Why Competition from a Multi-Channel E-Tailer Does Not Always Benefit Consumers

Transcription

1 Decision Sciences Volume 42 Number 1 February 2011 C 2011 The Auhors Decision Sciences Journal C 2011 Decision Sciences Insiue Why Compeiion from a Muli-Channel E-Tailer Does No Always Benefi Consumers Parick I. Jeffers Deparmen of Accouning, Law & CIS, Manhaan College, Riverdale, NY 10471, parick.jeffers@manhaan.edu Barrie R. Naul Haskayne School of Business, Universiy of Calgary, 2500 Universiy Drive NW, Calgary, Albera, Canada T2N 1N4, naul@ucalgary.ca ABSTRACT Empirical sudies have delivered mixed conclusions on wheher he widely acclaimed asserions of lower elecronic reail (e-ail) prices are rue and o wha exen hese prices impac convenional reail prices, profis, and consumer welfare. For goods ha require lile in-person pre- or possales suppor such as CDs, DVDs, and books, we exend Balasubramanian s e-ailer-in-he-cener, spaial, circular marke model o examine he impac of a mulichannel e-ailer s presence on reailers decisions o relocae, on reail prices and profis, and consumer welfare. We demonsrae several couner-inuiive resuls. For example, when he disuiliy of buying online and shipping coss are relaively low, reailers are beer off by no relocaing in response o an e-ailer s enry ino he reail channel. In addiion, such an enry a mulichannel sraegy may lead o increased reail prices and increased profis across he indusry. Finally, consumers can be beer off wih less channel compeiion. The underlying message is ha inferences regarding prices, profis, and consumer welfare criically depend on specificaions of he good, disuiliy and shipping coss versus ransporaion coss (or more generally, posiioning), and compeiion. Subjec Areas: Channels, E-Commerce, and Pricing. INTRODUCTION AND BACKGROUND Commercializaion of he Inerne has capured he aenion of researchers and businesses alike. Business-o-consumer (B2C) e-commerce or e-ailing promised compeiively deermined, convergen prices ha could improve profis and consumer welfare. However, he impac of on-line prices on reail prices, profis, and consumer welfare is no clear, in par because compeiion now includes We hank he Naural Science and Engineering Research and he Social Science and Humaniies Research Councils of Canada, and he David B. Robson Professorship Endowmen and he Informaics Research Cener in he Haskayne School of Business a he Universiy of Calgary for suppor. Corresponding auhor. 69

2 70 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers e-ailing as par of mulichannel reailing sraegies. In his research we ask wheher such a mulichannel sraegy helps o heighen or suppress he expeced impac of e-commerce on reail prices, profi, and welfare. Research has shown ha prices are influenced by hose in nearby markes (Asplund & Sandlin, 1999). Moreover, even online, or e-ail, sales are affeced by he proximiy of reailers (Forman, Ghose, & Goldfarb, 2009). Inuiively, e-ail prices should exer downward pressure on reail prices, as hey in urn converge (Goolsbee, 2001). Indeed, many well-known sudies hail he Inerne as a caalys for reduced prices. For example, Brynjolfsson and Smih (2000) showed ha e-ail prices for books were 9 16% lower han reail prices, and lower e-ail prices have also been found for cars (Sco Moron, Zeelmeyer, & Silva-Russo, 2001) and CDs (Lee, Chang, & Lee, 2003). E-ail prices for personal compuers (Goolsbee, 2001) and books (Chevalier & Goolsbee, 2003) were found o be sensiive o offline prices, showing ha reailers and e-ailers compee direcly. Tang & Xing (2001) found ha price dispersion was lower among e-ailers compared o mulichannel reailers for DVDs. Moreover, Xing, Yang, and Tang (2006) found mulichannel reailers charge higher prices for DVDs han e-ailers. Similar conclusions are echoed in oher empirical sudies (e.g., Brown & Goolsbee, 2002; Venkaesan, Meha, & Bapna, 2006). However, many sudies show ha e-ail prices are no always lower han reail prices and do no necessarily converge. Clay, Krishnan, Wolff, and Fernandez (2002) found similar average prices for books online as a reailers, wih subsanial dispersion online. Clemons, Hahn, and Hi (2002) found ha airline icke prices vary by as much as 18% online, Baylis & Perloff (2002) found price dispersion in cameras and scanners online, as did Baye, Margan, and Scholen (2004) for a range of consumer producs. Research on sofware and personal digial appliances concluded ha firms can avoid price compeiion by selling a wider variey of producs (Bailey, Faraj, & Yuliang 2007). Ancarani & Shankar (2004) showed ha for a variey of producs, inclusion of shipping coss resuled in mulichannel reailers having he highes prices, followed by e-ailers and reailers. Finally, some research shows insances where e-ail prices are higher han reail prices (Ancarani, 2002; Le Blanc & Folkman Curasi, 2002; Schmiz & Lazer, 2002). A good review can be found in Xing, Rachford, and Shankar (2004). Our Focus We consider a marke for goods ha require lile in-person pre- or possales suppor, so ha proximiy o a reailer is relaively unimporan for e-ail sales. Examples include CDs, DVDs, and books. Our model begins wih a baseline marke configuraion of wo reailers and an e-ailer as in Balasubramanian s (1998) model. From his baseline we address compeiion in he e-ail channel, and afer an e-ailer eners he reail channel. The resuls of his laer analysis depend on wheher reailers relocae. If hey do no relocae i is oo cosly or i is no profiable o do so hen here are hree equilibrium cases. We solve for equilibrium reail and e-ail prices, reailers and e-ailer s profis, and oal coss o consumers our measure of consumer welfare for each marke configuraion. The criical deerminan of prices, profis and consumer welfare in each marke configuraion is he raio of he e-ail ransacion coss relaive o he uni

3 Jeffers and Naul 71 ransporaion cos, a measure we call he e-ail cos raio. E-ail ransacion coss capure he disuiliy of purchasing online including limiaions in fully assessing he produc before purchase as well as shipping and handling coss. The alernaive o purchasing hrough he e-ail channel is physically raveling o he reailer a a uni ransporaion cos imes he disance raveled. Thus, he naure of he good is manifes in he e-ail cos raio: a low e-ail cos raio is indicaive of more homogeneous goods (books, CDs, ec.), as opposed o goods whose qualiy may be more difficul o assess (e.g., prepackaged Omaha seaks). Our main findings are educed from a comparison of he resuls obained from he differen marke configuraions and can be summarized as follows: firs, if reail relocaion is cosly and he e-ail cos raio is low, hen reailers should no relocae in response o an e-ailer enering he reail channel. A low e-ail cos raio means ha he e-ail channel is he main compeiion faced by each reail oule, and relocaion does no miigae ha hrea. Second, here are several condiions under which an e-ailer in he reail channel increases reail prices. Inuiively, reail prices should fall wih addiional reail locaions, bu his expeced oucome is confounded wih he e-ailer s mulichannel price-seing sraegy. Third, and relaed o he reail price resuls, indusry profis can increase as a resul of an e-ailer s enry ino he reail channel. Finally, we find condiions under which consumers are beer off wih less compeiion in reail locaions. Alhough our model is based in par on he physical locaion of reailers and is resriced o goods ha require lile pre- and possales service, he applicaion of our model, and he implicaions of he resuls, is broader. Raher han physical locaion, locaion could be considered as combinaions of cusomer service feaures or oher dimensions over which consumers have heerogeneous preferences. Wih his inerpreaion reail locaion and relocaion are choices of posiioning, and our resuls coninue o apply wihin his conex. We proceed by firs oulining he srucure of our model and solve for prices, profis, and consumer coss in each of he various marke configuraions deailed above. Then we presen our main resuls in a series of heorems. We finish wih conclusions summarizing he resuls. THE MODEL Our model seing is a circular spaial marke of he ype analyzed by Salop (1979) wih a coninuum of consumers, x [0, 1] spread uniformly around a uni circumference. Each consumer is in he marke for one uni of he good, consumpion of which yields uiliy U R +, ha we assume is large enough so ha demand is inelasic and reailers compee for heir business. All ransporaion occurs along he circle and is subjec o a uni cos R +. Consumers have equal access o informaion regarding prices. The consumers objecive is o maximize heir uiliy, which, wih inelasic demand, is equivalen o minimizing he sum of he ransporaion cos incurred, x, plus he price paid for he good, p r. Reailers operae brick-and-morar oules selling idenical producs wih marginal cos normalized o zero. Each reailer is aware of he oher s offering price, and faces a fixed enry cos f R +. To make our analysis more racable, we assume ha 4 /f < 9 which in he basic Salop model resuls in an equilibrium

4 72 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers Figure 1: E-ail enry. wih wo reailers (Tirole, 1988) when necessary. We index hese convenional reailers as r {A, B}. In his circular seing, each reailer gains by locaing as far as possible from compeiors (De Fruos, Hamoudi, & Jarque, 1999), hence our locaion of he wo reailers a opposie sides of he circle (Figure 1). In a sylized model of his ype he precise measuremen of /f is no obvious because of he way he parameers are scaled he issue is ha he relaionship beween ransporaion coss and enry coss deermines he number of reailers in Salop s model. The qualiaive characerisics of our resuls exend o a Salop model ha begins wih differen numbers of reailers. Our saring poin is Balasubramanian s (1998) model where we assume he marke is in equilibrium wih wo reailers and sunk enry coss, and an e-ailer ha compees wih each reailer. We hen model he following sequence of acions: (i) reailers decide wheher o ener he e-ail channel; (ii) he e-ailer decides wheher o ener he reail channel; and (iii) reailers decide wheher o relocae in response o he e-ailer s enry ino he reail channel. Our Saring Poin: Balasubramanian s 1998 Model Balasubramanian s model seup is Salop s model in equilibrium, in which each reailer has a fixed posiion a equal disance from each oher on he circumference and an e-ailer is sied a he virual cener wih equal access o he enire marke. The e-ailer offers he idenical good o consumers a an effecive price of p e + μ, where he e-ail price is p e and μ R + is he e-ail ransacion cos ha does no vary wih disance. I includes shipping and handling coss and could also capure a disuiliy cos (prospecive adverse selecion) of purchasing elecronically. The locaion of a consumer ha is indifferen beween purchasing from he e-ailer or a reailer is deermined by he indifference equaion p e + μ = p r + x, giving he indifferen consumer s disance away from a reailer as x = [p e p r + μ]/. Consumers closer o a given reailer han x purchase from ha reailer, while hose furher away purchase from he e-ailer. Figure 1 shows he wo-reailer Balasubramanian model. The e-ailer s and reailers marke shares are, respecively, m e = 1 4x and m r = 2x. Each reailer s profi maximizaion problem is [ max π r = max {p r 2 p ]} e p r + μ, (1) p r p r

5 Jeffers and Naul 73 and he e-ailer s profi maximizaion problem is [ max π e = max {p e 1 4 p ]} e p r + μ p e p e assuming no e-ail enry coss. The resuling e-ail and reail Nash equilibrium prices are pe b = /6 μ/3 and pb r = /12 + μ/3, (2) where we use he superscrip b o indicae Balasubramanian s model. Defining he e-ail cos raio as μ/, he e-ail price is posiive only if μ/ < 1/2, and we resric our aenion o his case for he remainder of he analysis. A he prices in Equaion (2) he indifferen consumer is locaed a x = 1/12 + μ/3. Each reailer s marke share is m r = 1/6 + 2μ/3 and he e-ailer s marke share is m e = 2/3 4 μ/3. Profis are π b r = [ + 4μ]2 /72 and π b e = [ 2μ]2 /9. (3) The oal cos o consumers is made up of profis plus he coss of ransporaion and disuiliy. Leaving he algebra for Appendix A his oal cos is ω b = μ 16μ 2. (4) 72 The reail price is higher han he e-ail price when μ/ > 1/8. For he e-ailer, prices are decreasing in μ, while for he reailer prices are increasing in μ. When μ = 0, he e-ailer s marke share is 2/3, leaving 1/3 of he marke o be shared beween he wo reailers. Boh he e-ailer s, and he reailers prices are increasing in, since increasing ransporaion coss implies increased differeniaion in he marke, which makes consumer response less elasic. Facing e-ail compeiion, he reailer s price is always lower han oherwise, and hus all consumers are beer off wih compeiion from an e-ailer. Reailers Decide Wheher To Go E-Tail One response reailers may choose when faced wih compeiion from an e-ailer is o ener he e-ail channel. Wihou differeniaion, oucome of compeiion in he e-ail channel is a unique equilibrium in which each charge marginal cos hrough he e-ail channel, which, wih marginal coss normalized o zero, yields p c e = 0, where he superscrip c indicaes e-ail compeiion. Consequenly here are zero e-ail profis. This is he classic Berrand Paradox whereby, wih undiffereniaed compeiion, prices fall o marginal cos. Marginal cos e-ail prices as a resul of eiher or boh reailers enering he e-ail channel diminish reail profis in all of our subsequen marke configuraions. Because all reail prices are affeced by price compeiion from he e-ail channel, firms are beer off avoiding direc compeiion (Judd, 1985; Bahn & Fischer, 2003). Consequenly, any marke configuraion ha follows from a reailer enering he e-ail channel canno be reached in equilibrium.

6 74 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers The E-Tailer Decides Wheher To Go Reail An addiional sraegy for he e-ailer is o ener he reail channel. An example of his is in he personal compuer indusry where boh Apple and Gaeway expanded ino he reail channel around 1997 (Prince, 2007). Since hen Dell and ohers have expanded ino exising reail sores like Bes Buy. The oucome of he e-ailer s reail presence depends in par on wheher he reailer compeior can relocae. Our analysis proceeds by considering he subsequen oucomes depending on wheher reailers can relocae. We solve for and compare prices, profis and welfare resuling from each possible marke configuraion given our model s consrains. Reailers relocae When reailers can relocae, he analysis proceeds in wo sages: firs, reailers decide where o relocae, and hen he e-ailer, he e-ailer s reail oule, and reailers compee in prices. We examine hese in reverse order. The price compeiion in he laer sage also arises if here were iniially hree reailers, and one was firs o ener he e-ail channel. Sage 2: Reail relocaion The criical issue in examining wha occurs when reailers relocae is wheher hey compee (i) wih each oher, (ii) wih he e-ailer s reail oule, or (iii) wih he e-ailer. The following lemma shows ha if he e-ail channel has posiive marke share, hen he reailers and he e-ailer s reail oule all compee wih he e-ail channel. Proofs are available in Appendix A. Lemma 1: Reail relocaion is such ha eiher (a) boh reailers and he e-ailer s reail oule compee wih he e-ail channel, or (b) he e-ail channel has no marke share, and he e-ailer s reail oule and reailers compee. Taking he e-ail cos raio, μ/, o be small enough so ha he e-ail channel has posiive marke share, he consequence of Lemma 1 is ha relocaion serves o disance he reailers from he e-ailer s reail oule and from each oher so ha hey all compee wih he e-ail channel. Indeed, here is no unique opimal relocaion poin for reailers avoiding direc compeiion wih oher reail oules is he crucial elemen of heir relocaion sraegy. Wih wo reailers in he model se-up, using resuls from Balasubramanian (1998), as μ/ becomes large such ha μ/ 1/2 he e-ail price becomes zero, and consequenly any fixed cos of enry is oo large for he e-ailer s reail oule o be launched profiably. Sage 1: Prices Assume for he momen ha he e-ail channel reains a posiive marke share afer e-ailer enry ino he reail channel and he reailers relocaion. Figure 2 depics when he wo reailers and he e-ailer s reail oule locae equidisanly from each oher. The consumer indifferen beween purchasing from a reailer or hrough he e-ail channel is defined by p r + x = p e + μ, giving x = [p e p r + μ]/. Because he e-ailer s reail oule is also compeing agains is e-ail channel, he consumer ha is indifferen beween purchasing from he e-ailer s reail oule

7 Jeffers and Naul 75 Figure 2: E-ailer goes reail, reailers relocae. and he e-ail channel is deermined by p er + y = p e + μ, where y = [p e p er + μ]/ represens he disance away from he e-ailer s reail oule. Each reailer s marke share is m r = 2x, he e-ailer s reail marke share is m er = 2y, and he e-ail porion of he marke is defined as uniy, less he sum of he wo reailer s shares and he e-ailer s reail share: m e = 1 2m r m er = 1 4x 2y. The e-ailer s profi maximizaion problem is now max p e,p er π e = max p e,p er [ {p e 1 4 p e p r + μ + p er [ 2 p e p er + μ The wo firs-order condiions are π e = 12p e + 4p r + 4p er 6μ = 0 p e 2 p e p er + μ ]}. (5) and π e = 4p e 4p er + 2μ = 0, p er (6) where he laer equaion can be more usefully wrien as p er = p e + μ/2. Because each reailer s marke share is deermined by he same indifference equaion as in Balasubramanian s model, each reailer s profi maximizaion problem is he same as Equaion (1), and he firs-order condiion yields p r = [p e + μ]/2. (7) Subsiuing hese wo prices ino Equaion (6) we can solve for p e, and hen for he remaining prices. Using superscrip r o indicae he case when he reailers relocae, his yields ] p r e = /6 μ/3, pr er = /6 + μ/6 and pr r = /12 + μ/3. (8) The e-ail and reail prices are he same as in Balasubramanian s model. Consequenly, each reailer s marke share and profi remains as before (Equaion (3)). Prices from Equaion (8) give x = 1/12 + μ/3 (same as Balasubrmanian s model) and y = μ/2. For here o be a posiive e-ail marke share requires m er + 2m r = 2y + 4x <1. Using Equaion (8) o find he values for x and y implies ha μ/ < 2/7 = (9)

8 76 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers Figure 3: E-ailer goes reail; all reailers compee wih e-ail channel. Thus, Equaion (9) defines he range of he e-ail cos raio where here is a posiive e-ail marke share. For he e-ailer, profis are πe r = pr e m e + per r m er = 17μ2 8μ = 14μ2 11μ μ 6 18 [ μ ] + 1, (10) where he erms on he righ hand side of he las equaliy are from he e-ailer s e-ail and reail channels respecively. Comparing Equaion (10) o he e-ailer s profi in Equaion (3), he ne gain in profi from he e-ailer s decision o go reail is μ 2 /2 >0, meaning ha i is individually raional for he e-ailer o ener he reail channel. Leaving he algebra for Appendix A, he oal cos o consumers is he sum of reail and e-ail profis, he e-ail ransacion cos and ransporaion coss ω r = μ 34μ 2. (11) 72 Reailers do no relocae Consider now when high relocaion coss fix he reailers locaions. If he e-ailer eners he reail channel, hen i mus be sied in one of he wo e-ail wedges (Figure 3) in order o locae as far as possible from oher reailers. There are hree cases: Case 1, all reail oules (including he e-ailer s) compee wih he e-ail channel, Case 2, he e-ailer s reail oule compees only wih he reailers, or Case 3, he e-ailer s e-ail channel affecs prices wihou direcly compeing wih is reail oule. Case 1: All reailers compee wih he e-ail channel This firs case is shown in Figure 3 assuming ha he e-ailer esablished is reail oule in he lower e-ail wedge. In his case all reailers, including he e-ailer s reail oule, compee wih he e-ail channel. The consumer indifferen beween purchasing from he e-ail channel or a reailer is defined by p r + x = p e + μ, orx = [p e p r + μ]/. Similar o when reailers relocae, le y represen he cusomer ha is indifferen beween

9 Jeffers and Naul 77 Figure 4: E-ailer has no presence in lower half. purchasing from he e-ail channel or he e-ailer s reail oule, such ha p er + y = p e + μ, giving y = [p e p er + μ]/. We assume for he momen ha x + y 1/4, ha is, he e-ailer has a (weakly) posiive e-ail marke share in he lower half of Figure 3. The oal e-ail marke share is represened by he wedge on he upper half of Figure 3 and he wo smaller segmens beween x and y on he lower half, m e = 2[1/4 x] + 2[1/4 x y] = 1 4x 2y. The e-ailer s reail marke share is m er = 2y hereby giving he e-ailer a oal marke share of 1 4x. The e-ailer s profi maximizaion problem is max π e = max p e,p er p e,p er [ {p e 1 4 p e p r + μ + p er [ 2 p e p er + μ ]}, 2 p ] e p er + μ (12) which is idenical o Equaion (5). In addiion, he reailers profi maximizaion is he same as Equaion (1), and he firs order condiion yields Equaion (7). The same facors deermine marke share for he reailers and he e-ailer in his case as when he reailers can relocae; consequenly, prices are as in Equaion (8), reailer profis are he same as in Equaion (3), and e-ailer profis are as in Equaion (10). As before, he ne gain o he e-ailer enering he reail channel is posiive, so i is individually raional for he e-ailer o do so. Moreover, because he same proporions of consumers are covered by he wo reailers, he e-ailer s reail oule, and he e-ail channel, he oal e-ail ransacion cos and ransporaion coss are given by Equaion (A2) in Appendix A, and he oal cos o consumers is given by Equaion (11). Consider he consrain x + y 1/4. A he equilibrium prices in his case given by Equaion (8) and Equaion (10), his consrain is saisfied if μ/ 1/5. (13) Thus, Equaion (13) defines Case 1, and when his consrain is saisfied prices and profis are he same regardless of wheher reailers can relocae. Case 2: E-ailer s reail oule compees direcly wih reailers This case is depiced in Figure 4. There is no e-ail share in he lower porion of he marke, and he e-ailer s reail oule compees direcly wih he reailers, while he e-ail channel compees wih he reailers in he upper porion of Figure 4.

10 78 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers In he upper porion of Figure 4, as before, he consumer ha is indifferen beween purchasing from he e-ail channel or from a reailer is defined by p r + x = p e + μ, giving x = [p e p r + μ]/. In he lower porion of Figure 4 he consumer ha is indifferen beween purchasing from he e-ailer s reail oule or a reailer is represened by z and is defined by p er + [1/4 z] = p r + z, giving z = [p er p r ]/2 + 1/8. For he e-ail channel o have no marke share in he lower porion of Figure 4, he cos a z of purchasing from he e-ail channel mus be (weakly) greaer han he cos of purchasing from eiher reailer, or he e-ailer s reail oule: p er + [1/4 z] = p r + z p e + μ. (14) Wih hese definiions we can wrie he hree marke shares as m r = x + z, m e = 1/2 2x, and m er = 1/2 2z. For reailers he profi maximizaion problem is { [ pe p r + μ max π r = max{p r [x + z]} =max p r + p er p r + 1 ]}, p r p r p r 2 8 and heir firs-order condiion is π r = p e 3p r + μ + p er + 1 = 0. (15) p r 2 8 For he e-ailer he profi maximizaion problem is max π e = max{p e M e + p er M er } p e,p er p e,p er [ ] [ ]} {p e 2x + p er 2z = max p e,p er = max p e,p er { [ ] [ 1 p e 2 2p e p r + μ 1 + p er 2 2p er p r 2 The wo firs-order condiions are π e = 1 p e 2 4p e 2p r + 2μ = 0 and π e = 1 p er 4 2p er p r 2 8 ]}. = 0. (16) Using he superscrip n2 o denoe his second case when reailers canno relocae, soluions o he hree firs-order condiions in Equaion (15) and Equaion (16) give he following prices p n2 e = 7/36 7μ/18, p n2 er = 7/36 + μ/9 and pn2 r = 5/36 + 2μ/9. (17) Prices from Equaion (17) give x = 1/18 + 7μ/18 and z = 11/72 μ/18. The profis for he reailers and for he e-ailer are, respecively πr n2 = μ + 64μ 2 and 864 π n2 e = p n2 e m e + p n2 er m er = μ + 136μ Checking our consrain Equaion (14) we have μ μ 18, (18)

11 Jeffers and Naul 79 which simplifies o 7/32 μ/. (19) The inequaliy in Equaion (19) represens he upper limi of he e-ail cos raio such ha he e-ailer s reail oule and e-ail channel do no direcly compee, and defines he range over which Case 2 applies. Wih Equaion (19), he ne gain for he e-ailer from enering he reail channel is posiive and i is raional for he e-ailer o ener. Again leaving he algebra for Appendix A, he oal cos o consumers is he sum of reail and e-ail profis, and he e-ail ransacion cos and ransporaion coss: ω n2 = μ 136μ 2. (20) 864 Case 3: E-ail channel affecs prices wihou gaining a share in lower porion of he marke Consider he consrains from Cases 1 and 2, ha is Equaion (13) and Equaion (19). Combining hose consrains leaves 1/5 μ/ 7/32. (21) In his case Case 3, he e-ail channel does no share in he lower porion of he marke (Figure 3), alhough is e-ail prices can impac reail prices by providing consumers an alernaive channel and price. This is analogous o he kinked equilibrium in he Salop (1979) model. To deermine prices and profis based on μ/ in his inerval, we reformulae he e-ailer s profis in Case 1 as a consrained opimizaion using a Lagrangian, where he marke shares are as in Case 1, ha is, m e = 1 4x 2y and m er = 2y: max L e = max p e,p er p e,p er [ {p e 1 4 p e p r + μ [ + p er 2 p e p er + μ ] 2 p ] e p er + μ [ 1 + λ 4 p e p r + μ p e p er + μ ]}, where he las erm embeds he consrain x + y 1/4. When he consrain is no binding we have he same problem as Equaion (12). When he consrain is binding he firs wo necessary condiions are similar o Equaion (6) bu wih an addiional erm from he consrain, L e = 12p e + 4p r + 4p er 6μ 2λ = 0, p e L e = 4p e + 2μ 4p er + λ = 0, p er and he hird condiion is L e / λ = 0 which resuls in he consrain saisfied wih equaliy. When his consrain is binding he relevan compeing price for reailers

12 80 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers is p er, so we can use he reailers firs-order condiion from Case 2, Equaion (15), as he necessary condiion for reailers o maximize profis. Using he superscrip n3 o denoe he case when he consrain x + y 1/4 binds, he prices ha resul from hese four equaions are p n3 e = 7/26 19μ/26, p n3 er = 7/52 + 5μ/13 and pn3 r = 2/13 + 2μ/13, (22) and he shadow price of he consrain is λ = 32μ/ /13. The e-ail price, p n3 e, is posiive if μ/ < 7/19, which is saisfied by he combined consrain Equaion (21). We can solve for marke share and profis of he reailers and he e-ailer. As in Case 2, in he upper porion consumers are indifferen beween a reailer and he e-ail channel a x, and in he lower porion beween a reailer and he e-ailer s reail channel a z. The marke share for he e-ail channel is m e = 1/2 2x and for he e-ailer s reail oule i is m er = 1/2 2z. Each reailer s marke share is m r = x + z. By subsiuing he resuls obained in Equaion (22), which are differen from he prices ha resuled in Case 2, we find x = 11/26 41μ/26 and z = 3/26 + 3μ/26. The profis from he e-ail channel and e-ailer s reail oule respecively are ( μ + 114μ 2 )/676 and ( μ 120μ 2 )/1352. Togeher his yields a oal profi of πe n3 = μ + 36μ 2. (23) 1352 Wih Equaion (21) he ne gain from enering he reail channel is posiive, and i is raional for he e-ailer o do so. Each reailer s profi is πr n3 = μ + 6μ 2. (24) 169 In Case 3, leaving he edious algebra for Appendix A, he oal cos o consumers is he sum of reail and e-ail profis, he e-ail ransacion cos and ransporaion coss ω n3 = μ μ 2. (25) 2704 MAIN RESULTS Our main resuls concern reail relocaion, reail prices, profis, and consumer welfare and all make use of he e-ail cos raio, μ/. Reail Relocaion When reailers do no relocae in response o he e-ailer s reail oule, our hree separae cases can be idenified using he e-ail cos raio: Case 1: The e-ail cos raio is low (μ/ 1/5 =.2). Case 2: The e-ail cos raio is high (μ/ 7/32 =.2188). Case 3: The e-ail cos raio is moderae (1/5 =.2 <μ/<.2188 = 7/32).

13 Jeffers and Naul 81 Our firs heorem saes when reailers should choose no o relocae in response o an e-ailer s enry ino he reail channel. Table 1 summarizes he profis and oal cos o consumers from our earlier analysis. Theorem 1: When an e-ailer eners he reail channel and relocaion coss are posiive, if he e-ail cos raio is less han.2623, hen reailers should no relocae. When he e-ail cos raio is low, he e-ail channel is compeiive even for consumers ha are beween reailers locaed relaively close o each oher. Therefore, a reailer s locaion relaive o he locaion of oher reailers does no affec heir profis so ha relocaion a any cos is no profi-maximizing. Moreover, even when he e-ail cos raio is moderae or in he lower segmen of high (less han.2623), profis are higher for reailers if hey do no relocae because he e-ail channel is a sronger compeiive force han he locaion of he e-ailer s reail oule. As we saw in he previous secion, when he e-ail cos raio is above.2857, from Equaion (9) where reailers can relocae, e-ailer enry ino he reail channel is no profiable, furher limiing he e-ail cos raio range where reailers should relocae. In pracice, if he e-ail cos raio is in he range defined in Theorem 1, hen i favors he e-ail channel o he exen ha all reail oules effecively compee wih he e-ail channel raher han wih each oher, and relocaion is no a profiable response. If he e-ail cos raio is low, hen reail relocaion also has implicaions for social welfare. This is given in he following corollary. Corollary 1: When an e-ailer eners he reail channel and relocaion coss are posiive, if he e-ail cos raio is less han.2, hen i is social welfare maximizing for reailers no o relocae. In Case 1 neiher individual reail or e-ail profis, nor consumer coss, are posiively impaced by relocaion; hus, he relocaion coss are a ne loss of social welfare. Reail Prices I is sraighforward ha compeiion in he e-ail channel causes reail prices o fall relaive o Balasubramanian s model. Addiional reail compeiion, however, does no always decrease prices. Our second heorem shows ha under cerain circumsances addiional reail compeiion from an e-ailer in he reail channel can increase reail prices. Table 2 summarizes prices from our analyses. Theorem 2: If reailers relocae, hen an e-ailer s reail oule weakly increases reail prices. Oherwise, if he e-ail cos raio is less han.2 (Case 1) or if i is beween.2188 and.25 (subse of Case 2), hen an e-ailer s reail oule increases reail prices. When here are no relocaion coss for reailers, heir response o reail enry by he e-ailer is o relocae and mainain heir prices as before o compee wih he e-ail channel. The e-ailer, however, ses is reail oule price o compee wih

14 82 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers Table 1: Profis and oal cos o consumers (DNR: do no relocae). Model Reailer Profi E-Tailer Profi Cos o Consumers Balasubramanian π b r = [ + 4μ]2 /72 π b e = [ 2 μ]2 /9 ω b = μ 16μ 2 72 Reailers Relocae π r r = [ + 4μ]2 /72 π r e = 17μ2 8μ ω r = μ 34μ 2 72 Reailers DNR Case 1 π n1 r = [ + 4μ] 2 /72 πe n1 = 17μ2 8μ ω n1 = μ 34μ 2 72 Reailers DNR Case 2 π n2 r = μ + 64μ π n2 e = μ + 136μ ω n2 = μ 136μ Reailers DNR Case 3 π n3 r = μ + 6μ π n3 e = μ + 36μ ω n3 = μ μ

15 Jeffers and Naul 83 Table 2: Prices. Model Conv. Reail E-Tail E-Tailer Reail Balasubramanian pr b = μ/3 + /12 pb e = /6 μ/3 Reailers Relocae pr r = /12 + μ/3 pr e = /6 μ/3 pr er = /6 + μ/6 Reailers DNR Case 1 p n1 r = /12 + μ/3 p n1 e = /6 μ/3 p n1 er = /6 + μ/6 Reailers DNR Case 2 p n2 r = 5/36 + 2μ/9 p n2 e = 7/36 7 μ/18 p n2 er = 7/36 + μ/9 Reailers DNR Case 3 p n3 r = 2/13 + 2μ/13 p n3 e = 7/26 19μ/26 p n3 er = 7/ is e-ail channel price (boom of Figure 2) and in his way is a mulichannel monopolis. As a resul, he e-ailer charges a higher price a is reail oule han reailers so ha i may gain greaer profi from hose consumers whose nex bes alernaive is o purchase from he e-ail channel. Therefore, compared o he presence of a pure e-ailer, reail prices faced by consumers are he same for hose closer o he reailers and are higher for hose closer o he e-ailer s reail oule. If relocaion coss are posiive such ha reailers do no relocae, hen here are differen cases o consider. If he e-ail cos raio is low (Case 1), hen he resuls are he same as when he reailers relocae (described above) reail prices are he same as, and he e-ailer s reail oule prices are higher han, reail prices in he Balasubramanian model. If he e-ail cos raio is high (Case 2), hen reail prices are higher han reail prices in he Balasubramanian model because compeiion on one end of each reailer s marke is wih he e-ailer s reail oule raher han wih he e-ail channel. If he e-ail cos raio is high bu no oo high hen prices a he e- ailer s reail oule are higher han reail prices in he Balasubramanian model for he same reason he e-ailer s reail oule compees wih reailers. In spie of his, if he e-ail cos raio is higher han.25, hen compeiion from he e-ail channel is miigaed by a relaively high disuiliy and shipping coss, and reail prices in he Balasubramanian model are greaer han hose a he e-ailer s reail oule. Ineresingly, when he e-ail cos raio is moderae he same siuaion arises whereby relaive o reail prices in he Balasubramanian model, reail prices are higher bu he e-ailer s reail oule price is lower. Profis Table 1 shows reail profis and e-ail profis for each marke configuraion. The addiional presence in he marke of a mulichannel e-ailer can increase profis. The nex heorem shows ha an e-ailer in he reail channel increases indusry profis. Theorem 3: Indusry profis are higher when he e-ailer sells hrough boh he e-ail and reail channels han when he e-ailer sells only hrough he e-ail channel. A mulichannel e-ailer yields higher profis for boh reailers as well as for he e-ailer. Allowing he e-ail and reail channels o compee direcly faciliaes opimizaion by way of marke forces, raher ha arificially imposing an upper limi on he marke share of any given channel (Figure 3). Even when he e-ail channel does no have marke share in he lower porion of he marke, his

16 84 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers is miigaed by he posiive exernaliies resuling from he reailers proximiy (Sahl, 1982; Tirole, 1988), while he e-ailer explois access o more remoely locaed segmens of he marke. Consumer Welfare Our measure of consumer welfare is he oal cos o consumers. This includes paymens o reailers and e-ailers plus he ransporaion coss, aggregaed over all consumers. Table 1 shows he oal cos o consumers for each marke configuraion. When he e-ailer eners he reail channel i adds anoher reail locaion from which consumers can purchase. We expec ha an addiional reail locaion increases reail compeiion, hereby decreasing reail prices, which in urn pus downward pressure on e-ail prices, making consumers beer off. Bu, as our nex heorem shows, when he e-ail cos raio is moderae and relocaion coss are such ha reailers do no relocae, he e-ailer in he reail channel decreases consumer welfare. Theorem 4: If he e-ail cos raio is moderae, beween.2 and.2947, and reailers do no relocae, hen consumers are worse off when he e-ailer eners he reail channel. Inuiively, when he e-ail cos raio is low (Case 1) consumers are affeced more significanly by ransporaion coss, and each reailer, including he e-ailers reail oule, compees wih he e-ail channel. As he e-ail cos raio increases ino he range covered by our Case 3, he e-ail channel has no share in he lower porion (of Figure 3), meaning all consumers in he lower porion purchase from reail locaions and pay ransporaion coss. Because he e-ailer chooses is e-ail price o compee wih reailers on he upper porion, and is reail price o compee wih reailers on he lower porion, consumer coss are increased due o he addiional ransporaion coss incurred in he lower porion. However, as he e-ail cos raio increases, addiional ransporaion coss paid by consumers in he lower porion is less significan, and he addiional reail locaion increases consumer welfare. CONCLUSIONS Our research has yielded four main resuls. Firs, if he e-ail cos raio is low, hen reailers do no relocae when faced wih reail channel enry from an e-ailer. When he e-ail cos raio is even lower, hen no relocaion is social welfare maximizing. Second, when reailers can relocae, enry of an e-ailer ino he reail channel increases reail prices. Third, indusry profis increase wih an e-ailer s enry ino he reail channel. Finally, when he e-ail cos raio is moderae, consumers are beer off wihou e-ailer enry ino he reail channel. We believe hese resuls hold even when here is differeniaed compeiion in he e-ail channel, as long as he differeniaion is independen of he locaion differeniaion in he reail channel. There are hree key messages from hese resuls. When he e-ail cos raio is low when he disuiliy of buying online and shipping coss are low hen reailers should reain heir original locaions and no relocae, because he

17 Jeffers and Naul 85 e-ail channel always compees direcly wih each reail oule boh reailers and he e-ailer s reail oule. The implicaion for managemen is ha under hese condiions relocaing is no an effecive sraegy for reailers o avoid direc e- ail compeiion. The nex message for managemen is ha an e-ailer s reail presence a mulichannel sraegy is a way for he indusry o increase reail prices and indusry profis. Consequenly, and perhaps surprisingly, consumers are no necessarily beer off wih an e-ailer in he reail channel. Indeed, here is a moderae range of he e-ail cos raio where consumer welfare is higher if he e-ailer does no ener he reail channel ha is, some consumers are beer off having fewer reail locaions o selec from. This is because in his range of he e-ail cos raio he reailers compee wih he e-ail channel on one side, and he e-ailer s reail channel on he oher side. In his siuaion he e-ailer s wo channels do no compee so is pricing decisions are separae, removing he downward pressure on is wo prices. This leads o our main message for researchers, which is ha even in his simple model, prices, profis, and consumer welfare are deermined by a variey of facors, and his may underlie he equivocal empirical resuls o dae concerning he impac of online reail compeiion on hese measures. For he ypes of goods o which our model applies, locaion is bes hough of as a physical locaion. However, as we indicaed in he inroducion, he applicaion of our model, and he implicaions of he resuls, is broader. Considering, for example, feaures of cusomer service such as service qualiy and cusomer relaionship managemen, he disribuion of consumers around he Salop model circle could be inerpreed as a disribuion of consumer preferences over combinaions of cusomer service feaures. Wih his inerpreaion of locaion, all consumers view he e-ail channel he same way. For example, Amazon s cusomer service feaures may be equally valued by all consumers. In urn, differen reailer locaions may be viewed by consumers as alernaive combinaions of cusomer service feaures, and in his way consumers may differ in heir preference for a given reailer. Thus, reail locaion and relocaion can be inerpreed as a choice of differen combinaions of cusomer service feaures or more generally, posiioning and wihin ha conex our resuls coninue o apply. A direcion for fuure research is o consider consumers ha are heerogeneous in heir e-ail ransacion cos eiher hrough a random disribuion of high-low coss or based on he need for pre- and possales suppor. [Received: Ocober Acceped: May 2010.] REFERENCES Ancarani, F. (2002). Pricing and inerne: Fricionless commerce or pricer s paradise. European Managemen Journal, 20(6), Ancarani, F., & Shankar, V. (2004). Price levels and price dispersion wihin and across muliple reailer ypes: Furher evidence and exension. Journal of he Academy of Markeing Science, 32(2), Asplund, M., & Sandlin, J. (1999). Compeiion in inerrelaed markes: An empirical sudy. Inernaional Journal of Indusrial Organizaion, 17(3),

18 86 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers Bahn, D., & Fischer, P. (2003). Click and morar: Balancing brick and morar business sraegy and operaions wih auxiliary elecronic commerce. Informaion Technology Managemen, 4(2/3), Bailey, J., Faraj, S., & Yuliang, Y. (2007). The road more ravelled: Web raffic and price compeiion in inerne reailing. Elecronic Markes, 17(1), Balasubramanian, S. (1998). Mall vs. mail: A sraegic analysis of compeiion beween direc markeers and convenional reailers. Markeing Science, 17(3), Baye, M. R., Morgan, J., & Scholen, P. (2004). Price dispersion in he small and he large: Evidence from an inerne price comparison sie. Journal of Indusrial Economics, 52(4), Baylis, K., & Perloff, J. M. (2002). Price dispersion on he inerne: Good firms and bad firms. Review of Indusrial Organizaion, 21(3), Brown, J. R., & Goolsbee, A. (2002). Does he inerne make markes more compeiive? Evidence from he life insurance indusry. Journal of Poliical Economy, 110(3), Brynjolfsson, E., & Smih, M. (2000). Fricionless commerce? A comparison of inerne and convenional reailers. Managemen Science, 46(4), Chevalier, J., & Goolsbee, A. (2003). Measuring prices and price compeiion online. Quaniaive Markeing and Economics, 1(2), Clay, K., Krishnan, R., Wolff, E., & Fernandes, D. (2002). Reail sraegies on he web: Price and non-price compeiion in he on-line book indusry. Journal of Indusrial Economics, 50(3), Clemons, E., Hahn, I. H., & Hi, L. (2002). Price dispersion and differeniaion in online ravel: An empirical invesigaion. Managemen Science, 48(4), De Fruos, M. A., Hamoudi, H., & Jarque, X. (1999). Equilibrium exisence in he circle model wih linear quadraic ransporaion cos. Regional Science and Urban Economics, 29(5), Forman, C., Ghose, A., & Goldfarb, A. (2009). Compeiion beween local and elecronic markes: How he benefi of buying online depends on where you live. Managemen Science, 55(1), Goolsbee, A. (2001). Compeiion in he compuer indusry: Online versus reail. Journal of Indusrial Economics, 49(4), Judd, K. (1985). Credible spaial preempion. Rand Journal of Economics, 16(1), Le Blanc, L. A., & Folkman Curasi, C. (2002). Differenial pricing for elecronics on he inerne and compeing channels. Quarerly Journal of Elecronic Commerce, 3(2), Lee, H. G., Lee, S., Chang, K. H. Y., & Lee, R. H. (2003). Is he inerne making reail ransacions more efficien? Comparison of online and off-line CD reail markes. Elecronic Commerce Research and Applicaions, 2(3),

19 Jeffers and Naul 87 Prince, J. T. (2007). The beginnings of online/reail compeiion and is origins: An applicaion o personal compuers. Inernaional Journal of Indusrial Organizaion, 25(1), Salop, S. (1979). Monopolisic compeiion wih ouside goods. Bell Journal of Economics, 10(1), Sco Moron, F., Zeelmeyer, F., & Silva-Risso, J. (2001). Inerne car reailing. Journal of Indusrial Economics, 49(4), Schmiz, S. W., & Lazer, M. (2002). Compeiion in B2C e-commerce: Analysis issues and empirical evidence. Elecronic Markes, 12(3), Sahl, K. (1982). Consumer search and he spaial disribuion of reailing. Journal of Indusrial Economics, 31(1/2), Tang, F., & Xing, X. (2001). Will he growh of muli-channel reailing diminish he pricing efficiency of he Web? Journal of Reailing, 77, Tirole, J. (1988) The heory of indusrial organizaion. Cambridge, MA: MIT Press. Venkaesan, R., Meha, K., & Bapna, R. (2006). Undersanding he consequences of reailer characerisics, marke characerisics and online pricing sraegies. Decision Suppor Sysems, 42(3), Xing, X., Rachford, B. T., & Shankar, V. (2004). Price dispersion on he inerne: A review and direcions for fuure research. Journal of Ineracive Markeing, 18(4), Xing, X., Yang, Z., & Tang, F. (2006). A comparison of ime-varying online price and price dispersion beween mulichannel and docom DVD reailers. Journal of Ineracive Markeing, 20(2), APPENDIX Balasubramanian s (1998) Model: Toal Cos o Consumers The oal e-ail ransacion cos o consumers is τ b e = μm e = 2μ/3 4μ 2 /3. The average disance for any consumer o a reailer is x/2. Because he marke share of he wo reailers is 2m r, he oal ransporaion cos incurred is τ b r = [x/2]2m r = 2x 2 = [4μ + ] 2 /72. (A1) Togeher, he oal e-ail ransacion cos and ransporaion coss are τ b = τe b + τ r b = μ 80μ 2, 72 and he oal cos o consumers is as in Equaion (4): ω b = 2πr b + π e b + τ b = μ 16μ Proof of Lemma 1: By conradicion. Consider when he e-ail channel has a posiive marke share. Firs, suppose ha a he opimal locaion and a equilibrium prices here is no e-ail share beween reailers. This means reailers prefer o

20 88 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers compee wih each oher han wih he e-ail channel. For x half way beween he wo reailers, his means ha p r + x > p e + μ so a x hey have less compeiion. Bu if his is rue, hen he consumer a x will purchase from e-ail. Nex, suppose ha a he opimal locaion and a equilibrium prices here is no e-ail share beween he reailers and he e-ailer s reail oule. This means reailers prefer o compee wih he e-ailer s reail oule. Then for consumer y ha is indifferen beween reail and he e-ailer s reail oule his means p er + y > p e + μ. Bu if his is rue, hen consumer y will purchase from e-ail. The E-ailer Goes Reail and Reailers Relocae: Toal Cos o Consumers The oal e-ail ransacion cos o consumers is τ r e = μm e = μ[1 4x 2y] = μ[2/3 7μ/3] = 2μ/3 7μ 2 /3. Thus, for m e > 0 requires μ/ < 2/7. As in Balasubramanian s (1998) model, he ransporaion cos incurred o he wo reailers is [4 μ + ] 2 /72 from Equaion (A1). The average disance is y/2 = μ/4. The ransporaion cos incurred o he e-ailer s reail oule is hen [μ/4]m er = μ 2 /4, and he oal ransporaion cos incurred is τ r r = [4μ + ] μ2 4 = 2 + 8μ + 34μ Togeher, he oal e-ail ransacion cos and ransporaion coss are τ r = τe r + τ r r = μ 134μ 2, (A2) 72 and he oal cos o consumers is ω r = 2πr r + π e r + τ r = μ 34μ The E-ailer Goes Reail and Reailers do no Relocae: Toal Cos o Consumers in Case 2 The average disance for any consumer in he upper porion o a reailer is x/2. The oal e-ail ransacion cos o consumers is τ n2 e = μm e = μ[1/2 2x] = 7μ/18 7μ 2 /9. The average disance for any consumer in he lower porion o a reailer is z/2. The marke share for each reailer in he upper porion is x, and in he lower porion i is z. Thus, he ransporaion cos incurred o he wo reailers oules is 2[x 2 /2 + z 2 /2] = [x 2 + z 2 ] = μ + 800μ The average disance from a consumer purchasing from he e-ailer s reail oule is [1/4 z]/2. The ransporaion cos incurred o he e-ailer s reail oule is m er [1/4 z]/2 = [1/2 2z][1/4 z]/2 = /16 z/2 + z 2 = μ + 16μ 2, 5184

21 Jeffers and Naul 89 and he oal ransporaion cos incurred is τr n2 = μ + 136μ Togeher, he oal e-ail ransacion cos and ransporaion coss are τ n2 = τe n2 + τr n2 = μ 536μ 2, 864 and he oal cos o cusomers is ω n2 = 2π n2 r + πe n2 + τ n2 = μ 136μ The E-ailer Goes Reail and Reailers do no Relocae: Toal Cos o Consumers in Case 3 The srucure of oal e-ail ransacion coss and ransporaion coss is he same as in Case 2, bu wih prices from Equaion (22). The average disance for any consumer in he upper porion o a reailer is x/2. The oal e-ail ransacion cos o consumers is τ n3 e = μm e = μ[1/2 2x] = 9μ/ μ 2 /26. The average disance for any consumer in he lower porion o a reailer is z/2. The ransporaion cos incurred o he wo reailers oules is 2[x 2 /2 + z 2 /2] = [x 2 + z 2 ] = μ + 65μ The average disance for a consumer purchasing from he e-ailer s reail oule is [1/4 z]/2, so he ransporaion cos incurred o he e-ailer s reail oule is m er [1/4 z]/2 = μ + 36μ 2, 2704 and he oal ransporaion cos incurred is τr n3 = μ μ Togeher he oal e-ail ransacion and ransporaion coss are τ n3 = μ μ 2, 2704 and he oal cos o consumers is ω n3 = 2π n3 r + πe n3 + τ n3 = μ μ Proof of Theorem 1: When he e-ail cos raio is low (Case 1), reail profis are he same wheher or no reailers relocae (Equaion (3)). When he e-ail cos raio is moderae (Case 3), reail profis if reailers do no relocae (Equaion (24)) are greaer han he reail profis if hey relocae (Equaion (3)). Finally, for

22 90 Why Compeiion from a Mulichannel E-Tailer Does No Always Benefi Consumers μ/ <.2623 (a subse of Case 2), reail profis if reailers do no relocae are given in Equaion (18), and hese reail profis are greaer han he reail profis if hey relocae (Equaion (3)). Proof of Corollary o Theorem 1: If he e-ail cos raio is low (Case 1), hen reail profis, e-ail profis, and he oal cos o consumers are given in Equaions (3), (10), and (11) respecively independen of wheher reailers relocae. Proof of Theorem 2: If reail relocaion is cosless, hen reailers relocae and he reailers prices are he same as in Balasubramanian s model. From Equaion (8) (and Equaion (2)) we find ha pr r (= pb r ) <pr er. Oherwise, Case 1 applies for μ/.2 and Case 2 for.2188 μ/ <.25. Comparing pr b from Equaion (2) wih reail prices in Cases 1 and 2 (pr r from Equaion (8) as Case 1 reail prices are he same as when reailers can relocae; p n2 r from Equaion (17)) we find ha pr b = pr r <pn2 r. Thus, reail prices are equal or higher when he e-ailer has a reail oule. For Case 1 from Equaions (2) and (8) we have pr b <pr er. For Case 2 from Equaions (2) and (17) we have pb r <pn2 er if μ/ <.25. Proof of Theorem 3: Firs consider when reailers relocae. Reail profis are he same as when he e-ailer sells only hrough he e-ail channel. For he e-ailer, profis from Equaion (10) are greaer han hose in Equaion (3). Now consider when reailers do no relocae. In Case 1 reail profis are he same as when he e-ailer only sells hrough he e-ail channel, and e-ailer profis from Equaion (10) are greaer han hose in Equaion (3) boh as above. In Case 3 reailer profis in Equaion (24) are greaer han hose in Equaion (3), and e-ailer profis in Equaion (23) are greaer han hose in Equaion (3). Finally, in Case 2 e-ailer profis are higher in Equaion (18) han hose in Equaion (3). However, reailer profis in Equaion (18) are only greaer han hose in Equaion (3) if he e-ail cos raio is less han.3061, and he sum of e-ailer and reail profis (noing here are wo reailers) in Equaion (18) is greaer han he sum of hose in Equaion (3). Proof of Theorem 4: If.2 <μ/.2188, hen from a comparison of Equaion (25) and Equaion (4) i is sraighforward ha ω 3 >ω b. If.2188 μ/ <.2947, hen from a comparison of Equaions (20) and (4) i is sraighforward ha ω 2 > ω b. Parick I. Jeffers is an assisan professor in he Deparmen of Accoun, Law, and CIS a Manhaan College, Bronx, New York. He holds a PhD in managemen informaion sysems from The Ohio Sae Universiy. His research ineress include he sraegic deploymen of informaion sysems in logisics and supply chains, elecronic commerce, and e-governmen. His work has been published in Inernaional Journal of Operaions and Producion Managemen, IEEE Transacions, and he Journal of Global IT Managemen.