Exercising Market Power in Proprietary Aftermarkets

Transcription

1 Exercising Mrket Power in Proprietry Aftermrkets SEVERIN BORENSTEIN Hs School of Business University of Cliforni Berkeley, CA nd NBER JEFFREY K. MACKIE-MASON School of Informtion Deprtment of Economics nd School of Public Policy University of Michign Ann Arbor, MI JANET S. NETZ Deprtment of Economics Purdue University West Lfyette, IN Over 20 recent ntitrust cses hve turned on whether competition in complex durble-equipment mrkets prevents mnufcturers from exercising mrket power over proprietry ftermrket products nd services. We show tht the price in the ftermrket will exceed mrginl cost despite competition in the equipment mrket. Absent perfectly contingent long-term contrcts, firms will blnce the dvntges of mrginl-cost pricing to future genertions of consumers ginst the pyoff from monopoly pricing for current, locked-in equipment owners. The result holds for undifferentited Bertrnd competition, differentited duopoly, nd monopoly equipment mrkets. We lso exmine the effects of mrket growth nd equipment durbility. 1. Introduction In the pst decde, mny independent providers of service for hightechnology products hve sued equipment mnufcturers for llegedly excluding them from providing mintennce services. Over twenty ntitrust cses hve been brought ginst mnufcturers such 2000 Msschusetts Institute of Technology. Journl of Economics & Mngement Strtegy, Volume 9, Number 2, Summer 2000,

2 158 Journl of Economics & Mngement Strtegy s Kodk, Prime Computer, Dt Generl, Northern Telecom, Picker, Unisys, Xerox, Rolm, Hewlett-Pckrd, EDS, Generl Electric, nd Siemens. 1 The common feture in these cses is tht the defendnts mnufcture complex durble equipment for which customers demnd service, support, prts, ndor upgrdes for mny yers fter the initil sle. The economic interction between the originl equipment mrket nd ftermrkets is centrl to the nlysis. Most of the cses hve similr plot. The mnufcturer sells one brnd of complex equipment in mrket tht is firly competitive Ž e.g., the mrket for minicomputers.. In ddition, the mnufcturer sells ftermrket products to customers who purchsed the originl equipment. Exmples of ftermrket products include hrdwre mintennce contrcts, spre prts, nd softwre upgrdes. Due to proprietry rights, the originl mnufcturer is often the exclusive seller of t lest one ftermrket product, such s replcement prts or upgrdes to the operting-system softwre. Plintiffs chrge tht the mnufcturer exploits its ftermrket position in violtion of ntitrust lws, typiclly by tying the purchse of n ftermrket product tht is lso vilble from the plintiffs Ž usully service. to the mnufcturer s proprietry good, tht is, by leverging monopoly over prts into monopoly over service. Once customer purchses prticulr brnd of complex, durble equipment, she is likely to be locked in to tht mnufcturer to some extent. There re often significnt costs of switching to nother brnd: retrining, sunk investments in custom softwre, cpitl losses on the sle of the used equipment, etc. It would seem tht these switching costs could provide the mnufcturer with room to collect some monopoly rents by rising ftermrket prices bove cost. 2 However, mnufcturer tht exploits locked-in customers with high ftermrket prices might mke its equipment less ttrctive when it competes with other mnufcturers. The question we ddress is fundmentl: does substntil competition in the durble-equipment mrket necessrily discipline mnufcturers so tht they will not exercise mrket power in the ftermrket? This hs been the centrl clim in the mny ntitrust cses cited, supported by expert testimony from number of indus- 1. Ech of the uthors hs dvised prties to ftermrket ntitrust cses. 2. A number of ppers demonstrte how the presence of switching costs cn endow firm with mrket power fter consumers mke their initil choice. See, e.g., Klemperer Ž nd Frrell nd Shpiro Ž Well-known exmples include computers with proprietry operting softwre nd printer toner crtridges for lser nd inkjet printers.

3 Mrket Power in Proprietry Aftermrkets 159 tril orgniztion economists. 3 Although there is recent flurry of rticles concerning ftermrket mrket power, none provide forml nswer to this bsic question. 4 In this pper, we show tht equipment competition will not prevent firms from chrging suprcompetitive prices in their proprietry ftermrkets; the incentive to exercise t lest some degree of mrket power in the ftermrket is unmbiguous. Of course, this is not the only issue in the ntitrust cses we hve cited, nd we re not tking position with regrd to ny specific llegtions of ftermrket monopoliztion. Shpiro Ž hs wisely noted tht the socil welfre costs of some ftermrket inefficiencies my be smll, nd of course there re costs to fshioning policy remedy. Chen nd Ross Ž hve shown tht even when the equipment mrket is monopolized, the welfre consequences of some types of ftermrket exploittion re mbiguous. Our objective is to focus ttention on the use of ftermrket strtegies by durble-goods mnufcturers. As theoreticl mtter, the ssertion tht competitive equipment mrket prevents firm from exercising mrket power in the ftermrket is wrong. As policy issue, we believe the discussion should focus on the fcts of ech cse nd on n ssessment of how much hrm will occur in ech prticulr sitution. In Section 2 we review the recent legl history, emphsizing how the centrl economic question hs emerged from importnt fct contexts. In prticulr, we discuss the role of lock-in nd reputtionl effects. We develop differentited Bertrnd duopoly model in Section 3 to ddress the incentive to exercise mrket power in the ftermrket nd its effect on welfre. This model not only pproches perfect competition in the equipment mrket s the degree of differentition pproches zero, but it lso llows for the existence of some economic profits, which we rgue s necessry in order to study how reputtion might ffect the incentives to exploit ftermrkets. We find tht reputtion for low ftermrket prices does hve vlue nd tht firms will therefore price the ftermrket product below its monopoly level. However, we lso find tht firms lwys price bove cost for the ftermrket product. 3. For exmple, Kodk rgued before the Supreme Court tht this proposition must hold s mtter of theory: even if it concedes monopoly shre of the relevnt prts mrket, it cnnot ctully exercise the necessry mrket power for Shermn Act violtion...equipment competition precludes ny finding of monopoly power in the derivtive ftermrkets Kodk, 112 S. Ct Ž t , emphsis in originl. 4. See, e.g., Borenstein et l. Ž 1995., Chen nd Ross Ž 1993, 1999., nd Shpiro Ž

4 160 Journl of Economics & Mngement Strtegy Assertions tht equipment mrket competition will necessrily discipline ftermrket behvior tend to refer to the equipment mrket s highly competitive. Therefore, within the context of our differentited duopoly, we exmine two issues. First, we consider the effects on the ftermrket price s the degree of differentition between the two firms pproches zero, so tht we pproch stndrd Bertrnd competition. We continue to find tht service price remins higher thn cost. 5 Then, we consider how the option to scrp used equipment nd buy new rther thn purchse ftermrket service ffects the ftermrket price. We show tht if the option to scrp nd buy new is binding on the mrgin, the ftermrket price is incresing in the firm s degree of equipment mrket power. These results emphsize our min point for ntitrust nlysis: the exercise of ftermrket mrket power is not ruled out by highly competitive equipment mrkets, but is mtter of degree. Rther thn merely ssume tht ftermrket mrket power is nonexistent or is significnt s mtter of theory, some degree of fctul inquiry into the mrket conditions is pproprite. We extend the nlysis in Section 4 by studying the ftermrket pricing behvior of n equipment monopolist. The fundmentl result is the sme: we show tht the ftermrket price is bounded wy from mrginl cost, but lso is not t the full monopoly ftermrket level. We lso show tht the monopolist chrges less in the ftermrket thn does duopolist, t lest in our sptil competition model. We rgue tht this result hs n intuitive explntion: the monopolist cn extrct lrger shre of the surplus creted when it lowers the ftermrket price Ž by rising the equipment price. thn cn duopolist, so the monopolist hs stronger incentive to keep the ftermrket price down. We conclude in Section 5 by summrizing our findings nd discussing some other incentives to monopolize ftermrkets some of which my benefit nd others of which my hrm consumers tht re not modeled here. 5. Alterntively, in the ppendix, vilble t jmmppers ftmkt-ppendix.pdf, we develop model of perfectly competitive equipment mrket in which ech equipment firm monopolizes its service mrket. We find once gin tht service price will be bove cost. Competition in the equipment mrket cuses firms to mke zero profits overll, but welfre loss occurs due to n ftermrket price bove cost.

5 Mrket Power in Proprietry Aftermrkets Aftermrket Economic Power in the Courts There re numerous cses before the federl courts tht involve clims of ntitrust violtions in ftermrkets for service products. Two hve recently reched the Supreme Court. In the first, firms selling service for Kodk high-volume photocopiers nd microgrphic equipment lleged tht Kodk dopted restrictive policy on the vilbility of spre prts, including tying sles of spre prts to the purchse of other mintennce services from Kodk. The Court upheld the Circuit Court s denil of Kodk s motion for summry judgment, concluding tht it is clerly resonble to infer tht Kodk hs mrket power to rise prices nd drive out competition in the ftermrkets... nd...to infer tht Kodk chose to gin immedite profits by exerting tht mrket power where locked-in customers, high informtion costs, nd discrimintory pricing limited nd perhps eliminted ny long-term loss Kodk, 112 S. Ct Ž t The Kodk cse then went to tril; Kodk lost on this issue t tril nd on ppel Imge Tech Services v. Estern Kodk Co., 125 F3d Ž Ninth Circuit, In nother cse, n independent service compny lleged tht Prime Computer hd tied the sle of softwre support nd upgrdes to the purchse of hrdwre mintennce from Prime. Prior to the Supreme Court decision in Kodk, the Sixth Circuit hd ccepted Prime s rgument tht competition in the equipment mrket would necessrily discipline ftermrket prices. The Supreme Court overturned this decision shortly fter deciding Kodk. The Sixth Circuit then decided tht sufficient evidence hd been presented to support finding tht it ws profitble for Prime to monopolize the service ftermrket Virtul Mintennce v. Prime Computer, 11 F3d. 660 Ž Sixth Circuit, Two min fetures tht distinguish ftermrkets hve emerged in the mny ntitrust cses before the courts: the role of customer lock-in estblishing mrket power nd the possibility tht reputtion effects will prevent mnufcturers from profitbly exploiting whtever economic power they hve in service ftermrkets. We discuss these fctors now, before proceeding to our forml model. 6. Three recent cses hve nrrowly interpreted or prtilly conflicted with the Supreme Court in Kodk. See McKie-Mson nd Metzler Ž for discussion of these.

6 162 Journl of Economics & Mngement Strtegy 2.1 Customer Lock-In The vilbility of substitutes limits mnufcturer s bility to chrge bove-competitive prices for its ftermrket products. An ftermrket customer would choose to sell or scrp the used equipment nd purchse new from different mnufcturer if the originl seller rised the service price sufficiently. The extent to which switching costs discourge customer from chnging brnds ffects how much room the mnufcturer hs to rise the service price. The equipment involved in most of the recent ntitrust cses is quite sophisticted. The products include minicomputers, hospitl CT scnners, telephone PBX switches, high-volume photocopiers, nd microgrphic reproduction equipment. In every cse, users nd experts hve testified to the high costs of switching. 7 Evidence introduced in the Wng 8 cse showed tht typiclly bout 80 percent of minicomputer consumers buy the sme brnd when they replce their equipment. Previous work hs demonstrted the role of switching costs in creting mrket power, but it hs focused on single product to which the consumer becomes locked in. 9 There hs been little ttention to firm tht sells equipment in competitive mrket but sells service to locked-in customers. 10 When there re two interrelted mrkets, the centrl question becomes the bility of the mnufcturer to profitbly exercise economic power in one mrket without lrger dverse impct on profits in the other mrket. 2.2 Reputtion nd Imperfect Competition Mnufcturers fce two types of customers: those who lredy own equipment nd those who re purchsing for the first time. Although customers who lredy own equipment my fce significnt costs of switching brnds nd thus provide the mnufcturer with n opportunity to price suprcompetitively, de novo customers do not. Do potentil new customers provide sufficient competitive discipline in the ftermrket? The nswer depends on reputtion effects. It my 7. For exmple, senior design systems mnger for Ford Motor Co. testified in Virtul tht switching from Prime minicomputers to nother brnd would shut Ford down. See lso Kodk, 112 S. Ct Ž t Systemcre, Inc. v. Wng Lbortories, D.C. Colo., No. 89-B See, for exmple, Frrell nd Shpiro Ž 1987., Klemperer Ž 1987., nd Beggs nd Klemperer Ž For n exception, see Chen nd Ross Ž In tht pper the uthors rgue tht firms chrge bove-cost service prices to recover higher costs from hevy users during wrrnty period.

7 Mrket Power in Proprietry Aftermrkets 163 not be profitble for mnufcturer to chrge bove-competitive ftermrket prices to locked-in service customers if the informtion esily spreds, inducing potentil new consumers to purchse other brnds. The direction of this reputtion incentive is cler, but its mgnitude hs not been shown to be gret enough to keep ftermrket prices t competitive levels. In prticulr, it is necessry to study reputtion effects, tking into ccount the incentives fcing other mnufcturers. The pressure from new customers my not be sufficient if the other mnufcturers re lso chrging bove-competitive ftermrket prices. The trde-off between erning profits by exercising mrket power in ftermrkets nd losing profits in equipment sles from reputtion for exploiting locked-in service customers hs cused some confusion in the courts. The ppellte court in Virtul originlly rgued tht lock-in theory is vible only when the producer cn chrge its customer monopoly prices without fer of being replced by competitors due to the customer s substntil investments ŽVir- tul, 957 F.2d 1318 t However, it is not necessry to chrge the full monopoly ftermrket price in order to exploit economic power, nor does the loss of some customers for new equipment necessrily offset the profits from service. The Supreme Court observed in Kodk tht even monopolists hve to give up sles when they rise prices, yet they find it profitble to chrge higher thn competitive prices 112 S. Ct Ž t 2084, nd tht short of chrging the full monopoly price for service, there could be middle, optimum price t which the incresed revenues from the higher-priced sles of service nd prts would more thn compenste for the lower revenues from lost equipment sles Ž id...the proper question, then, is the severity of the impct nticompetitive behvior in n ftermrket will hve on profitbility in the equipment mrket. The incentive to estblish reputtion for low ftermrket prices depends on the mnufcturer nticipting the possibility of erning bove-norml profits fter it hs built such reputtion. Thus, there must be some product differentition or other source of profits or qusi-rents in the equipment mrket. In fct, vigorous but imperfect competition chrcterizes mny durble-equipment mrkets. Complex, high-technology products tend to be differentited, even if they re similr enough tht customers cn consider them s prtil substitutes. For exmple, Wng minicomputers tended to be fvored by customers who needed strong document nd imgeprocessing cpbilities; DEC computers by scientific nd engineering users; nd IBM minicomputers by those with lrge dtbses to process. Northern Telecom PBX telephone switches were designed to

8 164 Journl of Economics & Mngement Strtegy mintin complete upwrd comptibility so tht customers cn expnd nd upgrde their system without replcing it; AT & T produced different lines of switches tht re not ll upwrdly comptible. In this section, we hve shown tht the courts hve begun to recognize tht durble-equipment mnufcturers fce trde-off between bove-competitive ftermrket profits from locked-in customers nd competitive losses in the equipment mrket. In the next section, we nlyze this trde-off in model with imperfectly competitive equipment sellers in Section 3 nd in Section 4 with monopoly equipment seller. We use these models to study the role of reputtion. 3. A Model of Competition with Monopolized Aftermrkets In this section, we present simple chrcteristic-spce model of competition between two differentited products where the mrkets for the ssocited ftermrket goods re monopolized by the originl equipment mnufcturers. The model hs the ttrctive feture tht s the trnsporttion costs pproch zero, the model pproches one of undifferentited Bertrnd competition. It lso cn be dpted for comprison with monopoly supplier of both the primry nd the ftermrket good, s we show in the following section. Using this model, we show tht competitive firms will lwys hve n incentive to price their Ž monopoly. ftermrket sles bove competitive levels, even s the degree of differentition between the firms becomes rbitrrily smll nd the foremrket becomes rbitrrily close to undifferentited Bertrnd competition. We demonstrte tht no equilibrium cn exist in which the price of the ftermrket product lwys is set equl to mrginl cost. 3.1 Model Assumptions Consider the mrkets for durble good, which we cll equipment, nd n ssocited ftermrket product, which we cll service. We suppose there re two firms, nd b, from whom the customer my purchse new equipment, but tht ech equipment mnufcturer is the only seller of service ssocited with its brnd. 11 Thus, fter 11. For now we suppress subscripts denoting different equipment brnds, becuse the modeling ssumptions hold for ech brnd. We introduce brnd subscripts below when we begin to nlyze consumer choice between brnds.

9 Mrket Power in Proprietry Aftermrkets 165 buying nd using equipment in period t, in period t 1 the consumer cn Ž. 1 use the product in its deprecited stte with no ddition of service, Ž. 2 buy some quntity of service from the sme mnufcturer to enhnce the equipment, or Ž. 3 scrp the used equipment nd purchse new equipment gin, from either mnufcturer. 12 The equipment nd service products ech hve constnt unit production costs, C nd c respectively, identicl for ll firms. We ssume tht consumers re locked in to their equipment mnufcturer if they wnt to purchse service: n owner of firm s equipment cnnot buy service from firm b. However, we do not need to ssume lock-in costs for subsequent equipment purchses, nd thus for simplicity do not introduce equipment brnd switching costs. 13 Tht is, consumer cn buy ny brnd from ny vendor with no penlty, regrdless of which brnd she my hve purchsed in the pst. We further ssume tht there is no symmetric informtion between buyers nd sellers. The firms re locted t opposite ends of unit-length chrcteristic-spce line. Consumers most preferred points in the spce re distributed uniformly long the line, with the totl number of consumers normlized to one. Ech consumer hs reservtion vlue, s, for the idel good locted t the consumer s most preferred point in chrcteristic spce. This vlue is high enough tht ech consumer buys one unit of the good from the deler tht offers the highest expected discounted consumer surplus. All consumers hve equl trvel costs, per unit distnce, tht reflect the loss in consumer surplus from hving to consume good tht differs from the consumer s most preferred chrcteristic. Since this cost is ssocited with persistent product differentition, it is incurred in every period, whether the consumer uses new or old equipment. Thus, consumer locted t distnce d from firm receives gross surplus from owning the equipment: CS 1 s d from using 2 Ž. new product nd CS s d h f q from using period-old product tht hs been ugmented with q units of service, where h represents the deprecition in the vlue of the product from one Ž. period of use. The function f is the consumer surplus from q units 12. We ssume enough homogeneity cross consumers tht there will be no polymorphous equilibrium with some consumers buying used equipment from others who then buy new. Allowing for enough heterogeneity to support trde in used goods does not chnge our min result. 13. Adding brnd-switching costs would strengthen our results; tht is, with brnd-switching costs ftermrket prices would devite even frther from mrginl cost.

10 166 Journl of Economics & Mngement Strtegy of service, nd is simply the integrl of the inverse demnd for service, with fž. 0 0, f Ž. 0, nd f Ž. 0. To mke the nlysis informtive, we ssume for ech brnd tht Ž. 1 s d h fžž.. q c cqž. c s d C for some q 0 nd Ž. 2 f Ž. 0 c. The first ssumption ensures tht reusing the period-old product would be preferred to buying new unit of the sme brnd ech period if both new equipment nd service were priced t cost. The second ssumption ssures tht purchse of t lest smll quntity of service would give positive net consumer surplus if it were priced t cost. Together, the two ssumptions imply tht in first-best solution consumers use unit of equipment for two periods nd purchse some positive quntity of service in the second period. We need to specify the flow of consumers into the mrket over time. For now, we ssume tht there re two equl-sized consumer cohorts who first wnt to purchse new equipment in successive periods. If consumers use equipment for two periods, then they repper s customers for new equipment in the third period, nd we hve sttionry overlpping-genertions model. 14 We ssume consumers live forever nd hve n infinite decision horizon subject to discounting with fctor per period. We will return to the issue of mrket growth or decline below. The fundmentl ssumption of our nlysis is tht firms cnnot credibly commit to future service prices. Therefore, to complete the model we must specify consumer beliefs bout future service prices, since they re purchsing equipment with useful life of two periods, nd the vlue of new equipment tody will depend on the expected service price tomorrow. We tke simple pproch to beliefs: consumers tke the firm s service price in period t to be the best indictor of the price the firm will chrge in period t 1. There re severl points tht support our use of this simple ssumption. First, costs nd the number of consumers re constnt over time in our model nd the horizon is infinite, so there re no exogenous drivers tht would tend to mke prices chnge over time. Second, this model of consumer beliefs corresponds closely to ctul behvior suggested by the evidence of mny ftermrket ntitrust cses. 15 Third, nd most importntly, our gol is to exmine the clim 14. Alterntively, one could view this s new equl-sized cohorts ppering every period nd living for two periods. 15. Testimony in mny of the legl cses cited in the previous section indictes tht consumers who consider service costs t ll in choosing mong brnds mke roughly this ssumption. We re wre of no cses in which ttempts to clculte lifetime costs of equipment hve included forecsts of future chnges in service prices beyond simple extrpoltion or infltion djustment.

11 Mrket Power in Proprietry Aftermrkets 167 tht the service price will lwys be set t the competitive level. Since costs do not chnge over time in the model, consumers expecttions of constnt prices over time will be fulfilled if this clim holds true. For now we suppose tht in equilibrium the price of service is sufficiently low reltive to the price of new equipment from ech firm tht consumers will lwys prefer to keep nd service used equipment fter one period, rther thn scrp it nd buy new ech period. We return to this ssumption below in order to study the constrining effect tht the option to scrp used nd buy new hs on service pricing. We summrize the model before we undertke the nlysis: A stedy number of new customers rrive to purchse equipment from one of two firms in ny period. Equipment is sufficiently durble tht consumers choose to keep it for two periods, while purchsing service to enhnce its secondperiod vlue. Consumers expect future service prices to be the sme s current prices. Firms re monopolists over service for their own brnd of equipment, but set the service price knowing tht current service prices ffect current consumer willingness to py for new equipment. Equipment prices re set under conditions of differentited product duopoly competition, with uniform distribution of consumer types long chrcteristics line seprting the two equipment brnds. 3.2 Anlysis of the Duopoly Model We hve specified rther generl infinite-horizon overlpping-genertions duopoly gme. Our gol is not to find ll equilibri of this gme, however. We re motivted by the fundmentl question repetedly rised in ntitrust lwsuits nd the ensuing cdemic discussion: will competition in the equipment mrket sufficiently discipline ftermrket service pricing so tht there is no exercise of monopoly power in the ftermrket? We interpret n exercise of ftermrket mrket power to imply tht p t c for t lest some periods t, where p is the ftermrket price. Therefore, we sk the following question: is there n equilibrium in the mrket described in which firms choose constnt service price equl to mrginl cost in every period: p t c, t? Our pproch is to use the necessry conditions for constntt price equilibrium to show tht if such n equilibrium exists, p p c, i.e., service price will lwys be bove cost. Tht is sufficient to nswer the min question, since if nonconstnt-price equilibrium

12 168 Journl of Economics & Mngement Strtegy exists, it is strightforwrd to show tht it must hve p t c in t lest some periods t. 16 After we show tht in constnt-price equilibrium Ž if one exists. service price is bove cost, we will estblish tht Mrshllin welfre is less thn it would be if mrginl-cost service pricing previled in ll periods, thus estblishing tht this exercise of mrket power hs dverse welfre consequences. After estblishing the min result, we further interpret the necessry conditions to chrcterize the effects of the discount rte or mrket growth rte on service pricing. We then exmine how vritions in the degree of equipment competition from undifferentited Bertrnd competition to monopoly mrkets ffect the result tht service is priced bove cost. Finlly, we consider the effect tht competition from new equipment hs on service prices, nd with this generlized model we cn lso exmine how the degree of equipment durbility ffects service pricing. Consider the consumer surplus from equipment purchsed in the current period nd service on tht equipment in the next period. If consumer locted t distnce d from firm ssumes tht she will fce the sme price for service next period s offers currently, p, she gets expected net consumer surplus from brnd of Ž Ž.. Ž. Ž. CS s d P s d h f q p pq p, 1 where cpitl P refers to equipment nd smll p nd q refer to the service product. The consumer is distnce 1 d from firm b, so her expected consumer surplus from firm b is given by CS s Ž 1 d. P b b Ž. Ž Ž.. Ž. Ž. s 1 d h f q p pq p. 2 b b b The consumer who is indifferent between buying from firm nd from firm b mrks the boundry between the two firms mrkets. Setting the consumer surpluses equl nd solving for d yields the mrket boundry, denoted d: ˆ Ž 1. Ž P P. b dˆ, Ž 3. 2 Ž After we prove our min result, it is esy to show tht no equilibrium exists in t ˆt which p c for some t nd p c for ll other ˆt t.

13 Mrket Power in Proprietry Aftermrkets 169 where, function of p nd p b, is the difference in the net surplus of ech brnd, nd b, tht the consumer would receive in the second period fter buying service: 17 csž p. csž p. b Ž Ž.. Ž. Ž Ž.. Ž. f q p pq p f q p pq p. b b b We ssume tht production costs of both the equipment nd service products re liner in quntity; without further loss of generlity, we tke these costs to be zero, so tht firm s equipment nd service profit on one genertion of equipment sles is given by Pd ˆ pqž p. d ˆ dˆ P, Ž 4. where pqž p., the profit per unit of equipment from sles of service, nd similrly for firm b. We now proceed to chrcterize the profit-mximizing equipment nd service prices for ech firm through nlysis of necessry conditions for n equilibrium. To do this, we derive the infinite-horizon vlue function for ech firm t given moment in time, ssuming n rbitrry initil mrket shre, d 0. Recll tht we restrict our nlysis to constnt pricing strtegies, so the choice vribles re P t P nd p t p, t, for ech firm. If firm expects to fce stedy strem of customers choosing between brnds for new equipment in tht period, then it will ern profits from ech customer genertion of dˆp. If the firm expects sttionry equilibrium behvior from its competitor, 18 then, given current mrket shre of d 0 for customers lredy locked in, the present vlue of its strem of profits forevermore will be / 0 V d Ž p. dˆ Ž P, P, p, p. P Ž p. 1. Ž 5. b b ž 1 A strtegy choice is simultneous nnouncement of Ž P, p., so necessry conditions for n optiml strtegy cn be found from the 17. To gurntee tht the duopolists cover the entire mrket, we lso ssume tht the gross surplus from service-ugmented equpiment is sufficiently lrge compred to the trvel cost: s s h fžqž p Ž 1.. If the inequlity does not hold, then the duopolists will ern higher profits by pricing in such wy tht the mrkets of the two do not overlp; tht is, ech duopolist chooses to be locl monopolist. 18. If constnt-price equilibrium exists, then these expecttions will be fulfilled when tht equilibrium is relized.

14 170 Journl of Economics & Mngement Strtegy sttionry points of V with respect to Ž P, p.. Substituting for dˆ from Ž. 3 nd setting the derivtive of Ž. 5 with respect to P equl to zero, we obtin firm s best-response function: Ž 1. P Ž. b P. Ž 6. 2 Doing likewise for P, nd then solving the two equtions simultneb ously, yields two necessry conditions for equilibrium equipment prices tht re solely function of service prices nd exogenous fctors: P Ž 1. Ž p, p. Ž p. 2 Ž p. Ž 7. b b b 3 nd P Ž 1. Ž p, p. Ž p. 2 Ž p.. Ž 8. b b b b 3 We cn substitute these expressions into V nd tke the deriv tive with respect to the service price p to obtin Ž. Ž. b V d, Ž 9. p Ž 1. 3 where primes indicte derivtives with respect to p. The first term is the chnge in current-period profits on service from rising p. The second term hs three fctors, the first of which is the present-vlue fctor for the infinite-horizon strem of profits. The second fctor is equl to the firm s equilibrium mrket shre or quntity sold of equipment, d, ˆ fter substituting in the solutions for optiml equipment prices P nd P b. The third fctor is proportionl to the difference between the loss in consumer surplus nd the gin in profits from n increse in the price for service p. The difference is the mrginl dedweight loss from rising the price of service. To evlute this expression, note tht t p 0 Ž mrginl cost., totl surplus is mximized, nd thus mrginl surplus 0. Tht is, to first-order, slight increse in the price of service from mrginl cost rises service profits by the sme mount tht it lowers

15 Mrket Power in Proprietry Aftermrkets 171 consumer surplus. Then V p p 0 0 Ž. d 0, 10 nd profit-mximizing firm with n instlled bse will lwys set the price of the service product bove mrginl cost. We hve now proven our min result: Result 1: No equilibrium exists in which the firms chrge service price equl to mrginl cost in every period. If constnt-price equilibrium does exist, the firms chrge service price bove mrginl cost. This result is quite generl, not n rtifct of the specific model. If the price of service is equl to its mrginl cost, smll increse in tht price will hve only second-order effect on future profits once the price of the equipment is optimlly djusted downwrd, becuse this cretes only second-order dedweight loss; but it will hve first-order effect on current-period profits from selling the service product, becuse the ssocited equipment units lredy hve been sold. For this reson, it will lwys be profitble for the firm to rise the price of service bove mrginl cost. In fct, this result relies on none of the ttributes of the sptil model beyond the vlue function Ž. 5. Eqution Ž. 5 mkes it cler tht there re two fundmentl forces t work in the firm s optimiztion problem t ny point in time. The second term on the right-hnd side of Ž. 5 is the present vlue of profits the firm could ern in ggregte from every genertion of buyers except those who hve lredy purchsed from it. Given the consumer beliefs we hve posited, the firm could chrge price equl to mrginl cost for service strting tody, nd in tht wy could exctly mximize the profit it erns on ll future genertions of buyers Žrecll t p c we hve 0.. If tht were the entire clcultion, the firm would simply price service t its mrginl cost. But t ny point in time, the firm will lso hve the first term on the right-hnd side of Ž. 5. This term represents the profit it cn ern on the consumers who hve lredy purchsed their equipment. This term is mximized by chrging the monopoly price for service. As we show in the next subsection, the firm would like to chrge the monopoly service price to these locked-in customers while still ssuring future customers tht it will chrge lower price Ž equl to mrginl cost. when they return to buy service. This is exctly wht the firm would do if it could mke binding

16 172 Journl of Economics & Mngement Strtegy commitment to future prices, but we re interested in the typicl cse in which long-term complete contrcts re not fesible. 3.3 Locked-in Customers nd Commitment Since the result relies crucilly on the instlled bse of customers who lredy own equipment, d 0, one might wonder if our conclusion fils when there is no instlled bse Žor for new entrnt in model tht permits entry.. Our result is robust to this concern. We hve exmined the necessry conditions for n equilibrium in which the firms choose to restrict themselves to constnt pricing over time. It is esy to show, however, tht t t 0, with no instlled-bse customers, constnt-price strtegy with p c cnnot be optiml in the wider strtegy spce tht includes the possibility of nonconstnt pricing over time. To see this, suppose tht the firm did nnounce p c in the first period. In the second period it would hve some instlled 0 Ž bse d P, P, p, p 0. b b. At this point, it would py to devite from p c by reverting to the strtegy we nlyzed bove, with p c. The min clim holds: if the firm cnnot precommit to service prices over the lifetime of equipment, it will not be profitble to follow strtegy of constnt service prices equl to cost. Further exmintion of the first-order condition Ž. 9 lso leds to the conclusion tht the firm will not choose to chrge the sttic monopoly price for service, where 0, either. At tht point, the first term in Ž. 9 would be zero. The second term, however, would be negtive, 19 so the derivtive of the vlue function with respect to p would be negtive. Thus, if constnt-price equilibrium exists, it will occur with price of service tht is strictly greter thn mrginl cost, but strictly less thn the sttic monopoly price. 20 Would the firms prefer to commit to mrginl-cost pricing if they could? Suppose commitment technology Že.g., fesible longterm complete contrcts. were introduced t some dte when the two firms lredy hve some locked-in customers. We show tht in this cse it would be n equilibrium for both firms to chrge the full monopoly service price to current locked-in service customers, but to commit to chrge service price equl to mrginl cost therefter. 19. The fctor Ž 1. is positive for the relevnt rnge of Ž 0, 1.. The second fctor is positive so long s firm hs positive mrket shre. The fctor is negtive for p 0, becuse price increses bove mrginl cost decrese consumer surplus by more thn they increse profits, thus creting incresed dedweight loss. Hence, the product of these three fctors will be negtive. 20. The two results on the first-order condition for the vlue function t p 0 Ž mc. nd p pm re sufficient to gurntee tht there is t lest one locl mximum for mc p p m.

17 Mrket Power in Proprietry Aftermrkets 173 First, reconsider firm s necessry condition for optiml service pricing in Ž. 9. With commitment technology, firm cn now chrge different price to current locked-in service customers nd future equipment purchsers, so the two terms in Ž. 9 re decoupled nd the firm optimizes by setting them seprtely to zero. This occurs when the current service price is the monopoly price Ž 0., nd the future service price is set to mrginl cost Žso tht totl mrginl surplus 0.. The symmetric nlysis holds for firm b. From Ž. 7 nd Ž. 8, both firms then chrge n equipment price P P Ž 1. b. With equl service nd equipment prices they ˆ 1 split the mrket, d from Ž. 2 3, nd ech firm erns profits 1 Ž 1. on ech two-period genertion of equipment sles 2 from Ž. 4. By comprison, without commitment, Ž. 7 nd Ž. 9 would led firm to chrge P Ž 1., nd two-period genertionl 1 profits would still be Ž 1. from Ž Thus, if both firms did commit, the profits on ll future genertions of equipment sles would be the sme s in the no-commitment cse. However, they would be ble to chrge the monopoly service price on current locked-in customers, nd, s we showed bove, the no-commitment price is less thn the monopoly price. Thus, both firms re better off with commitment thn without. When commitment is possible, it is n equilibrium for both firms to commit to chrging p mc in the ftermrket in ll future periods. To see this, suppose firm devites to noncommitment strtegy. The future service price will be set bove mrginl cost, nd the current service price will be set equl to the future price Žby ssumption., below the monopoly price s shown bove. Obviously, profits on current locked-in customers will fll. In ddition, when p increses for future customers, fžqž p.. fžqž p.. b pqž p. b b decreses becuse consumer surplus decreses, nd thus per-customer genertionl profits on new equipment sles fll. The sme clcultion on implies tht P increses, nd thus firm s mrket shre, not surprisingly, will fll, so it erns smller genertionl profits on fewer customers. Thus, ech term in the vlue function Ž. 5 decreses, nd firm does not wish to devite from committing to future mrginl cost pricing of service. The symmetric nlysis holds for firm b, nd simultneous commitment is Nsh equilibrium. Consumers lso benefit from the introduction of commitment technology. As the price of the ftermrket product rises, consumers lose on the infrmrginl nd mrginl units of service. Becuse the duopolists compete for the consumers in the equipment mrket, the loss to consumers on the infrmrginl units is recovered vi lower

18 174 Journl of Economics & Mngement Strtegy equipment price. The consumers do not, however, recover the loss of net consumer surplus on the mrginl units. Thus mrginl-cost service pricing is Preto improvement. 21 It might pper tht in our nlysis effectively we hve llowed the firm to commit to future prices, since consumers ssume tht tomorrow s price is the sme s tody s. However, this merely implies tht if the firm follows constnt-price strtegy, consumer beliefs will be fulfilled. There is nothing bout the beliefs ssumption tht stops the firm from rising price. It is true tht for our proof of Result 1 we ssumed the firms follow constnt-price strtegies. We did not, however, llow the firm to mke n enforceble commitment to chrge constnt price Ž equl to mrginl cost.. Thus, it is not possible in our model for the firm to chrge the monopoly price to current locked-in customers nd mrginl cost to ll future customers, which is wht it would do if commitment were possible. 3.4 The Effect of the Discount Rte nd Mrket Growth Ž. From 9 we cn see the effect of the discount rte: Result 2: If constnt-price equilibrium exists, the exercise of mrket power in the service mrket will be greter the higher is the discount rte. As goes to zero, so tht future profits receive decresing weight, service is priced closer to the sttic monopoly level Ž 0.. As goes to one, so tht future profits receive n incresing weight, service is priced closer to mrginl cost Žusing L Hopitl s ˆ rule, the first-order condition requires 0, which implies p 0.. Although is the discount fctor, it cn be interpreted s mesuring chnge in the expected size of the mrket. If the mrket is growing over time, then higher mrket shre for future equipment sles is of greter vlue, ssuming tht new customers in the mrket lern of ftermrket pricing reputtions. The greter weight on future sles 21. Similr resoning llows us to rule out n equilibrium in which p t c for some ˆt t nd p c for ll other ˆt t. A price below mrginl cost for service rises Ž expected. consumer surplus by less thn it lowers producer profits, so even ignoring the incentive to exploit locked-in consumers with higher service price, producer could increse its profits nd consumers expected surplus t the time they buy the equipment by rising its service price to be lwys equl to mrginl cost nd lowering its equipment price commensurtely.

19 Mrket Power in Proprietry Aftermrkets 175 cn be expressed s n increse in. 22 If the mrket is declining in size, then future mrket shres is less vluble, implying lower nd n increse in the price of service towrds the monopoly level. 3.5 The Effect of Incresing Competition The ntitrust cses tht in prt motivted this inquiry generlly ssume tht the mrket for equipment is highly competitive. It is not lwys cler just wht is ment, but in mny cses there is little disgreement tht the equipment mrket is competitive. Therefore, we would like to nswer the question whether perfectly competitive equipment mrket sufficiently disciplines the service mrket tht the ftermrket price will be equl to mrginl cost. Elsewhere we present finite-horizon model with perfectly competitive equipment mrket. ŽPlese see the ppendix vilble t for forml nlysis of the perfectly competitive equipment mrket model.. Our min result holds: there is not n equilibrium in which service prices re lwys equl to mrginl cost. In fct, we cn show the stronger result tht in equilibrium service prices re lwys bove mrginl cost; indeed, in some prts of the prmeter spce the service price is set t the monopoly level. However, when we try to solve n infinite-horizon model comprble to the model in this section, n equilibrium does not exist. 23 The problem is simple, but fundmentl: with free entry in the equipment mrket, there re no intrinsic rents to equipment mnufcturing. With zero profits, there is no incentive to build nd mintin reputtion for low service prices. Insted, with the sttic expecttions tht we ssume for consumers, firms lower service prices to build mrket shre, nd then revert to high prices to exploit their customer bse. This dynmic prevents the existence of n equilibrium. However, we cn show tht the min result continues to hold by demonstrting tht setting service prices equl to mrginl cost in every period is not n equilibrium. 22. Strictly speking, this interprettion only holds precisely if the mrket growth rte is such tht it cn represented by once-nd-for-ll increse in, so tht is t higher level but still constnt over time. If chnges for firm, however, we would expect firms to chnge their ftermrket pricing e.g., rising ftermrket prices s it becomes pprent tht product is likely to exit the mrket erlier thn hd previously been expected. In such cses, the consumers sttic expecttions would not be fulfilled over the periods in which chnges. 23. Anlogous existence problems rise in the qulity-reputtion literture. See, e.g., Klein nd Leffler Ž

20 176 Journl of Economics & Mngement Strtegy In this section we tke different pproch to showing the effect tht incresing equipment competition hs on the pricing of ftermrket service. As we let the trnsport cost go to zero, the degree of product differentition in our duopoly model goes to zero. In the limit, we hve n undifferentited Bertrnd duopoly gme, nd the usul outcome obtins: industry profits re competed to zero. Even with undifferentited product Bertrnd competition, service is still priced bove cost, nd our min result holds: equipment mrket competition does not induce competitive ftermrket pricing. To see the result, exmine the necessry conditions for constnt-pricing equilibrium, Ž. 9. As 0, the second term in squre brckets hs denomintor tht goes to zero. In order to stisfy this first-order condition, then, the service price must be chosen so tht the numertor lso goes to zero. Tht is, s 0 then b 0. Using this fct nd tking the limit of the equipment mrket price in Ž. 7 s 0, we get P, which is to sy tht the two-period profits in eqution Ž. 4 go to zero. By pplying L Hopitl s ˆ rule to expression Ž. 3 for the mrket-shre boundry d, ˆ we see tht ˆ 1 the mrket is evenly split Ž d. 2. Thus, s product differentition goes to zero, we get the stndrd Bertrnd duopoly result Žwith symmetric costs. tht industry profits re competed to zero nd the mrket is eqully divided. If we now evlute the limit of the necessry condition Ž. 9 with service price equl to cost, p 0, s we did before, we see tht the sme result holds: if there is constnt-price equilibrium, it must be tht the service price in tht equilibrium is bove cost, becuse the derivtive of the vlue function with respect to price is positive when evluted t mrginl cost, s in expression Ž 10.. This result for undifferentited Bertrnd duopoly shres nother feture with our finite-horizon perfect-competition model: we cn show tht equipment is priced below its mrginl cost. Service prices re bove cost, nd thus service profits re positive. However, we hve shown bove tht two-period profits from the sle of equipment nd service re zero. Thus, equipment profits re negtive, or P C; undifferentited Bertrnd competitors lower equipment prices to compete wy ll of the nticipted service profits. As in the differentited duopoly cse, the bility to commit to efficient service prices yields Preto improvement. Although firm profits remin t zero nd thus re not improved, consumers re mde better off. The intuition for the forml rgument is the following: ll consumers buy equipment in either cse, so first-period socil welfre is unchnged. The reduction in second-period service price

21 Mrket Power in Proprietry Aftermrkets 177 reduces dedweight loss from the choice of how much service to purchse, so second-period nd overll welfre is incresed. Firm profits re zero in both cses, so consumers must be better off. More generlly, we cn evlute the role of competition by looking t the conditions for stedy stte in this model. Eqution Ž. 9 nd the equivlent condition for pb implicitly define best-response functions tht together determine n equilibrium t ny point in time. 0 In stedy stte, however, third condition must hold, d d. ˆ In this cse, the sttic expecttions bout service prices tht we hve ssumed for consumers re fulfilled. Imposing this condition on Ž. 9, gin substituting for dˆ from Ž.Ž. 3, 7, nd Ž. 8, nd then fctoring out the dˆ expression gives the stedy-stte conditions Ž. Ž. b Ž. V 1 2 0, p Ž. 11 nd the equivlent expression for p b. The first fctor is the equilib- rium mrket shre, so for the equilibrium to exist t n interior solution, the second term must be equl to zero. We cn see from this tht the degree to which the price of service exceeds the cost of providing service depends only on the shpe of the demnd curve for service nd the degree to which the firm discounts future profits. Notbly, does not pper in the second fctor. The extent of substitutbility mong brnds in the equipment mrket, which determines the severity of competition, does not ffect the equilibrium price of the ftermrket product in this model. 24 This surprising result depends on the ssumption tht consumer s strength of preference between brnds,, nd loction on the line is uncorrelted with her demnd for the ftermrket product. When this is true, the service price is not useful policy instrument for mximizing profits s the level of competition chnges. The firm sets service price to optimlly blnce the reputtion nd lock-in mrket power incentives. It responds to chnges in competition only by djusting its equipment price. In some situtions, however, my not be independent of the demnd for service or the importnce of reputtion. In those cses, the chnges in cn influence the ftermrket price, s we discuss in Section 5. More importntly, this result 24. This result is conditionl on our current ssumption tht new equipment is not n economiclly vible lterntive to servicing used equipment. We relx this ssumption below.

22 178 Journl of Economics & Mngement Strtegy will not necessrily hold if consumers consider bndonment of the equipment fter one period relistic lterntive, s we will discuss below. While eqution Ž 11. nd the equivlent expression for pb to- gether chrcterize the stedy stte in this mrket, we hve not studied the dynmic pth to the stedy stte. Awy from the stedy stte, the optimum conditions for service prices will not be exctly s shown in Ž 11., becuse there will be dynmic considertion: given shre of equipment sles this period will ffect the optiml service price next period, which will help determine the shre of equipment sles next period nd thus the optiml service price in two periods, etc. In tht process, it ppers tht might ffect the degree of bove-cost pricing of the ftermrket product. Nonetheless, competition will still fil to drive the ftermrket price to mrginl cost. 3.6 Competition between Service nd New Equipment We hve thus fr nlyzed the model without recognizing the possibility tht consumers might bndon equipment fter one period nd purchse new equipment rther thn servicing the used equipment. Given the structure of the model in which consumers re homogeneous except for their loction on the line nd must py the trnsporttion cost ech period regrdless of whether they service used equipment or buy new it is cler tht there will be threshold price of service reltive to equipment tht would induce ll of the customers of firm to bndon their used equipment. This would never be efficient under the ssumptions of the model, nd firm would lwys be better off setting price just below this threshold thn inducing equipment bndonment. Thus, there re two types of equilibri tht could occur, depending on whether or not the equipment bndonment constrint is binding. To ssure tht the consumer services equipment in the second period rther thn bndoning it nd buying new, the necessry condition is tht s d P s d h fžqž p.. pqž p., or P h fžqž p.. pqž p.. This constrint is more likely to bind if equipment is inexpensive Ž P smll. reltive to the loss in vlue from using second-period piece of equipment fter optiml servicing h fžqž p.. pqž p.. If equipment is very expensive nd used equipment hs high vlue reltive to new, then this constrint won t bind nd the discussion bove will correctly chrcterize the mrket. If the constrint does bind, then new equipment competes with servicing used equipment, which chnges the effects of competition