Q9. Two used car dealerships compete... [FREE SOLUTION]

Chapter 17: Q9. (page 673)

Two used car dealerships compete for side by side on a main road. The first, Harry鈥檚 Cars, always sells high-quality cars that it carefully inspects and, if necessary, services. On average, it costs Harry鈥檚 $8000to buy and service each car that it sells. The second dealership, Lew鈥檚 Motors, always sells lower-quality cars. On average, it costs Lew鈥檚 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鈥檚 cars and only $7000 on average for Lew鈥檚 cars.
Without more information, consumers do not know the quality of each dealership鈥檚 cars. In this case, they would figure that they have a 50鈥�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鈥檚 profit if he does not offer a one-year warranty? If he does offer a one-year warranty?
ii. What is Harry鈥檚 profit if Lew does not offer a one-year warranty? If he does offer a one-year
warranty?
iii. Will Lew鈥檚 match Harry鈥檚 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

Expert verified

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.
If Lew does not offer a warranty, Harry will make a profit of $1500/car; if Lew offers a warranty, Harry鈥檚 company will make no profit.
Lew will match Harry鈥檚 one-year warranty.
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鈥檚 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鈥檚 car quality.

Harry鈥檚 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鈥檚 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鈥檚 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鈥檛 offer such a warranty.

Thus, Harry shouldn鈥檛 offer a warranty until he is sure of Lew鈥檚 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鈥檚 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鈥檚 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鈥檚 profit will be $10,000 鈭� 8000 鈭� 500(1.5) = $1250.