Buscar

Impacto da tecnologia de e-books na indústria editorial

Prévia do material em texto

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/220066702
Impact of e-book technology: Ownership and market asymmetries in digital
transformation
Article  in  Electronic Commerce Research and Applications · September 2010
DOI: 10.1016/j.elerap.2010.06.003 · Source: DBLP
CITATIONS
38
READS
508
2 authors:
Some of the authors of this publication are also working on these related projects:
Platform Complements View project
2D materials View project
Yabing Jiang
Florida Gulf Coast University
29 PUBLICATIONS   190 CITATIONS   
SEE PROFILE
Evangelos Katsamakas
Fordham University
49 PUBLICATIONS   872 CITATIONS   
SEE PROFILE
All content following this page was uploaded by Yabing Jiang on 08 February 2018.
The user has requested enhancement of the downloaded file.
https://www.researchgate.net/publication/220066702_Impact_of_e-book_technology_Ownership_and_market_asymmetries_in_digital_transformation?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_2&_esc=publicationCoverPdf
https://www.researchgate.net/publication/220066702_Impact_of_e-book_technology_Ownership_and_market_asymmetries_in_digital_transformation?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_3&_esc=publicationCoverPdf
https://www.researchgate.net/project/Platform-Complements?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_9&_esc=publicationCoverPdf
https://www.researchgate.net/project/2D-materials-39?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_9&_esc=publicationCoverPdf
https://www.researchgate.net/?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_1&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Yabing_Jiang?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_4&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Yabing_Jiang?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_5&_esc=publicationCoverPdf
https://www.researchgate.net/institution/Florida_Gulf_Coast_University?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_6&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Yabing_Jiang?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_7&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Evangelos_Katsamakas?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_4&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Evangelos_Katsamakas?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_5&_esc=publicationCoverPdf
https://www.researchgate.net/institution/Fordham_University?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_6&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Evangelos_Katsamakas?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_7&_esc=publicationCoverPdf
https://www.researchgate.net/profile/Yabing_Jiang?enrichId=rgreq-7d8034f35d071f1fbb7c060d2dbb1cdf-XXX&enrichSource=Y292ZXJQYWdlOzIyMDA2NjcwMjtBUzo1OTE3OTMyNTUxMjA4OTZAMTUxODEwNTkxNTY0Nw%3D%3D&el=1_x_10&_esc=publicationCoverPdf
This article appeared in a journal published by Elsevier. The attached
copy is furnished to the author for internal non-commercial research
and education use, including for instruction at the authors institution
and sharing with colleagues.
Other uses, including reproduction and distribution, or selling or
licensing copies, or posting to personal, institutional or third party
websites are prohibited.
In most cases authors are permitted to post their version of the
article (e.g. in Word or Tex form) to their personal website or
institutional repository. Authors requiring further information
regarding Elsevier’s archiving and manuscript policies are
encouraged to visit:
http://www.elsevier.com/copyright
http://www.elsevier.com/copyright
Author's personal copy
Impact of e-book technology: Ownership and market asymmetries
in digital transformation
Yabing Jiang *, Evangelos Katsamakas
Information Systems, Graduate School of Business Administration, Fordham University, 113 W. 60th Street, New York, NY 10023, United States
a r t i c l e i n f o
Article history:
Available online 1 July 2010
Keywords:
Product differentiation
E-books
Book industry
Information goods
Digital goods
E-commerce
Channel competition
Economic analysis
Ownership
Transformation
a b s t r a c t
The book industry is undergoing a digital transformation enabled by the Internet and e-book technology,
which offers a novel channel for delivering books to consumers who mostly purchase paper books from
physical or online bookstores. With a game theory model that introduces the concepts of paper book mar-
ket asymmetry and e-book market asymmetry, we examine how the entry of an e-book seller affects stra-
tegic interaction in the book markets and impacts sellers and consumers. We show that market
asymmetries, ownership of the e-book seller, and consumers’ preferences for e-books are important
determinants of prices, market shares and total book readership. We find that prices in the book market
may increase after the e-book entry. Total readership may decrease after e-book entry, if the e-book seller
is owned by one of the paper book sellers. The lowest total readership occurs when the online paper book
seller owns the e-book seller.
� 2010 Elsevier B.V. All rights reserved.
‘‘Like many other parts of the media industry, publishing is being
radically reshaped by the growth of the Internet. Online retailers
are already among the biggest distributors of books. Now e-books
threaten to undermine sales of the old-fashioned kind.” (The
Economist 2010)
1. Introduction
Publishing and book markets are undergoing a transformation
due to the Internet and the emerging e-book technology. In
November 2007, Amazon, the dominant online book seller, un-
veiled Kindle, a lightweight e-book reader that many observers
called the ‘‘iPod of books”, as it is likely to transform how people
read books. The Kindle device is only one component of the e-book
platform provided by Amazon. Other components include an
e-book store that provides the e-books as well as the software that
encodes and protects the books once they are downloaded into the
device. Customers can browse books and download the purchased
books through a 3G network. The original Kindle holds up to 1500
titles and features e-ink screen technology that makes reading as
pleasant as reading paper.1 Using a Kindle software application, cus-
tomers may also read their e-books on their iPhones or personal
computers. In addition to Amazon’s Kindle, Sony offers Reader, an-
other popular e-book device, and its own e-book store. Barnes and
Noble announced its own e-book store and its Nook e-book reader
in late 2009. In April 2010, Apple released its iPad tablet computer,
which targets several media markets including e-books.
E-book technologyoffers a new way for book delivery to read-
ers, whereby a digital copy of a book (e-book) is delivered to a de-
vice that a consumer uses. The American Association of Publishers
estimates that e-book sales in the US reached $113 million in 2008.
This is still a fraction of the $24.3 billion book market, but e-book
sales grew 68.4% in 2008, while total book sales decreased 2.8%
(AAP 2009). In addition to purchasing a paper book through a phys-
ical bookstore or an online store, customers can now download an
e-book from an e-book seller. According to Publishers Weekly, book-
chains and online stores hold 32.5% and 30% shares of consumer
physical book purchases in 2008 (Milliot 2008). Competition be-
tween online and physical sellers of products has been analyzed
in the literature on e-commerce and related channel-competition
1567-4223/$ - see front matter � 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.elerap.2010.06.003
* Corresponding author. Tel.: +1 212 636 6131; fax: +1 212 765 5573.
E-mail addresses: yajiang@fordham.edu (Y. Jiang), katsamakas@fordham.edu
(E. Katsamakas).
1 The popularity of the first Kindle motivated Amazon to introduce Kindle 2 (costs
$259 as of January 2010) and Kindle DX, a larger screen device targeting the
newspaper and textbook markets. Prices for Kindle e-books and newspaper
subscriptions are typically cheaper than the paper versions. For instance, most
best-sellers and new releases are $9.99, while the list price of the paper book is
typically more than $20.
Electronic Commerce Research and Applications 9 (2010) 386–399
Contents lists available at ScienceDirect
Electronic Commerce Research and Applications
journal homepage: www.elsevier .com/locate /ecra
Author's personal copy
(Balasubramaniam 1998, Viswanathan 2005, Cheng and Nault
2007), but this early literature has not considered competition be-
tween digital and physical products across different channels.
As shown in Fig. 1, this paper analyzes the novel phenomenon
of the competition between the e-book seller who sells digital
goods and pre-existing sellers of physical goods. The paper focuses
on the strategic interaction between the selling of e-books and that
of physical books in the book market.
In the book market of Fig. 1, consumers must decide whether to
buy a paper book from either seller A or B, or buy an e-book, or not
buy any book. The e-book technology may enhance some users’
reading experience. For example, it provides value-added features
such as automatic bookmark, dictionary, note taking, search capa-
bility, and text-to-voice functions. The device can store multiple ti-
tles so that users can easily carry around a personal library.
However, there are also downsides to using the e-book device.
The e-books are often protected by a DRM technology, which limits
a book owner’s capability of sharing the titles they bought. In addi-
tion, some customers may prefer the experience of holding and
reading a paper book.
E-book technology alleviates the need to produce, store, and
distribute physical books. At the same time, it decreases the pro-
duction costs of book publishing. However, publishers are con-
cerned that e-books will cannibalize existing paper book sales
and that consumers will get used to low e-book prices, which
may put pressure on the prices of paper books (The Economist
2010). To examine this concern, this paper conveys three main
observations. First, e-books compete with paper books, which
may be sold by offline or online sellers. Consequently, one needs
to consider carefully how costs and consumer preferences for
e-books and paper books differ. Second, as e-books can be sold
by an independent e-book seller or by sellers that already sell
paper books (e.g. Amazon), it is important to consider whether
ownership has a significant effect on prices and total readership.
Third, the e-book market is currently small but growing as e-book
technology advances, so it is helpful to understand how improve-
ments in e-book technology can affect prices and the total reader-
ship in the future. The research question is: how do the ownership
of the e-book seller, the advances in e-book technology and the dif-
ferences between selling paper books and e-books affect prices and
the total readership in book markets?
We answer this question by means of a game theory model
based on the literature on product differentiation, channel compe-
tition, and information goods. In particular, we extend Salop’s
(1979) ‘‘unit circle” modeling idea2 to a new model that examines
how the entry of an e-book seller affects strategic interactions in
the book market. Introducing the concepts of book market asymmetry
and e-book market asymmetry, our model shows that these market
asymmetries affect not only the prices and total readership but also
the incentives of online and offline sellers to own the e-book seller.
Because e-book technology is new, we also examine whether the an-
swer to our main research question is sensitive to alternative
sequential pricing cases, where the e-book seller or the paper book
sellers set prices first.
Previous IS research on information and digital goods focused
on issues of piracy and the value of digital rights management
(DRM) technology (Chellappa and Shivendu 2005, Smith and
Telang 2009, Sundararajan 2004) and pricing issues such as ver-
sioning and bundling (Bakos and Brynjolfsson 2000). Multiple
empirical studies used online book sales data and found that price
dispersion does not disappear on the Internet (Brynjolfsson and
Smith 2000, Clay et al. 2001, 2002); social welfare increases sub-
stantially due to increased product variety offered by online sellers
like Amazon (Brynjolfsson et al. 2003); price rigidity does not
disappear and it differs across types of books and retailers
(Bergen et al. 2005); and only 16% of used-book sales cannibalize
new book sales at Amazon, leading to an increase of consumer
and social welfare (Ghose et al. 2006). This literature has paid less
attention to the theoretical analysis of the strategic interaction
between digital and physical information goods. An exception is
(Oestreicher-Singer and Sundararajan 2006) that analyzes the
value of digital rights in the context of a monopolist selling a
physical and a digital book, and finds that the monopolist should
restrict certain digital rights in the presence of piracy.
We find that in response to the entry of an e-book seller, firms
may increase or decrease their prices on paper books, depending
on market conditions. Similarly, as the e-book technology becomes
acceptable to more customers, the price competition between the
paper book sellers and the e-book seller is sometimes relaxed. This
means that the prices for both the paper book and e-book can
increase. Another counter-intuitive result is that the entry of an
e-book seller does not always expand the total readership. We
show that when a firm offers both the paper books and e-books
and competes with a pure paper book seller, more customers are
left un-served than when both firms only sell paper books. In addi-
tion, we find that a paper book seller may prefer to compete with
an integrated book seller that offers both paper books and e-books
rather than compete with an independent e-book seller. Our
analysis provides strategic insights for managers in the book and
publishing industry, but it is also relevant, more generally, to
managers of industries that undergo a digital transformation. Thus,
we answer the call for more research on how digitization progres-
sively transforms information-goods industries, as managers need
to understand and manage this transformation (Agarwal and Lucas
2005).
The article is structured as follows: Section 2 defines the model
whereas Sections 3–5 analyze and discuss the results. In particular,
Section 3 analyzes the physical book duopoly before the entry of
the e-book seller. Section 4 discusses the entry of an e-book seller
and its impact on the market when the market is symmetric. Sec-
tion5 discusses the effects of market asymmetries. Section 6 pro-
vides a few concluding remarks.
Transformation of book market due to e-book technology 
Physical books e-books Physical books 
Consumers 
Book seller A Book seller B E-book seller E Book seller A Book seller B
Consumers 
(a) Physical book market (a firm 
can be an online or offline seller) 
(b) E-book seller enters into the book market (strategic 
interaction of selling e-books and physical books) 
Fig. 1. Overview of research framework.
2 Building on Salop’s (1979) ‘‘circular” market is a well-established approach in IS
economics, e.g. the analysis of search costs (Bakos 1997) and mass-customization
strategies (Dewan et al. 2003).
Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 387
Author's personal copy
2. The model
We consider a book market in which consumers have a unit de-
mand and a common reservation value V for a given book title that
is independent of its electronic or physical format. Consumers are
heterogeneous along two dimensions, which define consumers’
preferences for physical books and e-books.
The first dimension conveys the consumer’s preferences for
physical books in a circular spatial market, as in Salop (1979). Cus-
tomers are distributed uniformly on a circle of unit circumference
and their total mass is equal to 1. Two firms A and B, selling iden-
tical paper books, are located on the circle symmetrically at equal
distance apart from each other. Depending on their locations on
the circle relative to firms A and B, customers who buy a paper
book from B incur a disutility t per unit distance, whereas custom-
ers who buy from A incur a disutility kt per unit distance, with
k 6 1.
We use the distance-related disutility term to capture the fact
that customers have a different willingness to pay for books and
different preferences for sellers. The source of this customer heter-
ogeneity could be due to different transportation costs, opportu-
nity costs, brand or service differentiation, convenience of
shopping, loyalty to one firm rather than to another, or other
transaction costs or sources of disutility (Ellison and Ellison 2005,
Forman et al. 2009). Capturing the potential asymmetry of firms
A and B, the parameter k constitutes a novel extension of Salop’s
(1979) circular model. When k = 1, the circular component of our
model is identical to Salop’s (1979) setup. But when k < 1, firm A
is associated with a lower unit-distance disutility than firm B. As
a result, the physical book market is asymmetric.
While there can be many potential sources of such asymmetry,
we will focus on the case that A is an online seller of physical books
and B an offline seller of physical books. Now, some consumers of
paper books may prefer buying online, while others may prefer
buying offline. Online channels have shipping costs and delayed
gratification. However, the unit-distance disutility of the online
channel is lower than that of the offline channel, because the for-
mer allows for greater personalization and flexibility (Viswanathan
2005). In addition, customers who buy offline do incur a physical
transportation (travel) cost and a cost of traveling but not finding
the book (Forman et al. 2009). Because of a limited selection of off-
line sellers, online sellers face significant competition when they
sell popular products, but little competition when it comes to niche
products (Brynjolfsson et al. 2009). This suggests that, everything
else being equal, the physical book market asymmetry may in-
crease, the less popular the book is.
The consumers’ preferences for e-books are defined by three
assumptions: (a) consumers have a disutility te of buying the
e-book that is either3 te1 or te2, (b) te1 < V < te2 and (c) for a consumer
in the neighborhood of A, her disutility of e-books is te1 with proba-
bility q, while for a consumer in the neighborhood of B, her disutility
of e-books is te1 with probability mq, where 0 < m 6 1.
Assumption (a) says that consumers have a different willing-
ness to pay for e-books as they differ in their disutility te of buying
the e-book. This disutility may be due to the need to purchase an
e-book device, install e-book software, set up an e-book store
account, and learn how to use the device. It may also be caused
by the inconvenience of reading electronic texts or digital restric-
tions regarding sharing the e-book with friends, or more generally
the ‘‘quality” of e-book technology and other related costs.
Assumption (b) means that customers of type te1 (low e-book
disutility) will consider e-books in their purchase decision and
they may buy the e-book if it offers them greater surplus than
the physical book. Customers of type te2 (high e-book disutility)
do not like e-books in general and they do not consider e-books
in their purchase decisions. These consumers may not be techno-
logically sophisticated (Oestreicher-Singer and Sundararajan
2006), they may not be early adopters, or they may not like e-
books for some other reason (AAP 2009).
Assumption (c) suggests that when compared to consumers
close to B, consumers close to A may be differentially attracted
to e-books. This assumption conveys the e-book market asymme-
try. When parameter m = 1, there is no systematic difference be-
tween physical book sellers A and B’s customers. However, when
m < 1, more of firm A’s consumers are likely to consider e-books
than firm B’s consumers. This asymmetry may happen when A is
an online seller of paper books, whereas B is an offline seller of
physical books, in which case consumers close to A are likely to
be more technologically sophisticated or be more attracted to try-
ing e-books. For instance, consumers close to A may feel more
comfortable about using an e-book reader, and they may already
have accounts at the online bookstore that can be accessed through
the e-reader device. By introducing this e-book market asymmetry,
we are able to further investigate the impact of e-book technology
when it has a differential impact on physical book sellers’ customer
bases.
Another difference between paper books and e-books is the cost
structure. Both the paper book sellers and the e-book seller have to
pay the publisher/author for royalty. However, while the paper
book sellers incur a marginal production and distribution cost c,
the e-book seller has a near zero marginal production/distribution
cost, which is typical in the literature on information goods (Bakos
and Brynjolfsson 2000). Thus, we normalize the royalty cost for
both the paper book sellers and the e-book seller, and assume that
the former incurs a marginal cost c whereas the latter has a zero
marginal cost.
The closest paper to our model setup is Balasubramaniam
(1998), which considers retailers located on a Salop (1979) circle
competing with a direct marketer located in the middle of the cir-
cle. But that paper focuses on the number of retailers and on the
strategic role of information at equilibrium. It does not consider
the two types of market asymmetry that we discuss above; it does
not consider the issue of ownership of the direct seller; and also it
does not consider sequential entry as we do. Another related model
is (Viswanathan 2005), which considers online and offline channel
competition in the presence of a ‘‘hybrid” firm that operates in
both channels, but that paper has two touching Salop (1979) circles
and the main focus is on channel network effects and on switching
costs. We advance the line of research in Balasubramaniam (1998)
and Viswanathan (2005) by considering the competition between
digital and physical products across different channels. At the same
time, we discuss the implications of our new results in the context
of emerging book markets that are being transformed by the
e-book technology and IT. Table 1 summarizes the modeling
notations.
3. Duopoly market of physical book sellers
Let us consider the book market in which only the physical book
sellers A andB are active and e-books are not available. We use the
superscript D to represent results of this duopoly market. Let PDA be
the price charged by firm A and c be the common marginal cost. The
net valuation of a customer located at distance x apart from firm A is
given by V � PDA � ktx. Similarly, the net valuation of a customer lo-
cated at distance x apart from firm B is given by V � PDB � tx.
We focus on the market-uncovered case such that some
customers are priced out of the market. We analyze the market-
uncovered case here because we are interested in examining the
3 This discrete distribution significantly simplifies our model analysis versus even
the simple uniform distribution case (Dewan et al. 2000), without loss of generality.
388 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399
Author's personal copy
potential market-expansion effect of the e-book technology. If the
physical books market was fully covered before the entry of e-book
seller, then one would not be able to examine what factors may af-
fect the potential expansion of book readership.
Now, let yDA be the location of a customer who is indifferent be-
tween purchasing the title from A and not participating in the mar-
ket. Since V � PDA � kty
D
A ¼ 0, we deduce that yDA ¼ ðV � P
D
A Þ=kt. Firm
A will choose the optimal price PDA to maximize its net profit, which
is given by:
PDA ¼ 2yDA P
D
A � c
� �
: ð1Þ
The duopoly pricing equilibrium (Lemma 1) states that custom-
ers located within (V – c)/(2kt) distance from firm A or (V – c)/(2t)
from firm B will purchase the physical book, and customers located
further away from the firms will not purchase any book. As ex-
pected, prices increase in the marginal cost c, but shares and profits
decrease in c. Shares and profits also decrease in the disutility
parameter t, but prices are independent of t, because by our
assumption of (V � c)(k + 1) < kt the market is uncovered and both
sellers set prices like a local monopolist. We assume that this
parameter condition holds for the rest of the analysis so that we
can focus on the market-uncovered case.
It is interesting to note that the ratio of shares and profits for the
two firms is fixed: SDB=S
D
A ¼ k and P
D
B=P
D
A ¼ k. Because in general
the market asymmetry parameter k 6 1, the equilibrium condition
implies that A’s share and profit are in general greater than or
equal to B’s share and profit, respectively. The total market cover-
age (SDA þ S
D
B ) decreases in k, because A’s market share decreases in
k. Both prices are independent of k.
4. The symmetric market with an e-book seller
In this section, we analyze and discuss the entry of an e-book
seller when the market is symmetric with k = m = 1. The symmetric
market implies that there are no systematic differences between
sellers A and B’s customers in terms of their physical book prefer-
ences or their e-book preferences. This simplification allows for
greater expositional clarity and a detailed examination of the im-
pact of e-book entry.
In particular, we study two types of ownership of the e-book
seller: an independent e-book seller and an integrated e-book sell-
er owned by one of the paper book sellers, in three cases of sequen-
tial actions:
Case 1: Entry of an independent e-book seller, who sets the
price on e-books first, whereas physical book sellers set the
prices second.
Case 2: Entry of an independent e-book seller when physical
book sellers set the prices first, and the e-book seller sets the
price second; and,
Case 3: Entry of an e-book seller, who is integrated with the
physical book seller A, and A sets the prices first.
We focus on sequential pricing action because e-book technol-
ogy is new: the new e-book seller either responds to the paper
book sellers’ prices or takes the lead in setting the price.4
Table 1
Table of modeling notation.
Notation Definition Comments
b, D, 1, 2, 3 Superscripts representing results of the simultaneous move
benchmark, duopoly market, Case 1, Case 2, and Case 3,
respectively
c Paper book sellers’ marginal production and distribution cost
i Subscript index i = A, B, representing paper book sellers A and B,
respectively
k k 6 1 is a parameter that captures the paper book market
asymmetry concept (the market is symmetric when k = 1, and
asymmetric when k < 1)
Consumers who purchase from seller A incur kt disutility per
unit distance, whereas consumers who purchase from seller
B incur t disutility per unit distance on the circle
m m 6 1 is a parameter that captures the e-book market asymmetry
concept (the market is symmetric when m = 1, and asymmetric
when m < 1)
When the e-book seller enters, mq of seller B’s consumers
will consider e-books whereas q of seller A’s consumers will
consider e-books
Pi Price charged by paper book seller i When PA = PB, we occasionally use PA/B to stand for the price
charged by sellers A and B
Pe Price charged by the e-book seller E
Si The paper book seller i’s market shares When the paper book seller i also owns the e-book seller E, i’s
total market shares are given by Si + Se
Se Market shares of the e-book seller E
t Consumers’ unit-distance disutility of purchasing a paper book
te Consumers’ disutility of purchasing an e-book, and te is either te1
or te2 with te1 < V < te2
Type te2 consumers do not consider e-books in their
purchasing decision, whereas type te1 consumers do consider
e-books.
TR Total readership Subscript IE, AE, and BE representing the total readership
when E is independent, owned by A, owned by B, respectively
V Consumers’ common reservation value for a book title
x A customer’s distance from a paper book seller on the circle
y The location on the circle of the customer who is indifferent
between purchasing the paper book from a paper book seller and
not participating in the market
yDA represents the location of a customer who is indifferent
between purchasing the title from A and not participating in
the duopoly market
yp The location on the circle of the customer who is indifferent
between purchasing the paper book and the e-book
Gi Paper book seller i’s profit When the paper book seller i also owns the e-book seller E, i’s
total profits are given by Gi + Ge
Ge The e-book seller’s profit
q The mass of paper book seller A’s consumers who have a low
disutility te1 on e-books
The mass of paper book seller B’s consumers who have a low
disutility te1 on e-books is mq
4 As a benchmark, we also derived the pricing equilibrium when the paper book
sellers and the e-book seller set prices simultaneously (Appendix Lemma 2). We use
the superscript b to represent results of this simultaneous price move scenario.
Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 389
Author's personal copy
4.1. Entry of an independent e-book seller
Let us consider the same firms A and B selling physical books
whereas a new independent entrant E obtains the right to sell
the same titles as e-books through an e-book platform that may
consist of a specialized reading device, a digital rights management
(DRM) technology, and e-book software. A customer’s net valua-
tion for the e-book depends on the price of the e-book Pe and the
customer’s disutility te, and it is independent of the customer’s
location on the circle.
Due to the symmetry of the model, we illustrate the half-circle
market on A’s side and omit the subscript A for the moment in or-
der to simplify the notation. As shown in Fig. 2, let seller A be lo-
cated at point 0; thus, A’s potential customers are located [0, 1=4]
away from its location on both sides, before the entry of the e-book
seller. This half-circle market has two segments: y and 1=4 � y
where y = (V � P)/t, representing the location of the marginal cus-
tomer for seller A. First, consider the 1=4 � y segment after the entry
of the e-book seller. Customers in this segment will not purchase
the paper book. However, customers with a low disutility te1 in this
segmentmay purchase the e-book. Since a customer’s transaction
cost te is independent of her location, the demand for e-book in the
1=4 � y segment is given by 2q(1=4 � y). Next, consider the y segment.
We only focus on the case with Pe + te1 > P, which means that firm
A always has some loyal customers who prefer paper books even
though they have a low disutility of e-books. The marginal cus-
tomer who prefers the paper book over the e-book is located at
yp = (Pe + te1 � P)/t since V� P� typ = V� Pe� te1. Thus, the demand
for the e-book in this segment is given by 2q(y � yp).
The profit functions for the paper book sellers and the indepen-
dent e-book seller can be simplified as:
PA ¼ PB ¼ 2ðP � cÞ½ðV � PÞ=t � qðV � Pe � te1Þ=t� ð2Þ
Pe ¼ 4qPe½1=4� ðPe þ te1 � PÞ=t�: ð3Þ
Paper book sellers and the e-book seller will set the optimal
prices to maximize their profits. We consider two cases of the Stac-
kelberg game depending on whether the e-book seller moves first
(Case 1), or the physical book sellers move first (Case 2).
4.1.1. Case 1: the independent e-book seller anticipates the move of
physical book sellers
In the first case, the e-book seller sets the price first, anticipat-
ing the move of paper book sellers. This case applies when the pa-
per book sellers do not foresee the entry of the new comer E, who
secretly developed the electronic device and worked through deals
with content providers. It also applies when the paper book sellers
cannot observe which titles will be available on firm E’s electronic
device. We use the superscript 1 to represent results of Case 1. The
pricing equilibrium of this Stackelberg game is presented in
Appendix Lemma 3.
Comparing Pbe , the e-book price when all players move simulta-
neously, with P1e , the e-book price when the independent E moves
first, we find that P1e > P
b
e . That is, when E moves first, anticipating
paper book sellers’ price response, it will set a higher price than
when they move simultaneously. As a result, E captures a smaller
market share (S1e < S
b
e). However, the profit comparison shows that
P1e > P
b
e . Hence, compared with the simultaneous move scenario,
the e-book seller E gains a higher profit level since E can determine
its price taking into account the paper book sellers’ pricing
response.
In response to E’s price, the paper book sellers as the followers
will also raise their prices from the simultaneous-move level
(P1A=B > P
b
A=B). Because the price increase on the e-book is higher
than that on the paper book, the market shares of the paper book
sellers are actually higher than the simultaneous-move levels
(S1A=B > S
b
A=B). Thus, the paper book sellers also benefit when the
e-book seller acts first rather than when they move simultaneously.
Compared with the physical book duopoly case, here the paper
book sellers charge a lower price in response to the entry of the
independent e-book seller, P1A=B < P
D
A=B. However, the market shares
of the paper book sellers are reduced (S1A=B < S
D
A=B), even with re-
duced prices. Thus, the paper book sellers’ profits are lower as well
(P1A=B < P
D
A=B).
We illustrate the impact of the entry of an independent e-book
seller on the book market in a numerical example. Fig. 3 represents
the one-quarter circular market in Case 1with firm A located at
zero. Parameter values for this example are: V = 26, c = 10, t = 35,
te1 = 20, and q = 0.2. Customers are uniformly distributed in the
x–y space, with the x-axis representing the customer location on
the circle and the y-axis representing the customer preference
for the e-book. For example, customers below the line of q = 0.2
have a low disutility te1 on e-books and will consider e-books in
their purchase decision.
The vertical dotted line represents the customers who are indif-
ferent between purchasing the paper book and not buying in the
physical book duopoly case before E’s entry. The solid vertical line
y represents the new marginal customers when an independent
e-book seller enters. In this case, the price of the paper book is
Firm A 
y 
¼ - y
y 
¼ - y 
Fig. 2. Illustration of the half-circle market on firm A’s side.
Case 1
0
1
0 0.25
Circular 
location
D
is
tr
ib
ut
io
n 
of
 d
is
ut
ili
ty
 
on
 e
-b
oo
ks
A y 
ρ =0.2 
te2
te1
yp 
 A 
 E 
Fig. 3. An illustration of market shares for the 1=4 circular market in Case 1.
390 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399
Author's personal copy
lower than that in the duopoly case, so some customers who were
previously priced out of the market are able to purchase the paper
book when the independent e-book seller enters. The solid vertical
line yp represents the marginal customers who are indifferent
between the paper book and e-book. For firm A, customers located
in [yp, y] and with type te1 will now purchase the e-book instead of
the paper book. Thus, when the independent e-book seller enters
and acts as the leader in the Stackelberg game, the paper book sellers
gain some new customers by lowering their prices, but they also lose
some customers to the e-book seller. The entry of the e-book seller
further expands the total book consumption because some type te1
customers (located between the dotted line and 0.25), who did not
participate before E’s entry, now purchase an e-book. In summary,
the total book market expands with some new customers purchas-
ing physical books, and some other new customers purchasing the
e-book. Thus, in Case 1 consumer surplus and social welfare increase
with the entry of an independent e-book seller.
4.1.2. Case 2: the physical book sellers anticipate the entry of the
independent e-book seller
In the second case, the paper book sellers move first. This spe-
cial case enables the study of e-book entry under adverse market
conditions for the entrant firm. We use the superscript 2 to repre-
sent results of case 2. The pricing equilibrium of this Stackelberg
game is presented in Appendix Lemma 4. This case is similar to
Case 1 in that not only the paper book sellers benefit by acting
as the leaders in the price game, but the e-book seller also gains
a higher profit level than when they move simultaneously. That
is, P2A=B > P
b
A=B and P
2
e > P
b
e .
However, when the paper book sellers are leaders in the
Stackelberg game, the price of the paper book can be lower or high-
er than the price in the duopoly case depending on the parameter
conditions. It is a little surprise to see that the entry of an indepen-
dent e-book seller can sometimes lead to a price increase for the
paper books. This happens when consumers’ disutility is high rel-
ative to their reservation value (V < te1 + t/4). In this case, the entry
of e-book seller forces paper book sellers to focus more on loyal
customers near the sellers’ locations only. However, when consum-
ers’ disutility is low relative to their reservation value (V > te1 + t/4),
the price of paper book is lower than the price in the duopoly case.
Whether the price of paper book is lower or higher than that in the
duopoly case, paper book sellers’ market shares are lower than
those in the duopoly case, and so are their profits.
Proposition 1 (Conditions for prices to increase and readership to
decrease after e-book entry in Case 2). When the physical book
sellers anticipate the entry of an independent e-book seller, the price of
physical book may increase and the paper book readership may
decrease from the physical book duopoly case. The condition for that to
happen is V < te1 + t/4, i.e., the disutility is relatively large.
We illustrate the scenario described in Proposition 1 with Fig. 4,
which only shows one-quarter of the circular market with firm A
located at zero. Comparing Fig. 4 with Fig. 3, we see that the entry
of the e-book seller actually leads to an increase of the price of the
paper book—the new marginal paper book customers represented
by the solid line y are located to the left of the dotted line, which
represents themarginal customers before the entry of seller E.
Thus, the entry of an independent e-book seller can lead to the exit
of some potential readers from the book market.
4.2. Entry of an e-book seller owned by one of the two physical book
sellers
Let us consider the case in which A and E are an integrated com-
pany. In other words, firm A, while competing with B in the paper
book market, also starts selling e-books. By developing an e-book
technology, including a specialized electronic device and possible
DRM technology, firm A is able to obtain the right to sell some book
titles in an electronic format. Customers who acquire the electronic
device from firm A can then purchase and consume e-books offered
by A.
4.2.1. Case 3: the integrated firm A sets its prices (PA and Pe)
anticipating the move of firm B
Clearly, e-books compete directly with A’s paper book, raising
cannibalization concerns. However, firm A may gain by taking
market share from firm B and serving previously un-served
customers. The analysis of the e-book and paper book sellers’
markets discussed in Section 4.1 still applies here, except that
now A also owns the e-book seller E, and A and B may charge
different prices for the paper book. Firm B’s profit function (5) is
the same as (2) while firm A’s (4) includes a term of profit from
e-books as well, and firm A will decide both Pe and PA:
PA ¼ 2ðPA � cÞ½ðV � PAÞ=t � qðV � Pe � te1Þ=t� þ 2qPeDe; ð4Þ
PB ¼ 2ðPB � cÞ½ðV � PBÞ=t � qðV � Pe � te1Þ=t�; ð5Þ
where De = ½ � (pe + te1 � PA)/t � (Pe + te1 � PB)/t. We focus on the
Stackelberg game with firm A as the leader. Firm A maximizes its
profit by determining the optimal prices of the paper book and
e-book and by anticipating the price response of firm B. We use
the superscript 3 to represent results of Case 3. The pricing equilib-
rium of this Stackelberg game is presented in Appendix Lemma 5. In
this case, the two paper book sellers may charge different prices for
the paper book.
0
1
0 0.25
Circular location
D
is
tr
ib
ut
io
n 
of
 d
is
ut
ili
ty
 o
n 
e-
bo
ok
s
A
te2
te1
y 
 A 
yp 
ρ =0.2 
E
Fig. 4. An illustration of market shares for the 1=4 circular market in Case 2.
Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 391
Author's personal copy
When firm A also offers e-books and acts as the leader in the
Stackelberg game, it will charge a higher price than that in the
duopoly case, but in response, firm B will charge a lower price than
before, P3A > P
D
A=B > P
3
B. This suggests that the introduction of e-
books by an integrated firm such as Amazon creates a price pres-
sure on a pure paper book seller such as Barnes and Noble, and that
explains the interest of Barnes and Noble to move into the e-book
market segment.
4.3. The impact of e-book technology on symmetric book market
We now discuss the comparative statics5 of Cases 1–3. We begin
with a discussion of how factors such as consumers’ e-book prefer-
ences, cost and disutility terms of paper and e-books may affect
the competition in the book market. We then compare the prices,
market shares, and profits with and without e-book entry in a
numerical example.
4.3.1. Distribution of consumers’ e-book preferences
It is interesting to note that the change in q, the fraction of cus-
tomers with type te1, has a different impact on prices depending on
parameter values or who leads the Stackelberg game. An increase
in q means more customers have a low disutility (te1) on e-books,
and this is in favor of the e-book seller.
When the independent e-book seller E is the leader (Case 1), E’s
price and market share both increase in q, which means that the e-
book seller has more market power as more customers accept the
e-book technology. However, when the paper book sellers are the
leaders (Case 2), the price of the e-book can increase or decrease
in q depending on parameter values. In particular, when the reser-
vation value of consumers is low relative to disutility, i.e.,
V < te1 + t/4, the prices of both paper and e-book increase in q,
but the former increases more (@P2i =@q > @P
2
e=@q > 0 (i = A, B)).
While more customers having a lower disutility of e-books should
intensify the competition between paper and e-book sellers, the
price competition is actually relaxed with both the paper book sell-
ers and the e-book seller increasing their prices. But when
V > te1 + t/4, as more customers have a lower disutility of e-books,
the price competition is in fact intensified. As paper book sellers
aggressively reduce their prices, in response the e-book seller also
reduces its price, but the paper book sellers reduce their prices at a
higher rate (@P2i =@q < @P
2
e=@q < 0 (i = A, B)).
Proposition 2 (Effect of q on prices in Case 2). When physical book
sellers anticipate the entry of an independent e-book seller, all sellers’
prices increase in q if V < te1 + t/4, and all prices decrease in q if
V > te1 + t/4.
Research and industry data (AAP 2009, Greco 2005, Oestreicher-
Singer and Sundararajan 2006) suggest that the book industry is in
its early stages of transformation due to IT and e-book technology.
This implies that there is a small but increasing fraction of consum-
ers that consider e-books in their purchase decisions (q is low and
increasing). We can also conjecture that the ‘‘quality” of e-book
technology is low, but it is improving, so te1 is high and decreasing.
Given these conditions, Proposition 2 suggests that as more con-
sumers consider e-books in their purchase decisions, prices in
the book market increase above a te1 threshold and decrease below
the same threshold.
In Case 3, when the fraction of customers considering e-books
increases, we have @P3A=@q > 0, @P
3
e=@q > 0, @S
3
A=@q < 0, and
@S3e=@q > 0. That is, when q increases, the integrated firm A will fo-
cus more on the loyal customers (customers close to A’s location)
in the paper book market and increase its price on e-books. Again,
in this case even though the e-book’s price increases in q, the mar-
ket share of the e-book also increases in q. As a result, the total
market shares of A increase (@ðS3e þ S
3
AÞ=@q > 0) and are higher than
the duopoly case (S3e þ S
3
A > S
D
A ). This means that the market-expan-
sion effect of e-books for A offsets the cannibalization effect. The
effect of q on B’s physical book-price and market-share could be
positive or negative depending on parameter condition.
4.3.2. Costs and differentiation
The three scenarios with an independent e-book seller and an
integrated e-book seller have some common properties. The paper
book sellers will increase prices when the marginal cost of paper
book increases. Consequently, the e-book seller will also increase
the price of e-books (@Pnj =@c > 0; j = A, B, e and n = 1, 2, 3).
When consumers’ unit-distance disutility of paper book t
increases, paper books become less attractive to consumers.
However, because paper book sellers are insulated from direct
competition, the price of paper book actually increases
(@Pni =@t > 0; i = A, B and n = 1, 2, 3). In response, the e-book seller
will also increase the price of e-books (@Pne=@t > 0; n = 1, 2, 3). As
a result, the market shares of both paper books and e-books de-
crease in t, (@Snj =@t < 0; j = A, B, e and n = 1, 2, 3).
As consumers’ disutility of e-book te1 decreases over time be-
cause of technology improvement, e-books become more attrac-
tive to consumers, and the e-book seller is able to increase its
price on e-books. To compete with the e-book seller, paper book
sellers will, however, reduce their prices on paper books as te1 de-
creases. Interestingly, even though the e-book seller increases its
price on e-books and the paper book sellers reduce their prices
on paper books, the market share of e-book increases and the mar-
ket share of paper book decreases (@Pni =@te1 P 0; @P
n
e=@te1 < 0; and
@Sni =@te1 > 0, @S
n
e=@te1 < 0, i = A, B and n = 1, 2, 3).
When seller A owns the e-book seller, A’s priceon paper
book is independent of the disutility parameter te1 (@P
3
A=@te1 ¼
0). Again in the context of Amazon, this means that the per-
ceived ‘‘quality” (inverse of disutility) of Amazon’s Kindle in
the eyes of customers considering e-books (type te1) does not
affect Amazon’s physical book prices. The market share of paper
books decreases and the share of e-books increases as te1 de-
creases over time, as in the case of the independent e-book sell-
er. However, the total market shares of the integrated book-
seller A increase (@ðS3e þ S
3
AÞ=@te1 < 0). This happens because, as
te1 decreases, the increased shares in e-books offset the decreased
shares in paper books. As e-book technology improves, the market-
expansion effect of e-books offsets the cannibalization effect,
benefiting an integrated company like Amazon that introduces
the e-book platform.
Proposition 3 (Effects of q and te1 in Case 3). When firm A owns the
e-book seller, its total market share decreases in te1, but it increases in
q. Firm B’s share and price can increase or decrease in q and A’s prices
(physical and e-book) increase in q.
This analysis suggests that investment in an e-book technology
that allows a paper book seller like Amazon to sell e-books to cus-
tomers is an important strategic factor in the competitive interac-
tion in the book market.
4.3.3. Prices, market shares, and profit comparison with and without e-
book entry
With the same numerical example used in Sections 4.1 and 4.2,
we summarize the prices, market shares, profits of each player in
the duopoly, simultaneous move with an independent e-book sell-
er, and three sequential move cases in Table 2. This numerical
example illustrates some interesting results. First, in Case 3 the
integrated firm A’s total profit is given by 3.781—the sum of profits5 A summary of the comparative statics formulas is provided in Appendix Table A1.
392 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399
Author's personal copy
from paper books and e-books. Thus, a paper book seller (A) prefers
to be an integrated book seller who offers both paper and elec-
tronic books than be just a paper book seller competing with an
independent e-book seller. The reason is that the integrated book
seller can internalize the competition between paper and elec-
tronic books.
However, comparing Case 3 with Cases 1 and 2, we see that the
paper book seller B also prefers to compete with an integrated
book seller rather than with an independent e-book seller. This
happens because the integrated book seller tends to charge a high-
er price on e-books. Thus, the paper book seller B loses less market
share to e-books. Also, comparing Case 1 with Case 2, we see that
the independent e-book seller can gain a higher profit level, if it
acts as the follower rather than the leader in the price competition
game. Similarly, the paper book sellers prefer to be the followers
when competing with an independent e-book seller. This validates
the result of the second-mover advantage in a price-setting
Stackelberg game (Gal-Or 1985), as prices are strategic
complements.6
Next, we compare the total market served in each case, which
includes both the paper book and e-book. Comparing with the
duopoly case without the entry of e-books, the entry of an
independent e-book seller increases the total readership in the
simultaneous-move case and Cases 1 and 2. The simultaneous-
move case leads to the highest readership. This happens because
in price-setting Stackelberg games, firms tend to increase their
prices compared to the simultaneous-move case. However, Case
3 actually reduces the readership. That is, an integrated book seller
may reduce the total readership when introducing e-books
through an e-book platform. This insight is generalized in
Section 5.3.
5. Effects of market asymmetries
Section 4 provided a detailed discussion of the effects of e-book
technology on a symmetric book market with k = m = 1. In this Sec-
tion, we offer an in-depth discussion of the effects of market asym-
metries when the e-book technology enters the book market. As
defined in Section 2, our model allows for two types of market
asymmetry: the physical book market asymmetry, captured by
parameter k, and the e-book market asymmetry, represented by
parameter m.
The implications of these asymmetries are best explained when
we assume that A is an online physical book seller (e.g., Amazon)
and B an offline physical book seller (e.g., a bookstore chain). The
physical book market asymmetry suggests that, everything else
being equal, customers that buy from A incur a lower disutility per
unit-distance than do customers that buy from B. This gives the on-
line seller an advantage in the physical book market, because the
online seller can capture a larger market share and be more profit-
able than the offline seller. This assumption reflects the greater on-
line seller’s ‘‘reach”, which is now a textbook concept (Laudon and
Laudon 2010).
The e-book market asymmetry suggests that there are more cus-
tomers that consider e-books in seller A’s customer base than in
B’s. Seller A’s customers are more likely to be technologically
sophisticated (Oestreicher-Singer and Sundararajan 2006) or early
adopters. These consumers may already be familiar with purchas-
ing and paying online, and they are likely to have accounts at on-
line bookstores that can be leveraged for e-books. For instance,
Amazon’s Kindle e-book store is an extension of the traditional
Amazon online physical book store. Kindle users benefit from using
the same payment and shipping information, as they maintain a
wish-list, read reviews posted by the Amazon community of book
readers, and receive personalized recommendations that leverage
their historical book preferences and purchase behavior at Ama-
zon. Consumers close to A may also feel more comfortable buying
and using an e-reader device or reading e-books via e-book soft-
ware. Amazon’s Kindle hardware is aggressively promoted at Ama-
zon’s website, and Kindle software can be easily downloaded. A
collection of thousands of public domain e-books is available for
consumers who are interested in trying the e-book experience
for free. It is thus plausible that the digital channel of selling e-
books is ‘‘closer” to the online than the offline channel of selling
physical books.
The concept of e-book market asymmetry reflects also the grad-
ual transformation of the book industry whereby both the distribu-
tion channel and the product are becoming digital: from selling
physical products through offline channels to selling physical prod-
ucts through online channels, and finally to selling e-books
through digital e-book distribution technologies like Kindle. This
gradual transformation can be represented in a pair (type of chan-
nel, type of product) that gradually shifts from (physical, physical) to
(digital, physical) to (digital, digital). Seen as a continuum, consum-
ers who are in the (digital, physical) state are more likely to switch
to the (digital, digital) state than consumers in the (physical, physi-
cal) state.
Now we discuss in detail how the interaction of market asym-
metries and ownership type is affecting market outcomes in the
following cases:
� An independent third party like Apple selling e-books (the equi-
librium is formally defined in Appendix Lemma 3 and was dis-
cussed for the symmetric market in Section 4).
� An established online seller like Amazon selling e-books (the
equilibrium is formally defined in Appendix Lemma 5 and was
discussed for the symmetric market in Section 4).
Table 2
Prices, market shares, and profits comparison.
Duopoly
(before E’s entry)
Simultaneous-move case
(with an independent E)
CASE 1
(E as the leader)
CASE 2
(A & B as the leaders)
CASE 3
(A owns E and as the leader)
Paper Book (A/B) Seller A Seller B
Price 18 17.724 17.742 18.153 18.559 17.979
Share 0.457 0.441 0.442 0.419 0.423 0.456
Profit 3.657 3.409 3.425 3.418 3.619 3.638E-book (E)
Price 3.237 3.417 3.451 5.794
Share 0.074 0.070 0.079 0.028
Profit 0.239 0.240 0.272 0.162
Total readership 0.914 0.957 0.955 0.917 0.907
6 It would be interesting to investigate which firm(s) will move first in equilibrium
(endogenous timing), but it is beyond the scope of this paper.
Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 393
Author's personal copy
� An offline seller of physical books selling e-books (the equilib-
rium is formally defined in Appendix Lemma 6).
5.1. Effects of market asymmetries with an independent e-book seller E
When an independent third party like Apple enters the book
market selling e-books, then the asymmetry parameters k and m
affect all prices and market shares (Appendix Lemma 3). The re-
sults are best discussed by examining the effects of m and k
separately.
When m = 1, then one interesting equilibrium property is that A
and B set equal prices, and their ratios of shares and profits (SB/SA,
PB/PA) remain fixed and equal to k, as in the duopoly case. The e-
book price increases in k. The prices of A and B are linear, increas-
ing functions of the e-book price, so they also increase in k but only
at a smaller rate. As k decreases, firm A can reach more paper book
customers, but at the same time price competition intensifies, be-
cause E reduces its price on e-books. Because the offline seller B
also faces intensified price competition, B’s price, market share,
and profit decrease. The share and profit of B increase in k, so the
offline seller is better off when the market is becoming more sym-
metric. Interestingly, before the entry of the e-book (Section 3), a
decrease of k does not affect paper book prices, but only increases
the online seller’s market share and profit.
When k = 1, the price of E is a U-shaped function of m (with
minimum at m� ¼
ffiffiffi
2
p
� 1). The price of A increases in m if and only
if the price of E increases in m, so the price of A is also a U-shaped
function of m. The share and profit of A (B) increase in m if and only
if the price of A (B) increases in m. The intuition is that a more
asymmetric e-book market (decrease of m) decreases the demand
for e-books in the neighborhood of firm B. As a result, firm E re-
duces its price and so does A. Firm B benefits because it faces less
competition from E, although E’s price is lower. But when m be-
comes lower than a critical value m� ¼
ffiffiffi
2
p
� 1, then E starts
increasing its price because E is better off making a higher profit
in the neighborhood of A than capturing the market in the neigh-
borhood of B. E’s price change benefits B even more, but also ben-
efits A because price competition is relaxed. However, the e-book
market asymmetry (m) does not affect the equilibrium of the paper
book duopoly before the e-book entry (Section 3) because the e-
book technology is not available and thus customers’ e-book pref-
erences do not affect their purchase behavior.
5.2. Effects of market asymmetries with E owned by either A or B
Because the market is asymmetric, we must discuss two distinct
ownership cases: the online seller A owns E (Appendix Lemma 5)
and the offline seller B owns E (Appendix Lemma 6). The effects
of market asymmetries are likely to be different in those two cases.
5.2.1. Online seller A owns E
When the online seller A owns E and maximizes the total profit
by selling a paper book and an e-book, then A’s paper book market
share is independent of m. This suggests that A sets its paper book
and e-book price so the e-book market asymmetry does not affect
its paper book market share. In addition, the strategic behavior of
the offline firm B is identical to its behavior in Lemma 3, when E
is independent. In particular, the formulas that give B’s price, share,
and profit are identical to those in Lemma 3: B sets a price that is a
mark-up over the e-book price, and k affects B’s behavior only indi-
rectly through the e-book price.
We can gain more insight in the strategic behavior of firms
when we consider the parameters k and m separately. When
m = 1, the prices of A’s electronic and paper books increase in k, be-
cause c + t > V is true. Thus, firm A increases its prices as the phys-
ical book market becomes more symmetric and B responds with an
increase of its price and price competition is relaxed. The relation-
ship between the e-book disutility parameter te1 and the produc-
tion cost of physical books c determines how A’s e-book market
share behaves. A’s e-book market share increases in k, if te1 > c
and decreases otherwise.7
5.2.2. Offline seller B owns E
When the offline seller B owns E and maximizes the total profit
by selling a paper book and an e-book (Appendix Lemma 6), then
the pricing and market-share behavior of the online seller A is
identical to A’s behavior when E is independent: A sets a markup
over the e-book price. The market share of B’s paper book is inde-
pendent of k. B’s paper book market share decreases in m, which
means that as the e-book market becomes more symmetric, B sells
fewer physical books. When k = 1, the effect of m on the market
share of B’s e-book depends on disutility and cost parameters; in
particular, B’s e-book market share increases in m if and only if
4(c � te1) + t > 0.
When m = 1, the prices of B’s physical book and e-book increase
in k. This suggests that, as the physical book market becomes more
symmetric, B increases its prices and, as a response, A increases its
price as well, and therefore price competition is relaxed. The effect
of k on the market share of B’s e-book depends on market param-
eters; in particular, B’s e-book market share increases in k, if and
only if (2 � q)te1 > V(1 � q) + c.
5.3. How ownership and market asymmetries affect total readership
Now, let us consider the total readership TR (total book sales)
when E is independent (TRIE), when E is owned by A (TRAE),
and when E is owned by B (TRBE). The total readership is the high-
est when E is independent, and the second highest when B owns E.
The following figure shows the total readership ratios (TRIE/TRAE)
and (TRIE/TRBE) as functions of (m, k) with parameter values, as in
Figs. 3 and 4.
As shown in Fig. 5, the total readership when E is independent is
larger than the total readership when E is owned by the offline sell-
er A or by the online seller B. A further comparison shows that the
total readership when E is owned by the offline seller B is larger
than the total readership when E is owned by online seller A. Inte-
grated ownership is inferior with respect to total sales and social
welfare because it internalizes competition and thus reduces total
sales. This result is different from the IS research in ownership of
Internet intermediaries that shows that integrated ownership is
superior (Bakos and Katsamakas 2008), because in that literature
the main effect of integrated ownership is to internalize network
externalities, which tends to increase total sales and social welfare.
Fig. 5 also shows that when E is owned by A, the readership
reduction effect gets stronger, when the market becomes more
asymmetric. However, when E is owned by B the readership reduc-
tion effect gets stronger, and when the market becomes more
symmetric.
Owning E is a ‘‘defensive” strategy for A when there are strong
market asymmetries, because the main benefit for A is avoiding
competition within its large paper book market. Thus, the larger
the market asymmetries, the stronger the ‘‘threat” of an indepen-
dent E to A, and the stronger A’s incentive to own the e-book seller.
As a result, the total readership is the lowest when the e-book sell-
er is owned by the online seller A. However, owning E is an ‘‘offen-
sive” strategy for B when there are strong market asymmetries,
because it is an opportunity to capture the market in the neighbor-
hood of A by selling e-books. The result is a larger total readership
7 The share of A’s paper book is increasing in k if and only if c > Vð1� qÞ þ qte1.
When k= 1, then the market share of A’s e-book is increasing in m if and only if
2ðV þ cÞ þ t þ 4mqte1 > 4ðmqV þ te1Þ.
394 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399
Author's personal copy
than the case of E owned by A, but a lower total readership than
when E is independent. Overall, market asymmetries have a signif-
icant effect on prices, market-shares, profits, total readership, and
the incentives of the online seller A and offline seller B to own
the e-book seller.
Fig. 6 compares the total readership in the three cases discussed
above (TRIE, TRAE, TRBE) and the total readership TRD in the duopoly
market, before the e-book technology is available. When E is
owned by the online seller A, the total readership is less than the
total readership before the e-book entry, and this effect is enlarged
the more asymmetric the e-book market is. When E is owned by
the offline seller B, the readership is less than the duopoly case
only if the e-book market asymmetry is small (i.e. m is large).
The total readership, when E is independent, is always higher than
the readership in the duopoly case. These results suggest that hav-
ing an independent e-book seller enter the book market increases
the total readership and leads to the highest possible readership
compared to all other ownership cases. A last interesting observa-
tion from Fig. 6 is that when the e-book market is perfectly asym-
metric (m = 0), then B owning E also results in the highest total
readership. This happens because in the perfect asymmetric case
there are no e-book customers in the neighborhood of B, so B sets
an e-book price that is identical to the e-book price of an indepen-
dent e-book seller.
6. Conclusion
The advances in Internet and IT enable the digitization of books,
transforming the competitive forces in the book industry. This pa-
per developed a stylized game theory model that captures the ef-
fects of e-book entry on the book market. Our analysis shows
that e-book entry leads to intricate price adjustments, and share
and profit changes. E-book technology offers the potential for mar-
ket expansion, which can be quantified in our research model. Sur-
prisingly, we find that the entry of an e-book seller does not
necessarily expand the total readership, and, additionally, that
the price competition between the paper book sellers and the e-
book seller can actually be relaxed when the e-book technology be-
comes acceptable to more customers.
In order to manage the entry of e-book technology (e.g., Ama-
zon) or respond to that entry, managers need to consider several
factors, including the differentiation and intensity of competition
in the pre-existing physical book market, the cost difference be-
tween e-books and physical books, the competitive ‘‘leadership”,
the fraction of customers considering e-books in their purchase
decisions, and the perceived ‘‘quality” of e-books for those custom-
ers that consider e-books an option. In high-velocity information-
goods markets, some of these factors may change fast, so optimal
decisions under the current market conditions may need to be ad-
justed in the near future.
Most importantly, companies involved in the transformation of
the book industry into digital products (e-books) and digital distri-
bution channels must consider carefully the effects of ownership
and market asymmetries. Expanding Salop’s circular model, this
paper introduces the concepts of physical book market asymmetry
(k) and e-book market asymmetry (m) and shows that these market
asymmetries affect not only the market interaction when the e-
book seller enters the market but also the incentives of an online
book seller (A) and an offline book seller (B) to own the e-book
seller.
Combining the physical book market asymmetry and the
e-book market asymmetry in the same model reveals opposing
effects affecting the paper book sellers: the physical book asym-
metry benefits A because it can reach more customers of physical
books, but at the same time it hurts A because price competition
intensifies, which also hurts B. The e-book asymmetry benefits the
offline seller B because customers close to B are less likely to
switch from paper books to e-books, but it may hurt or benefit
A, as it affects price competition in a non-linear way. In particular,
when the e-book market is not very asymmetric, price competi-
tion intensifies with a decrease of m and A’s profit decreases,
but price competition relaxes below a threshold, in which case
A’s profit increases.
The interaction of ownership and market asymmetries affect
total readership, and when the market asymmetries are strong,
k
TRIE 
/TRAE 
m
m
k
TRIE 
/TRBE 
Fig. 5. Total readership ratios (TRIE/TRAE) and (TRIE/TRBE) as functions of (m, k).
0.2 0.4 0.6 0.8 1.0
0.90
0.92
0.94
m
TRIE 
TRD 
TRBE 
TRAE 
Fig. 6. Total readership TRD, TRIE, TRBE, TRAE as functions of e-book market
asymmetry m with k = 1.
Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 395
Author's personal copy
ownership of E by the online seller leads to the lowest total read-
ership. This suggests that Amazon’s control of the e-book market
through the Kindle technology is socially inferior compared to that
of an offline book seller offering e-books or that of an independent
e-book seller entering the market. Two opposing forces drive these
results: the physical book asymmetry benefits A, because it can
reach more customers, but the e-book asymmetry hurts A because
customers close to A are more likely to switch from physical books
to e-books.
Research and industry data (AAP 2009, Greco 2005, Oestreicher-
Singer and Sundararajan 2006) suggest that the book industry is in
its early stages of transformation due to IT and e-book technology.
This early transformation suggests that there is a small but increas-
ing fraction of consumers that consider e-books in their purchase
decisions. It also indicates that the ‘‘quality” of e-book technology
is currently low, but it is improving. We have shown that, as con-
sumers that consider e-books in their purchase decisions increase,
prices increase above a threshold of e-book disutility and decrease
below the threshold.
As leading technology companies like Amazon, Google and
Apple are maneuvering strategically to benefit from the fast
growing e-book market, power changes in the book industry’s
value-chain are possible. Anecdotal evidence suggests that pub-
lishers are concerned about the increasing control of e-books by
Amazon’s Kindle platform and they ‘‘have turned to Apple to help
them twist Amazon’s arm” (The Economist 2010). Our analysis has
shown that even without considering e-book sellers’ competition,
the entry of a single e-book seller has a significant impact on book
markets, as e-book technology competes with the ‘‘old” book
technologies.
Appendix A. Proofs
Lemma 1 (Duopoly pricing equilibrium). When only the physical
book sellers A and B are active in the book market and (V
� c)(k + 1) < kt, at equilibrium the prices, market-shares, and profits
are as follows: PDA ¼ P
D
B ¼ Vþc2 ; S
D
A ¼ V�ckt ; S
D
B ¼ V�ct ; P
D
A ¼
ðV�cÞ2
2kt ;
PDB ¼
ðV�cÞ2
2t .
Proof. For seller A, since yDA ¼¼ ðV � P
D
A )/kt, taking y
D
A into seller A’s
profit function given in Eq. (1) the second-order derivative of PDA
with respect to PDA is given by �4/(kt) < 0. As the profit function
is concave in price, solving the first order condition (FOC) we have
PDA ¼ ðV þ cÞ=2 and yDA ¼ ðV � cÞ=ð2ktÞ. Similarly, we can solve for
seller B with PDB ¼ ðV þ cÞ=2 and yDB ¼ ðV � cÞ=ð2tÞ. For the market
to be uncovered it requires yDA þ yDB < 1=2, which gives the param-
eter condition (V � c)(k + 1) < kt (Note: we require that this param-
eter condition is satisfied in the proofs that follow). h
Derivation D1 (Derivation of demand for e-book and physical
books): We derive the demand for e-book and A’s and B’s physical
books for the article’s model defined in Section 2. Customerspref-
erences are defined in Section 2, and the e-book market asymmetry
mathematically implies that a customer’s e-book disutility te is te1
with probability f ðdÞ ¼ q; 0 6 d < 1=4
mq; 1=4 6 d 6 1=2
�
and te2 with proba-
bility 1 � f(d), where d is the customer’s distance from firm A’s
location, 0 6 q 6 1, 0 < m 6 1, and F is the c.d.f. of f.
Consider the half-circle market with A located at 0 and B at ½.
The indifferent consumers of paper book located at yA, yB for A and
B, respectively, satisfy yA = (V � PA)/kt and ½ � yB = (V � PB)/t. Cus-
tomers in the segment [yA, yB] will not purchase physical books,
but a mass of customers equal to F(yB) � F(yA) may purchase the
e-book. We only focus on the case with Pe + te1 > Pi (i = A, B), which
means A and B always have some loyal customers who prefer pa-
per book even though they have a low disutility of e-book.
Consider the [0, yA] segment. The marginal customer who pre-
fers A’s paper book over the e-book is located at ypA = (Pe + -
te1 � PA)/kt since V � PA � ktypA = V � Pe � te1. Thus, the demand
for the e-book in this segment is F(yA) � F(ypA) and the demand
for A’s physical book is yA � (F(yA) � F(ypA)).
Next consider the [yB, 1/2] segment. In this segment, the mar-
ginal customer ypB who prefers B’s paper book over the e-book sat-
isfies ½ � ypB = (Pe + te1 � PB)/t since V � PB –t(½ � ypB) = V � Pe
� te1. Thus, the demand for the e-book in this segment is
F(ypB) � F(yB) and the demand for B’s physical book is
½ � yB � (F(ypB) � F(yB)).
In summary, the total demand for A’s physical book is
SA ¼ 2ðyA � ðFðyAÞ � FðypAÞÞÞ; ðA1Þ
the total demand for B’s physical book is
SB ¼ 2ð1=2� yB � ðFðypBÞ � FðyBÞÞÞ; ðA2Þ
and the total demand for the e-book is
Se ¼ 2ðFðypBÞ � FðypAÞÞ: ðA3Þ
the profit from A’s physical book is
ðPA � cÞSA; ðA4Þ
the profit from B’s physical book is
ðPB � cÞSB; ðA5Þ
and the profit from the e-book is
PeSe: ðA6Þ
Lemma 2 (Simultaneous-move pricing equilibrium with the entry
of an independent e-book seller). When an independent e-book
seller enters the market and makes pricing decision simultaneously
with the paper book sellers, at equilibrium the prices and market-
shares are as follows8:
PbA ¼ P
b
B ¼
8c þ tqþ 4te1qþ 8V � 8Vq
16� 4q ;
Pbe ¼
2c þ t � 4te1 þ 2te1qþ 2V � 2Vq
8� 2q ;
SbA ¼ S
b
B ¼
8V � 8c þ 4cqþ qðt þ 4te1 � 8VÞ
ð8� 2qÞt ;
Sbe ¼
2qð2c þ t � 4te1 þ 2te1qþ 2V � 2VqÞ
ð4� qÞt :
Proof. In the simultaneous-move pricing game, the profit func-
tions for the paper book sellers and the e-book seller are described
in Eqs. (2) and (3). All three firms set prices simultaneously to max-
imize their profit. The equilibrium prices and market-shares
follow. h
Lemma 3 (Pricing equilibrium with the independent e-book seller
as the leader in the pricing game). When an independent e-book
seller enters the market anticipating the price response of physical
book sellers, at equilibrium the prices and market-shares are as
follows:
8 This lemma is proved only for the symmetric market with k = 1 and m = 1, since it
is applicable only to the discussion of the symmetric market in Section 4.
396 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399
Author's personal copy
If the market is symmetric (k = m = 1), the equilibrium
is simplified to the following: P1A ¼ P
1
B ¼
8Vþ8c�2cq�qð10V�t�4te1Þþ2q2ðV�te1Þ
16�8q ; P
1
e ¼
2ð1�qÞðV�te1Þþtþ2c�2te1
8�4q ; S
1
A ¼ S
1
B ¼
8V�8cþ6cqþqðtþ4te1�10VÞþ2q2ðV�te1Þ
ð8�4qÞt ; S
1
e ¼
qð2Vþ2c�2Vqþt�4te1þ2te1qÞ
2t .
Proof. We consider the Stackelberg game in which an indepen-
dent e-book seller E sets its price in the first stage, and firms A and
B set their prices simultaneously in the second stage. All firms are
maximizing their profits. The game is solved backwards for the
subgame perfect Nash equilibrium.In stage 2, firms A and B set
prices to maximize the profits from selling physical books defined
in (A4) and (A5), respectively, taking the price of E’s e-book as
given. Substituting these prices into E’s profit function (A6) we can
solve for the optimal price for E in stage 1. There exists a unique
equilibrium for which the prices and market-shares follow. h
Lemma 4 (Pricing equilibrium with the physical book sellers as
the leader in the pricing game). When the physical book sellers
anticipate firm E’s market entry and set prices first, at equilibrium
the prices and market-shares are as follows9:
P2A ¼ P
2
B ¼
8V þ 8c � 4cq� 8qV þ tqþ 4te1q
16� 8q ;
P2e ¼
2ð1� qÞðV � te1Þ þ t þ 2c � 2te1 þ te1q� cq� tq=4
8� 4q ;
S2A ¼ S
2
B ¼
8V � 8c þ 4cqþ qðt þ 4te1 � 8VÞ
8t
;
S2e ¼
q½ð1� qÞð8V þ 4c þ t � 12te1Þ þ 4c þ 3t � 4te1�
ð8� 4qÞt :
Proof. The profit functions for the paper book sellers and the e-
book seller are described in Eqs. (2) and (3). Since in Case 2 the
paper book sellers act as the leader in the Stackelberg pricing
game, they will set their prices on the paper book first, anticipating
the price response of the e-book seller. It is straight forward to
show that each player’s profit function is concave in its own price.
Thus we can derive the equilibrium prices by solving the FOCs. For
the e-book seller E, its FOC is given by:
FOC of E qð4P2 þ t � 4te1 � 8P2e Þ=t ¼ 0: ðA7Þ
Here, the superscript 2 represents Case 2, and we omit the subscript
A (B) of paper book price to simplify notation. From (A7), we can de-
rive that the e-book price is given by P2e ¼ ð4P
2 þ t � 4te1Þ=8. Since
the paper book sellers move first, they will take P2e into Eq. (2)
and solve through the FOC for the optimal paper book price, which
is given by P2 ¼ 8Vþ8c�4cq�8qVþtqþ4te1q16�8q .
When the e-book seller enters it will set its price in response to
the paper book price P2e ¼ ð4P
2 þ t � 4te1Þ=8. The market share of
each player can be derived accordingly, based on their profit
functions. h
Proof of Proposition 1 (Conditions for prices to increase and reader-
ship to decrease after e-book entry in Case 2). In Case 2 with a sym-
metric market (k = m = 1), a price comparison between P2 and PD
shows that PD � P2 ¼ qð4V � 4te1 � tÞ=ð16� 8qÞ, which can be
negative when V < te1 + t/4. That is, an entry of an independent e-
book seller can lead to a high price on paper book. Accordingly,
the paper book market shrinks. h
Proof of Proposition 2 (Effect of q on prices in Case 2). In Case 2
with a symmetric market (k = m = 1), @P2=@q ¼ ð8te1 � 8V þ 2tÞ=
8ð2� qÞ2 which means the paper book price is increasing in q
when V < te1 + t/4. h
Lemma 5 (Pricing equilibrium with seller A also selling e-books
and as the leader in the pricing Game). When firm A owns the e-
book seller E and it anticipates firm B’s price response to the introduc-
tion of e-book, at equilibrium prices and market-shares are as follows:
If the market is symmetric (k = m = 1), the equilibrium is
simplified to the following:
P1e ¼
2cð1þ kmÞ þ 2ðVð1� qÞ � ð2� qÞte1Þ þ kðð1þmÞt þ 2mðte1ðmq� 2Þ þ Vð1�mqÞÞ
4ð2� qþ kmð2�mqÞÞ ;
P1A ¼ ð1=2Þðc þ qte1 þ Vð1� qÞ þ qP
1
e Þ;
P1B ¼ ð1=2Þðc þmqte1 þ Vð1�mqÞ þmqP
1
e Þ; S
1
A ¼
2ðP1A � cÞ
kt
;
S1B ¼
2ðP1B � cÞ
t
; S1e ¼
qð2� qþ kmð2�mqÞÞ
t
P1e :
P3e ¼
2ckmþ 4ð1� qÞðV � te1Þ þ kðð1þmÞt þ 2mðte1ðmq� 2Þ þ Vð1�mqÞÞ
4ð2� 2qþ kmð2�mqÞÞ ;
P3A ¼
2cð2ð1� qÞ þ kmð2þ ð1�mÞqÞ þ 4Vð1� qÞ þ kð4mV þ qð1þmÞðt � 2mVÞÞ
4ð2� 2qþ kmð2�mqÞÞ ;
P3B ¼ ð1=2Þðc þmqte1 þ Vð1�mqÞ þmqP
3
e Þ;
S3B ¼
2ðP3B � cÞ
t
; S3A ¼
Vð1� qÞ þ qte1 � c
kt
;
S3e ¼
qð2cð2þ kmÞ � 4te1 þ kðð1þmÞt þ 2mðð1�mqÞV � te1ð2�mqÞÞÞ
4kt
:
9 This lemma is proved only for the symmetric market with k = 1 and m = 1, since it
is applicable only to the discussion of the symmetric market in Section 4.
Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 397
Author's personal copy
P3A ¼
4V þ 4c � 2cqþ tq� 4qV
8� 6q ;
P3e ¼
3ð1� qÞðV � te1Þ þ t þ c � te1
8� 6q ;
P3B ¼
cð8� 5qÞ þ qðt þ 4te1 � 11VÞ þ 3q2ðV � te1Þ þ 8V
16� 12q ;
S3A ¼
V � c þ qðte1 � VÞ
t
;
S3e ¼
qðV þ 3c � Vqþ t � 4te1 þ te1qÞ
2t
;
S3B ¼
8V � 8c þ 7cqþ qðt þ 4te1 � 11VÞ þ 3q2ðV

Outros materiais

Perguntas relacionadas

Perguntas Recentes