Electronic Commerce. and. Competitive First-Degree Price Discrimination

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1 Elctronic Commrc and Comptitiv First-Dgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg ondon, Gowr Strt, ondon WC1E 6BT. d.ulph@ucl.ac.uk. ** Dpartmnt of Economics, Univrsity of Bristol, 8 Woodland Road, Bristol BS8 1TN. n.vulkan@bristol.ac.uk Abstract As consumr -commrc maturs on-lin rtailrs ar adopting prsonalisation tchnologis which significantly incras thir ability to undrtak first-dgr pric discrimination by offring diffrnt prics to diffrnt consumrs. W prsnt a modl of duoplolistic comptition btwn firms capabl of using such tchnologis. Using firstdgr pric discrimination firms ar abl to xtract mor surplus from thir customrs, but also fac mor intns comptition, bcaus thy compt, in ffct, for ach and vry consumr in th markt. Whthr or not firms will choos to us this nw tchnology will dpnd on whthr or not th nhancd surplus xtraction ffct dominats th intnsifid comptition ffct. W prsnt a modl which maks ths idas prcis, and charactris th conditions undr which firms will choos to mploy firstdgr pric discrimination tchnologis. Acknowldgmnts W ar gratful to John Bath and Avnr Shakd for usful discussions. Both authors thank th financial support of th ESRC grant no. R

2 1. Introduction In rcnt yars an normous amount of consumr-spcific data has bn collctd by rtailrs and markting companis. For xampl, loyalty cards and air milag programms ar usd to collct data on th shopping pattrns of individual consumrs. By mploying data mining tchniqus companis ar abl to infr from ths massiv databass th prfrncs of individual consumrs. Companis which do not (or cannot) collct data thmslvs can still purchas rlvant consumr-spcific information from dirct mailing databass spcialists. This consumr-spcific information can in principl b usd by sllrs to undrtak firstdgr pric discrimination by offring consumrs th product thy want at a pric which thy ar likly to b willing to pay. Howvr, until now, such discrimination has bn too costly - for xampl, a physical catalogu which is individually tailord is hardly likly to b cost ffctiv. With th advnt of consumr -commrc, this nds no longr b th cas. In particular, prsonalisation tchnologis, such as agnts 1, significantly incrass th ability of firms to undrtak first-dgr pric discrimination. Using agnts, an on-lin catalogu can b individually customisd, for th agnt can idntify th shoppr and automatically rdsign th company s Wb sit to match th usr s likly rquirmnts. In particular th tchnology can b usd to offr diffrnt prics to diffrnt consumrs. Sinc on-lin mnu costs ar practically zro, on-lin rtailrs can chang thir prics to match what thy xpct th individual to b willing to pay for whatvr thy ar slling. Th qustion w wish to addrss in this papr is whthr, if such a tchnology is availabl, firms will ncssarily choos to us it. At first sight this may sm an odd qustion, sinc convntional thory tlls us that th ability of a firm to mploy first-dgr pric discrimination always raiss its profits, sinc it can xtract gratr surplus from consumrs. Call this th nhancd surplus xtraction ffct. Howvr, lik virtually all th analysis of pric discrimination, this conclusion is drawn in th contxt of pric discrimination by a monopolist. A ky fatur of th nvironmnt in which firms ar 1 An agnt is a program that is authorisd to act indpndntly on bhalf of its usr. This can rang from automatic sarch (for xampl, an agnt sarching for airlin tickts on th Wb can match prfrrd dats, pric-rang, class of travl, tctras, without consulting its usr) to automatic ngotiations (for xampl, agnts can plac binding bids in a Wb auction). Prsonalisation can b carrid out according to Wb sit dmographics (th usr profil for a givn sit); individual domains (attributs infrrd from th usr s browsr, for xampl by using cookis or agnts); larning (th agnt monitors and larns about th prfrncs of th usr), and corrlation (whr th agnt compars th usr s prfrncs with othr usrs with similar intrsts and suggsts possibl contnts basd on this corrlation. For xampl, Barns & Nobl and Firfly cratd a systm that rcommnds books basd on this mthod). An xampl of prsonalisation tchnology in us is MyYahoo! (my.yahoo.com), an agnt that allows th construction a individually tailord nws wb pag, whil at th sam tim customising th bannr advrtising on this pag according to th usr s profil. In a rcnt study, Intrnt rtailrs prics adjustmnts ovr tim wr found to b up to 100 tims smallr than convntional rtailrs pric adjustmnts (Brynjolfsson and Smith, 1999).

3 oprating using -commrc is that it is highly comptitiv. Intuitivly on suspcts that this will introduc a scond important consqunc of th dcision by firms to us firstdgr pric discrimination namly that it will intnsify comptition btwn firms, sinc thy will now b compting consumr-by-consumr. Call this th intnsifid comptition ffct. This will naturally lowr firms profits. Thus whthr or not firms will choos to us this nw tchnology will dpnd on whthr or not th nhancd surplus xtraction ffct dominats th intnsifid comptition ffct Th aim of this papr is to mak ths idas prcis, and to charactris conditions undr which firms might choos to mploy first-dgr pric discrimination in a comptitiv nvironmnt. Whil much of th litratur on pric discrimination has focusd on th cas of monopoly 3, a numbr of paprs hav analysd how pric comptition oprats in a comptitiv nvironmnt - Katz (1984), Bornstin (1985), Holms (1989), Corts (1998) and Armstrong and Vickrs (1999). Th lattr papr in particular provids an lgant framwork that incorporats much of th arlir work. Howvr this analysis concntrats on th cas of third-dgr pric discrimination in a comptitiv nvironmnt. As Armstrong and Vickrs (1989) show, th analysis of third-dgr pric discrimination can ssntially b split into two parts. Each firm first dtrmin how much profit it can mak for any givn lvl of gross utility that a typical consumr will obtain by buying from that firm. Dvics such as pric-discrimination and commodity bundling ar just ways of xtracting mor surplus from consumrs and so making mor profits for any givn lvl of gross utility. Firms thn compt in trms of th amount of gross utility thy offr thir customrs. Consumr spcific prfrnc charactristics will dtrmin th nt utility thy obtain from any gross utility providd by a particular firm. Th distribution of ths charactristics will dtrmin th dmand for ach firm as a function of th gross utilitis offrd by both firms. Firms cannot obsrv ths consumr spcific charactristics and so cannot influnc th nt utility a consumr obtains from any gross utility thy gt from buying from that firm. In contrast, in th modl of comptitiv first-dgr pric discrimination considrd hr, firms will fac a trivial problm of xtracting surplus from consumrs onc thy hav chosn to buy from thm. Howvr firms can obsrv individual consumr charactristics, and can us thir pricing policy to oprat dirctly on consumrs nt utility and hnc on th dcision to buy from on firm rathr than th othr. It is this that givs ris to th mor intns comptition btwn firms. W us th Hotlling framwork to modl pric comptition in diffrntiatd goods btwn two firms. Consumrs ar locatd along a lin rprsnting th dgr of product diffrntiation. Th two firms ar locatd at ithr nd of th lin. Th firms 3 Th survy by Varian (1989) has a small sction 3.6 covring th analysis for th cas of monoplistic comptition. 3

4 hav th sam tchnology with marginal costs indpndnt of output. Firms can ithr st mill prics, or offr ach consumr an individually tailord pric. W obtain th following major rsults. 1. If nithr firm pric discriminats, both firms will st pric abov marginal cost.. If a firm chooss to us first-dgr pric discrimination, thn th prics it sts and th profits it obtains ar indpndnt of whthr or not th othr firm chooss to us first-dgr pric discrimination. 3. If at last on firm oprats first-dgr pric discrimination, th consumr locatd half-way btwn th two firms will b offrd a pric qual to marginal cost by both firms th convntional Brtrand conclusion. 4. Whthr or not profits ar highr undr first-dgr pric discrimination dpnds crucially on th natur of th transport cost function. To laborat on this lattr point, considr th class of functions tz ( ) = tz. β, β 1, whr z is distanc travlld and β taks intgr valus. If this function is linar or quadratic (i.. β = 1,) thn, th prics that a firm offrs consumrs will b almost vrywhr 4 lowr than if nithr firm discriminats. Whn β 3 thn a firm that pric discriminats will charg highr prics to thos consumrs locatd clos to it, than it would if nithr firm discriminats. Howvr, sinc prics ar lowr for consumrs in th middl (rsult 3), profits ar highr if nithr firm discriminats. Only whn β 5 do firms mak mor profits if thy can pric discriminat than if nithr discriminats. Th intuition is straightforward. Whn transport costs do not incras vry fast with distanc, thn comptition btwn products is intns, and so th intnsifid comptition ffct is th dominant considration. Howvr, whn transport costs ris vry fast with distanc thn consumrs locatd clos to firms ar ffctivly lockd in, giving firms considrabl powrs to xtract surplus from thm, just as in th traditional monopoly analysis. Th xtra profits xtractd from ths consumrs can offst th rducd profits mad on th consumrs locatd in th middl whr comptition is intns. 4 Th xcption is th consumr locatd at th sam nd of th lin as th firm. 4

5 . Th Modl Suppos thr ar two firms, A and B, locatd at ithr nd-point of a lin of lngth. Consumrs ar uniformly distributd along this lin, and ach consumr buys a fixd amount of th good. Choos units so that thr is 1 unit of dmand at ach point on th lin. Th firms hav idntical constant marginal costs of production c>0. Consumrs hav to incur transport costs to visit firms. t tz ( ) b th transport costs of travlling distanc x. Assum t(0) = 0; t ( z) > 0; t ( z) 0. For latr purposs lt T( z ) b th intgral of t(z). So z T( z) = t( ydy ). 0 Cas I: No-Discrimination Suppos firm A chargs a pric p whil firm B chargs a pric q. Th consumr that is just indiffrnt btwn buying from A and B lis a distanc x from A whr p+ tx ( ) = q+ t ( x) (1) Givn th assumption on how w masur units, x is also th dmand for firm A, which is dfind through (1) as an implicit function of p and q. W hav x 1 = < 0 p t ( x) + t ( x) () For any givn q firm A chooss p to MAX ( p c). x( pq, ) p Th first ordr condition is x x( pq, ) + ( p c). = 0. (3) p In a symmtric Brtrand quilibrium p = q which implis () and (3) and thn substitut () into (3) to gt x =. Substitut this into 5

6 p = c+ t.. But thn th quilibrium profits that ach firm maks undr no-discrimination is π n =. t. (4) Cas II: Pric Discrimination: Only On Firm Discriminats Suppos now that firm A can pric discriminat, but firm B cannot. A can now st a pric schdul p(x). Suppos that B sts a pric of q c. Considr consumrs locatd a distanc x from A. If c+ tx ( ) < q+ t ( x) thn A can st a pric px ( ) = q+ t ( x) tx ( ) ε, pick up all th consumrs at x and still mak a profit. Thus w can tak A s bst rspons to any pric q to b to st a pric schdul [ ] px ( ) = MAX q+ t ( x) tx ( ), c (5) It is now straightforward to show that th only Brtrand quilibrium pric for B is q = c. Suppos that this wr not th cas and that B s quilibrium pric wr q > c, and that th corrsponding pric schdul st by A wr px ( ) = MAX q+ t ( x) tx ( ), c. Notic that th cost to any consumr locatd at a distanc x from A, of buying from A, is thn [ ] px ( ) + tx ( ) = MAX q + t ( x), c+ tx ( ) Notic that in such an quilibrium A would srv all consumrs that li a distanc x or lss from itslf whr q+ t( x) = c+ t( x) which implis x >. 6

7 This is illustratd in Figur 1 blow for th cas of a linar transport cost function. Th havy dark lin indicats th cost px ( ) + tx ( ) of buying from firm A. Figur 1 q + t c+t c c q A x B Hnc if q rally wr th quilibrium, firm B would mak a profit ( q c) ( x) ( q c). <.. Notic that if B maks th normal Brtrand/Nash assumption that A will carry on stting th pric schdul px, ( ) thn if it now sts a pric q ε whr q > q ε > c thn x, 0 x : q ε + t ( x) < q+ t ( x) px ( ) + tx ( ) = MAX q+ t ( x), c+ tx ( ). Thus B would pick up th ntir markt and mak a profit ( q ε c).. This is illustratd in Figur 1 by th brokn lin that rprsnts th cost q ε + t ( x) to a consumr locatd at x of buying from firm B if it has chargd a pric q ε. For sufficintly small ε, ( q ε c). > ( q c). > ( q c).( x) 7

8 Hnc q is not th profit-maximising rspons by B to th pric schdul px ( ) chosn by A. p ( x) = MAX c+ t ( x) tx ( ), c ; q = c. Hnc th only quilibrium is [ ] Onc again ach firm srvs half th markt. Th profits mad by firm B ar clarly zro, whil thos mad by A ar π d = [ t ( x) tx ( )] dx= T( ) T 0. (6) Cas III: Pric Discrimination: Both Firms Discriminat Firms compt for consumrs at ach point on th lin. Clarly th only outcom is that th firm that is at a distanc disadvantag will hav to st a pric = c, whil th othr firm will st a pric that just picks up all th consumrs. On th othr hand, at th mid-point of th lin both firms ar idntical, so th convntional Brtrand conclusion holds and both firms prics ar drivn down to costs. This mans that on th intrval 0 x th solution is as abov, namly, [ ] p ( x) = MAX c+ t ( x) tx ( ), c ; q = c. On th othr hand if w lt y = x dnot th distanc btwn a consumr and firm B, thn, on th intrval 0 y th solution is [ ] q ( y) = MAX c+ t ( y) t( y), c ; p = c. But thn, if both firms pric discriminat thy both mak profits π d = T( ) T. (7) From quations (6) and (7) w gt our first rsult: 8

9 d mma 1. If a firm pric discriminats it maks profits π = T( ) T whthr or not th othr firm pric discriminats. And by comparing quations (4) and (7) w gt: Proposition 1. Pric discrimination is profitabl if and only if d π = T( ) T > n. π = t Th following sction illustrats our rsult for a larg class of transport costs. 3 Exampls Considr th class of simpl transport cost functions tx ( ) = tx. β ; t > 0, β 1. From (4) From (7) π t. β n 1+ =. β. β ( ) t β β π d = β (1 + β ).. d π If w lt ρβ ( ) dnot th ratio of profits undr discrimination to nondiscrimination, thn w hav n π β ( 1) ρβ ( ) =. β.(1 + β) It is straightforward to show that Th function dfind by th abov ratio is monotonic incrasing in β for β>1.5. It is qual to lss than 1 for intgr valus of β 4, but gratr than 1 for intgrs gratr or qual to 5. To s what is going on in mor dtail considr what happns to th pric schduls undr discrimination and non-discrimination... W know that with non-discrimination. t β p = c+ t = c+ β 1 β 9

10 With discrimination w hav p (0) = c+ t ( ) = c+ t. β, and th pric thn falls with distanc until p = c. Considr thn th following cass. Th following tabl rports th valus of ths various variabls for diffrnt valus of β. β Tabl 1 p (0) 1 c+ t. c+ t. 1/ c+ t. c+ t. 1/ c+ t. 7/1 c+ t c+ t. 3/4 c+ t c+ t. 31/30 c+ t 16 p ρ Figur illustrats th pric paths for th cas of linar transport costs - β = 1. Figur p p = p (0) c 0 / x Hr th brokn lin rprsnts th quilibrium pric whn thr is no discrimination, and th havy lin th quilibrium pric path undr discrimination. 10

11 Figur 3 illustrats th situation whn β = 5. Figur 3 p p (0) p c 0 / x Onc again th brokn lin rprsnts th quilibrium pric whn nithr firm discriminats. Th curv rprsnts th pric path undr discrimination. So whn β is small - i.. β, thn p = p (0) and so prics ar almost vrywhr lowr undr discrimination. Whn β = 3 th ability to discriminat mans that prics ar highr undr discrimination for consumrs clos to firms. But, this is not nough to offst th fact that prics ar lowr for consumrs around th middl so profits ar lowr undr discrimination. As β gts largr so too dos th gain from bing abl to discriminat amongst consumrs clos to th firms, until, vntually, pric discrimination bcoms possibl. So, as w mntion arlir, thr ar two ffcts at work: Th intnsification of comptition btwn firms, and th ability to discriminat. Considr first th impact of ths two ffcts on prics. Th first ffct crtainly lowrs th prics of consumrs that ar last loyal to any firm thos in th middl. Whn transport costs do not ris vry fast with distanc, thn thr ar almost no loyal consumrs and so th first ffct mans that prics ar lowr for all consumrs. Howvr, whn transport costs ris mor sharply with distanc, thn consumrs clos to a firm ar lockd in much mor and so th firm can rally discriminat. This offsts th comptition ffct and mans that firms can now charg highr prics for thos closr to thm. Considr now th ffct on profits. Whn prics ar drivn down for all consumrs thn profits obviously fall with discrimination. Whn firms can ffctivly rais prics for thir most loyal consumrs, this may or may not b nough to offst th ffcts of low prics in th middl. Only whn th ability to discriminat is vry strong bcaus of sharply rising transport costs will discrimination actually b profitabl. 11

12 4. Discussion In rcnt yars th Intrnt has bcom a popular shopping channl. Th Intrnt offrs consumrs 4 hour shopping and th convninc of shopping from hom. It is also much asir to compar products and prics on-lin than it is in any othr mans of shopping. For homognous goods, lik CDs and books, consumrs can us shopping agnts (known as ShopBots), lik BargainFindr.com to compar prics and buy from th sllr which offr th chapst pric. Intrnt tchnologis offr gratr opportunitis for sllrs too. On-lin rtailrs fac much lowr ntry and st-up costs and mnu costs ar practically zro (onc th appropriat softwar is installd). Easy accss to information about thir usrs allows onlin rtailrs to bttr sgmnt th markt thy ar srving and to offr customrs products which thy ar likly to want to buy. It is not clar at this arly stag what ffcts ths tchnologis will hav on prics and markt structur. Evn in th simpl cas of homognous goods, it is not clar what th ovrall ffct on prics will b 5. Thr is clarly a nd for rigorous modls of lctronic markts whr intuitions can b put to th tst. This papr can thrfor b sn as a contribution to filling that gap. This papr focus on on particular fatur of lctronic markts - th ability of sllrs to first dgr pric discriminat. Prsonalisation tchnologis hav bn in th cntr of mdia attntion in rcnt yars. Many, including th US Justic Dpartmnt, hav voicd thir concrn about th possibl violation of individual privacy rights through th xchang of information btwn th usr s agnt and th host Wbsit, which taks plac automatically. In particular, th viw that th mor information th sllr hav about th usr, th mor surplus it is abl to xtract from hr, rmains highly popular. Whil this is always tru in a monopoly contxt, this papr qustions this intuition in th contxt of comptitiv markts. W hav shown that in that contxt thr ar two ffcts at work: (i) th nhancd surplus xtraction ffct - which is th ffct at work in th traditional monopoly analysis of first dgr pric discrimination; (ii) th intnsifid comptition ffct th fact that firms nd up compting consumr by consumr with th traditional Brtrand rsult that at last on of thm has its pric drivn down to marginal cost. W hav usd a simpl duopoly stting with product diffrntiation to undrstand th intraction btwn ths two ffcts, and to charactris th xact conditions undr which firms would prfr to mploy first-dgr pric discrimination. W showd that whn th avrag and marginal transport costs ris vry slowly with distanc mor 5 S Vulkan (1999) for a gnral discussion, and Ulph and Vaughan (1999) for an analysis that shows that incrasd pric transparncy can rais or lowr prics, dpnding on whthr producrs or consumrs can bttr xploit th tchnology. 1

13 prcisly whn transport costs ar linar or quadratic thn th intnsifid comptition ffct dominats th nhancd surplus xtraction ffct and almost all consumrs fac lowr prics undr pric discrimination. As transport costs ris mor stply with distanc thn this strngthns th surplus xtraction ffct. Now consumrs with th gratst brand loyalty will pay highr prics undr first-dgr pric discrimination, though thos with last loyalty will still fac lowr prics. Only whn transport costs ris sufficintly stply so that th incrasd profits xtractd from th most loyal consumrs xcds th loss in profits from th last loyal consumrs will first-dgr pric discrimination turn out to b profitabl for firms. Thus, in a wid class of cass, firms may choos not to us th pric-discrimination tchnology. Whil th analysis in this papr has bn motivatd by mrging -commrc tchnology, it can b applid in any contxt whr first-dgr pric discrimination is possibl, and can b usd to xplain why, whn thr is comptition, pric discrimination may not always b usd. Thr ar a numbr of dirctions in which th analysis can b xtndd. As pointd out abov, -commrc can b usd to tailor not just th pric, but also th product to individual consumr nds. This lattr phnomnon is oftn rfrrd to as mass customisation. In a companion papr 6 w xplor th implications of this for pric discrimination. 6 Ulph and Vulkan (000) 13

14 Rfrncs Armstrong, M. and J. Vickrs (1999), Comptitiv pric discrimination, Working Papr, Nuffild Collg, Oxford Univrsity. Bornstin, S. (1985), Pric Discrimination in Fr-Entry Markts, Rand Journal of Economics, 16, pp Brynjolfsson, E. and M. Smith (1999), Frictionlss Commrc? A comparison of Intrnt and Convntional Rtailrs, Working Papr MIT. Corts, K. (1998), Third-Dgr Pric Discrimination in Oligopoly: All-Out Comptition and Stratgic Commitmnt, Rand Journal of Economics, 9, pp Holms, T. (1989), Th Effcts of Third-Dgr Pric Discrimination in Oligopoly, Amrican Economic Rviw, 79, Hottling, H. (199), Stability in Comptition, Economic Journal, 39, pp Katz, M. (1984), Pric Discrimination and Monopolistic Comptition, Economtrica, 5, pp Varian, H. (1989), Pric Discrimination, in R. Schmalns and R. Willig, ds., Handbook of Industrial Organization, Volum 1, Amstrdam: North Holland. Ulph, D. and R. Vaughan (1999), Pric Transparncy and Markt Equilibria, mimo. Ulph, D. and N. Vulkan (000), E-Commrc, Mass Customisation and Pric Discrimination, in prparation. Vulkan, N. (1999), Economic implications of agnt tchnology and -commrc, Th Economic Journal, 453, pp