a multi-channel model of separating equilibrium in the face of...

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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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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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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

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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.

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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

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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

qq

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)



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−


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−


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)



−= 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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