CHAPTER 2 LITERATURE REVIEW
3.4 Findings and Discussion
Figure 3.2 summarizes the main results concerning a firm’s innovation. The innovative firm has a higher equilibrium price and equilibrium quantity than the non- innovative firm. Individual buyers also prefer an innovative product, since the expected utility EU(N ＝ 1) ＞ EU(N ＝ 0) if the firm sets a reasonable price.
Moreover, as the barrier to the firm’s engaging in innovative activities, the fixed innovation cost will be overcome only if the firm produces high-quality products.
Figures 3.4 and 3.5 show the strategic decisions of high-quality firms, low quality firms and rational consumers. Initially, only high-quality firms innovate to increase profit. Then, customers investigate the quality, price, and product innovativeness of the firms’ products as purchase information. Finally, only an innovative product of high quality can induce a consumer’s willing- to-buy because the failure of bad products causes the consumer to lose much money. Proposition 1 and Proposition 2 present these important results.
Researchers are divided on the causal relationship between product quality and product innovation. The findings of this paper, however, imply that product quality may be a determinant of product innovation.
(firm profit), (consumer expected utility)
Figure 3.4 Dynamic Game of Complete Information under q ＝ H
Figure 3.5 Dynamic Game of Complete Information under q ＝ L
[[H(1＋I) － CH]2/ 4 H － F，Hr－P+HI]
N=1 H
[(H－CH)2/ 4 H，H(r－P)＋(1-H)(－P)]
＝[(H－CH)2/ 4 H，Hr－P]
0
0 Buy
Not N=0
Buy
Not
N=1 L
[(L－CL)2/ 4 L，Lr－P]
0
0 Buy
Not N=0
Buy
Not
[L(1＋I) － CL]2/ 4 L － F，Lr－P+LI]
CHAPTER 4 PRODUCT QUALITY AND SERVICE INNOVATION: A GAME THEORY APPROACH
The service sector is important in the economy of most advanced countries.
Although service activities have been classified as business services, trade services, infrastructure services, personal services and public administration, distinguishing between products and services remains difficult. Several services, such as assembling and repairing, follow the selling of a product, yet restaurant service involves the production of many products. In fact, every purchase activity combines the consumption of products and services at different rates (Fitzsimmons & Fitzsimmons, 1994). Automotive industry represents an important example of the combination of products and services.
4.1 Service Innovations in the Automotive Industry
Most product markets are attracting increasing interest from firms that provide extended services to support their products. Unsurprisingly, most consumers prefer products that come with pre-sold and post-sold services, which generally promote their purchase motivation. Meanwhile, service innovations cover all financial and marketing innovations before products are sold, as well as all maintenance, repairing, warranty and repossessing activities after products are sold. By referring to the raw material, product, purchase and scrap stages of a product’s life cycle, depicted in Figure 4.1, customers can understand the differences between product and service innovations. Service innovation covers all innovative activities after the production of a product, before that product is discarded. Restated, service innovation involves a new service associated with increased willing-to-buy or consumer satisfaction before or after the product is sold. Service innovation in the automotive industry involves
financial innovation, pricing innovation, promotion innovation, placement innovation, maint enance innovation, repairing innovation, warranty innova tion and repossessing innovation, or the combination of at least two of these innovations. The points made so far apply in principle to most manufacturing and service industries. Half-priced warranties service, indeed, seems to be a representative service innovation widely provided by automotive firms and real estate companies in the recent years. Since service innovation remains difficult to be valued and modeled, it’s necessary to discuss representative cases for new services. Exhibiting originality and innovativeness, half-priced warranties service also provides important clues for better understanding of service innovation.
Figure 4.1 Product Stages and Corresponding Innovation Activities in the Automotive Industry
Raw material Product Purchase/
Usage
Scrap
Product innovation Process innovation Technical innovation
Service innovation Financial innovation Pricing innovation Promotion innovation Placement innovation Maintenance innovation Repair innovation Warranty innovation Repossessing innovation
4.2 Half-priced Warranties Service
Durable product markets show increasing interest from firms in providing extended warranties for new products. In the automobile industry, nearly all motor companies sell their new cars with new vehicle limited warranties. Not surprisingly most consumers prefer products with warranties because warranties generally boost their purchase motivation. Motor firms therefore provide long limited warranties to cater for consumer taste and establish confidence in their products. Furthermore, to ensure competitiveness many firms offer new vehicle limited warranties of up to 3 years or 36,000 miles. These warranties cover material or workmanship deficiencies in parts or components, and customers are not charged for warranty covered repairs made during the warranty period.
Moreover, to ensure competitiveness, several firms are providing innovative services, such as longer vehicle limited warranties and half-price warranties. The former warranties cover material or workmanship deficiencies in parts or components for up to five years or 50,000 miles, and customers are not charged for covered repairs during the warranty period. With the half-price purchase warranties offered by Ford Taiwan and Honda Taiwan, each consumer is permitted initially to pay just half of the price of the new car, and then, after the products reaches half of its service life, the consumer can decide whether to keep the product and pay the balance of the purchase price, or simply return the used product to the firm without paying any mo re. The latter service is a broad combination of pricing innovation, warranty innovation, and old product repossessing innovation. Accompanying their product innovations, motor firms are providing innovative services to build their reputations and to increase profit (Utterback, 1994). Focusing on durable products, the rest of this chapter examines the informational role and optimality of half-price purchase warranties in a signaling model with unknown product quality and risk-neutral consumers.
4.3 Basic Model
Consider a one-period model involving one monopolist and a group of rational consumers, and where the marketed products have a short life and thus service life is not a consideration. These products are goods with a short life rather than durable goods. For products where service life is not a consideration, consumers can discriminate between good and bad products the moment they use them.
In this basic model without warranties, product quality is known only by the firm, and is unknown to consumers before purchase. The firm sets its price according to quality, and then consumers read the price as a signal of product quality in making their purchase decisions. So, each firm producing fixed quality products will set its price to maximize profit given existing consumer demand and firm manufacturing cost. Simultaneously, rational consumers prefer high-quality products to maximize their utility. The model structure can be established based on the interaction between firms and consumers. For simplicity, the variables used here serve as indexes corresponding to interval [0, 1].
Product Quality. Following Milgram and Roberts (1986) and Shieh (1993), quality, denoted by q, is defined as the probability of a randomly selected consumer being satisfied with a product. Suppose q can only take two values, high (H) or low (L), with0 ≦ L < H ≦ 1. High-quality firms (H-type firms) will produce high-quality products (H-type products), which will satisfy the customers with a probability of H. Additionally, the probability of H-type product performing poorly and not satisfying customers is 1 － H. Meanwhile, L-type products have a probability of L of performing well and satisfying customers, and a probability of 1
－ L of performing poorly. The actual qualities of the products are uncertain, and will remain unknown until the product is purcha sed. All customers prefer H to L because H-type products have a higher probability of working well. 0 ≦ q ≦ 1.
Price. Product price, P is an index variable on the interval [0, 1], or 0 ≦ P ≦ 1.
That is, P＝ 1 represents the highest price set by the firm, and P＝ 0 represents the lowest price set by the firm. 0 ≦ P ≦ 1.
Cost. Let Cq denote the cost per unit at a q-type firm, which serves as an index
variable corresponding to the interval [0, 1], or 0 ≦ Cq ≦ 1. Cq represents the degree to which a company produces low-cost products.
Consumers. Following Bagwell and Riordan (1991), Al-Najjar (1995) and Shieh (1996), let r represent the monetary valuation made by a potential consumer of a working and satisfactory product. Assume that consumers have unit demand and that the consumer valuation of the product, r, serves as an index variable over the interval [0, 1], or, 0 ≦ r ≦ 1. That is, r＝ 1 represents the highest valuation made by consumers, and r＝ 0 represents the lowest valuation. A consumer knows his monetary valuation r, which follows a uniform distribution on [0, 1], before deciding whether or not to make a purchase. Hence, each consumer has a different r value. No warranty is offered and a consumer has no right to change his purchasing decision after purchase, so r is constant over the product’s service time once a consumer has bought the product. To realize their own valuation, an individual consumer will not buy if r ＜ P, and will only buy if r ＞ P. Consider a consumer who pays P for the product; the utility of this consumer is r － P if the product works satisfactorily, and is －P if the product breaks and is unsatisfactory. Notably, consumers who do not buy the product receive zero utility. Finally, assume the firm sets a reasonable price, that is, r ＞ P; otherwise no consumers will be willing to buy the product owing to it being overpriced. 0 ≦ r ≦ 1.
Demand. Let Ω denote the probability that q ＝ H after the consumer has randomly purchased a product in the marketplace and has used it, and let Q(Ω)
denote the probability that a randomly selected consumer is satisfied with a product after he has used it. 0 ≦Ω≦ 1. Hence , Q(Ω) ≡ ΩH ＋ (1 － Ω)L, and 0 ≦ Q(Ω) ≦ 1. A consumer with a monetary valuation of r will buy this product at price P if and only if his expected utility from buying this product is non-negative; that is,
EU ＝ Ω〔H(r － P) ＋ (1 － H)(－P)〕
＋ (1 － Ω)〔L( r－ P) ＋ (1 － L)(－P)〕 ≧ 0 (4–1)
Or, EU ＝ rQ(Ω) － P ≧ 0 (4–2)
Let D(P;Ω) be the demand function with an argument P and a given Ω. D(P;Ω) serves as an index variable on the interval [0, 1], or 0 ≦ D(P;Ω) ≦ 1. That is, D(P;
Ω)＝ 1 represents the highest quantity demanded, and D(P;Ω)＝ 0 represents the lowest quantity demanded. From Eq. (2), a consumer with a monetary valuation of r will buy this product if and only if rQ(Ω) － P ≧ 0. Hence r* ＝ P/ Q(Ω) represents the minimum r for which the consumer is willing to purchase the product under an argument P and a given Ω. A larger r* corresponds to a smaller demanded quantity. Therefore , D(P; Ω ) ＝ 1 － r*＝ 1 － P/ Q( Ω ). Notably, the quantity demanded is non-negative. Thus,
D(P;Ω) ＝Max{1－ P/ Q(Ω), 0} (4–3)
Profit. Given demand, the profit of the firm is,
ðq(P;Ω) ＝ (P－Cq)[1－ P/ Q(Ω)] (4–4)
Equilibrium under full information. Under full information, each consumer knows the quality of the products of all firms. Equation (4) can be rewritten as
ðq(P; q) ＝ (P－Cq)(1－ P/q) (4–5)
To obtain Max ðq, solving Eqn. (5) using its F.O.C. reveals the full information price P*q ＝ (q ＋ Cq)/2 , the quantity Q*q ＝ 1 － P/q ＝ Max {(q － Cq)/2q, 0} , the marginal buyer r*q ＝ P/ Q(Ω) ＝ P/q ＝ (q ＋ Cq)/2q and the maximum ð*q ＝ (q － Cq)2/ 4 q
4.4 Generalized Model of Durable Products with Half-Price Warranties Service Regarding durable products and their service life, the firms and consumers must make decisions interactively in this generalized model. First, the firms must decide whether to offer half-price purchase warranties, and then set their price based on this decision. Given the half-price purchase warranties, each consumer is permitted initially to pay just half-price for the new product, and then after the product reaches its half service life, the consumer can decide whether to hold onto the product and pay the balance of the purchase price, or simply return the used product to the firm without paying any more.
Second, customers read the price and warranty decisions of the firm as signals of product quality, and make their purchase decisions accordingly. Finally, when a consumer buys a product and initially pays half-price, P/2, then after the half service life has elapsed the customer will actually understand the quality of the product.
Consequently, the consumer will continue to hold the product and pay another P/2 if the product really works satisfactorily. Otherwise, the consumer will return the used
product to the firm. Because the firm is the first to decide and act, so it reveals a dynamic game in the nature. Figure 4.2 displays the extensive-form of the game corresponding to the generalized model. For later reference, some additional variables should be introduced or redefined.
Figure 4.2 Extensive-form Game Corresponding to the Generalized Model S=1
S=0
Buy Buy
Not buy Not buy
S=1 S=0
Buy Buy
Not buy Not buy
H
L
firm buyers
Warranties. Assume S = 1 if a firm offers a half-price purchase warranty service.
In this case, each consumer is permitted initially to pay just half-price for the new product, and after the half service life of the product, the consumer is allowed to decide whether to hold onto the product and pay the balance, or alternatively return the used product to the firm without paying any more should the product dissatisfy him. S = 0 no warranty is offered by the firm.
Time. For the service life, let t denote the time since product purchase.
Consequently, t ＝ 0 represents that the product has just been bought, t ＝ 1/2 shows the product has already reached its half service life, and t ＝ 1 shows the product reached the end of its service life; 0 ≦ t ≦ 1.
Consumers. If the firm offers a half-price purchase warranty then S=1. For durable products, let r(t) denote the monetary valuation a potential consumer places on repurchasing an identical product after use at time t. The decision point at which each consumer decides whether to retain ownership of the product is t ＝ 1/2, so r(t) at t
＜ 1/2 differs considerably from that at t ≧ 1/2. When t ＜ 1/2, since r(0) represents the initial monetary valuation of the product, using the same definition of r in the basic model, the consumer gains the maximum monetary value by buying a new product at time 0. With time, latent problems gradually arise in this durable product, which reducing the customer’s monetary valuation of it. Hence, r(t) is a non- increasing function of over t. When t ≧ 1/2, however, after the product reaches its half- service life, the consumer is fully aware of understands actual product quality of the product, and thus has finished revising the monetary valuation. Hence, r(t) is constant over t in this case. However, beyond the decision point (t ＝ 1/2), r(t) is constant over t because no consumer can change his mind when t ＞ 1/2.
The difference between r(t) in the generalized model and r in the basic model is that r is constant over the product’s service life after a consumer has bought it in the former model, whereas r(t) is a linear function over t when t ＜ 1/2 and r(t) is constant over t when t ≧ 1/2 in the latter model. Assume 0≦ r(t) ≦ 1, and that r(t) satisfies the following assumptions.
Assumption 1. r(t) is a linear function of t when t ＜ 1/2, and r(0) ≧ r(t) ≧ r(t
＋ △t), ∀ t ＜ 1/2.
Assumption 2. r(t) is constant over t when t ≧ 1/2.
Assumption 3. r(0) ＞ P. The firm is assumed to set a reasonable price, otherwise no consumers will wish to buy the product.
Assumption 4. When t ＝ 1/2, r(1/2) indicates consumer monetary valuation of the product after its half service life. If P ≦ r(1/2) ≦ r(0), rational consumers will continue to hold the product and pay another P/2. Since r(1/2) ≧ P, such a consumer will gain extra utility r(1/2) － P ≧ 0 as he continues to use this product. However, if 0 ≦ r(1/2) ≦ P, then the rational consumer will return the used product to the firm without paying the balance of the purchase price. Since r(1/2)
＜ P, the consumer would have negative utility r(1/2)－ P ＜ 0 if he continued to use the product.
In Assumption 4, notice that if a rational consumer continues to keep the product and pay another half price P/2, then the remaining utility of the used product exceeds P/2. Accordingly, a consumer should make one of the following decisions.
(a) The consumer simply holds the used product and obtains a positive utility.
(b) The consumer may switch the old product and buy a new one, and obtain a positive utility higher than in case (a).
(c) The consumer may buy a ne w product when t ＝ 1/2. At the same time, the consumer will hold on to the used product and obtain the highest utility, which equal (a) ＋ (b). Since the quality of the used product is proved to be high after use, the consumer may also choose to pay P/2 to the firm, and immediately sell the used product in the used product market at a price higher than P/2 if he needs only one product.
A rational consumer will hold on to a product of high quality since the utility in (c) is the greatest.
Consumer’s utility when a warranty is offered. If a consumer buys this product for half of the full purchase price, P/2, then after the product reaches its half service life, the monetary valuation of the consumer r(1/2) ＝ y ≧ P for use time, t ＝ 1/2.
Consequently, the working situation of the product can still satisfy the expectations of the consumer, and the rational consumer will hold the product continuously and pay another P/2. Simultaneously, the utility of this cons umer equals the area of the polygon r(0)y A B 0 in Figure 4.3 minus P. The conception of consumer utility is very similar to that of consumer surplus.
For q ＝ H, according to Assumption 1–4 consumer monetary valuation y is during the interval [P, r(0)]. Therefore, consumer utility r(0)y A B 0 － P varies with the value of y, and the average consumer utility must be calculated given q ＝ H. Let Area(y) denote consumer utility when r(1/2) ＝ y . Then Area(y) ＝ (3y ＋ r(0) － 4P)/4, and the probability density func tion of y are denoted by f(y) ＝ 1/(r(0)－
P). Consequently, average consumer utility is
∫
yf(y)Area(y) dy ＝ r(
∫
0)P
[1/(r(0) － P)][ (3y ＋ r(0) － 4P)/4] dy
Figure 4.3 Consumer Utility whe n P ≦ r(1/2) ＝ y ≦ r(0), or q ＝ H
So, when P ≦ r(1/2) ＝ y ≦ r(0), the consumer will hold onto the product and receive his average consumer utility.
Given q ＝ H, Average Consumer Utility ＝ (5r(0)－5P)/8 (4–6)
On the contrary, if a consumer initially pays half-price, P/2, for the product, after the product reaches its half service life, consumer monetary valuation r(1/2) ＝ y ＜ P given use time, t ＝ 1/2. It also means that the product fails to satisfy consumer expectations, and rational consumers will return the used product to the firm without paying any more. Simultaneously, the consumer utility equals the area of the polygon r(0)y B 0 in Fig 4.4 minus P/2.
When q ＝ L, then according to Assumption 1–4 consumer monetary valuation y is during interval [0, P]. Therefore, consumer utility r(0)y B 0 －P/2 varies with the value of y, and the average consumer utility must be calculated given q ＝ L. Let
B y
r(0)
P
r(t)
t t＝1/2
0 t＝1
A
Area(y) denote consumer utility when r(1/2) ＝ y . Then Area(y) ＝ (y ＋ r(0) － 2P)/4, and the probability density function of y is represented by f(y) ＝ 1/P.
Consequently, average consumer utility is
∫
yf(y)Area(y) dy ＝
∫
P0
(1/P)[(y ＋ r(0) － 2P)/4] dy
So, when 0 ≦ r(1/2) ＝ y≦ P , the consumer will return the used product to the firm and receive the average consumer utility.
Given q ＝ L, Average Consumer Utility ＝ (2r(0) － 3P)/8 (4–7)
Figure 4.4 Consumer Utility when 0 ≦ r(1/2) ＝ y ≦ P , or q ＝ L B
A
y r(0)
P
r(t)
t t＝1/2
0 t＝1
Lemma 1. When a firm offers half-price purchase warranties, then if P ≦ r(1/2) ＝ y ≦ r(0), the consumer will pay another P/2 to hold the product continuously and receive the average consumer utility ＝ (5r(0) － 5P)/8; On the other hand, if 0 ≦ r(1/2) ＝ y ≦ P, the consumer will not pay any more and will return the used product to the firm and also receive the average consumer utility ＝ (2r(0) － 3P)/8.
Optimal solutions for the generalized model under full information. According to Lemma 1 and the basic model, Eqn. (4–1) can represent that the expected consumer utility, EU(S ＝ 1) equals function of Eqn. (4–3) is rewritten as
D(P; S ＝ 1) ＝
Simultaneously, the firm profit function changes to
ðq(P; S ＝ 1) ＝
To obtain Max ðq, solving (10) using its F.O.C. obtains the full information price
Figure 4.5 displays the optimal solutions for offering half-price purchase warranties (S ＝ 1) and offering no warranty (S ＝ 0) under the assumption of linear demand function. Under full information, Figure 4.5 shows that the provision of half-price purchase warranties in the durable product market shifts the demand curve upwards from q to
q . Unsurprisingly, most consumers prefer products with
warranties because these warranties generally increase their purchase motivation.
Simultaneously, these warranties also increase the equilibrium quantity from (q － C q )/2q to
. Consequently, the equilibrium price is higher because of the cost of the warranties. However, the equilibrium profit also increases when warranties are offered, from (q － C q ) 2 / 4 q to
Figure 4.5 Full-information Solutions in the Subforms of S = 0 and S = 1
Moreover, if the firm provides no warranty (S ＝ 0), then from Eqn. (4–2) the expected utility of the consumer, EU(0) ＝ rQ(Ω) － P＝ r q － P. Moreover, if half-price purchase warranties are offered (S ＝ 1), then from Eqn. (4–8), expected consumer utility, EU(1) ＝ r(0)[3Q(Ω) ＋ 2] － P [2Q(Ω) ＋ 3] ＝ r(0)(3q＋2)
－ P(2q＋3). It can also be proven that if the firm sets a reasonable price, namely r(0)
＞ 3 2
EU(S ＝ 0). This pattern indicates that if the consumer has faith in firm warranties, they will obtain higher expected utility under r(0) ＞
2 equilibrium solutions between S = 1 and S = 0 only change slightly when the product quality, q approaches 1. Under full information, should the firm offer a half-price
Q*q (S=0) Q*q (S=1) 1
purchase warranty? Furthermore, should consumers accept the warranties and buy the product without hesitation despite the firm increasing the price? The above analytical
purchase warranty? Furthermore, should consumers accept the warranties and buy the product without hesitation despite the firm increasing the price? The above analytical