Investigating Firm Strategies on O¤ering Consumer-Customizable Product Zheyin (Jane) Gu University of Connecticut 2100 Hillside Rd, Unit 1041, Storrs, CT, 06269 Email:
[email protected] Tel: (860) 486-0493. Giri K. Tayi State University of New York at Albany 1400 Washington Avenue, Albany, NY 12222. Email:
[email protected], Tel: (518) 956-8320 February 25, 2015
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Investigating Firm Strategies on O¤ering Consumer-Customizable Product Abstract
Advances in the digital economy have driven the trend among manufacturers, particularly those in the IT industry, to o¤er products that consumers can self-customize so as to satisfy their idiosyncratic needs. This study examines …rm strategies on o¤ering such consumercustomizable products. Our analysis shows that a monopolistic …rm obtains a greater pro…t from o¤ering a consumer-customizable product than from o¤ering a pre-con…gured standardized product only if consumers are su¢ ciently capable to conduct the customization task; otherwise, it is more pro…table for the …rm to o¤er a standardized product. Moreover, consumers obtain a greater surplus when the …rm o¤ers the customizable product. We also consider the case when the …rm is capable of o¤ering both a customizable product and a standardized product and …nd that the …rm bene…ts from o¤ering both products than either if consumer customizing capability and the customization cost are not too high. Interestingly, when the …rm o¤ers both products, its e¤ort in enhancing consumer customizability (e.g., o¤ering free consumer training) always bene…ts both the …rm and consumers, but its e¤ort in increasing the value of the standardized product (e.g., o¤ering more functions) can hurt both the …rm pro…t and consumer surplus. Our theoretical results explain many interesting business practices and provide useful insights for marketing practitioners. Key words: Consumer Customization, Consumer-Customizable Product, Standardized Product, IT products, Game Theory
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1
Introduction
The idea of consumer customization has been around for long ever since the futurist Alvin To- er predicted its emergence in 1970’s, but business implementations of this idea have not been very successful until recently with IT products. For example, Apple is famous for allowing consumers to customize the appearance and functionality of its computers and mobile phones. Probably the most ubiquitous consumer-customizable product is the platform-based mobile device, which consumers customize by downloading and installing apps. And most recently in January 2015, Google announced the plan to launch a modular smartphone, Project Ara, which allows a consumer to pick components from a range of selections including battery, camera, and screen, and piece them together to make her own phone. As commented by Project Ara’s head product designer, "You could change the design all the time....Conceptually it’s the …rst time a major electronic object, your phone, will not only be designed but also manufactured, if you wish, by the end user." (Dezeen.com, Jan. 15, 2015). Other successful examples of consumer-customizable products in the IT industry include Facebook and Pandora. As shown in these examples, “consumer customization”for a product is conducted by consumers for themselves so that the product will best suit their own unique needs, which is distinct from “product customization” as discussed in existing studies that is conducted by …rms for consumers as in the case of Mini Cooper (e.g., Dewan, Jing, and Seidmann 2003; Syam, Ruan, and Hess 2005; Ghose and Huang 2009). The purpose of this study is to examine …rm strategies on o¤ering a product that consumers can self-customize. In particular, we examine the following questions: First, what are the bene…ts for a …rm to o¤er a consumer-customizable product? Second, is it always pro…table for a …rm to o¤er a consumer-customizable product over a standardized product? And third, what are the strategic implications of a …rm o¤ering a consumer-customizable product on consumer surplus? The bene…ts of o¤ering a consumer-customizable product can be illustrated by an interesting life example of Steve Jobs. “Chris Espinosa found a way to Satisfy Jobs’s Design Demands And Control Freak Tendencies. . . [Chris] Espinosa kept re…ning [the calculator] in response to 3
Jobs’s critiques, day after day, but with each iteration came new criticisms. So …nally one afternoon, when Jobs came by, Espinosa unveiled his inspired solution: ‘The Steve Jobs Roll Your Own Calculator Construction Set.’ It allowed the user to tweak and personalize the look of the calculator by changing the thickness of lines, the size of button, the size of buttons, the shading, the background, and other attributes." Instead of just laughing, Jobs plunged in and started to play around with the look to suit his tastes. After about ten minutes he got it the way he liked. His design, not surprisingly, was the one that shipped on the Mac and remained the standard for …fteen years.” – Steve Jobs (2011), Chapter 12, “Design: Real Arts Simplify,” by Walter Isaacson, Simon and Schuster US. In information systems and marketing literature, “product customization” generally refers to the manufacturer practice of interacting with a client, understanding the client’s preference, and then producing a product that suits the client’s needs. This strategy is illustrated by the initial e¤ort of Steve Jobs’s design team when they tried to design a calculator that Steve (as the user) liked. In this case, the …rm internalizes the cost of product customization, and the success of customization depends on e¤ective communication between the …rm and its client. In contrast, our study focuses on “consumer customization,”wherein a …rm o¤ers a product that the client can self-customize. This strategy is illustrated by the later e¤ort of Steve Job’s team when they provided a “calculator construction set” to Steve so that he could design the calculator as he liked. In this case, the …rm outsources the customization task and the related costs to consumers, and the success of customization depends on consumers’customizing capability. Besides saving on customization costs, a …rm by o¤ering a consumer-customizable product also avoids the cost and hassle to communicate with clients, and therefore can satisfy consumers’peculiar needs better and more e¢ ciently. This notion is perfectly illustrated in the Steve Jobs’calculator example. O¤ering consumer-customizable product is particularly bene…cial for a …rm selling experience products about which consumers have diverse tastes. Consumers learn about their …t with an experience product only after a period of use. For example, a consumer may …nd out whether a smart phone …ts her needs only after having experienced its various functions. 4
Moreover, consumers may have time-varying preferences (Hoe- er and Ariely 1999) or may be uncertain about their own preferences at the time of purchase (Lynch and Ariely 2000). In these situations, o¤ering a consumer-customizable product grants consumers ‡exibility to adjust the product to best suit their needs when they are ready to do so.1 Furthermore, when consumers have diverse tastes, it is too costly and so infeasible for the manufacturer to customize the product for each individual consumer. For example, each individual person can have distinct habits of using computers or smart phones. In this case, the …rm by o¤ering a customizable product allows each individual consumer to enjoy a good …t with the product through self-customization, as opposed to o¤ering a standardized product that may fail to suit most consumers’needs. Interestingly, while in the IT industry o¤ering consumer-customizable product has become fairly common, in other industries …rms’e¤ort in o¤ering consumer customization is still rare and much less successful. Some examples in the non-IT industries include Kraft, Hallmark, M&Ms, Wrigley, and Nike. And one recent attempt is Coca-Cola’s launching of “freestyle machine,”which lets consumers make their own beverages by mixing more than 40 ingredients, including lemon, orange, raspberry, Coke, and Dasani (York and Cancino 2011). Beyond the easy explanation that o¤ering consumer customization for IT products is easier and less costly owing to their digital nature, we are interested in investigating other factors that cause such di¤erences in the practice of o¤ering consumer customization between the IT and non-IT industries. Moreover, even within the IT industry, we also see variations in …rm strategies on o¤ering consumer-customizable product. We would also like to investigate factors that have caused such variations. In understanding …rm strategies on o¤ering consumer customizable products, it is important to note that consumers’capability to make a customizable product best suit their own needs di¤er. Depending on consumers’skills, experiences, and knowledge about their own preferences, the results of consumer customization can di¤er considerably, as can be evidenced from the work of a professional and an amateur carpenter. Consumers with poor customizing capability are likely to desire a standardized product pre-con…gured by the 1
Recent research has also shown the “Ikea E¤ect,” that is, consumers even derive utility from self-
customizing the product (Norton, Mochon, and Ariely 2011).
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professionally-skilled manufacturer over a product that needs their own e¤ort. Overall consumer customizing capability may vary across markets. For example, in general consumers are more experienced with IT products such as computers and electronics and therefore are more capable of customizing these products than with many non-IT products such as apparel and beverages. Moreover, an individual consumer may develop di¤erent customizing capability for di¤erent product categories. While a tech guru is likely to have higher customizing capability for IT products than for beverage, a cook, on the other hand, may have higher customizing capability for beverages than for IT products. Although consumers can enhance customizing capability with any product category through learning, with limited time and cognition capacity they naturally choose to develop such capability only in key categories more important to their lives. Consumer heterogeneity in customizing capability has important implications for …rm strategies on o¤ering customizable products. In particular, each of the two product o¤ering strategies has its unique advantage and the heterogeneous customizing capability of consumers a¤ects the relative strengths of their advantages. On the one hand, when the …rm o¤ers a standardized product, the value of the product is uniform to all consumers, enabling the …rm to fully exploit consumer surplus using a uniform price. Nonetheless, the highest price the …rm can charge and the maximum pro…t the …rm can obtain is bounded by the manufacturing attributes of its product. On the other hand, when the …rm o¤ers a customizable product, consumers’perceived values with the product di¤er, and increase with their customizing capability. The …rm can set a higher price for the same product when consumers have higher customizing capability, but has to make a trade-o¤ between collecting a greater demand and acquiring a higher pro…t margin. Summary of Results Our analysis shows that for a monopolistic …rm, o¤ering a customizable product is more pro…table than o¤ering a standardized product only if the overall customizing capability of the consumer market is su¢ ciently high; otherwise, o¤ering a standardized product is more pro…table. This insight might explain why o¤ering consumer-customizable products is more popular in the IT industry. Owing to the rapid advancement of digital technologies in the past decades, a large population of consumers has accumulated a high level of knowledge 6
and experience about IT products. The extensive digital experiences and knowledge make consumers more interested in and also more capable of customizing IT products. Note that consumers are not just individual people; they can also be individual institutions such as companies and organizations. We also consider the case when the monopolistic …rm is capable of o¤ering both the customizable and the standardized product. We …nd that o¤ering both products is more pro…table than o¤ering either, if the overall consumer customizing capability and consumers’ cost of customization are not too high. Under this condition, demand is split between consumers with high customizing capability, who buy the customizable product, and consumers with low customizing capability, who buy the standardized product. Consumer surplus when the …rm o¤ers both products is greater than when the …rm o¤ers the standardized product only, but is lower than when the …rm o¤ers the customizable product only. Interestingly, we …nd that when the …rm o¤ers both products, an increased overall consumer customizing capability enhances both …rm pro…t and consumer surplus, but an increased value of the standardized product can hurt both the …rm and the consumers. Related Literature Our study follows a long tradition of research on product …t and monopolistic competition, which dates back to the early works of Hotelling (1929), Chamberlin (1948), and later, Shaked and Sutton (1982) and later continues in the information systems and marketing literature. While in recent years advances in information technology have provided consumers with unprecedented price and product information, consumers’ intrinsic and idiosyncratic needs continue to challenge marketers to facilitate the revelation of product …t information and assist consumers in …nding suitable products. Consumer uncertainty on product …t can be resolved through seller-induced learning, such as money-back guarantees (Davis et al. 1995), demonstrations (Heiman, et al. 2001), or sampling (Gu and Xie 2013). Gu and Liu (2013) shows that a big retailer can manipulate consumers’…t search process through store layout designs. Consumer …t uncertainty may also be resolved through experiential learning. Jing (2011a) studies a dynamic scenario in which …rst-period buyers of a durable product inform second-period consumers about the product speci…cs. In a similar setup, Jing (2011b) examines how the seller can promote social learning so that the same number 7
of …rst-period buyers informs more second-period consumers about the durable product. Our study makes a novel contribution to this research by demonstrating that a …rm can resolve consumer …t uncertainty by allowing consumers to self-customize the product according to their own tastes, which increases the product value for a broad set of horizontally di¤erentiated consumers at little cost on the …rm side. The concept of consumer self-customization is new to the literature and makes distinctive impact on …rm strategies and consumer welfare. And the …rm strategy of facilitating consumer self-customization constitutes an important new dimension of product di¤erentiation and design that digital technologies make possible, which adds to the traditional strategies of increasing product quality or investing on one set of product features at the cost of others. While the current study does not explore all aspects of consumer self-customization, we aim it to serve as the starting point for this new and exciting research direction. By examining …rm strategies on o¤ering products that consumers can self-customize, our study complements the literature on …rm strategies to customize products for consumers. Dewan, Jing, and Seidmann (2003) considers a …rm that o¤ers a variety of products that spread around the Salop circle of consumer tastes and examines how the cost of providing such products a¤ect …rm pricing and market entry deterrence. Syam, Ruan, and Hess (2005) considers a model in which two competitive …rms have to decide between two product attributes which one to customize for consumers after a costly interaction, and …nd that both …rms customize an identical attribute but not both. Ghose and Huang (2009) investigates a duopoly market where one or both …rms tailor its product qualities and prices based on consumers’ willingness to pay. Other research examines customized pricing for the same product (see Arora et. al. 2008 for a review). For example, Choudhary et. al. (2005) examines the competitive implications of personalized pricing when a …rm knows a consumer’s willingness to pay for a product. While these studies model how …rms can internalize the customization task, in our study the same task is outsourced to consumers. This outsourcing of customization is particularly feasible with IT products. Our study is also related to the literature on co-creation. Co-creation is the process during which consumers create value together with the company (Prahalad and Ramaswamy 2004). Recent technical advances in information and communication technologies (ICTs) provide 8
the opportunity for consumers to engage directly in an organization’s innovation process through virtual customer environments (Di Gangi et al. 2009). In an empirical study, Nambisan and Baron (2007) shows that customers’perceptions of interaction-based bene…ts will shape their future participation in product support in the virtual customer environments and customers’interactions will also generate changes in their a¤ective states, and these, in turn, in‡uence their attitude towards the …rm. Kohler et. al. (2011) generates a set of design principles for virtual co-creation systems through synthesizing the insights gained from an action research. It is important to note that co-creation typically occurs during the product development process, when the manufacturers involve consumers in product development activities such as generating and evaluating new product ideas, elaborating, evaluating, or challenging product concepts, and creating virtual prototypes (Kohler et. al. 2011). In contrast, consumer customization that we study occurs during product consumption process after the product development stage. Our study is also related to the product line literature. O¤ering more products help a …rm to serve consumers with di¤erent needs (Villas-Boas 2004; Klemperer 1992; Randall et al. 1998), but the information load involved in product search may cause poor-quality choices or a failure to purchase (Hu¤man and Khan 1998; Iyenger and Lepper 2000; Lurie 2004; Kuksov and Villas-Boas 2010). By o¤ering a consumercustomizable product, the …rm helps alleviate the cognition cost consumers incur in searching for the product that best suits the consumer’s needs. The rest of the paper proceeds as follows. In Section 2, we set up the general model. We examine strategies of a monopolistic …rm in Section 3. In Section 4, we illustrate two examples with speci…c model formats. Section 5 concludes the study while highlighting several areas for future research.
2
Model
The market has a demand of unit mass. A consumer’s utility from buying a standardized product is UN =
pN ,
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(1)
where
0 is the consumer’s value from the product and pN is the product’s price. Note
that all consumers perceive the same value with the standardized product. A consumer’s utility from buying a customizable product is UM = V ( )
pM
c,
(2)
0 is the consumer’s value from the product after customizing it, pM is the
where V ( )
product’s price, and c > 0 is the cost the consumer incurs in customizing the product.2 The consumer’s perceived value of a customizable product V depends on her customizing capability
1), with V 0 > 0 and V 00
(0
V and therefore
0
In particular, we assume being f ( ) =
1 ; 1 m
00
> 0 and
m(0
0. We let ( ) denote the inverse function of
0. Consumers have heterogeneous customizing capability.
is evenly distributed on the interval [m; 1], with the p.d.f. of m
1) captures the overall consumer customizing capability in a
market. We focus on demand side factors that a¤ect …rm strategies and abstract away the impact of …rm production costs. We assume a …rm incurs zero cost to o¤er a standardized product of value
and an in…nite cost to o¤er a higher value; the …rm incurs zero cost to o¤er a
customizable product. A …rm decides its product o¤erings and product prices to maximize its pro…t. We examine the product o¤ering strategy of a monopolistic …rm in a three stage game. In the …rst stage, the …rm decides whether to o¤er a standardized product (case N), a customizable product (case M), or both products (case MN). In the second stage, the …rm decides the price(s) for the product(s) it o¤ers. And in the third stage, consumers make purchase decisions. 2
We assume that the customization cost is known to consumers ex-ante, which is consistent with many
cases like that of platform-based mobile devices like the iPhone or the Samsung Galaxy since downloading apps is now part of the cultural dialog. Moreover, product reviews and online word of mouth may serve a role in informing customers upfront about what customization costs need to be incurred. For some product categories, the customization cost may be unknown to consumer ex-ante, which could represent an interesting direction for further work.
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3
Analysis
We solve the game through backward induction by …rst solving the …rm’s optimal strategies in cases N, M, and MN separately and then comparing the …rm’s payo¤s in the three cases to derive its optimal product o¤ering strategy.
3.1
Firm Strategy in Case N and Case M
We …rst consider case N when the …rm o¤ers a standardized product only. In this case, all consumers buy the standardized product as long as they obtain a non-negative utility, UN =
pN
0. The …rm’s optimal strategy is to serve the entire market and fully exploit
consumer surplus by charging pN = . At this price, the …rm’s maximized pro…t is
N
=
and consumer surplus is S N = 0. We next consider case M where the …rm o¤ers a customizable product only. In this case, a consumer buys the customizable product if and only if U M = V ( )
pM
c
0, which is
satis…ed when her customizing capability is su¢ ciently high, M
where
M
(pM ) = (pM + c);
(3)
is the customizing capability of the marginal consumer. The market is partially
covered if m
> > < > > > > > > > :
Z1 M
(V ( )
pM
c)f ( )d
Z1
(V ( )
c)d
Z1
peM
(V ( )
V (m))d
(10)
;mg
1 1 m
M
1 1 m
if
m
0, that is, the …rm cannot fully exploit consumer surplus for a customizable product. This contrasts the case when the …rm o¤ers the standardized product, where consumers are left with zero surplus, S N = 0. We examine how the …rm pro…t
M
and consumer surplus S M vary with the overall consumer customizing capability m in the market, and obtain the the following proposition. Proposition 1: When the …rm o¤ers a customizable product and the overall consumer customizing capability m increases: (1) the …rm pro…t always increases; (2) the consumer surplus increases only if m
m e = :
1
(e pM +c) M
( + c)
pe
if if
otherwise, o¤ering a standardized product is more pro…table.
< peM
peM ;
(11)
(2) Consumer surplus is always greater when the …rm o¤ers a customizable product than when the …rm o¤ers a standardized product. Proof: See Appendix. Proposition 2 shows a monopolistic …rm may be worse o¤ by o¤ering a customizable product rather than a standardized product. O¤ering either product has its unique advantage and the relative strengths of their advantages depend on the overall consumer customizing capability m. On the one hand, when the …rm o¤ers the standardized product, consumers’ 13
willingness to pay for the product is homogeneous, which allows the …rm to fully exploit consumer surplus while serving the entire market. This constitutes a unique advantage comparing to the case when the …rm o¤ers the customizable product, where consumers’heterogeneous willingness to pay forces the …rm to make a trade-o¤ between charging a higher price and covering a larger market. When m increases, the customizing capability of the entire market is improved. Consumer heterogeneity in customizing capability is reduced, weakening the bene…t of o¤ering the standardized product. On the other hand, when the …rm o¤ers the customizable product, consumers’willingness to pay for the product increases with their customizing capability, which allows the …rm to charge a higher price for the same product. This constitutes an advantage comparing to the case when the …rm o¤ers the standardized product, where consumers’willingness to pay is bounded by the product’s manufacturing attributes. When m increases, more consumers have high customizing capability, strengthening the bene…t of o¤ering the customizable product. Collectively, o¤ering a customizable product brings the …rm a pro…t advantage over o¤ering a standardized product when m is su¢ ciently high. Since consumers’customizing capability is generally higher for IT products, our result may explain why o¤ering customizable product is more common in the IT industry than in non-IT industries. Proposition 2 also shows that consumers always obtain a greater surplus when the …rm o¤ers a customizable product. This is because the …rm cannot fully exploit consumer surplus when their willingness to pay for the product is heterogeneous. Our result thus suggests an interesting win-win situation when the …rm o¤ers the customizable product.
3.2
Firm Strategy in Case MN
We let pM N
M
and pM N
N
denote the prices of the customizable product and the standard-
ized product respectively when the …rm o¤ers both, and denote d = pM N
M
pM N
N
. A
consumer buys the customizable product if gaining a higher utility, UM = V ( )
pM N
M
c > UN =
pM N
N
:
(12)
Condition (12) is satis…ed when the consumer’s customization capability is su¢ ciently high, >
MN
(d) = (d + c + ): 14
(13)
MN
And consumers with low customizing capability ( < Note that if
MN
) buy the standardized product.
1 all consumers buy the standardized product, and if
MN
m all con-
sumers buy the customizable product. Consumer demand is split between the two products only if m
0 is always satis…ed; therefore, the …rm can fully exploit
consumers’willingness to pay for the standardized product by charging the optimal price of pM N
N
= . We let deM N denote the interior solution to
m
0, that is, the optimal price of the customizable product is higher than that of the standardized product, pM N
M
> pM N
N
. We summarize the …rm’s optimal
strategy in Case MN in the following lemma. Lemma 2. When the …rm o¤ers both a customizable product and a standardized product, it obtains demand from both products if m
in equilibrium, the …rm pro…t and consumer surplus are respectively MN
=
SMN
=
1
(c + pM N 1 m 1 Z p (
M
)2
pM N
pM N
M
M
+ c)
p 1 (c+ 3+c2 )2 9
(c + pM N M )2 1 m 1 1
m
d .
m
pM N
N
; and
(29) (30)
Based on the above analysis, Propositions 1-5 can be proved.
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Conclusion
Our study makes the …rst attempt to examine …rm strategies on o¤ering a product that consumers can self-customize to satisfy their idiosyncratic needs. Our analysis shows that it is more pro…table for a monopolistic …rm to o¤er a consumer-customizable product than to o¤er a standardized product if the overall customizing capability of the consumer market is su¢ ciently high; otherwise, o¤ering a standardized product is more pro…table. We also consider the case when the …rm is capable of o¤ering both a customizable and a standardized product and show that o¤ering both products is more pro…table than o¤ering either if the overall consumer customizing capability and consumers’ customization cost are both low. Interestingly, when the …rm o¤ers both products, enhanced overall consumer customizability always bene…ts both the …rm and consumers, but increased value of the standardized product can hurt both …rm pro…t and consumer surplus. Furthermore, the total surplus of consumers
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when the …rm o¤ers both products is higher than when the …rm just o¤ers the standardized product, but lower than when the …rm o¤ers the customizable product. While our study focuses on the monopolistic case, it is interesting to consider a competitive market where each of two competing …rms decides whether to o¤er a customizable product or a standardized product. Our preliminary results show that in equilibrium the two symmetric …rms adopt di¤erentiated product o¤ering strategies, with one …rm o¤ering the customizable product to serve consumers with high customizing capability and the other …rm o¤ering the standardized product to serve consumers with low customizing capability. This result is interesting because it shows that facing market competition, the two symmetric …rms are likely to adopt asymmetric product o¤ering strategies. This is because in a market characterized by consumer heterogeneity in customizing capability, o¤ering di¤erent types of products (customizable or standardized) creates product di¤erentiation and consequently reduces price competition between the two …rms. The strategic di¤erentiation in …rms’product o¤ering strategies can also be achieved when the two competing …rms o¤er products with di¤erent levels of customizability. This insight may explain the variation in …rm product o¤ering strategies in the IT industry. A limitation of the current study is that we do not consider consumer learning on customizing capability or market dynamics related to consumer learning. There are many interesting future research directions to pursue in this regard. For example, consumer may improve their customizing capability for a …rm’s product through experiencing that product or through experiencing the …rm’s other related products. Moreover, early buyers who acquire customizing capability for a product may share such knowledge with late buyers through online tutorials or word-of-mouth. Such experiential learning and social learning on consumer customizing capability can have important implications for a …rm’s dynamic marketing strategies including sequential product launches, dynamic pricing, and product line design. Another interesting future research direction is to examine strategies of two-sided platforms, where developers on the one side produce customizability that consumers on the other side could consume. We leave these interesting issues for future explorations. We acknowledge, with thanks, the insightful suggestions and constructive comments offered by Senior Editor, Associate Editor, and the review team which have greatly enhanced 21
the quality of the paper.
6
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7
Appendix
7.1
Proof of Lemma 1
The interior solution peM sustains only if m
m2 = ( + c);
=
is satis…ed if m > m1 =
is satis…ed if and only if
is satis…ed if and only if peM . We then conclude that M > 8 < m = 1 (1 (epM +c)) pe if < peM 1 m
S N = 0.
7.4
Proof of Lemma 2
Consumer demand is split between the customizable product and the standardized product MN
only when m < c < V (1)
deM N
(deM N ) = (deM N + c + ) < 1, that is, when {m
N
MN
(b)
M
pM N
M
=
M
m
(36)
:
. As of comparing the equilibrium …rm pro…t in case MN and
in case M, we consider the following two situations. (a) m < (pM N
+ c) m
> , selling two products is always more pro…table than selling just a stan-
dardized product,
MN
M
) increases with pM N
MN
(pM N
< m < > V (m)
MN
M
M
for pM N
= deM N + ) >
: In this case,
MN
MN
M
M
M
M
= peM )
M
= V (m)
: In this case, since
(pM = peM ) =
M
:
(37)
c is always satis…ed since
c:
Next, we compare the total consumer surplus. Since consumer surplus is positive in case MN and zero in case N, we obtain S M N > S N . And since pM N
26
M
> pM is satis…ed, we
obtain SMN =
Z1
1 1
m
(pM N
(V ( ) pM N
M
M
c)d < S M =
1 1
m
Z1
(V ( ) pM
c)d :
(pM +c)
+c)
(38)
7.6
Proof of Proposition 4 MN
We take f.o.c. of MN
@
=
w.r.t. m and obtain
1 [(1 (1 m)2
@m 1 (1 = (1 m)2
(deM N + c + ))(deM N + ) + ( (deM N + c + )
(deM N + c + ))deM N > 0:
Moreover, since deM N and
MN
do not depend on m, consumer surplus S M N =
c)d increases with m.
7.7
Proof of Proposition 5 MN
To examine how MN
@
1
m (39)
1 1 m
Z1
(V ( )
MN
deM N
@
m) ]
varies with , we obtain
(deM N + c + ))(deM N + ) @( (deM N + c + ) m) ) + ] 1 m @ @ 1 @ (deM N + c + ) eM N @(deM N + ) MN e = [ (d + ) + (1 (d + c + )) 1 m @ @ MN e @ (d +c+ ) + + ( (deM N + c + ) m)] @ 1 @ deM N @ deM N = ( 0 deM N + +1 m): (40) (1 m) @ @ =
1
[
It can be proved that m < (1 Moreover, we have @S M N 1 = @ 1 m
Z1
MN
@(1
@
MN
@
> 0 if
0 eM N
d
@V ( )
) + (1
)
@ deM N = @
( + deM N ) @
c
d =
+ (1
)
1 1
m
@ deM N < @ Z1
(deM N +c+ )
27
MN
(1 +
:
(41)
@ deM N )d < 0: @ (42)
Proof of Results in Example 1: V ( ) =
7.8
The …rm’s pricing strategy and market payo¤ in case N is the same as in the main model. In case M, the consumer buys the product if U M = M
> m, the …rm’s pro…t function is Z Z 1 M M p dF ( ) = = M
@ M @pM
The interior solution to
1
p
pM +c V
pM
pM (1 d = m 1
1
M
0
1
1 (V 2
= 0 is peM =
c > 0, or if
M
>
pM +c ) V
m
= p + c. If
(43)
: M
c), and at this price,
=
1+c . 2
In
particular, we consider the following two conditions: M
(a) m
R1
m
pM dF ( 0 ) =
pM = m
Z
m
c+1 2
=
Z1
(
p
M
M
c)
1 1
m
It is easy to prove that
0
c)dF ( ) =
&c>1
Z
1
(
m)
m
M
1 1
1 d = (1 m 2
M
N
>
only if {m > 1
(44) M
=
, that is, if
(45)
m):
(1 c)2 4
&c
1
M
2 } or
2 }. We have thus proved Propositions 1 and 2.
In case MN, a consumer buys the customizable product if U M = N
(1 c)2 : 8(1 m)
always increases with m; S M increases with m only if m
c +
c)
pM 1 1m df ( 0 ) = pM . The …rm optimally charges the highest price possible,
c, and obtains a pro…t of S
1 (V 2
( V
: In this case, all consumers buy product 1. The …rm pro…t is
R1
M
1
>
MN
= c + d + . If m
UN =
, consumer demand is split between
the standardized product and the customizable product, and the …rm’s pro…t function is Z 1 Z MN 1 1 MN MN M = p d + pM N N d (46) MN 1 m 1 m m =
MN
1
1
m
MN
( + d) + 28
1
m : m
(47)
MN
Taking f.o.c of
, we obtain
@ MN @pM N N
the …rm’s optimal pricing strategy is {deM N = 1 (1 2
m< MN
MN
c)}, which renders the
+
MN
=
=
c+1+ 2
1
(c+2d+( 1+ )) ( 1+m)
=
1 (1 2
c+1+ 2
=
MN
@d
c), pM N
N
= 0. Therefore, =
, pM N
M
=
. This interior solution sustains only if
< 1. Under this condition, the …rm’s equilibrium pro…t is
c+1+ 2
1
@
= 1 and
1 (1 + m 2
c) +
c+1+ 2
m
1
=
m
1 + c2 + 2c( 1 + ) + (2 4(1 m)
2
4m) +
: (48)
This pro…t increases with m, since MN
@
@m
=
(c + ( 1 + ))2 > 0: 4(1 m)2
And @
MN
@
8
M
= mV
c+1 , 2
c) and therefore, MN
>
M
=
MN
MN )2
=
>
(c V 4V (1 m)
M
c+1+ 2
< 1. In this case, pM N
M
=
. In comparing the …rm pro…t, we
is always satis…ed, and when m
c+1 , 2
c is always satis…ed. In comparing the consumer surplus, we obtain
S M N > S M = 12 (1 m)V for 12 (1 c + ) < m < 1 and S M N > S N = 0 is always satis…ed. We have thus proved Propositions 3-5.
7.9
Proof of Results in Example 2: V ( ) =
p
The …rm’s pricing strategy and market payo¤ in case N are the same as in the main model. p In case M, a consumer buys the product only if U M = pM c > 0, that is, if 29
M
= (p + c)2 . When m < M , the …rm’s pro…t function is Z 1 Z 1 1 1 (pM + c)2 M M M p dF ( ) = pM d = p : (52) = M 1 m 1 m (p+c)2 p M The interior solution pM = peM = 31 ( 3 + c2 2c) solves @@p = 0. At pM , the threshold is p M = 19 (c + 3 + c2 )2 . We consider the following conditions. p (a) If m < M = 91 (c + 3 + c2 )2 , the interior solution sustains; the …rm pro…t can be >
derived as M
=
1 27(1
m)
p ( 3 + c2
N
=
is greater than the pro…t when the seller o¤ers a p p if m > 1 272 ( 3 + c2 2c)(3 c2 c 3 + c2 ).
The consumer surplus at pM = peM can be derived as
S
Z1 p = (
M
p
(53)
M
which increases with m. Moreover, standardized product
p ( 3 + c2 + c)2 );
2c)(3
c)dF ( ) =
1
1
m
M
Z
p (
1
1 (c+ 9
p
3+c2 )2
1 p ( 3 + c2 3
2c)
c)d :
(54)
It is easy to see that S M increases with m. M
(b) If m
, the interior solution does not sustain. All consumers buy product 1 and R1 R1 the …rm pro…t is M = m pM dF ( ) = m pM 1 1m df ( ) = pM . The …rm optimally charges p M the highest price that satis…es m , that is, pM = m c, and obtains a pro…t of p M = m c. This pro…t is greater than N = if m > ( + c)2 . p The consumer surplus at pM = m c can be derived as S
M
Z1 p = (
p
0
c)dF ( ) =
Z
1
p (
m)
m
m
It is easy to see that S M > 0 and
@S M @m
=
1 1
1
m p
d =
2 3
m
2 3 m 2 + m2 : 3
(55)
m + 2m < 0. We have thus proved
Propositions 1 and 2. In case MN, a consumer buys the customizable product if and only if U M = pM N
M
c > UN =
pM N
N
, that is, if
>
MN
= (c + d + )2 . If m
0:
(c + deM N + )2 (c + deM N + )2 m ( + deM N ) + 1 mp 1 m 2 2 2 p 9 ( + c + 3 + c + 2c + ) = ( 2c + + 3 + c2 + 2c + 27(1 m) p 1 ( 3 ( + c + 3 + c2 + 2c + 2 ) + c)2 m + : 1 m 1
=
MN
It can be proved that
always increases with m; and
1 m < (3 + 2c2 + 4c + 2 9
2
)+
MN
2p 2 3c + c4 + 6c + 4c3 + 3 9
increases with 2
+ 6c2
2
+ 4c
2)
(58) if
3
+
4:
(59)
Given the …rm’s optimal prices, the total consumer surplus can be derived as MN
S
MN
Z
=
(
p
MN N
m
=
)
1 1
m
Z1 p d + (
pM N
M
c)
1 1
m
d
MN
1 1
m
Z1 p (
1 ( 2c + 3
+
p 3 + c2 + 2c +
2)
(60)
c)d :
MN
It is easy to see that S M N increases with m. Also, it can be proved that @S M N @
=
1 1
m
+
Z1
q ( (
p @(
p 1 @ MN ( 2c + + 3 + c2 + 2c + 2 ) c) 3 @ p 1 ( 2c + + 3 + c2 + 2c + 2 ) c) 3 d ) < 0. @
MN
(61)
MN
Moreover, since pM N satis…ed, we obtain
M MN
p = 13 ( + 3 + c2 + 2c + >
M
2
p 2c) > pM = 13 ( 3 + c2 2c) is always
. We can then prove that
MN
>
M
and
MN
>
N
are
always satis…ed and that S M N > S M and S M N > S N = 0 are always satis…ed. We have thus proved Propositions 3, 4, and 5. 31
