1
A Multi-Channel Model of Separating Equilibrium in the Face of the Digital Divide
Frederick J. Riggins Carlson School of Management
University of Minnesota, Minneapolis, MN [email protected] Phone: 612-624-5760 Fax: 612-626-1316
December 2001
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A Multi-Channel Model of Separating Equilibrium in the Face of the Digital Divide
Abstract
We develop a multi-channel model of separating equilibrium where a monopolist markets a durable good to high and low type consumers in two different channels – an online Internet storefront and an offline brick-and-mortar store. We show how the digital divide, where high type consumers dominate the online channel and low type consumers dominate the offline channel, artificially segments the marketplace thereby mitigating the classic cannibalization problem. This allows the seller to more efficiently market its goods to each consumer segment. We show conditions under which low type consumers are initially served in the offline channel, but subsequently bridging the divide results in low type consumers not being served in either channel. We also examine the implications of bridging the digital divide when the seller employs personalization technology in the online channel and uses delay by engaging in intertemporal price discrimination.
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A Multi-Channel Model of Separating Equilibrium in the Face of the Digital Divide
1. Introduction
The success of the Internet as a viable channel for commerce is dependent upon
achieving a critical mass of users who are willing to make purchases using the online
channel. However, examination of the growth in the number of Internet users indicates
that the adoption of the Internet has not been uniform across all segments of society,
creating what has come to be called the “digital divide.” Empirical studies have
investigated the existence of the divide according to several different individual
characteristics including race, gender, level of education, and age (Hoffman and Novak
1998; 2000). For example, the U.S. Commerce Department reports that in 2000
(Commerce Department 2000):
• persons with a disability are about half as likely to have access to the Internet as those without a disability;
• access to the Internet for Black and Hispanic households was about 23.5% and 23.6%
versus a national average of 41.5%; • less than one third of people 50 years or older were Internet users; and • children in dual-parent households are nearly twice as likely to have Internet access
as children in single-parent households. The presence of the digital divide should be a concern for all members of society;
whether it be policy makers seeking to promote societal welfare, educators concerned
with the intellectual development of those without access, or online sellers that seek to
increase their marketing base.
The digital divide exists, in part, because individuals differ in their propensity to
try out and adopt new innovations such as the Internet. Rogers (1995) outlines several
key characteristics that distinguish early innovation adopters from late adopters. These
characteristics can be grouped into three different categories: socioeconomic
characteristics, personality variables, and communication behaviors. Among other
things, early innovation adopters have more education, have higher socioeconomic status,
are more interconnected via interpersonal networks, are more cosmopolitan, have more
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exposure to mass media, and have more contact with change agents who promote the
innovation. As the Department of Commerce study indicates, those with Internet access
are more likely to live in better suburban neighborhoods as opposed to the less connected
who tend to reside in inner city or rural areas. The fear that we are creating two societies
– an online society where children are “growing up digital” with rich access to online
information resources, and an offline society where there is limited or no access to such
information – has profound social, political, and economic implications (Tapscott 1997).
It would seem that bridging the digital divide is an important goal if electronic
commerce is to grow into a widely accepted form of commerce. However, bridging the
divide may have certain negative consequences that have not been previously considered.
This paper will examine the implications of a firm that sells its goods in a multi-channel
marketplace where action is taken to bridge the divide. Specifically, we develop an
analytical separating equilibrium model examining the pricing and quality levels of a firm
that sells in two channels simultaneously – an online channel and an offline channel.
Prior analytical modeling has examined the classic cannibalization problem that can exist
when high and low type consumers exist in the same shopping channel (Stokey 1979;
Landsberger and Meilijson 1985; Moorthy and Png 1992). In the present analysis, we
show how the digital divide artificially segments the marketplace allowing the seller to
more efficiently market its goods to each consumer segment, thereby mitigating the
cannibalization problem. Subsequently bridging the divide increases the distortion from
the cannibalization problem, causing the seller to lower the quality of the low quality
product in the physical store. Indeed, we show conditions under which low type
consumers are initially served in the offline channel, but subsequently bridging the divide
results in low types not being served in either channel. We extend the multi-channel
model to examine the implications of bridging the divide when the seller employs
personalization technology to target market to specific customers and uses delay by
offering product introductions in sequential periods.
The organization of the paper is as follows. In the next section, we review the
relevant literature upon which we construct our model. The formal model is developed in
§3, where we examine the seller’s optimal selling strategies in the face of the digital
divide and examine the implications of bridging the divide. We expand the model in §4
5
where we include the use of personalization technology by the seller. We examine the
use of intertemporal price discrimination with the existence of the digital divide in §5.
We conclude with a summary of our findings in §6.
2. Previous Modeling
Several researchers have examined pricing strategies of sellers that practice
intertemporal price discrimination or that operate in multiple channels simultaneously.
Stokey (1979) showed how a monopolist could use delay as a way of selling to multiple
consumers who have differing reservation prices. Landsberger and Meilijson (1985) built
on that idea to show that intertemporal price discrimination works when the seller and
buyers have different discount rates. Conner (1988) illustrates how a firm may spend
aggressively on research and development to create a new version of an old product, and
then delay introduction of the new product until the old one is challenged by a
competitor. Besanko and Winston (1990) model the monopolist’s optimal timing and
pricing strategy in the introduction of a new product when consumers are intertemporal
utility maximizers versus being myopic. They show that prices are always lower when
consumers act rationally as opposed to myopic, which allows the seller to practice
intertemporal price discrimination. Similarly, Levinthal and Purohit (1989) show how
expectation of a future product improvement cannibalizes sales of the current version of
the product. They show conditions under which the seller should phase out the old
product versus instituting a buy-back policy when the new product is introduced.
Purohit (1997) develops a two-period model of a manufacturer that markets its
goods in a multi channel setting. By comparing an automotive rental agency structure
versus a dealership structure, he determines the profitability of a manufacturer under
three different channel scenarios to best coordinate rental and dealership relationships.
Zettelmeyer (2000) examines how the size of the Internet affects the firm’s pricing and
communications strategies. He shows that when the Internet is relatively small in size,
firms will provide more information online and prices will be lower than in conventional
channels. However, as the number of users on the Internet increases, the amount of
information the firm provides through the Internet channel and the firm’s online pricing
policy will eventually become similar to that in the conventional channel.
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Another useful model for analyzing online retailers is Balasubramanian’s (1998)
adaptation of Salop’s (1977) circular city model. In that paper, he compares the direct
mail efforts of a physically unconstrained catalog retailer with the efforts of traditional
retailers who cater to neighboring customers. While he indicates the model can be used
to illustrate the efforts of an online Internet retailer he doesn’t examine the use of online
features such as personalization. In another model, Roy (2000) examines how targeted
direct marketing can result in complete market segmentation between two competing
firms.
Mason and Milne (1994) conduct an empirical study of the cigarette industry to
show how the proliferation of brands results in cannibalization of other product lines,
leading firms to reduce the number of brands they sell. They develop a method of
identifying the degree of cannibalization in mature retail markets.
The current analysis is most closely related to Moorthy and Png (1992) who
develop a model of separating equilibrium in a single-channel market. They consider a
monopolist that produces a durable product that can be differentiated along some
dimension of “quality”. The monopolist sells to a market that is made up of high and low
type consumers, where high types have a higher valuation for a given level of quality
than low type consumers. In this situation, the seller will produce two versions of the
product to be targeted at the two consumer segments. Because of the lack of information
about a specific consumer’s type, the seller must practice second-degree price
discrimination and price the two products such that the consumers self-select into their
appropriate market segments. The cannibalization problem arises because the seller is
not able to prohibit the high type consumer from buying the low quality good. The
authors show that the optimal solution to the problem is to give high type consumers a
price discount and lower the quality (and corresponding price) of the low quality good to
the point that high type consumers are not interested in that version of the product.
Depending upon the relative consumer valuations of the good, it is possible that the seller
may need to lower the quality of the low quality product to the point that it essentially
doesn’t exist. In that case, the cannibalization problem is so strong that low type
consumers are not served in the marketplace.
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This distortion in the marketplace due to high type cannibalization essentially has
two important effects on the market. First, low type consumer choice is reduced since
they receive a lower quality product, and in fact may not be served at all if the
cannibalization potential is high enough. Second, this distortion lowers the profits of the
seller who must contend with the moral hazard problem associated with second-degree
price discrimination. To combat the cannibalization distortion, the seller may employ
intertemporal price discrimination by offering the high quality good at an earlier point in
time than the low quality good. By using delay to degrade the low quality good, the
seller may be able to mitigate the cannibalization problem if consumers are sufficiently
impatient relative to the seller. In the next section, we extend the Moorthy and Png
(1992) model by allowing the seller to sell in two channels at the same time.
3. A Multi-Channel Model of Separating Equilibrium
We consider the monopolist’s problem where the seller markets its goods in two
channels simultaneously, the online (Internet) channel (I) and an offline (brick-and-
mortar) channel (B). The seller sells a durable good that can be differentiated according
to some dimension of quality, q. There are two types of consumer segments in the
market, h and l, where nh is the number of high types and nl is the number of low types.
Further, high type consumers value a given level of quality q at vhq, while low types
value the same item at vlq. Let vh > vl > 0 such that high types value a given level of
quality more than low types. Let hlv =vh/vl, h
ln =nh/nl and R= hln ( h
lv –1) where R is a
measure of the degree of cannibalization as shown in Moorthy and Png (1992). Finally,
assume that a consumer buys at most one unit of the durable good and then exits the
marketplace.
Due to a favorable online transaction cost structure, we assume that the marginal
cost of providing an additional good in the online channel is less than or equal to the
marginal cost of an additional good in the offline channel. Therefore, the seller can
market the good in the online channel and/or the offline channel, where the marginal cost
of supplying one unit with quality q is ciq2 and cbq2 respectively, where cb > ci > 0. Let α
and β be the fraction of low and high type consumers, respectively, who have migrated to
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the online channel. We assume that a particular consumer shops in only one channel and
her decision to remain in the offline channel or migrate to the online channel is
independent of the market for the one durable good under consideration.1 Based on
empirical and theoretical grounds, we assume that a digital divide potentially exists, i.e.
0 < α < β < 1, such that high type consumers migrate to the online channel of commerce
faster than low type consumers.
When some portion of high and low type consumers are located in both channels,
that is when 0 < α < β < 1, the seller will potentially sell high and low quality versions of
the good in both channels. Therefore, with two consumer segments and two channels,
there can be at most four “products” or levels of qualities – a high quality good offered
online targeted to high type consumers, a high quality good offered offline targeted to the
high types, a low quality good offered online to the low type consumers, and a low
quality good offered offline to the low types. Due to the difference in transaction costs
between the two channels, the high (low) quality good offered online need not be the
same as the high (low) quality good offered offline. Indeed, we can calculate the efficient
qualities of the four products as the qualities that maximize the difference between the
targeted customer’s valuation and the firm’s marginal cost of quality. Specifically, the
efficient qualities for the four products are
high quality good offered in the online channel i
hih c
vq 2
* = (1)
high quality good offered in the offline channel b
hbh c
vq 2
* = (2)
low quality good offered in the online channel i
lil c
vq 2
* = (3)
low quality good offered in the offline channel b
lbl c
vq 2
* = . (4)
The efficient levels of quality are shown in Figure 1. In general, we know that
** bh
ih qq ≥ ,
** il
ih qq > ,
** bl
il qq ≥ , and
** bl
bh qq > .
1 We make the assumption that a consumer shops in one channel or the other to simplify the analysis, however, the results would still hold if we assumed a consumer type has a certain propensity to shop either online versus offline.
9
Segment h
Segment l
Internet Costs
Brick-and-Mortar Costs
qlb* qh
b* qli * qh
i* quality
$
Figure 1. Customer Reservation Values and Marginal Costs for Quality
We now turn our attention to the situation where the seller introduces all products
in the same period and commits to no further product introductions. When the seller
targets the appropriate good to the appropriate consumer segment in each channel, the
seller’s problem is
max,,,
,,,,bl
bh
il
ih
bl
bh
il
ih
ppppqqqq
( ) ( )
−−+
−−+
−+
− 222211 b
hbbhh
blb
bll
ihi
ihh
ili
ill qcpnqcpnqcpnqcpn βαβα (5)
subject to:
ih
ihl
il
ill pqvpqv −≥− (6a) b
hbhl
bl
bll pqvpqv −≥− (6b)
il
ilh
ih
ihh pqvpqv −≥− (7a) b
lblh
bh
bhh pqvpqv −≥− (7b)
il
ill pqv ≥ (8a) b
lbll pqv ≥ (8b)
ih
ihh pqv ≥ (9a) b
hbhh pqv ≥ . (9b)
The constraints (6) and (7) are the self-selection constraints for the two consumer
segments in the two channels. Since the seller must practice second-degree price
10
discrimination, he must set the quality and price levels so that each segment chooses the
appropriate quality and price offering. Constraints (8) and (9) are the participation
constraints that ensure that each consumer type will participate in the market.
As pointed out by Moorthy and Png (1992), because high type consumers value a
given level of quality more than low types, the seller cannot extract all of the consumer
surplus from both types by binding constraints (8) and (9) at the same time. If this were
the case, the high type consumers would forgo purchasing the high quality good and
instead purchase the low quality good, thereby gaining some positive surplus. Instead,
the seller will bind constraint (8) such that
ill
il qvp = and b
lbll pqv = . (10)
Also, the seller should set the price for the high quality goods so that the high types in
each channel are indifferent between the high quality good and the low quality good.
This is accomplished by making constraint (7) bind and then using (10), such that
( ) illh
ihh
ih qvvqvp −−= and ( ) b
llhbhh
bh qvvqvp −−= . (11)
Substituting the four prices into the objective function and maximizing with respect to the
four levels of quality, we see that
−= R
cv
qi
lil α
β1
2 and
−−−= R
cv
qb
lbl α
β11
12
(12)
i
hih c
vq
2= and
b
hbh c
vq
2= . (13)
The seller’s profits are
b
hh
b
ll
i
hh
i
ll
cvn
Rc
vncvn
Rcvn
4)1(
11
14
)1(4
14
222222 βαβαβ
αβα −+
−−−−++
−=Π . (14)
The four terms in equation (14) represent the profit from selling to low types online, high
types online, low types offline, and high types offline, respectively. This four-product
solution is feasible, if and only if 0>ilq , i.e., when
βα<R . When
βα≥R , the seller is
able to increase profits by lowering the quality of the low quality online product, and
does so until the point that it essentially doesn’t exist – the low type consumer is not
served in the online market. However, a three-product solution is feasible where the low
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type segment is still served in the offline marketplace provided 0>blq , which occurs as
long as βα
−−<
11R . When
βα
−−≥
11R , the seller again is able to increase profits by
lowering the quality of the low quality offline product until the point that the low type
consumer is not served in either channel, resulting in a two-product solution. In terms of
selling to the high type consumers, the seller should supply the high types their efficient
qualities from (1) and (2) and price them according to (11). In the appropriate regions,
profits are increased as ilq and/or b
lq go down. In the limit, no four-product solution can
have profits greater than
b
hh
i
hh
blb
blll
b
hbl
b
hh
bllh
ili
illl
i
hil
i
hh
illh
cvn
cvn
qcqvnc
vq
cv
vqvn
qcqvnc
vq
cv
vqvn
bl
il
4)1(
4
)1(42
)1(
42lim
22
22
22
0,0
ββ
αβ
αβ
−+=
−−+
−
−+−
+
−+
−
−+
↓↓
Therefore, the seller’s profit for the single period introduction case is
−−≥−+
−−<≤
−−−−+−+
<
−−−−+
−+−+=
Π
.11
if4
)1(4
)15(11
if11
14
)1(4
)1(4
if11
14
)1(
144
)1(4
22
2222
22
2222
βαββ
βα
βα
αβαββ
βα
αβα
αβαββ
Rc
vncvn
RRc
vnc
vncvn
RRc
vn
Rcvn
cvn
cvn
b
hh
i
hh
b
ll
b
hh
i
hh
b
ll
i
ll
b
hh
i
hh
p
p
Notice that the profits reduce to the Moorthy and Png (1992) case when cb = ci
and when α = β. Our purpose here is not to duplicate that analysis for the multi-channel
case, but rather examine the implications of the digital divide. If 0 < α < β < 1, the
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seller’s strategy can be determined from equation (15). If βα<R , the seller will sell high
and low quality goods in both channels. If βα
βα
−−<≤
11R , the seller can increase profits
by lowering the quality of the low quality good online, and will do so to the point that it
does not exist – the low type consumer will only be served in the offline channel, while
high types will be served in both channels. If βα
−−≥
11R , the cannibalization is so great
that the seller does not serve low type consumers in either channel, but still sells to high
types in both channels. Specifically, the seller’s strategy is stated in Proposition 1.
PROPOSITION 1. If the seller chooses to introduce products in one period only, then
he will do so in the first period, and offer four qualities, qhb, qh
i, qlb, and ql
i, if βα<R , or
offer three qualities, qhb, qh
i, and qlb, if
βα
βα
−−<≤
11R , or two qualities, qh
b and qhi, if
βα
−−≥
11R .
The seller’s strategy is readily illustrated in Figure 2, where we show the case
where β = .8. The three regions in Proposition 1 and equation (15) are labeled in Figure 2
as Sell 4, Sell 3, and Sell 2, which represent the number of unique product qualities
offered. When R is relatively low, the threat of cannibalization is low, allowing the seller
to sell to both consumer types in both channels, provided the digital divide is not too
great. However, even when R is low, a huge digital divide will result in low types being
served only in the offline market, since there would not be enough low type consumers in
the online market to make it profitable for the seller to offer a low quality good online.
When R is very large, the potential for cannibalization is so large that the seller will sell
only to the high type consumers in both channels. Moorthy and Png (1992) show that in
the single-channel, one-period case, the seller will sell to both high and low types when
R < 1, and only to the high type consumers when R > 1. In Figure 2, this corresponds to
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the situation where α = β = .8 where the appropriate strategy is Sell 4 when R < 1, and
Sell 2 when R > 1. However, when α < β, the digital divide opens up a new opportunity
for the low types to be served in the offline channel via the Sell 3 strategy. The greater
the digital divide, the more the Sell 3 strategy dominates the seller’s strategic options.
What is the impact of the digital divide on the seller’s profits? It is easily shown
that 0≥∂Π∂β
, such that having the high type consumers migrate to the online channel
increases the seller’s profits. This is so for two reasons. First, increasing the digital
divide further segments the marketplace; thereby lessening the distortion due to
cannibalization and increasing profits for the seller. In addition, the seller enjoys the cost
advantages of selling to the high type consumers in the more efficient online market.
However, bridging the digital divide by bringing more low type consumers into the
online channel does not necessarily increase the seller’s profits. This is because the seller
benefits by selling to the low type consumers in the cost efficient online channel, but is
harmed by the exacerbated cannibalization problem that results from unsegmenting the
market as the high and low type consumers mix in both channels.
Consider equation (12) for the situation where β is considerably large relative to
α. In that case, the high type consumers dominate the online commerce channel such that
the seller is forced to lower the quality, ilq , of the low quality online good to keep the
Sell 4Sell 2
Sell 3
β= .8
R
αβR =
1 − α1 − βR =
1
01
αh
Sell 2:offer q , q
Sell 3:offer q , q , q
Sell 4:offer q , q , q , q
bhi
hb
hi
hb
hi
lb
lb
li
Figure 2. The Seller’s Response to the Digital Divide
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high types from cannibalizing sales of the high quality good. In this scenario, it is quite
likely that the low types will not be served in the online channel as the seller sets ilq = 0
and chooses to focus its online marketing efforts on selling the high quality good to the
high type consumers. In addition, notice that as β increases, the seller is able to raise the
level of quality of the low quality good in its brick-and-mortar stores, that is 0≥∂∂
β
blq
.
Indeed, in the extreme case where α is some positive value and 1→β , the seller is able
to serve its offline low type consumers with an efficient level of quality *b
lq from
equation (4). Therefore, as more and more high types migrate from traditional brick-and-
mortar shopping environments to Web-based shopping, and thereby visit physical stores
less frequently, we should expect to see physical stores raise the quality, and by (11) the
corresponding price, of their discount merchandise. In this case, we see that the digital
divide acts as a mitigating factor for the cannibalization problem that exists when
different types of consumers co-exist in the same marketplace. The digital divide lessens,
or may in fact eliminate, the distortion that occurs when high type consumers are tempted
to purchase low-end goods due to their higher valuation of quality. We summarize this
result in Proposition 2.
PROPOSITION 2. If the seller chooses to introduce products in a single period setting,
the digital divide, where 0 < α < β < 1, segments the market and lessens the distortion
due to the cannibalization problem, resulting in higher quality goods at higher prices for
low types consumers in the offline channel.
The intuition is quite straightforward. When high type consumers are faster to
adopt the innovation of Web-based shopping, the digital divide naturally segments the
market into two channels: the online Internet channel where high quality goods are
targeted to the high type adopters, and the offline brick-and-mortar channel where low
quality goods are targeted to low type consumers. When the two consumer types are
segmented in this way, the low type consumers are better served in the brick-and-mortar
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store because the seller is not forced to lower quality to avoid the cannibalization
distortion.
This type of online/offline segmentation is seen in the market for personal
computers. Manufacturers are attempting to simultaneously sell in traditional brick-and-
mortar electronics retail stores and through the direct channel via their company Web
sites. Products offered on the Web site are typically high-end workstations and servers,
while those sold at retail electronic stores are typically slower, low-end processors. In
fact, many of the low-end products found in the physical store are not available at all in
the online storefront. Even when a new processor is introduced into the online storefront,
rather than add the new model to its existing product line, the manufacturer will typically
remove the slowest machine previously offered online – even though the slower model is
readily available in the brick-and-mortar stores for some time to come. In part, this is to
keep the high type online consumer’s attention focused on the more profitable powerful
desktop models, rather than cannibalize these sales.
The situation can be illustrated is Figure 3. The assumption that α < β means that
we need only concern ourselves with the area to the right of line AB. Provided that
βα<R , we can summarize the key points as follows:
• at point A, no consumer has migrated to the online channel – the seller sells a high and low quality good in the offline channel only with the maximum cannibalization distortion;
• at point B, all consumers have migrated to the online channel – the seller sells a high
and low quality good in the online channel only with the maximum cannibalization distortion;
• along the diagonal line from A to B, there is no digital divide as an equal percentage
of high and low type consumers have migrated to the online channel – the seller may sell high and low quality goods in both channels with the maximum cannibalization distortion;
• the distortion due to the cannibalization problem decreases as we move further from
the AB diagonal; • at point C, the markets are perfectly segmented such that there is no distortion due to
the cannibalization problem at all – the low types enjoy the efficient quality level in the offline channel and the seller’s profits are maximized;
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• the solid/dashed arc beginning at point A is a hypothetical adoption path.2 Note that
the distortion is minimized at point D for α* and β*; • the dotted line indicates the hypothetical adoption path where an effort is made to
bridge the digital divide. Note that the effort to bridge the digital divide rotates the arc counter-clockwise toward the AB diagonal, thus increasing the distortion due to the cannibalization problem.
Figure 3. Adoption of an Online Commerce Channel
β
00 1
1
α
β*
α *
A
B
C
D
MaximumDistortion
OnlyOnline
ChannelServed
AdjustedAdoption Path
OnlyOfflineChannelServed
DistortionOnly inOfflineChannel
DistortionOnly inOnline
Channel
HypotheticalAdoption Path
(projected)
Total MarketSegmentationNo Distortion
HypotheticalAdoption Path
Percentageof High Types
Online ( )
Percentageof Low Types
Online ( )
Now suppose the seller considers offering less than four different product
offerings in the two channels. As shown in Figure 3, if α = β = 0 (α = β = 1), the seller
sells only in the offline (online) channel. If α = 0 and β = 1, the seller sells only the low
2 The arc endpoint could certainly be at point B. The projected arc is drawn to emphasize the possibility that some low type consumers may never adopt the online channel. Of course, the same could be said for laggard high types as well.
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quality good in the offline channel and only the high quality good in the online channel
with no cannibalization distortion. If α = 0 and 0 < β < 1, the seller will sell the high
quality good in both channels, will not sell any low quality goods online, and will sell a
low quality good in the offline channel if (1–β) R < 1. If (1–β) R > 1, the low type
consumer will not be served in either channel.
What happens when the potential for cannibalization is high and an effort is made
to bridge the digital divide? Refer back to Figure 2 and consider the region where
bR
−−<<
11
1α
, such that the seller pursues the Sell 3 strategy due to a combination of the
cannibalization problem and the digital divide. In this case, a sufficient increase in α will
force the seller to revert to the Sell 2 strategy. In other words, bridging the digital divide
could make the low type consumers worse off because the cannibalization problem will
force the seller to cease sales of the low quality good in the brick-and-mortar stores, but
will not provide adequate incentives to begin sales of the low quality good in the online
channel! This rather surprising result shows that conditions could exist where low type
consumers were previously served in one channel, but bridging the digital divide could
cause them to be not served in either channel. More formally, we can summarize this
result in Proposition 3.
PROPOSITION 3. If 1 < R < β−
−11 a , low type consumers will be served in the offline
channel only, where qlb > 0, provided that 0 < α < β < 1. Subsequently increasing α
such that R > β−
−11 a will result in ql
b = 0 such that low type consumers will not be served
in either channel.
In fairness to those advocating bridging the digital divide, providing Internet
access to low type consumers should have positive effects on these individuals. In
particular, the Internet increases people’s connectivity to information resources, other
individuals, ideas and cultures, and new shopping experiences. Theoretically, bridging
18
the digital divide potentially has two diametrically opposed long-term potential impacts
on the cannibalization parameter, R, that are not taken into account in our model.
First, consider the implications of bridging the divide on the differences in quality
valuations, vh and vl. Having access to the Internet could make low type consumers more
cosmopolitan and aware of more product opportunities in the marketplace, thereby
altering their consumer tastes. If having access to the Internet causes vl to increase, the
gap between vh and vl could decrease, lowering hlv and thereby lowering R. We call this
long-term change in R the moderating valuation effect. Referring back to Figure 2, if
R > 1, bridging the digital divide could move the seller from the Sell 3 strategy to the Sell
2 strategy. However, over a longer period of time, a reduction in R due to the moderating
valuation effect would cause the seller to revert to the Sell 3 strategy and eventually to
the Sell 4 strategy. A long-term increase in vl lessens the cannibalization problem and the
ensuing distortion. Indeed, inspection of equation (14) reveals that the seller’s profit
increases in vl, 0≥∂Π∂
lv.
On a more individual level, having access to the Internet may cause a low type
consumer to adopt high type characteristics, essentially causing some low types to
become high type consumers. If providing access to the Internet causes nl to decrease
and nh to increase, the proportion of high types to low types, hln , will increase, thereby
increasing R. We call this long-term change in R the type transformation effect. Again,
referring to Figure 2, if R < 1, bridging the digital divide could move the seller from the
Sell 3 strategy to the Sell 4 strategy. However, over a longer period of time, an increase
in R due to the transformation of some low type consumers into high type consumers
would cause the seller to revert to the Sell 3 strategy and eventually to the Sell 2 strategy
thereby harming the remaining low type consumers. In this case, an increase in hln
increases the cannibalization problem and the ensuing distortion. What is the impact of
the type transformation effect on the seller’s profit? In the Sell 4 region, increases in R
would tend to lower profits, however, the seller compensates by lowering qli and ql
b.
Likewise, in the Sell 3 region, the seller compensates for the increased distortion by
lowering qlb. However, in the Sell 2 region the seller avoids the cannibalization problem
19
entirely by not selling a low quality good. Therefore, as shown in equation (15), when
R > β−
−11 a , the type transformation effect increases the seller’s profits by providing more
high type consumers in the marketplace.
Whether the moderating valuation effect and/or the type transformation effect
actually exist is an issue open to debate and empirical study. Longitudinal studies on the
impact of Internet access on low type users is an important area for researchers to
examine in the coming years.
4. The Use of Personalization Technology in the Online Channel
We now consider an extension to the model developed in the previous section by
considering the implications of the seller employing personalization technology in the
online channel. When the seller is not able to distinguish between high type consumers
and low type consumers, the seller must practice second-degree price discrimination and
set the price and quality levels so that each consumer self-selects into his or her
appropriate category. As discussed earlier, we bind constraint (8) so that without
knowing which consumers are low types, the seller sets the price of the low quality good
at the price that the low types are willing to pay. The seller is able to do this to the low
types because he doesn’t try to do this to the high types. Instead, the seller gives the high
type consumers a price discount allowing the high types to gain some surplus from the
transaction, but sets the price of the high quality good so that the high types are
indifferent between buying the low quality good versus the high quality good by binding
constraint (7).
One of the most useful tools available to sellers in the online channel is the ability
to collect information about the user and personalize the site and product offerings
accordingly.3 Collection of information is both passive (tracking user actions on the site)
and active (having the user fill out forms with personal information). As the seller is able
to collect user information and thereby personalize the online offering, the seller is able
to move away from second-degree price discrimination and move closer to first-degree
3 For a more extensive analytical treatment of the use of personalization technology in the online channel only see Riggins and Narasimhan 2001.
20
price discrimination. Indeed, in an environment where the seller is able to gather perfect
information about the user, he would be in a position to extract all of the high type
consumer’s surplus by setting the price of the high quality good at the high type’s
willingness-to-pay. For example, once enough information is collected, an online high
type user would only have access to pages promoting high quality goods and may never
see low quality goods in the online channel. It is easy to see how in the extreme this
would eliminate the cannibalization distortion.
In this section, we introduce a personalization parameter, ω ∈ (0, 1), which
measures the extent to which the online seller is able to know the user’s likes and
dislikes, and correspondingly personalizes the online channel offerings. When ω is near
zero, the seller is not able to personalize at all. When ω is near 1 the seller knows
everything about the user and is able to practice first-degree price discrimination.
The seller’s problem is to choose qualities and prices to solve
max,,,
,,,,bl
bh
il
ih
bl
bh
il
ih
ppppqqqq
( ) ( )
−−+
−−+
−+
−2222
11 bhb
bhh
blb
bll
ihi
ihh
ili
ill qcpnqcpnqcpnqcpn βαβα (16)
subject to:
])[1( ih
ihl
il
ill pqvpqv −−≥− ω (17a) b
hbhl
bl
bll pqvpqv −≥− (17b)
])[1( il
ilh
ih
ihh pqvpqv −−≥− ω (18a) b
lblh
bh
bhh pqvpqv −≥− (18b)
il
ill pqv ≥ (19a) b
lbll pqv ≥ (19b)
ih
ihh pqv ≥ (20a) b
hbhh pqv ≥ . (20b)
With the seller’s problem stated in (16) thru (20), we can proceed in the same
manner as in the previous section to find that the prices for the four levels of quality are
ill
il qvp = and b
lbll pqv ≥ . (21)
( ) ( ) ][1 illh
ihh
ihh
ih qvvqvqvp −−−+= ωω and ( ) b
llhbhh
bh qvvqvp −−= . (22)
Substituting the four prices into the objective function and maximizing with respect to the
four levels of quality, we see that
21
( )
−−= ω
αβ
112
Rcv
qi
lil and
−−−= R
cv
qb
lbl α
β11
12
(23)
i
hih c
vq
2= and
b
hbh c
vq
2= . (24)
The seller’s profits in this case are
( )i
hh
i
ll
cvn
Rcvn
411
4
222 βωαβα +
−−=Π
b
hh
b
ll
cvn
Rc
vn4
)1(111
4)1( 222 β
αβα −+
−−−−+ (25)
when ( )ωβα
−<
11R and
βα
−−<
11R . Here is it important to notice that unlike the model
in the non-personalization case, it is possible that ( )ωβα
βα
−<
−−
11
11 for certain values of
ω. In particular, consider the case when ω is relatively high, such that the seller is able to
personalize extensively in the online channel. In that case, the online cannibalization
distortion will be much lower, potentially to the point that the seller will sell to the low
type consumer in the online market, but not in the offline channel. The maximum profits
while introducing products in the two channels when personalization is possible are
( ) ( )
( )( )
( ) ( ) ( )
( ) ( )( )
( )( )
−−
−≥−+
−−<≤
−
−−−−+−+
−<≤
−−
−−+−+
−−
−<
−−−−+
−−+−+=
Π
βα
ωβαββ
βα
ωβα
αβββ
ωβα
βαωβββ
βα
ωβα
αβ
ωαβββ
11
,1
1maxif
41
4
11
11
if11
14
14
14
)26(1
111
if1144
14
11
,1
1minif
11
14
1
1144
14
22
2222
2222
22
2222
Rc
vncvn
RRc
vnac
vncvn
RRac
vanc
vncvn
RRc
vna
Rcvan
cvn
cvn
b
hh
i
hh
b
ll
b
hh
i
hh
i
ll
b
hh
i
hh
b
ll
i
ll
b
hh
i
hh
p
p
p
22
Therefore, there are four strategies the seller can choose: Sell 4 and Sell 2 as in
§3, and Sell 3i and Sell 3b, where the seller offers the low quality good in the online
channel only, and the offline channel only, respectively. More formally, we can state
Proposition 4.
PROPOSITION 4. If the seller is able to personalize his online product offerings
according to the parameter ω and he chooses to introduce products in one period only,
then he will do so in the first period and offer four qualities, qhb, qh
i, qlb, and ql
i, if
( )
−−
−<
βα
ωβα
11
,1
1minR , or offer three qualities, qh
b, qhi, and ql
i, if
( )ωβα
βα
−<≤
−−
11
11 R , or three qualities, qh
b, qhi, and ql
b, if ( ) βα
ωβα
−−<≤
− 11
11 R , or
two qualities, qhb and qh
i, if ( )
−−
−≥
βα
ωβα
11
,1
1maxR .
These results are illustrated in Figure 4 for the β = .8 case and where ω = .5.
Comparing Figure 4 with Figure 2 (which is the ω = 0 case), the reader should note that
not only does ω create the potential for the Sell 3i region, but also increases the size of the
Sell 4 region. Sell 3i comes at the expense of the Sell 2 region, while Sell 4 is at the
expense of Sell 3b, as personalization makes selling to low types online more feasible.
α
Case for β = .8, ω = .51
01
Sell 4
Sell 2
Sell 3
R
R = 1βα
R βα
−−=
11
Figure 4. The Seller’s Response with Personalization
Sell 3
Sell 2: offer q , q
hb
hi
Sell 3 : offer q , q , q
hb
hi
li
Sell 4: offer q , q , q , q
hb
hi
lb
li
i
Sell 3 : offer q , q , q
hb
hi
lb
bi
b
(1 − ω)
23
We can now state two follow-up propositions to Proposition 3. As shown in
Figure 4, for relatively high values of R, increasing α by bridging the digital divide can
once again move low type consumers from being served in the offline market (Sell 3b) to
not being served in either channel (Sell 2). However, further increases in α could result
in low type consumers being served in the online channel if the seller engages in online
personalization. More formally, we can state Proposition 5.
PROPOSITION 5. If βω−1
1 < R < β−
−11 a , low type consumers will be served in the
offline channel only, where qlb > 0, provided that 0 < α < β < 1.4 Subsequently
increasing α such that R > β−
−11 a will result in ql
b = 0 such that low type consumers will
not be served in either channel. For
−−
− βωβ 11
,1
1max
aa < R < ( )ω−11
, further
increasing α such that R < ( )ωβα
−11 will result in ql
i > 0 such that low type consumers
will be served in the online channel only.
The intuition is that when the seller uses the online channel to engage in high
levels of personalization with its online customers, the distortion due to cannibalization
goes away in the virtual storefront, but continues to exist in the real-world store.
Therefore, selling to both high and low type consumers online becomes more attractive,
relative to that in the offline channel. Similarly, we can state Proposition 6 for lower
values of R.
4 The reader should note that
βω−=
11
R is the point at which ( )ωβ −=
11a
R and β−
−=11 a
R intersect.
24
PROPOSITION 6. If 1 < R <
−−
− βωβ 11
,1
1min
aa , low type consumers will be served
in the online and offline channels, provided that 0 < α < β < 1. Subsequently increasing
α such that R > β−
−11 a will result in ql
b = 0 such that low type consumers will not be
served in the offline channel.
In this situation, for moderate values of R, a moderate digital divide will allow the
seller to serve the low type consumers in both channels (Sell 4), however, subsequently
bridging the divide will result in the seller serving low type customers in the online
channel only (without personalization the low types would not be served in either
channel).
So we see that personalization in the online channel allows the seller to practice
first-degree price discrimination, which can eliminate the cannibalization distortion in
that channel. Inspection of equation (25) shows that the seller’s profit is increasing in
personalization, i.e. 0>∂Π∂ω
, however the reader should recall that we have not
considered the explicit costs of personalization. Riggins and Narasimhan (2001) explore
additional implications of employing personalization technology in the online channel.
There, they show that the seller should direct all of its personalization efforts toward the
high type consumers only.
Again, observe Figure 4. When ω is very large, Sell 4 becomes much more
attractive, even for extremely high values of R. High levels of personalization can
eliminate the cannibalization distortion, allowing the seller to engage in first-degree price
discrimination to all customers within that channel. The result is that the seller is able to
set qualities (and prices) for both products in the online channel and the high quality
product in the offline channel at the efficient levels shown in equations (1) to (3). One
could argue that those that seek to bridge the digital divide could better help low type
consumers by encouraging personalization in the online channel. However, what we
observe in practice is quite the opposite. Many consumers express concern when online
retailers collect massive amounts of information about its users and threaten a potential
25
backlash to violations of stated corporate privacy statements. Privacy and security
concerns consistently rank near the top of surveys examining the public’s apprehension
about online commerce. The debate seems to be moving toward efforts to curtail sellers’
data collection and subsequent personalization efforts. “Web-lining”, a new form of the
old practice of red-lining, where online storefronts target high levels of service for its
most promising customers and provide lower levels of service to less promising visitors,
has become a concern to many consumers and public officials (BusinessWeek 2000).
5. Sequential Product Introductions
Moorthy and Png (1992) extend their original model to examine the possibility
that the seller introduces the high and low quality goods in different periods.
Specifically, they show that if the consumers are relatively less patient than the seller, the
cannibalization problem can be mitigated by offering the high quality good in the first
period and the low quality good in the second period. Essentially, the seller uses
sequential product introductions to make time another differentiating attribute along with
product quality. They also show that when R is particularly large, the low type
consumers may be served in an after-market when simultaneous product introductions
would shut the low types out of the market. The implications are somewhat analogous to
the results in the previous section where the digital divide artificially segments the
marketplace to the benefit of the low type consumers. As stated earlier, our goal is not to
duplicate their analysis, but rather investigate the implications of bridging the digital
divide in the multi-channel context. We will consider the no-personalization case when
the seller can pre-commit to future actions.5
In our case, the seller could choose to introduce products in two different periods
by introducing the high quality goods in both channels in the first period in order to reap
the profits from the higher-quality goods as soon as possible, followed by the low quality
goods in period 2, if it is profitable to do so.6 This corresponds to the Sell 2 strategy in
5 For a discussion of the commitment versus no-commitment cases see Moorthy and Png (1992) and Riggins and Narasimhan (2001). 6 The two-period scenario is feasible due to our original assumption that a particular consumer shops in only one channel at a given point in time. Because of this, the high (low) quality product offered offline does not cannibalize the high (low) quality product offered in the online channel. Relaxing this assumption
26
the first period, followed by either the Sell 2, 3, or 4 strategy in the second period. Let
δc ∈ (0, 1) be the consumer’s discount factor of waiting until the second period to make a
purchase. When consumers are very patient, δc will be close to 1, while δc will be close
to 0 if consumers are very impatient. Likewise, let δs ∈ (0, 1) be the seller’s discount
factor of waiting until the second period for profits from the sale of the low quality
goods. Denote δc/δs by csδ .7
The seller will now choose qualities qhi and qh
b at prices phi and ph
b for release in
period 1, and possibly qli and ql
b at prices pli and pl
b for release in period 1 or 2, to solve
max,,,
,,,,bl
bh
il
ih
bl
bh
il
ih
ppppqqqq
−+
−
22 ihi
ihh
ili
ills qcpnqcpn βαδ
( ) ( )
−−+
−−+22
11 bhb
bhh
blb
blls qcpnqcpn βαδ (27)
subject to:
( ) ( )ih
ihl
il
illc pqvpqv −≥−δ (28a) ( ) ( )b
hbhl
bl
bllc pqvpqv −≥−δ (28b)
( ) ( )il
ilhc
ih
ihh pqvpqv −≥− δ (29a) ( ) ( )b
lblhc
bh
bhh pqvpqv −≥− δ (29b)
il
ill pqv ≥ (30a) b
lbll pqv ≥ (30b)
ih
ihh pqv ≥ (31a) b
hbhh pqv ≥ . (31b)
Proceeding in the same manner as in the previous section, we find that the prices for the
four levels of quality are
ill
il qvp = and b
lbll pqv ≥ . (32)
( )lhilc
ihh
ih vvqqvp −−= δ and ( )lh
blc
bhh
bh vvqqvp −−= δ . (33)
Substituting the four prices into the objective function and maximizing with respect to the
four levels of quality, we see that
−= R
cv
q cs
i
lil δ
αβ
12
and
−−−= R
cv
q cs
b
lbl δ
αβ
11
12
(34)
creates the potential to introduce four levels of quality over four periods. However, depending on the values of α, β, and R, it is not clear what products are introduced in what order. 7 Similarly denote δs/δc by s
cδ .
27
i
hih c
vq
2= and
r
hrh c
vq
2= . (35)
The seller’s profits are
i
hhcs
i
lls
cvn
Rc
vn4
14
222 βδαβαδ +
−=Π
b
hhcs
b
lls
cvn
Rc
vn4)1(
11
14
)1( 222 βδαβαδ −+
−−−−+ (36)
when βαδs
cR < . More generally, the maximum profits while introducing four products
sequentially over two periods are
( )
( )
( ) ( )
( )
−−≥−+
−−<≤
−−−−+−+
<
−−−−+
−+−+=
Π
βαδββ
βαδ
βαδδ
αβδββ
βαδδ
αβδ
δαβδββ
11
if4
14
)37(11
if11
14
14
14
if11
14
1
144
14
22
2222
22
2222
sc
b
hh
i
hh
sc
sc
cs
b
lls
b
hh
i
hh
sc
cs
b
lls
cs
i
lls
b
hh
i
hh
Rc
vncvn
RRc
vnac
vncvn
RRc
vna
Rc
vanc
vncvn
p
p
For our purposes, the important point to notice regarding the two period case is
that when α < β, the seller can use time and/or the market segmentation due to the digital
divide to mitigate the cannibalization problem, thereby increasing the quality of the low-
end good and increasing profits. Unfortunately, the problem for the two-channel case
becomes intractable if we try to solve for the specific conditions under which the seller
offers products simultaneously or sequentially. However, we can state that market
segmentation due to the digital divide has a similar effect on the marketplace as delayed
product entry, which makes delaying the offering of the low quality good less attractive
to the seller. It could well be the case that allowing the digital divide to exist allows the
low type consumers to be served in the marketplace faster by providing the seller the Sell
3 option as shown in the previous section. Without the digital divide, the low type
28
consumers may be forced to wait until a later time period for a product that is suitable for
them.
6. Conclusion
In this analysis we have shown that efforts to bridge the digital divide could have
some potentially negative consequences. While we certainly recognize the societal value
of providing full access to the information and communications capabilities associated
with using the Internet, we also recognize certain inefficiencies that result from bridging
the divide. Specifically, we have shown that the digital divide artificially segments the
marketplace into two distinct shopping channels. This allows a seller of a durable good
to more efficiently market its goods to different types of consumers – benefiting both the
seller and the buyers. In particular, we have shown how bridging the digital divide can
harm low type consumers when the likelihood of cannibalization of high quality goods is
relatively high. The digital divide allows low type consumers to be served in the offline,
brick-and-mortar channel when they otherwise might not be served at all. We have
shown how bridging the divide could cause the seller to cease marketing to low type
consumers entirely.
We have also examined how personalization technology allows the seller to move
from second-degree price discrimination toward first-degree discrimination where each
individual consumer is served according to his or her unique wants and needs. We have
shown how personalization allows the seller to increase prices to their high type
consumers in the online channel, and lessens the distortion caused by the cannibalization
problem. This reduction in the distortion increases the seller’s profits and decreases the
harm to low type consumers caused by high type cannibalization. We have shown that
significant personalization efforts can result in complete elimination of the
cannibalization inefficiencies in the online channel.
While certain parties seek to bridge the digital divide, this analysis suggests that
the buyers and sellers alike might be better served by efforts to improve the seller’s
ability to personalize its online offerings. Mechanisms that prohibit online merchants
from abusing collected information and consumer information databases would
encourage users to willingly submit personal information to online storefronts. User
29
apprehension regarding privacy abuses currently encourages Web users to avoid
submitting information or submitting inaccurate information. Inaccurate information
creates another distortion in the seller’s efforts to engage in personalization.
By examining the implications of the cannibalization problem and its relations to
the digital divide we have focused on only one of many issues related to the difficulties of
selling in multiple channels. The problems associated with channel conflict exist in many
forms. However, the distortion that occurs when high type consumers are allowed to
purchase products that are targeted at low type consumers is a serious problem that
affects the seller and the low type consumers. This analysis offers several implications
that those involved in the digital divide debate should consider.
30
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