Reach Versus Competition in Channels with Internet and Traditional Retailers

Transcription

1 Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Bai R Nault Haskayn School of Businss, Univsity of Calgay, Calgay, Albta, Canada, nault@ucalgayca Mohammad S Rahman Haskayn School of Businss, Univsity of Calgay, Calgay, Albta, Canada, ahman@ucalgayca W xamin th statgic and wlfa implications of comptition btwn taditional (tail) and Intnt channls fo goods wh chaactistics such as tust in th sll, tuns, aft-sals suppot, and physical inspction a impotant Tming ths as fixd onlin disutility costs, w dvlop xtnsions to two paadigm modls th Salop (1979) cicl aound th lak modl and th Balasubamanian (1998) pu -tail in th cnt modl to includ taditional tails slling though th Intnt channl In ths xtnsions, w concptualiz and spcify how th onlin disutility costs of puchasing can b mitigatd if th puchas is fom a dual-channl tail, dfining th xtnt of mitigation as a function of distanc fom th taditional physical outlt W compa ths fou modls in pics, pofits, consum, and social wlfa W find that th impact of comptition fom a pu -tail and ach fom dual-channl tails in th Intnt channl impovs consum wlfa whil at th sam tim lowing social fficincy This is bcaus consums incu gat onlin disutility costs than tanspotation costs in od to obtain low pics that sult fom onlin comptition W also find that consums do not civ th advantags of mitigation of onlin disutility costs whn ths costs a high as dual-channl tail pics in both channls a gat than thy a in th psnc of a pu -tail Yt th vs occus whn onlin disutility costs a low as this incass th comptition btwn th dual-channl tails Intnt channls Howv, it is only pofitabl fo taditional tails to xtnd into th Intnt channl if th onlin disutility costs a high nough to fostall a pu -tail Takn togth, ou sults show how th xtnsion of makt ach whn taditional tails also sll though th Intnt channl can confound th ffcts of comptition Ky wods : makt ach, channl comptition, onlin disutility costs, consum wlfa, social wlfa Histoy : 1 Intoduction & Backgound Consums gnally bliv that a wid slction of channls fom which to puchas bnfits thm and socity a vsion of mo is btt This is spcially tu in th lctonic tail, o -tail, wold of Intnt commc wh in addition to gat ach, gat comptition fom, and in, Intnt channls is commonly viwd as having advantags fo consums Howv, this blif is basd on th assumption that mo channls do not ngativly alt conditions consums xpinc in xisting channls Dspit th psnc of dual-channl (taditional and Intnt) 1

2 2 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails tails in most industis, th a fw sults that valuat th bnfit of having a taditional tail sto linkd to th Intnt channl, fo consums and fo socity Fo xampl, w do not find quivocal vidnc about whth th psnc of dual-channl tails matts vn in pics In paticula, Clay t al (2002) found simila book pics though th Intnt and taditional tail In contast, Chvali and Goolsb (2003) found Intnt pics fo books w snsitiv to dual-channl tail pics, and Goolsb (2001) found that th dcision to buy computs onlin is snsitiv to th lativ pic of such in taditional tail stos What is cla fom pio sach is that Intnt pics a highly vaiabl Clay t al (2002) found gat pic dispsion fo books though Intnt channls, as did Baylis and Ploff (2002) fo camas and scanns, Tang and Xing (2001) fo DVDs, Clmons t al (2002) fo ailin tickts, and Bay t al (2004) fo oth tail poducts Most of this sach studid homognous sach goods such as CDs, books, and DVDs (Iy and Pazgal 2003), a typ of good fo which th is limitd impact of channl and sll chaactistics This suggsts that, spcially in cass wh th is a significant ffct of channl and sll attibuts, it is not staightfowad to chaactiz th statgic and wlfa implications of comptitiv makt stuctus that may involv only dual-channl tails, o dual-channl tails in addition to pu -tails thos that sll though th Intnt channl only W concptualiz and modl a vital aspct of dual-channl tailing mitigating th disutility of buying fom th Intnt in studying goods fo which channl and sll chaactistics matt in th contxt of taditional and Intnt channl comptition Th xtant litatu suggsts that ky componnts that undli th disutility of buying fom th Intnt includ tust (Javnpaaa t al 2000, Stwat 2003), challngs in tuning th poduct (Foman t al 2009), and th lack of touch and fl (Balasubamanian 1998) Bcaus taditional tail stos hav a physical location to intact with consums, thy dominat Intnt tails on svic, aft-sals suppot, and tust (Vhof t al 2007) Consquntly, accss to a taditional tail sto of a dual-channl tail hlps mitigat th costs duc th disutility of buying fom th Intnt channl, ssntially incasing tail ach Tust plays a significant ol in consum dcision making whn buying onlin (Hoffman t al 1999) Not supisingly, th taditional sto of a dual-channl tail nhancs consum tust whn thy a puchasing though th Intnt Using an xpintial suvy, Javnpaaa t al (2000) found that fo tust to xist a consum must bliv that th sll has both th ability and motivation to liably dliv goods of th quality xpctd, and this tust is mo difficult to ngnd fo an Intnt sto than a taditional tail sto Thy spculat that th psnc of a physical sto o th cognition of th mchant s nam might hav an ffct on consum tust in an Intnt-basd sto (Javnpaaa t al 2000) This tust is somtims fd to as

3 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 3 institution-basd tust, and is takn to b high whn an Intnt tail also dos businss in th taditional tail channl Expimntal sults fom Stwat (2003) hav shown that a connction to a taditional tail sto had a significant positiv ffct on intntion to buy, suggsting that institutional factos a impotant to tusting intntions Hnc, dual-channl tails a abl to bnfit fom institution basd tust bcaus th tust tansfs fom a taditional tail sto to th Intnt channl (Stwat 2003) Th vidnc fom this sach indicats that th taditional sto of a dual-channl tail povids a distinct advantag to th tail s Intnt countpat by mitigating th onlin disutility cost, whil a pu -tail dos not njoy this bnfit Fo xampl, most consums would cogniz and lat Bstbuycom with a Bstbuy taditional sto and, consquntly, would mo comfotably tust and tansact with Bstbuycom Howv, a consum may not plac th sam lvl of tust in Buycom, a sit that is not associatd with taditional stos A citical disadvantag of buying fom th Intnt channl is poblms latd to tuning a poduct (Foman t al 2009) Th poblms onlin consums fac in making tuns can b substantially ducd by visiting a taditional sto of th dual-channl tail If th a postpuchas issus consums can div to th sto and tun th poduct o gt satisfactoy svic Indd, vn th option of going to th nast taditional tail sto givs a consum pac of mind and ducs th onlin disutility cost Basd on a suvy of tansaction costs, Liang and Huang (1998) found that som poducts a mo suitabl fo slling though th Intnt channl than oths, and this dpnds on th nd fo chaactistics such as post-puchas svic Fo xampl, Bstbuycom consums hav th option of going to a naby taditional Bstbuy sto to talk to somon in pson if th a issus to solv Not bing abl to touch and fl th poduct oftn maks onlin consums unctain about th fit with thi nds and this inducs disutility cost (Balasubamanian 1998) Th litatu on consum bhavio suggsts that th consum dcision pocss can b dividd into fiv stags: nd cognition, infomation sach, altnativ valuation, puchas, and outcom (Engl t al 1990, Kotl 2002) Accodingly, a taditional sto of th dual-channl tail may hlp in th infomation sach stag as a consum may go to th sto fo oth asons and inspct availabl poducts Lat, if th consum dcids to buy a poduct onlin that s/h alady saw at th sto o a poduct clos to th on s/h saw at th sto, th is lss unctainty about th poduct o th tail that slls it Thus, th taditional sto of th dual-channl tail can povid th touch and fl fo its Intnt consums In this cas, th consum dos not incu any tavling cost in puchasing th focal poduct bcaus th inspction was don in a tip that was not mad fo this poduct

4 4 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails In sum, th psnc of a taditional tail sto naby mitigats th onlin disutility cost of buying fom th Intnt channl of th dual-channl tail, and this mitigation dpnds on how fa a consum is fom a taditional sto Bynjolfsson t al (2009) mpiically dmonstat that having taditional stos naby ducs th Intnt dmand fo popula poducts, which a likly to b availabl locally Similaly, using data on bookslling Foman t al (2009) show that whn a local taditional tail sto opns, consums substitut away fom th Intnt channl, which implis that th compaison btwn onlin disutility costs and tanspotation costs matts vn fo books Consquntly, it is citical to undstand th statgic and wlfa implications of mitigating th onlin disutility costs Th novlty in ou wok is to fomally aticulat and modl th mitigation of onlin disutility costs and div insights by compaing consum wlfa and social wlfa btwn commonly obsvd makt stuctus Accodingly, in xamining th impact of mitigating onlin disutility costs, w concptualiz an impotant componnt of -commc, which plays a significant ol in th comptition within th Intnt channl and btwn Intnt and taditional channls W study this channl comptition whn slling th typs of goods fo which a sll s physical psnc is valuabl to consums whn thy mak puchass onlin W spcify a modl of how dual-channl tails, whn thy also sll though th Intnt channl, mitigat onlin disutility costs to consums basd on th consums distanc fom th taditional tail sto Using this spcification w thn fomulat and solv an xtnsion to ach of th paadigm analytical modls Salop s (1979) cicl aound th lak and Balasubamanian s (1998) pu -tail in th cnt whby taditional tails also sll though th Intnt channl so that, fist, th tails a dual-channl tails (Salop modl with an Intnt channl) and, scond, th is comptition in th Intnt channl (Balasubamanian modl with tails in th Intnt channl) Fo xampl, considing th makt fo hom impovmnt poducts, Hom Dpot and Low s a th main comptitos both in taditional tail stos and though th Intnt, which matchs ou fist xtnsion (Salop modl with an Intnt channl) Th makt fo unning shos, on th oth hand, has dual-channl tails (g, Finish Lin and Foot Lock) as wll as pu -tails (g, Zapposcom) (Balasubamanian modl with taditional tails in th Intnt channl) In ou modls, th tnsion btwn a dual-channl tail s ach via two channls vsus comptition in th Intnt channl yilds supising sults fo consum and social wlfa W find that th impact of comptition fom a pu -tail and ach fom dual-channl tails in th Intnt channl impovs consum wlfa whil at th sam tim lowing social fficincy This is bcaus consums incu gat onlin disutility costs than tanspotation costs in od to obtain low pics that sult fom onlin comptition, and this ducs social wlfa noting that pics a a tansf and only includd in consum wlfa W also find that whn taditional

5 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 5 tails nt th Intnt channl, consums do not civ th advantags of mitigation of onlin disutility costs whn ths costs a high bcaus dual-channl tail pics in both channls a gat than thy a in th psnc of a pu -tail Th vs occus whn onlin disutility costs a low as this incass th comptition btwn th dual-channl tails Intnt channls, ducing pics to th xtnt that vn with lss mitigation th mitigation ffct is stong Howv, ou pofitability sults suggst that it is only pofitabl fo taditional tails to xtnd into th Intnt channl if th onlin disutility costs a high nough to fostall a pu -tail Bcaus comptition btwn dual-channl tails and comptition fom a pu -tail a th two most commonly obsvd makt stuctus, ths supising sults a paticulaly lvant fo mpiical studis, and fo th fomulation of futu analytical modls Finally, in ou analyss, lik Balasubamanian (1998), w xclusivly focus on tail-lvl comptition and abstact fom sach, fom sgmntation apat fom distanc in th Salop (1979) modl, and fom supply chain ffcts such as vtical intgation and doubl maginalization Ou analysis pocds as follow Fist, w bifly viw th Salop (1979) and Balasubamanian (1998) modls, and xplain ou spcification of how a taditional sto can mitigat onlin disutility costs facd by consums whn puchasing fom a tail s Intnt channl Using a consistnt famwok, w show th solutions to th Salop and Balasubamanian modls, and thn obtain th simila solutions fo th xtnsions to ach of ths modls whn taditional tails a also in th Intnt channl Subsquntly, w dvlop ou main sults in th fom of popositions that compa th solutions of th diffnt modls in tms of pic, tail pofits, consum wlfa, and social wlfa W conclud with a discussion of ou findings, ou contibutions, and implications fo futu sach 2 Ou Modl Salop Modl Ou modl and its vaiants a basd on th wll-known Salop modl (Salop 1979) of a cicl aound th lak cating a cicula spatial makt, which itslf is an xtnsion of th Hotlling (1929) modl of hoizontal diffntiation along a lin Salop s modl has a continuum of consums, x [0, 1], spad unifomly aound a cicl of unit cicumfnc Each consum is in th makt fo on unit of th good, consumption of which yilds utility U R +, which w assum is lag nough so that dmand is inlastic and tails compt fo th businss All tanspotation occus along th cicl and is subjct to a unit cost of t R + All customs hav accss to infomation gading pics Th consums objctiv is to maximiz thi utility by puchasing fom on of th (taditional) tails, which, with inlastic dmand, is quivalnt to puchasing fom th tail that minimizs th sum of th tanspotation cost incud, t tims distanc fom th tail, plus th pic paid fo th good

6 6 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Rtails opat taditional stos slling idntical goods with a maginal cost nomalizd to zo Each tail is awa of th oth s offing pic, and facs a fixd nty cost f R + This fixd nty cost togth with th unit tanspotation cost dtmins th numb of tails in th makt To mak ou analysis mo insightful and tactabl, w assum that 4 t/f < 9 which in th oiginal Salop modl sults in an quilibium with two tails (Tiol 1988) This paticula inquality is scald by th siz of th cicumfnc, which in tun scals t W indx ths tails by {A, B} In this cicula stting, ach tail gains by locating as fa as possibl fom comptitos (d Futos t al 1999), hnc ou location of th two tails at opposit sids of th cicl Although w obtain simila qualitativ sults with n tails, xpssing th sults is mo tdious and lss insightful, so w us th two-tail fomulation in ou analyss Figu 1 Balasubamanian Modl Two Taditional Rtails (A & B) and On Pu E-tail Balasubamanian Modl Balasubamanian s (1998) modl xtnds th Salop modl to includ a pu -tail which offs a good idntical to that of th taditional tails In Balasubamanian s modl, th pu -tail has qual accss to any point on th cicumfnc In Figu 1, th pu -tail is locatd at th cnt of th cicl, with a adius distanc to ach point on th cicumfnc As an altnativ to puchasing fom on of th taditional stos as in th Salop modl, consums can puchas fom th -tail and incu a fixd onlin disutility cost plus th pic paid fo th good In lin with Balasubamanian (1998), th fixd onlin disutility cost, which w dnot as µ R +, may includ shipping and handling costs as wll as disutility costs of puchasing lctonically Ths disutility costs may com fom th pivacy and scuity isks of

7 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 7 puchasing onlin, th lack of tust in an -tail s ability and motivation to liably dliv th quality xpctd, gat difficultis in gtting hlp with o tuning th good should th b poblms post-puchas, and th lack of touch and fl In this modl, th -tail has no nty costs Ou Fomulation Ou fomulation is basd on taditional tails also slling though th Intnt channl, offing idntical goods though both channls To b consistnt with Balasubamanian s modl, w tak tails as having no onlin nty costs Whn a dual-channl tail slls though th Intnt channl, consums that puchas though th Intnt channl incu th fixd onlin disutility cost, plus th pic of th good Howv, bcaus of th xistnc of taditional tail stos, th disutility in th fixd onlin disutility cost of th Intnt channl whn puchasing fom such tails can b in pat mitigatd along th th dimnsions mntiond bfo: tust, aft-sals suppot, and th lack of touch and fl Th xtnt of th mitigation dpnds on th distanc fom th taditional sto Fo xampl, whn puchasing fom Bstbuycom, a consum who is 30 mils away fom a Bstbuy sto has a high disutility mitigation compad to a consum who is 60 mils away In addition, in ou quilibium, tails compt fo thos consums that a closst to thm: givn pics a symmtic in quilibium, thn with a distanc cost (though th taditional channl) o gat mitigation with poximity (though th Intnt channl of dual-channl tail), consums cannot b btt off choosing th tail that is fath away Figu 2 Salop Modl with an Intnt Channl Two Dual-Channl Rtails

8 8 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Ou fomulation has two spaat cass Th fist is two tails that compt acoss th taditional tail and Intnt channls, which is ssntially th addition of an Intnt channl to th oiginal Salop modl with two tails (s Figu 2) Th scond is two tails that compt acoss th tail and Intnt channls, and a pu -tail, which is ssntially th addition of taditional tails in th Intnt channl to th oiginal Balasubamanian modl (s Figu 3) W st up ou modls as a simultanous gam of pic stting, following th classic Salop and Balasubamanian aticls As such, in th two cass w dvlop, w implicitly assum that both taditional tails nt th Intnt makt Givn tails act symmtically, th is no nd to fomally dvlop th stp of whth taditional tails nt th Intnt makt bcaus it is lativly staightfowad Considing that th a no costs of nting th Intnt channl (noting that is th cas in Balasubamanian s modl), and that ou modl is not about squntial nty, w also ffctivly modl tails dciding to nt th Intnt channl simultanously Du to th symmty in ou modl, th is no pu statgy quilibium in which only on taditional tail opns th Intnt channl Nonthlss, w povid conditions that dscib whn taditional tail nty can b pofitabl in th Intnt channl Figu 3 Balasubamanian Modl with Rtails in th Intnt Channl Two Dual-Channl Rtails (A & B) and On Pu E-tail To incopoat th mitigation of th fixd onlin disutility costs that th xistnc of a taditional tail sto bings to consums, w dfin two additional paamts Fist is th maginal dop in mitigation of onlin disutility costs with distanc, a R +, and th scond is th maximum amount

9 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 9 of mitigation of onlin disutility costs, ac wh c R + Thus, if a consum at distanc x fom a taditional tail puchass fom that tail s Intnt channl, h costs of using th Intnt channl is µ a(c x) = µ ac + ax (1) A consum adjacnt to th taditional sto facs a fixd onlin disutility cost lss mitigation of µ ac, and that cost iss with x by a Givn this cost of distanc cannot b high than th tanspotation cost, w hav a < t, and fo th mitigation to b positiv w hav c > x Finally, th fixd onlin disutility cost can nv b compltly mitigatd, µ > ac Fo asi fnc, w includ ths th inqualitis blow: (i) a < t, (ii) c > x, (iii) µ > ac (2) This lina fom in (1) is th simplst fom w can us that is compatibl with th Salop modl W dnot th taditional tail pics as p, th tail pics though th Intnt channl as p, and th pu -tail pic as p W us supscipts to dnot th modls, so that supscipt s is th Salop modl, b is th Balasubamanian modl, s is ou fomulation of th Salop modl with taditional tails in th Intnt channl, and b is ou fomulation of th Balasubamanian modl with taditional tails in th Intnt channl 21 Modl Solutions Salop Modl Solutions ( s) Two tails off idntical goods A consum at th distanc x [0, 1/2] fom tail is indiffnt btwn puchasing fom ith tail if p A +tx = p B +t[1/2 x] Basd on this indiffnc quation w can dtmin tail A s makt sha as m A = 2x = [p B p A ]/t + 1/2 Rtail A s pofit maximization poblm is { [ pb p A max π A = max p A + 1 ]} p A p A t 2 Rtail B has an idntical makt sha and pofit maximization poblm Th sulting symmtic Nash quilibium pic is p s = t/2, (3) and th is no asymmtic quilibium Each tail s makt sha is 1/2 and pofits a π s = t/4 Th maximum distanc fo any consum to a tail is x = 1/4 and th minimum distanc is 0, giving an avag distanc of 1/8 so that th total tanspotation cost incud is t/8 Th total cost to consums is th sum of th tail pofits plus th tanspotation costs: ω s = 2π s + t/8 = 5t/8 (4) Th social cost, which accounts fo tansfs btwn consums and fims, is simply qual to th tanspotation cost in th Salop modl: γ s = t/8 (5)

10 10 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Balasubamanian Modl Solutions ( b) Th pu -tail offs th idntical good at an ffctiv pic of p + µ Th location of a consum that is indiffnt btwn puchasing fom th -tail o a taditional tail is dtmind by th indiffnc quation p + µ = p + tx, giving th indiffnt consum s distanc away fom a tail as x = [p p + µ]/t Consums clos to a givn tail than x puchas fom that tail, thos that a fath than x puchas fom th -tail Th -tail s makt sha is 1 4x, and ach tails makt sha is 2x Each tail s pofit maximization poblm is and th -tail s pofit maximization poblm is Th sulting Nash quilibium pics a [ max π = max {p 2 p ]} p + µ, p p t [ max π = max {p 1 4 p ]} p + µ p p t p b = t/6 µ/3 and p b = t/12 + µ/3, (6) and th is no quilibium wh tail pics a asymmtic Th -tail makt sha is positiv if x < 1/4, and consquntly th pu -tail pic and makt sha a positiv only if µ/t < 1/2, (7) and w stict ou attntion to wh (7) holds It is woth noting that th magnituds in this lation may appa unnatual until w call that th cicl is of unit cicumfnc and thus th magnitud of distanc, x, is small Pofits a π b = [t + 4µ] 2 /72t and π b = [t 2µ] 2 /9t (8) Th total cost to consums is th sum of th fixd onlin disutility costs, th tanspotation costs, and tail and -tail pofits: ω b = µ[1 4x] + 2t[x/2][2x] + 2π b + π b = 11t2 + 40µt 16µ 2 (9) 72t Th social cost is th sum of fixd onlin disutility and tanspotation costs: γ b = µ[1 4x] + 2t[x/2][2x] = t2 + 56µt 80µ 2 (10) 72t

11 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 11 Salop Modl with an Intnt Channl ( s) Th two dual-channl tails compt acoss taditional tail and Intnt channls In th Intnt channl, ach tail offs th idntical good at p + µ ac + ax W dfin two indiffnt consums Th fist, x 1, is indiffnt btwn th sam tail s taditional sto and Intnt channl This indiffnt consum is dfind by p + tx 1 = p + µ ac + ax 1, giving th distanc away fom th taditional tail sto as x 1 = [ac + p p µ]/[a t] Th scond, x 2, is indiffnt btwn th two tails Intnt channls This indiffnt consum is dfind by p A + µ ac + ax 2 = p B + µ ac + a[1/2 x 2 ] Fom ou modl fomulation, w can show that bcaus th tails a idntical, x 2 = 1/4 Each tail s makt sha fom its tail channl is 2x 1, and fom its Intnt channl is 2[x 2 x 1 ] = 1/2 2x 1 Thi pofit maximization poblms a [ max π = max {p 2 ac + p ] [ p µ 1 + p p,p p,p a t 2 2ac + p ]} p µ a t Th two tails hav idntical bst spons functions, and th sulting Nash quilibium pics a p s = [a ac + µ]/2 and p s = a/2, (11) both of which a positiv, th fist fom (2)(i) Both channls hav positiv makt shas if 0 < x 1 = [µ ac]/2[t a] < 1/4 Th fist inquality is tu fom (2)(i) and (iii), and th scond is tu if Fo th to b positiv mitigation, (2)(ii) quis c > x 2, o Rtail pofits a π s t a > 2[µ ac] (12) c > 1/4 (13) = a2 2a 2 c 2 at + 4acµ 2µ 2 (14) 4[a t] Th total cost to consums is th sum of fixd onlin disutility costs lss mitigation, tanspotation costs, and tail pofits: ω s = [µ ac + a[1/4 + x 1 ]/2][1 4x 1 ] + 2t[2x 1 ][x 1 /2] + 2π s = 5a2 + 4a 2 c 2 8a 2 c + 8act 5at 8acµ + 8aµ 8µt + 4µ 2 (15) 8[a t] Th social cost is simply th sum of fixd onlin disutility costs lss mitigation, plus tanspotation costs: γ s = [µ ac + a[1/4 + x 1 ]/2][1 4x 1 ] + 2t[2x 1 ][x 1 /2] = a2 + 12a 2 c 2 8a 2 c at + 8act + 8aµ 24acµ 8µt + 12µ 2 (16) 8[a t]

12 12 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Balasubamanian Modl with Rtails in th Intnt Channl ( b) Two dual-channl tails compt acoss taditional tail and Intnt channls, and with a pu -tail in th Intnt channl Th addition to th Balasubamnian modl is th taditional tail in th Intnt channl In th Intnt channl, th tail offs th idntical goods at p +µ ac+ax W dfin two indiffnt consums Th fist, x 1, is indiffnt btwn th sam tail s taditional sto and Intnt channl, and is dfind as in th Salop modl with an Intnt channl abov Th scond, x 2, is indiffnt btwn a dual-channl tail s Intnt channl and th pu -tail This indiffnt consum is dfind as p + µ ac + ax 2 = p + µ, giving x 2 = [ac + p p ]/a Th tail s makt shas a as dfind in th Salop modl with an Intnt channl, xcpt that in this cas x 2 is not qual to 1/4 Th pu -tail makt sha is 1 4x 2 Each tail s pofit maximization poblm is max π = max p,p p,p {p [ 2 ac + p p µ a t Th -tail s pofit maximization poblm is max π = max p p ] [ ac + p p + p 2 ac + p ]} p µ a a t {p [ 1 4 ac + p p a ]} (17) Again, as th dual-channl tail bst spons functions a symmtic, th only quilibium is wh tail pics a symmtic, and th sulting Nash quilibium pics a p b = [a 2ac + 6µ]/12, p b = [a + 4ac]/12, and p b = [a 2ac]/6 (18) Pics a positiv fom (2)(i) and whn c < 1/2 Th makt shas dpnd on x 1 and x 2 which a x 1 = [µ ac]/2[t a] and x 2 = c/3 + 1/12 x 1 is positiv fom (2)(i) and (iii), th sam as in th Salop modl with an Intnt channl Fo th pu -tail to hav positiv makt sha quis x 2 < 1/4, o c < 1/2, which is th sam as th positiv pic condition Fo th tail to hav a positiv Intnt makt sha quis x 2 x 1 > 0, o t a > 6µ 2ac 4ct (19) Fo th to b positiv mitigation, (2)(ii) quis c > x 2, o c > 1/8 Stating th bounds on c: 1/2 > c > 1/8 (20) Rtail pofits a π b = a2 20a 2 c 2 + 8a 2 c a[1 + 4c] 2 t + 72acµ 36µ 2, (21) 72[a t]

13 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 13 and -tail pofits a π b = a[1 2c] 2 /9 (22) Th condition in (19) is sufficint fo th dual-channl tails Intnt channl to hav positiv makt sha, and (22) bing positiv is sufficint fo th pu -tail to b pofitabl thus th Balasubamanian modl with tails in th Intnt channl obtains whn (19) is tu Th total cost to consums is th sum of fixd onlin disutility costs on puchass fom th -tail, th sum of fixd onlin disutility costs lss mitigation on Intnt puchass fom dual-channl tails, tanspotation costs, and tail and -tail pofits: ω b = µ[1 4x 2 ] + [µ ac + a[x 2 + x 1 ]/2][4[x 2 x 1 ]] + 2t[x 1 /2][2x 1 ] + 2π b + π b = 11a2 + 20a 2 c 2 32a 2 c 11at + 32act + 16ac 2 t 72acµ + 72aµ 72µt + 36µ 2 (23) 72[a t] Th social cost is sum of fixd onlin disutility costs on puchass fom th -tail, th sum of onlin disutility costs lss mitigation on Intnt puchass fom dual-channl tails, plus tanspotation costs: γ b = µ[1 4x 2 ] + [µ ac + a[x 2 + x 1 ]/2][4[x 2 x 1 ]] + 2t[x 1 /2][2x 1 ] 3 Main Rsults = a2 + 28a 2 c 2 16a 2 c at + 16act + 80ac 2 t 216acµ + 72aµ 72µt + 108µ 2 (24) 72[a t] In som of popositions that follow ath than stat th poof dictly in th txt w us constaint plots to mo claly dmonstat ou sults Th poofs that undli ths popositions a povidd in th Appndix 31 Pics and Pofits Pics To bgin, th psnc of an Intnt channl in th Salop modl (s) ducs taditional tail pics as th Intnt channl incass ach by spaating th makt into thos consums that incu tanspotation costs and thos that incu onlin disutility costs To undstand why this occus, in th Salop modl (s), ach consum xcpt th indiffnt consum has a low tanspotation cost with on o th oth tail Howv, with th Intnt channl vn with mitigation fo a givn consum th diffnc in th onlin disutility costs is small than th diffnc in tanspotation costs As a consqunc, th pic comptition btwn th tails Intnt channls affcts Intnt pics and causs th taditional tail channl pics to b low Thus, th additional ach ngnds incasd comptition Nxt, compaing th Balasubamanian modl (b) to taditional tails in th Intnt channl in th Salop modl (s), comptition fom a pu -tail, supisingly, dos not always xtt

14 14 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails downwad pssu on pics so long as th fixd onlin disutility cost is not too high In oth wods, if th onlin disutility cost is not too high, comptition fom a pu -tail can suppot high taditional tail and Intnt pics than can additional ach fom dual-channl tails Othwis, tails in th Intnt channl suppots high taditional tail and Intnt pics Th following poposition povids th fomal statmnt Poposition 1 Th Effct of Rach vsus Comptition on Pics If fixd onlin disutility costs a high (low), thn dual-channl tails chag high (low) taditional tail and Intnt pics W show th sult numically though th constaint plots in Figus 4 and 5 Without loss of gnality, w st th unit tanspotation cost to unity so that t = 1 By constuction t > a, so that th maginal dop in mitigation with distanc is a < 1 W incas th onlin disutility costs, µ, succssivly moving fom Figu 4(a) to 4(c) Th shadd aas flct ou constaints: th makt sha condition fom (12) as wll as th constaints on th mitigation paamts in (2) As µ incass, an incasing popotion of th paamt spac suppots p s pattn is tu fo Intnt pics in Figu 5, i, p s > p b > p b A simila (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 4 Compaing taditional tail pics in th Balasubamanian modl (b) to tails in th Intnt channl in th Salop modl (s) Poposition 1 is impotant and supising bcaus it shows that th ffct of ach vn with tails as dual-channl monopolists dos not ncssaily lad to high pics as compad to comptition fom a pu -tail, th Balasubamanian modl Th conditions und which this occus is low onlin disutility costs and a low maginal dop in mitigation with distanc Th latt mans that th mitigation applis to a gat ang of consums, which in tun, intnsifis

15 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 15 (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 5 Compaing Intnt pics in th Balasubamanian modl (b) to tails in th Intnt channl in th Salop modl (s) th comptition btwn th Intnt channls of th dual-channl tails This intnsifid onlin comptition cats pssu on taditional tail pics, incasing th ivaly btwn th two tails In contast, th pu -tail in th Balasubamanian modl compts dictly with ach taditional tail and dos not incas th ivaly btwn th tails (s Figu 1) With high onlin disutility costs o as th maginal dop in mitigation incass and mitigation bcoms lss substantial ov distanc, th ivaly btwn th Intnt channls of th two dual-channl tails (s) is ducd, and high Intnt and taditional tail pics can b sustaind Fo Intnt pics, th poposition shows that whn µ is low, both dual-channl tail and pu -tail pics a high in a comptitiv makt as opposd to dual-channl monopolis fo a lag paamt spac A low µ facilitats this bcaus th pu -tail is lss disadvantagd, whas th Intnt channl of th dual-channl tail facs gat comptition fom its ival Howv, whn onlin disutility costs a high, thn mitigation fom gat ach matts mo, and dual-channl tails can sustain high Intnt pics Finally, taditional tail and Intnt pics a low whn th is comptition fom a pu -tail in th Intnt channl (b) vsus dual-channl tails (s) as th comptition fom a pu -tail ducs Intnt pics offd by th dual-channl tail, and this in tun futh lows taditional tail pics Hnc, comptition is mo powful than ach in dtmining pics Using ou sults, th lationship btwn pics is p s > p s > p b > p b and p s > p b > p b, p s > p b, (25) wh th compaison btwn tails in th Intnt channl (s) and th Balasubamanian modl (b) a fom Poposition 1 whn onlin disutility costs a high

16 16 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Pofits In compaisons btwn th oiginal Salop modl (s) and th Salop modl with tails in th Intnt channl (s), and btwn th oiginal Balasubamanian modl (b) and th Balasubamanian modl with tails in th Intnt channl (b), dual-channl tail pofits fom on modl vsus th oth can b high o low dpnding on th valu of th additional channl Gnally, w xpct that a low fixd onlin disutility cost and a high maximum mitigation favos tail pofits fom th -tail channl, and vic vsa Not supisingly, dual-channl tail pofits a high whn th is no pu -tail sinc th pu -tail adds dict comptition to th Intnt channl, and indict comptition to th taditional tail channl whn th tails sll though both channls Supisingly, tail pofits a high in th Salop modl as compad to th Salop modl with tails in th Intnt channl bcaus th additional channl incass comptition btwn th tails Consquntly, π s π s, π b, π b and π s > π b Coollay 1 compas pofits in th Balasubamanian modl (b) to tails in th Intnt channl in th Salop modl (s) Th pofit lationship follows th gnal tnd in pics psntd in Poposition 1: whn onlin disutility costs a high, thn th ffcts of ach with mitigation dominat thos of incasd comptition btwn dual-channl tails in th Intnt channl, and vic vsa Figu 6 (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Rtail pofits in th Balasubamanian modl (b) compad to th dual-channl tails (s) Coollay 1 If fixd onlin disutility costs a high (low), thn dual-channl tails a mo (lss) pofitabl than taditional tails with a pu -tail in th Intnt channl W show th sult numically though th constaint plots in Figu 6 Without loss of gnality, w st th unit tanspotation cost to unity so that t = 1 By constuction t > a, so that th maginal dop in mitigation with distanc is a < 1 W incas µ succssivly moving fom Figus 6(a) to 6(c) Th shadd aas flct ou constaints: th makt sha condition fom (12) as wll

17 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 17 as th constaints on th mitigation paamts in (2) As µ incass, an incasing popotion of th paamt spac suppots π b > π s Ou nxt poposition compas pofits in th Balasubamanian modl (b) to thos fom th Balasubamanian modl with tails in th Intnt channl (b) Poposition 2 Th Effct of Rach on E-tail Comptition Enty into th Intnt channl and consqunt ach is aly pofitabl fo a taditional tail W show th sult numically though th constaint plots in Figu 7 Without loss of gnality, w st th unit tanspotation cost to unity so that t = 1 By constuction t > a, so that th maginal dop in mitigation with distanc is a < 1 W incas µ succssivly moving fom Figu 7(a) to 7(c) Th shadd aas flct ou constaints: th makt sha condition fom (19) as wll as th constaints on th mitigation paamts in (2) π b > π b a In th small fasibl aas abov th lin, th opposit is tu acoss most of th ang of c and (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 7 Rtail pofits in th Balasubamanian modl (b) compad to th xtndd th Balasubamanian modl (b) Anoth way to show Poposition 2 is though Coollay 1 and π s > π b As Figu 7 shows, Poposition 2 holds ov a substantial ang of th paamt spac (mo than Coollay 1), and th convs holds only ov a small pat of th paamt spac As in som of ou picing sults, th additional ach fom taditional tails in th Intnt channl incass comptition in that channl, and this incasd comptition cais though to th taditional tail channl Using ou sults fom Coollay 1 and Poposition 2, w hav th following pofit lationships fo th tails: π s π s π b π b (26)

18 18 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Th chang in pu -tail pofits whn th is additional comptition fom taditional tails slling though th Intnt channl is staightfowad as th additional comptition dissipats pofits: 32 Consum Wlfa π b > π b (27) W now xamin th impact of ach as compad to comptition on consum wlfa In consum wlfa w account fo pics, th onlin disutility costs lss mitigation and th tanspotation costs Thus, ou analysis is basd on total costs to consums, cognizing that with ou implicit assumption that th makt is covd, ach consum divs th sam valu fom consumption acoss modls and, consquntly, thy only diff in thi costs Nonthlss, w dscib ou sults in tms of consum wlfa bcaus it is a mo common and natual dsciption Ou fist sult is that stating fom th Salop modl, consum wlfa is incasd with a pu -tail in th makt This sult, that w choos not to stat fomally in a poposition, is that th total cost to consums is low in th Balasubamanian modl than in th Salop modl: ω s > ω b (28) This is staightfowad fom (4) and (9), cognizing that th constaint fo th lationship btwn th fixd onlin disutility cost and th tanspotation cost in (7) must hold Th following poposition, statd in two pats, shows that both ach and comptition contibut to consum wlfa Th fist pat of th poposition compas th Salop modl (s) and th Salop modl with tails in th Intnt channl (s) Th scond pat compas th Salop modl with tails in th Intnt channl (s) and th Balasubamanian modl with tails in th Intnt channl (b) Poposition 3 Th Effct of Rach and Thn Comptition (i) Th additional ach of taditional tails in th Intnt channl incass consum wlfa (ii) Th additional comptition fom a pu -tail in a makt with dual-channl tails incass consum wlfa Poof: (i) Fom th total costs to consums in (4) and (15), [ω s ω s ] c = a(a ac t + µ) a t and 2 [ω s ω s ] c 2 = a2 a t > 0 so that [ω s ω s ] is convx In addition, [ω s ω s ] has no al oots, but only complx oots Hnc, ω s > ω s

19 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 19 (ii) Fom th total costs to consums in (15) and (23), and using th constaints in (13) fo th Salop modl with tails in th Intnt channl togth with thos in (20) fo th Balasubamanian modl with tails in th Intnt channl: ω s ω b = 20c 8c 2 17 > 0 c 1/2 c 1/4 QED Taditional tails in th Intnt channl a ffctivly dual-channl monopolists Howv, th duction in onlin disutility costs fom a sufficintly low maginal dop in mitigation with distanc fo consums that puchas though th Intnt mo than offsts th potntially high tail pics fo thos customs that puchas though th taditional tail channl Consquntly, fom Poposition 3(i), an avag consum is btt off with taditional tails in th Intnt channl gat ach whn th makt involvs dual-channl tails only Poposition 3(ii) is impotant bcaus it shows that fo th avag consum, th possibl incass in onlin disutility costs that occus fom comptition in th Intnt channl whby th pu -tail as wll as th dual-channl tails in both channls hav a positiv makt sha a dominatd by th dcass in pics that coms fom th sam comptition Th possibl incass in onlin disutility costs is du to th lack of mitigation of onlin disutility costs offd by dual-channl tails in th Intnt channl whn th pu -tail has a positiv makt sha As dscibd ali, comptition in th Intnt channl ducs Intnt pics, which in tun puts downwad pssu on taditional tail pics Consquntly, comptition compounds th ffcts of ach on consum wlfa Ovall, Poposition 3 stablishs that taditional tails slling though th Intnt channl incas consum wlfa as compad to th Salop modl, and that comptition in th Intnt channl fom a pu -tail futh incass consum wlfa In tms of total costs to consums, w hav ω s > ω s > ω b (29) It mains to dtmin whth consums a btt off as a sult of incasd taditional tail ach th Salop modl with tails in th Intnt channl (s) o incasd comptition only a pu -tail in th -tail channl, th Balasubamanian modl (b) Poposition 4 Th Effct of Rach vsus Comptition on Consum Wlfa If fixd onlin disutility costs a high (low), thn a pu -tail incass (dcass) consum wlfa lativ to dual-channl tails

20 20 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails W show th sult numically though th constaint plots in Figu 8 Without loss of gnality, w st th unit tanspotation cost to unity so that t = 1 By constuction t > a, so that th maginal dop in mitigation with distanc is a < 1 W incas µ succssivly moving fom Figu 8(a) to 8(c) Th shadd aas flct ou constaints: th makt sha condition fom (12) as wll as th constaints on th mitigation paamts in (2) Whn µ incass, and incasing popotion of th paamt spac suppots ω s > ω b (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 8 Consum wlfa in th Balasubamanian modl (b) lativ to that with th Intnt channl in th Salop modl (s) Poposition 4 is impotant and supising bcaus it shows that th consum wlfa-incasing ffct of mitigating onlin disutility costs ovcoms th consum wlfa-incasing ffcts of comptition on pics in th Balasubamanian modl mostly at low lvls of th onlin disutility costs As onlin disutility costs incas, th ffcts of comptition a gat than thos of mitigation ov an incasingly gat ang of th paamt spac Consquntly, mitigation is only consum wlfa-incasing if th maginal dop in mitigation (a) is low and th maximum mitigation is high (ac) It is also possibl to show that adding tails in th Intnt channl to th Balasubamanian modl incass consum wlfa bcaus both comptition and ach wok to low pics in both channls (s (25)) Putting th lations togth ov th diffnt makt configuations, w hav ω s > ω s > ω b > ω b, (30) wh th compaison btwn tails in th Intnt channl (s) and th Balasubamanian modl (b) a fom Poposition 4 whn onlin disutility costs a high

21 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Social Wlfa Accounting fo th fact that pics, and thus pofits, a a tansf btwn slls and consums, social costs a a subst of total costs to consums that only includ onlin disutility costs lss mitigation and tanspotation costs Consquntly, th lativ ffcts of diffnt channl configuations on social wlfa may diff fom th lativ ffcts of diffnt channl configuations on consum wlfa As with consum wlfa, with th makt covd, ach consum divs th sam valu fom consumption acoss modls Although ou analysis of social wlfa is don basd on social costs, w dscib ou sults in tms of social wlfa as it is mo common and natual 331 Th Effcts of an Intnt Channl W bgin by stablishing th condition that dtmins if social wlfa is incasd by th addition of a pu -tail to a makt that only contains taditional tails, that is, whn th Balasubamanian modl (b) incass social wlfa ov th Salop modl (s) Th following poposition povids th condition Poposition 5 Th Effct of a Pu E-tail on Social Wlfa fom th Salop Modl If fixd onlin disutility costs a mo (lss) than 20% of unit tanspotation costs, thn th addition of a pu -tail to th Salop modl th Balasubamanian modl dcass (incass) social wlfa Poof: Dictly fom (5) and (10), if t < 5µ thn γ b > γ s QED Th impact in Poposition 5 coms fom th combind ffct of som consums substituting onlin disutility costs fo tanspotation costs and of additional pic comptition fom th pu - tail dtmining how many consums mak that substitution Although it is phaps supising, calling th constaint fom th Balasubamanian modl in (7), 2µ < t, and th condition in th Poposition, th is a substantial ang in th lationship btwn onlin disutility costs and tanspotation costs whby ith a taditional tail only channl makt o comptition btwn channls can hav gat social wlfa Ou nxt social wlfa poposition compas th social costs in th oiginal Salop modl (s) to th Salop modl with tails in th Intnt channl (s) Poposition 6 Th Effct of Rtail Rach on Social Wlfa If fixd onlin disutility costs a high, thn social wlfa is low with taditional tails in th Intnt channl W show th sult numically though th constaint plots in Figu 9 Without loss of gnality, w st th unit tanspotation cost to unity so that t = 1 By constuction t > a, so that th maginal dop in mitigation with distanc is a < 1 W incas µ succssivly moving fom Figu 9(a) to 9(c) Th shadd aas flct ou constaints: th makt sha condition fom (12)

22 22 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails and th constaints on th mitigation paamts in (2) To b consistnt acoss modls, w also impos µ 1/2 fom (7) Whn µ is modat to high in Figus 9(b) and 9(c), thn γ s > γ s ov most of th paamt spac Whn µ is low thn fom Figu 9(a), γ s > γ s (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 9 Social wlfa in th Salop modl (s) lativ to that with th Intnt channl in th Salop modl (s) Poposition 6 is impotant bcaus it shows that count to intuition, consums can incu gat costs in oth wods, social wlfa is ducd with th addition of taditional tails slling though th Intnt channl Hnc, w hav th supising sult that xclusiv of pics, an xta channl can ffctivly incas costs to socity Ths social costs a high whn onlin disutility costs a sufficintly lag and whn th maximum mitigation (i, ac) is not sufficintly lag to offst th high onlin disutility costs, in th contxt of a dual-channl tails that pic disciminat btwn channls such that som consums incu th high nt onlin disutility costs in xchang fo possibly low pics (not p s p s fom (25)) Poposition 6 also shows that th low a th onlin disutility costs lativ to tanspotation costs (having nomalizd t = 1), th gat is th social gain fom consums substituting th Intnt channl fo th taditional tail channl Combining Popostions 5 and 6 w find th supising sult that whn onlin disutility costs a sufficintly high, thn th addition of an Intnt channl whth fom a pu -tail o fom th taditional tails in th Intnt channl dcass social wlfa In tms of social costs w hav γ s, γ b > γ s

23 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails Th Effcts of Comptition in th Intnt Channl W xamin th ffcts of comptition in th Intnt channl, and compa ths ffcts with thos of ach W bgin with a conclusiv thom that shows comptition in th Intnt channl (b) dcass social wlfa lativ to ach fom taditional tails in th Intnt channl (s) Poposition 7 Th Effct of Comptition fom a Pu E-tail in th Intnt Channl on Social Wlfa Compad with taditional tails in th Intnt channl, additional comptition in th Intnt channl fom a pu -tail dcass social wlfa Poof: Using (16) and (24), w find γ s γ b = a (1 + c(10c 7)) Thfo, if (7 10c)c > 1, thn 9 γ s < γ b Combining constaints fom (13) and (20) to obtain th ang of 1/4 < c < 1/2, th inquality is tu fo all c (1/4, 1/2), and social costs a qual if c = 1/2 QED This poposition is impotant and supising bcaus it shows that social wlfa is ducd by comptition in th Intnt channl fom a pu -tail It is also a stong thom in that it dos not dpnd on conditions outsid th two modl s solutions Th ason wlfa is ducd is bcaus nt of pics which a taditional tail and Intnt pofits and do not nt into social costs consums locatd fa fom a dual-channl tail puchas fom th pu -tail and do not bnfit fom mitigation of thi onlin disutility costs as thy would if thy puchasd fom a tail s Intnt channl In oth wods, with only taditional tails in th Intnt channl, th onlin disutility costs a always mitigatd fo consums that buy though th Intnt channl Th vsal of th ffcts on costs, total vsus social, fom Poposition 3 is bcaus pics fall with comptition btwn dual-channl tails and a pu -tail in th Intnt channl (s (25)), and mo than offst th diffncs in tanspotation and onlin disutility costs Nxt, w compa social wlfa in th Balasubamanian modl (b) with that fom th Salop modl with tails in th Intnt channl (s) Poposition 8 Th Effct of Dual-Channl Rtails vsus a Pu E-tail in th Intnt Channl If fixd onlin disutility costs a high and th maginal dop in mitigation is low, thn social wlfa is high with a pu -tail in th Intnt channl than with taditional tails in th Intnt channl W show th sult numically though constaint plots in Figu 10 Without loss of gnality, w nomaliz th unit tanspotation cost to unity, t = 1 By constuction t > a, so that th maginal dop in mitigation with distanc fom (1) is a < 1 W incas µ succssivly moving fom Figu 10(a) to 10(c) Th shadd aas flct ou constaints: th makt sha condition fom (12) as

24 24 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 10 Social wlfa in th Balasubamanian modl (b) lativ to that with th Intnt channl in th Salop modl (s) wll as th constaints on th mitigation paamts in (2) As µ incass acoss Figus 10(a) though 10(c), whn a is low, thn γ s > γ b Poposition 8 is impotant and vy supising bcaus it shows that comptition btwn a pu -tail in th Intnt channl and taditional tails can incas social wlfa lativ to th incasd ach and consqunt mitigation of onlin disutility costs fom taditional tails in th Intnt channl dual-channl tails This occus bcaus whn pic is xcludd, th calculation of social costs is basd on tanspotation costs and onlin disutility costs Th onlin disutility costs a mitigatd fo consums with dual-channl tails slling though th Intnt channl lativ to th cas whn th pu -tail is alon in th Intnt channl Examining th pmis of th thom, a low maginal dop in mitigation of onlin disutility costs with distanc favos a pu -tail lativ to taditional tails in th Intnt channl in tms of low social costs Moov, a low maginal dop in mitigation also ducs th maximum mitigation of onlin disutility costs, which impacts th nt onlin disutility costs incud by consums Ou last poposition compas social wlfa in th Balasubamanian modl (b) to th xtndd Balasubamanian modl wh a pu -tail compts with dual-channl tails in th Intnt channl (b) Poposition 9 Th Effct of Comptition in th Intnt Channl If fixd onlin disutility costs a high o th maximum mitigation of fixd onlin disutility costs o th maginal dop in mitigation a low, thn social wlfa is low with comptition in th Intnt channl W show th sult numically though constaint plots in Figu 11 Without loss of gnality w nomaliz th unit tanspotation cost to unity, t = 1 By constuction t > a, so that th maginal

25 Nault and Rahman: Rach Vsus Comptition in Channls with Intnt and Taditional Rtails 25 dop in mitigation with distanc fom (1) is a < 1 W incas µ succssivly moving fom Figus 11(a) to 11(c) Th shadd aas flct ou constaints: th makt sha condition fom (19) as wll as th constaints on th mitigation paamts in (2) As µ incass acoss Figus 11(a) though 11(c), whn a is low, thn γ b > γ b (a) Pic: µ = 015, t = 1 (b) Pic: µ = 030, t = 1 (c) Pic: µ = 045, t = 1 Figu 11 Social wlfa in th Balasubamanian modl (b) lativ to that in th xtndd Balasubamanian modl (b) Rflcting th sult fom Poposition 7, th pmis in Poposition 9 is wak than that in Poposition 8 Poposition 9 is impotant in that xclusiv of pics, consums can incu gat social costs with th addition of taditional tails slling though th Intnt channl this tim byond an Intnt channl svd by a pu -tail Thus, w find th supising sult that th combination of comptition in th Intnt channl btwn a pu -tail and taditional tails in th Intnt channl togth with ach fom th dual-channl tails can also duc social wlfa Bcaus of low pics with gat comptition, th Intnt channl both th pu -tail and taditional tails in th Intnt channl has gat ach wh high onlin disutility costs a offst by low pics Thus, social costs a high bcaus mo consums incu gat onlin disutility costs Combining th sults of Popositions 7, 8 and 9, if onlin disutility costs a sufficintly lag thn gat comptition and ach in th Intnt channl can duc social wlfa Moov, togth with thos fom Popositions 5 and 6 w hav γ b > γ s > γ b > γ s (31) This is a damatic sult in that und asonabl conditions maximum social wlfa is th Salop modl without an Intnt channl In oth wods, fo typs of goods wh a sll s tail psnc is valuabl to consums, an Intnt channl ducs social fficincy This is in dict contast to