Readings
Baye “Signaling” (see the index)
Dixit Chapter 9
BA 445 Lesson C.4 Signaling Product Quality 1

Overview
BA 445 Lesson C.4 Signaling Product Quality 2

Overview
Service Warranties can signal product quality. — So, producers of good quality can distinguish themselves from bad quality by offering low-price service warranties that producers of bad quality avoid.
Replacement Warranties can signal product quality like service warranties when the expected cost of replacing high-quality products is lower than the expected cost of replacing low-quality products.
BA 445 Lesson C.4 Signaling Product Quality 3

Example 1: Service Warranties
BA 445 Lesson C.4 Signaling Product Quality 4

Example 1: Service Warranties
Overview
Service Warranties can signal product quality. — So, producers of good quality can distinguish themselves from bad quality by offering low-price service warranties that producers of bad quality avoid.
BA 445 Lesson C.4 Signaling Product Quality 5

Example 1: Service Warranties
Comment: Warranties can signal information about the quality of a product for manufacturers who have not yet established a reputation for high quality. Warranties signal high quality because warranties are more expensive to offer when the product is of low quality.
For example, Korean automaker Hyundai had some success in selling to the U.S. market in the late 1980s. Sales then slipped. It developed a reputation for low quality, and by 1997 its sales had slipped to the
1985 level. Starting in 1999, Hyundai raised the quality of their cars, but this had not yet been recognized by U.S. consumers. To get its claim of quality across in a credible way, the company signaled its quality by offering an unprecedented 10-year, 100,000-mile warranty on the power train and 5 years, 50,000 miles on the rest. That worked well, and sales in 1999 increased 82%, and sales in 2000 were up a further 49%.
BA 445 Lesson C.4 Signaling Product Quality 6

Example 1: Service Warranties
Question: Suppose Hyundai has produced a high quality car that has
$10,000 unit cost and that, during any given year, costs $1,000 in repairs with 5% probability. Hyundai knows the quality of its car, but consumers do not. Suppose consumers think it possible that Hyundai has produced the high quality car, but it is also possible that Hyundai has produced, instead, a low quality car that has $9,000 unit cost and that, during any given year, costs $2,000 in repairs with 20% probability. Suppose potential buyers value the high-quality car at
$16,000 and the low at $12,000.
Finally, suppose Hyundai can make a price demand for the car purchase and for a service warranty that any potential buyer must either accept or reject (but not counter).
Determine the number of years of warranty Hyundai should offer.
BA 445 Lesson C.4 Signaling Product Quality 7

Example 1: Service Warranties
The Car is a
High Q Low Q
Value/Cost to Buyer $16,000 $12,000 to Seller $10,000 $9,000 of Warranty $0 $350
Answer: With the warranty, the average cost of repair service each year is $50 (5% of $1,000) for the high-quality car, and is $400 (20% of $2,000) for the low-quality car.
Consider finding an appropriate integer number N so the
Seller should demand a price of $16,000 for each car that is offered with a warranty that costs $50N for N years of service coverage. In particular, the net profit per year to the Seller of offering the warranty is 0 if the car were High
Quality, and negative $350 if the care were Low Quality.
BA 445 Lesson C.4 Signaling Product Quality 8

Example 1: Service Warranties
The Car is a
High Q Low Q
Value/Cost to Buyer $16,000 $12,000 to Seller $10,000 $9,000 of Warranty $0 $350
Incentive compatibility constrains the number N of years to be high enough so Low Quality cars (to be sold for
$12,000) do not bother to offer the warranty, and so that
High Quality cars (to be sold for $16,000) will offer it.
Incentive compatibility for Low Quality requires
$12,000 > $16,000 - $350 x N, or N > 11.43, meaning N >
12.
Incentive compatibility for High Quality requires
$16,000 - $0 x N > $12,000, which is true regardless of N.
BA 445 Lesson C.4 Signaling Product Quality 9

Example 1: Service Warranties
The Car is a
High Q Low Q
Value/Cost to Buyer $16,000 $12,000 to Seller $10,000 $9,000 of Warranty $0 $350
Participation constrains the number N of years so High
Quality cars (to be sold for $16,000) are offered, and so that consumers think it possible that Hyundai has produced the low quality car.
Participation for High Quality cars requires
$16,000 - $0 x N > $10,000, which is true regardless of N.
Participation for Low Quality cars requires
$12,000 > $9,000, which is true regardless of N.
BA 445 Lesson C.4 Signaling Product Quality 10

Example 1: Service Warranties
The Car is a
High Q Low Q
Value/Cost to Buyer $16,000 $12,000 to Seller $10,000 $9,000 of Warranty $0 $350
Therefore, Hyundai should make a take-it-or-leave-it (no haggle) price demand of $16,000 for the car purchase and $50 per year for a service warranty of up to 12 years. That way, Hyundai breaks even on the warranty, and makes $6,000 on each car, which is more profit than is possible with Low Quality cars.
Consumers are willing to pay $16,000 for the car purchase because the option to buy the service warranty signals the car is high quality. In this example, the option to buy the service warranty is the signal. It is not important to Hyundai whether consumers actually buy the service warranty.
BA 445 Lesson C.4 Signaling Product Quality 11

Example 2: Replacement Warranties
BA 445 Lesson C.4 Signaling Product Quality 12

Example 2: Replacement Warranties
Overview
Replacement Warranties can signal product quality like service warranties when the expected cost of replacing high-quality products is lower than the expected cost of replacing low-quality products.
BA 445 Lesson C.4 Signaling Product Quality 13

Example 2: Replacement Warranties
Comment: Replacement warranties can signal information about the quality of a product like service warranties quality because warranties are more expensive to offer when the product is of low quality.
For example, Sears Craftsman-brand tools enjoy a strong reputation for quality. This reputation arises from its unlimited lifetime replacement warranty on broken tools.
Indeed, Sears used to run a television advertisement featuring a middle-aged man returning a wrench to Sears for the guaranteed replacement; the wrench had been purchased by the man’s father decades before. The warranty is so strong that, in consumers’ minds, Sears could not afford to offer it unless the tools rarely broke.
BA 445 Lesson C.4 Signaling Product Quality 14

Example 2: Replacement Warranties
Question: Suppose Sears has produced a high quality Craftsman wrench that has $10 unit cost and that, during any given year, breaks with 2% probability. Sears knows the quality of its wrench, but consumers do not. Suppose consumers think it possible that Sears has produced the high quality wrench, but it is also possible that Sears has produced, instead, a low quality wrench that has $9 unit cost and that, during any given year, breaks with 10% probability. Suppose potential buyers value the high-quality wrench at $16 and the low at
$12.
Finally, suppose Sears can make a price demand for the wrench purchase and for a free-replacement warranty that any potential buyer must either accept or reject (but not counter).
Determine the number of years of warranty Sears should offer.
BA 445 Lesson C.4 Signaling Product Quality 15

Example 2: Replacement Warranties
The Wrench is a
High Q Low Q
Value/Cost to Buyer to Seller
$16
$10 of Warranty $0.00
$12
$9
$0.70
Answer: With the warranty, the average cost of replacement each year is $0.20 (2% of $10) for the high-quality wrench, and is $0.90 (10% of
$9) for the low-quality wrench.
Consider finding an appropriate integer number N so the Seller should demand a price of $16 for each wrench that is offered with a replacement warranty that costs $0.20N for N years of replacement coverage. In particular, the net profit per year to the Seller of offering the warranty is 0 if the wrench were High Quality, and negative $0.70 if the care were Low Quality.
BA 445 Lesson C.4 Signaling Product Quality 16

Example 2: Replacement Warranties
The Wrench is a
High Q Low Q
Value/Cost to Buyer to Seller
$16
$10 of Warranty $0.00
$12
$9
$0.70
Incentive compatibility constrains the number N of years to be high enough so Low Quality wrenches (to be sold for
$12) do not bother to offer the warranty, and so that High
Quality wrenches (to be sold for $16) will offer it.
Incentive compatibility for Low Quality requires
$12 > $16 - $0.70 x N, or N > 5.71, meaning N > 6.
Incentive compatibility for High Quality requires
$16 - $0 x N > $12, which is true regardless of N.
BA 445 Lesson C.4 Signaling Product Quality 17

Example 2: Replacement Warranties
The Wrench is a
High Q Low Q
Value/Cost to Buyer to Seller
$16
$10 of Warranty $0.00
$12
$9
$0.70
Participation constrains the number N of years so High
Quality wrenches (to be sold for $16) are offered, and so that consumers think it possible that Hyundai has produced the low quality car.
Participation for High Quality cars requires
$16 - $0 x N > $10, which is true regardless of N.
Participation for Low Quality cars requires
$12,000 > $9,000, which is true regardless of N.
BA 445 Lesson C.4 Signaling Product Quality 18

Example 2: Replacement Warranties
The Wrench is a
High Q Low Q
Value/Cost to Buyer to Seller
$16
$10 of Warranty $0.00
$12
$9
$0.70
Therefore, Sears should make a take-it-or-leave-it (no haggle) price demand of $16 for the wrench purchase and $0.20 per year for a replacement warranty of up to 6 years. That way, Sears breaks even on the warranty, and makes $6 on each wrench, which is more profit than is possible with Low Quality wrenches.
Consumers are willing to pay $16 for the wrench purchase because the option to buy the replacement warranty signals the wrench is high quality. In this example, the option to buy the replacement warranty is the signal. It is not important whether consumers actually buy the replacement warranty.
BA 445 Lesson C.4 Signaling Product Quality 19

Review Questions
Review Questions
 You should try to answer some of the review questions (see the online syllabus) before the next class.
 You will not turn in your answers, but students may request to discuss their answers to begin the next class.
 Your upcoming cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.
BA 445 Lesson C.4 Signaling Product Quality 20

BA 445 Managerial Economics
BA 445 Lesson C.4 Signaling Product Quality 21