Question

Two used car dealerships compete for 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 \(8000to buy and service each car that it sells. The second dealership, Lew’s Motors, always sells lower-quality cars. On average, it costs Lew’s only \)5000 for each

car that it sells. If consumers knew the quality of the used cars they were buying, they would pay \(10,000on average for Harry’s cars and only \)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 lastingYyear will cost \)500Yon average, and he also knows that if Lew tries to offer the same warranty, it will cost Lew $1000Yon 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 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?

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.

Short answer

a.

1. If Lew does not offer a one-year warranty, his profit will be $2000/car, and if he offers a one-year warranty, his profit will be $2500/car.
2. If Lew does not offer a warranty, Harry will make a profit of $1500/car; if Lew offers a warranty, Harry’s company will make no profit.
3. Lew will match Harry’s one-year warranty.
4. Harry should not offer one year warranty.

b. If Harry offers a two-year warranty, he will make a profit of $1000 per car, and Lew will not be able to make a two-year warranty. Therefore, this will be considered as a good signal of quality. If Harry offers a three-year warranty, then he will make $500 profit per car, leaving him indifferent.

c. Harry must be advised to provide a 1.5-year warranty so that Lew would not be able to match him and he still can make better profits than in the case of a two-year warranty.

Step-by-step solution

Explanation for part (a)

1^st subpart:

• If Lew does not offer a warranty: the consumers will think his cars are of low quality.

Lew’s cost is $ 5000, and he will get $7000 as a selling price in case of no warranty.

Therefore, Lew will make a profit of; 7000-5000= $2000.

• If Lew offers a warranty: the consumers will be unaware of the quality.

If he were to offer a warranty, each car would cost $6000 (=$5000+ $1000 warranty). He will receive $ 8500 as a selling price. Therefore, his profit would be: 8500-6000=$2500.

2^nd subpart:

• If Lew does not offer a warranty: the consumers will know Harry’s car quality.

Harry’s car costs $8500 (=$8000 + $500 of warranty), and Harry will sell them at a $10,000 selling price (as the quality is assured). Therefore, Harry will make a profit of10000-8500= $1500.

• If Lew offers a warranty: the consumers will be unaware of Harry’s car quality.

If Lew offers the warranty, Harry will be able to sell his car at $8500, making zero profits.

3^rd subpart:

If Lew matches Harry’s policy of warranty, he will be able to make higher profits ($2000 to $2500). Thus, he will offer one year warranty.

4^th subpart:

Without any warranty, Harry will make $500 as profit (8500-8000). With a warranty, he can increase his profits to $1500, provided Lew doesn’t offer such a warranty.

Thus, Harry shouldn’t offer a warranty until he is sure of Lew’s action. Harry will only benefit from offering a one-year warranty only if Lew does not match his action.

Explanation of part (b)

If Harry offers a two-year warranty, then each car will cost him $9000 (including $500 of warranty for each year). By offering two years of warranty, Harry will earn $1000/car (=10,000-9000) as profit, as consumers will recognize the higher quality of its cars.

Lew’s profit will only be $1500/car (8500-7000) in case he offers a two-year warranty, which is less than the $2000 that Lew will make without offering the warranty. So the two-year warranty will serve as a credible signal of quality.

If Harry gives a three-year warranty, he would be making $500 per car, which is the same that Harry would have made had it not signalled the higher quality with a warranty. Therefore, Harry would not offer a three-year warranty.

Explanation of part (c)

Harry needs to offer a warranty of sufficient length. Doing so will discourage Lew from offering the same warranty since it will not be feasible for him to do so then.

Let tdenote the number of years of the warranty; then Lew’s will offer a warranty according to

the following inequality:

Therefore, Harry should offer a 1.5-year warranty on his cars, since Lew will not find it profitable to match this warranty; Harry’s profit will be $10,000 − 8000 − 500(1.5) = $1250.