buy.

HMI is considering providing a free warranty that will cover all repairs on its cars for a specified length of time after purchase; it believes that SUC is also considering offering a similar free warranty. HMI knows that a warranty that lasts Y years will cost it $500*Y; it also knows that, if SUC were to provide a similar warranty, SUC's costs would be $1,100*Y. HMI is contemplating offering a one-year, a two-year, or a three-year warranty. You are an advisor to HMI.

1) Should HMI provide a warranty? If so, of what length? Why? (If not, why not?)

2) If HMI does provide a warranty, are there any potential problems related to the warranty that HMI ought to be aware of? Explain.