Inducing Downstream Selling Effort with Market Share Discounts

Transcription

1 Inducng Downstream Sellng Effort wth arket Share Dscounts Davd E. lls 1 Department of Economcs P.O. Box Unversty of Vrgna Charlottesvlle, VA (phone) (fax) mlls@vrgna.edu September, 2009 Forthcomng n the Internatonal Journal of the Economcs of Busness

2 Inducng Downstream Sellng Effort wth arket Share Dscounts JEL Classfcaton L11 & L41 Keywords: arket Share Dscounts, Loyalty Dscounts, Exclusonary Behavor, Procompettve Effects Abstract Loyalty dscounts and rebates are prcng schemes that offer ncentves to buyers for reachng or exceedng certan sales thresholds. In the case of market share dscounts, thresholds are expressed as a percentage of the buyer s total purchase requrements. Although market share dscounts may have exclusonary effects under certan crcumstances when a seller has sgnfcant market power, there are plausble nonexclusonary reasons for offerng them as well. Two such reasons rent extracton and nducng downstream sellng effort are explored n ths paper. The paper consders the case of a manufacturer who sells a dfferentated good through a network of heterogeneous, non-exclusve retalers. The manufacturer offers market share dscounts to nduce non-contractble sellng effort such as brand-specfc nformaton or customer servce from those retalers who possess certan unobservable characterstcs. In some nstances, market share dscounts nduce ncreased sellng effort and mprove market performance as compared to lnear prcng. In other nstances, they have no effect on aggregate benefts, but merely shft the rents created by nduced sellng effort upstream to the manufacturer. In no nstance, as long as the producers of substtute goods retan suffcent sales to reman vable, do market share dscounts mpar market performance. 2

3 I. Introducton Loyalty dscounts and rebates are prcng schemes that offer ncentves to buyers for reachng or exceedng certan sales thresholds. There are many knds of loyalty dscounts. Quantty dscounts have thresholds expressed n terms of a buyer s unt purchase volume. Some quantty dscounts are appled to all of the unts purchased by the buyer f the sales target s acheved. Others are appled only to those unts purchased n excess of the target. 2 arket share dscounts have thresholds expressed as a percentage of the buyer s total purchase requrements. These dscounts typcally are appled to all of the unts purchased f a buyer reaches or exceeds a market share target (Patrck Greenlee and Davd Retman, 2005). 3 Whle some loyalty dscounts arse n retal markets, market share dscounts usually arse n wholesale or ntermedate goods markets. In recent years, the offer of loyalty dscounts by domnant frms has become a promnent anttrust ssue. 4 Loyalty dscounts, ncludng those wth market share thresholds, have been challenged under the anttrust laws n the U. S. as well as n Europe for ther putatve exclusonary effects. 5 These practces typcally receve harsher treatment n Europe than n the U. S. In Europe, the cheln court concluded that a domnant frm s loyalty dscounts are abusve unless they are justfed by the frm s cost structure. In the U. S., courts generally have been more permssve because they recognze that loyalty dscounts are not always or necessarly exclusonary. arket share dscounts are controversal because they explctly nvte buyers to substtute the seller s goods for those of rvals. 6 Ths feature s not problematc n markets that are structurally compettve. But n markets where there s a domnant frm, 3

4 that frm s market share dscounts may reduce the demand for ts rvals goods to levels so low that these rvals cannot recover ther fxed costs. The domnant frm s market share dscounts may deter small-scale entry for smlar reasons. 7 Of course the ratonale for market share dscounts, even n the case of a domnant frm, may not be excluson. Non-exclusonary reasons for ths knd of prcng are rent extracton and mproved effcency n producton or dstrbuton. Lke other forms of prce dscrmnaton, dscounts based on market share performance may be offered by sellers to extract surplus from buyers rather than to weaken or elmnate compettors. Rent extracton per se usually s not an anttrust offense. Denns W. Carlton and Kenneth Heyer dstngush frm conduct that extracts surplus from conduct that extends market power and propose that [c]onduct merely to extract surplus the frm has created ndependent of the conduct s effect on rvals should be permtted. Conversely,... conduct that extends the frm s market power by mparng the compettve constrants mposed by rvals... presents a legtmate cause for concern (p. 1). Another non-exclusonary reason for offerng market share dscounts s that, n some crcumstances, they ncrease the effcency of dstrbuton channels. Ths paper demonstrates that manufacturers who dstrbute ther goods through non-exclusve retalers may use market share dscounts to nduce non-contractble downstream sellng effort that mproves market performance. The paper consders a manufacturer who sells a dfferentated good through a network of retalers who also dstrbute substtute goods. The manufacturer could be a domnant frm, but even f not the frm stll has some degree of market power because of 4

5 product dfferentaton. Retalers serve separate retal markets wth dfferent numbers of consumers. Each retaler, due to ts sze, locaton, or some other dstngushng characterstc, has market power when resellng the goods to consumers n ts own market. For nstance, many retalers have some degree of market power n the sale of one good because consumers shop for bundles of several goods. Shoppng for bundles to reduce shoppng costs reduces consumers n-store demand elastctes for specfc goods. 8 Some consumers are wllng to pay a premum for the manufacturer s dfferentated good, but others are not. Retalers are postoned to supply brand-specfc nformaton or perform brand-specfc customer servces that ncrease the number of consumers who are wllng to pay a premum for the manufacturer s good. Ths sellng effort s non-contractble because montorng performance would be costly or nfeasble. The retaler s sellng effort must be drected at all of ts consumers because the retaler cannot dstngush (ex ante) whch consumers are susceptble to ts nfluence. For one type of retaler, the surplus created by brand-specfc sellng effort s greater than ts cost. But for another type of retaler, sellng effort costs more than the surplus t creates. The manufacturer cannot observe (ex ante) a retaler s type or sze. Interactons between the manufacturer and the retalers are modeled as a two-stage game where the manufacturer offers terms of sale frst followed by retalers responses. The paper shows that n ths settng the manufacturer can use an across-theboard market share dscount to separate retalers by type but not by sze. Low-cost retalers of any sze are nduced to provde sellng effort and are compensated accordngly. 9 Hgh-cost retalers are nether nduced nor compensated. Wth more 5

6 retaler types, further separaton can be acheved usng mult-ter market share dscounts. To assess the welfare effects of ths prcng tactc, outcomes are compared to scenaros where the manufacturer s constraned by anttrust or regulaton to charge unform wholesale prces. Based on ths comparson, market share dscounts mprove market performance by nducng otherwse underproduced sellng effort n some crcumstances. In other crcumstances the same dscounts merely shft rents created by retalers sellng efforts upstream to the manufacturer. Ths analyss ndcates that ntroducng market share dscounts never mpars market performance. Ths result even extends to a domnant frm s market share dscounts as long as the producers of substtute goods retan suffcent sales to reman vable. Other across-the-board prcng schemes, such as quantty dscounts, mnmum purchase requrements, and resale prce mantenance cannot acheve the same result. The dstngushng feature of market share dscounts s that they utlze proportonal targets that do not dscrmnate by frm sze. Prevous papers nvestgatng market share dscounts have focused on rent extracton and exclusonary effects. None have explored ther use for nducng downstream sellng effort. Patrck Greenlee and Davd Retman (2004) examne rent extracton n a model where dfferentated-products Bertrand duopolsts sellng to compettve buyers compete va market share dscounts. Among other results they fnd that, n equlbrum, buyers take advantage of only one of the sellers market share dscounts. The other seller s not excluded from the market and the effect of market share dscounts on consumers s ambguous. 6

7 Lesle. arx and Greg Shaffer also focus on the rent shftng effects of market share dscounts n a model wth two sellers and a sngle buyer who contracts sequentally wth the sellers. In ther analyss market share dscounts only shft rents and have no effect on the prces consumers pay, product varety, or welfare (p. 26). Emphaszng the smlarty of market share dscounts and exclusve dealng, Wllard K. Tom, Davd A. Balto and Nel W. Avertt focus on potental exclusonary effects. They reason that snce complete foreclosure from the market s not necessary for an exclusve dealng arrangement to be held llegal, market share dscounts wth suffcent foreclosure also may be antcompettve. 10 Of course, the smlarty of market share dscounts and exclusve dealng also suggests procompettve effects. Benjamn Klen and Andres V. Lerner observe that [a] procompettve justfcaton for... preferred dstrbuton contracts [such as market share dscounts]... may appear to be related to the procompettve justfcaton for exclusve dealng contracts, wth exclusve dealng merely nterpreted as an extreme form (100%) of preferred dstrbuton (p. 562, footnote omtted). There s some dscusson n the lterature of procompettve market share dscounts. 11 Davd Spector observes that, as compared to quantty dscounts, the proportonal target feature of market share dscounts makes them a superor nonlnear prcng tactc where the sellers goal s to ncrease sales to dfferent szed buyers by offerng margnal prces that are below average prces. He also suggests that market share dscounts may be used by a manufacturer to protect ts nvestment n tranng retalers by lmtng the extent to whch competng manufacturers could free rde on that 7

8 tranng. 12 The use of market share dscounts as a mechansm for nducng effcent downstream sellng effort s not wdely recognzed. II. Ordnary Lnear Prcng Suppose frm produces a dfferentated good and dstrbutes t to consumers through retalers that serve separate retal markets. Undfferentated versons of the same good are produced by compettve manufacturers and are sold to consumers through the same retaler network. Every producer has constant margnal costs whch to smplfy matters are assumed to be zero. Frm s cost of dfferentatng ts brand s fxed and sunk. Retalers markets have dfferent numbers of consumers, but the manufacturer cannot observe (ex ante) the exogenous sze of any retaler s market. Retalers margnal costs of dstrbuton are constant and also are assumed to be zero. Suppose retaler s market has a contnuum of h consumers, where h 0 R. Every consumer (n every market) has a reservaton prce of 1 for a sngle unt of an undfferentated brand of the good. Some consumers recognze and value brand s dstngushng characterstcs and have a reservaton prce of 1 z for a sngle unt of that brand, where z (0,1). 13 The -preferrng fracton of consumers n every market s (0,1). The remanng consumers are ndfferent among all brands ncludng brand. Every consumer (n every market) maxmzes her surplus by purchasng one unt of an undfferentated brand, one unt of brand, or nether, dependng on retal prces. 8

9 Just as frm s unable to observe (ex ante) the sze of a retaler s market, the retaler s unable to observe (ex ante) whether a gven customer s -preferrng. However every retaler and frm know the values of z and that characterze the entre populaton of consumers and therefore are the same n every market. The compettve wholesale prce for unts of the undfferentated brands s w0 0. arket sze s the only retaler-specfc characterstc n the model and s unobservable to frm. Ths means there s no reason for the manufacturer to negotate or mpose retaler-specfc terms of sale. Instead, frm offers every retaler the same lnear prce w. Let the frms nteractons be depcted by a two-stage game: n the frst stage frm announces w, and n the second stage each retaler R responds ndependently by settng ts retal prces p and p and purchasng the correspondng 0 quanttes. Begnnng wth stage two, retaler has the opton to earn profts of at least h no matter what wholesale prce frm announces. Ths s because the retaler can resell h unts of the undfferentated brands for 0 p 1 and refuse to carry brand. Because ths opton assures the retaler a proft of 1 from each consumer t serves, frm would be able to sell the retaler h unts of brand f wm zor none otherwse. Thus constraned, frm s proft s maxmzed by chargng are as follow. w z. Equlbrum outcomes 9

10 Proposton 1: For all feasble values of the model s parameters, there s a perfect equlbrum n whch frm charges w z and earns profts of zh from the sale of h unts of brand to retaler, R. Retaler s prces are R p 1 z and p 1 and ts profts are h, R. Every -preferrng consumer (n every market) buys a unt of brand and all other consumers buy unts of an undfferentated brand. Consumers rectangular demands, coupled wth retalers market power, precludes any consumers surplus n equlbrum. Although frm captures the entre ncremental rent created by brand, the avalablty of undfferentated brands allows retalers to retan part of the proft from the sale of brand. Any change n the characterstcs of the undfferentated brands that rases consumers reservaton prces more than the compettve wholesale prce for those brands would ncrease retalers profts on all sales, ncludng sales of brand. The same change would reduce frm s profts. 14 III. Dscounts to Induce Servce Now suppose that retalers can supply useful brand-specfc nformaton about brand, or perform brand-specfc customer servces on behalf of frm. Ths sellng effort ncreases the fracton of a retaler s consumers who wll pay a premum for brand. Some knds of brand-specfc sellng effort by retalers can be specfed and montored by manufacturers wth suffcent ease and precson that ther performance can be nduced contractually. Examples mght nclude advantageous shelf poston or promnent n-store sgnage to call attenton to the brand. Other knds of brand-specfc 10

11 sellng effort, such as featurng a brand n sales presentatons or consultatons wth consumers, are less easly specfed and montored. Some forms of sellng effort are unobservable (to frm ) or are dosyncratc and retaler-specfc. As a practcal matter, ths knd of downstream sellng effort s non-contractble. It s not economcally feasble for a manufacturer to wrte an explct, enforceable, contract wth a dealer for the supply of desred dealer servce (Benjamn Klen and Kevn. urphy, p. 267). Assume that every retaler has the ablty, by provdng relevant nformaton or customer servce, to ncrease the fracton of ts consumers who attach a premum of z to brand from to, where (0,1 ). The reservaton prces of the retaler s remanng consumers are unchanged by the retalers sellng effort. One nterpretaton of ths assumpton s that a fracton of every retaler s consumers have a latent preference for brand that can be unlocked by the nformaton or servce suppled by the retaler. Of course, there s a cost to the retaler of supplyng ths nformaton or servce. And for some retalers the cost exceeds the jont value of that effort to frm- and the retaler. To capture ths knd of heterogenety, we assume that the cost of supplyng the ndcated sellng effort s dfferent for dfferent retalers. Specfcally, assume that there are two types of retalers, L and H. Retaler types and szes are uncorrelated. Every retaler knows ts type and sze, but frm cannot dstngush retalers by type or sze ex ante. The retaler s cost to supply the ndcated sellng effort depends on the frm s sze because the requste nformaton or servce must be made avalable to all of the retaler s customers. Because the retaler cannot dstngush (ex ante) those consumers 11

12 who are susceptble to ts sellng effort, t cannot supply sellng effort to susceptble consumers alone. For retaler RL ths cost s L fh, and for retaler j RH t s H j fh, where f H z f L 0. These nequaltes mean that t s only the type-l retalers (of any sze) whose sellng effort costs less than the benefts t contrbutes. Suppose retalers decde whether to supply the ndcated sellng effort n the second stage of the game when, as before, they set retal prces. Although type-l retalers sellng effort would ncrease jont profts wth frm by ncreasng brand- s share of sales, these retalers have no ncentve to supply that sellng effort unless frm charges a wholesale prce low enough for the retalers to recover ther costs on the ncremental sales those actvtes produce. If frm lacks a less expensve mechansm for conveyng the relevant nformaton or provdng the relevant customer servce, the frm may try to nduce sellng effort from these retalers wth ts prcng. Frm could acheve ths by reducng enough to make t worthwhle for type-l retalers to nvest n the necessary promotonal actvtes. However, an across-the-board prce cut that s just suffcent to nduce sellng effort from type-l retalers would transfer rents to type-h retalers who would not promote brand. Inducng type-l retalers sellng effort n ths way may or may not be w more proftable for frm than settng w z and forgong that sellng effort. In any case, there s a more proftable prcng strategy for frm that employs a market share ncentve. Ths strategy nduces type-l retalers, but not type-h retalers, to put forth the sellng effort sought by frm. It also avods a transfer of rents to type-h retalers whose neffcent sellng efforts are nether sought nor nduced. 12

13 Notce that f frm charges a wholesale prce of fl ŵ z (1) or less for brand, ths would nduce every retaler R to put forth the sellng effort L sought by the manufacturer. Ths s because the retaler s cost fh L would be offset by the ncremental savngs from ncreasng brand- unt sales to ( )h. The prce ŵ would not nduce retaler j RH to supply sellng effort because the retaler s cost fh H j would be greater than the ncremental savngs fhfrom L j ncreasng brand- unt sales to ( )h j. As seen n the followng proposton (proof n the Appendx), frm can offer retalers a prcng menu that ncludes a market share dscount to separate retalers by type. Type-L retalers pay ŵ and provde promotonal support for brand, and type-h retalers pay w z and provde no promotonal support. Proposton 2: For all feasble values of the model s parameters, there s a perfect equlbrum n whch frm sets ts wholesale prce equal to and offers a dscounted prce of w z ŵ to any retaler whose brand- share of retal sales s at least. Retaler s prces are p 1 z and p 1, R R L H, but only type-l retalers supply brand-specfc sellng effort R and collect the dscount. Retaler s profts are h R R. Frm L H s profts from the sale of ( )h R unts of brand to each retaler L are [ z( ) f ]h and ts profts from the sale of hj unts of brand L to each retaler j R are zh. H j j 13

14 Equlbrum prces and quanttes are shown n Fgure 1. Retaler j R H provdes no brand-specfc sellng effort and pays a wholesale prce of w z for hj unts of brand. Retaler RL nvests L fh n brand-specfc sellng effort and recovers ths nvestment by qualfyng for frm s market share dscount that reduces ts prce to ŵ. Usng a market share ncentve, frm nduces type-l retalers to promote brand and captures all of the rent created by these promotonal actvtes. Ths holds no matter what the relatve number of retalers of the two types s. It also holds no matter what the frms szes are. Because the market share requrement serves as an effectve screenng devce, effcent promoton and complete capture of the resultng rent are acheved wthout sacrfcng any of the frm s proft from sales to type-h retalers. Although market share dscounts generally are appled to all of the unts a customer purchases once the market share requrement s met, a dscount of f / L appled only to the ncremental unts h purchased by retaler L would gve the same result as n Proposton 2. Sreya Kolay, et al. show the same equvalency between all-unts dscounts and ncremental-unts dscounts n a blateral monopoly model of retal contractng where the frms contract wth complete nformaton about demand. In ther model, however, these dscounts are not equvalent f the upstream frm cannot observe the downstream frm s demand. Wth ncomplete nformaton, the upstream frm can extract more proft usng an all-unts dscount n ther model. 14

15 Notce that frm could not acheve the same result as n Proposton 2 usng an across-the-board quantty dscount, regardless of whether that dscount appled to all unts of the brand a retaler purchased or only the ncremental unts elcted by retaler promotons. Nor could t be acheved by mposng an across-the-board mnmum purchase requrement. These measures would not perform as well as a market share dscount because the ncrease n unt sales frm seeks to nduce s retaler-specfc. It s the proportonalty of the output threshold that trggers the dscount that makes an across-the-board market share dscount advantageous for the manufacturer. 15 Notce also that frm could not acheve the result n Proposton 2 by usng resale prce mantenance (RP). anufacturers sometmes fnd t advantageous to use RP requrements to prevent downstream competton from makng t unproftable for retalers or dstrbutors to provde promotonal servces n support of the manufacturers brands. By assurng retalers of an adequate retal margn to recover ther nvestments n ths knd of servce, manufacturers nduce those nvestments wth an RP requrement (Lester G. Telser, and Howard P. arvel and Stephen ccafferty). In the present nstance, RP s nether necessary for frm to control retalers margns, nor suffcent for compensatng only those frms who promote brand. The result that frm captures the entre rent created by nduced downstream sellng effort stems from the assumpton that the manufacturer has the frst move and can make a take-or-leave offer to retalers. A dfferent assumpton about nteractons between frm and the retalers may alter that dstrbuton. One alternatve would be blateral barganng arrangements where frm negotates separate terms of sale wth every retaler nstead of settng terms of sale that apply to all transactons. Wth full 15

16 nformaton (e.g., frm knows the sze and type of each retaler), the Nash barganng soluton would dstrbute the rents created by promotonal actvty n a way that reflects the frms relatve barganng power. 16 Ths outcome can be shown to reproduce the result derved here that effcent sellng effort s elcted and that retalers who can supply that effort acheve greater brand- market shares and pay lower wholesale prces (Davd E. lls, 2007). The results n Proposton 2 generalze to some cases where retalers have heterogeneous consumer populatons. For nstance, let (0, ) be the -preferrng fracton of retaler s consumers RL RH, where 1. Assume that retalers values of ths fracton are uncorrelated wth ther types and szes. Next suppose that by provdng relevant nformaton or customer servce, any retaler s -preferrng fracton ncreases to, where (, 1). Ths means that the -preferrng fracton of consumers s dfferent for retalers before they supply brand-specfc sellng effort, but s the same for all retalers who supply that sellng effort. In ths nstance, frm can acheve a result smlar to that n Proposton 2 by makng the wholesale prce dscount equal to f / and by makng the market share that trggers the dscount equal to. L 17 The dstrbutonal effects of market share dscounts mght be markedly dfferent f retalers have access to two brands of the good (or more) where each s preferred by some consumers, and where other consumers wth no preference can be nduced to prefer each when retalers supply exclusve brand-specfc sellng effort. When two manufacturers compete wth market share dscounts to wn retaler loyalty, varous outcomes are possble. For nstance f the cost of provdng sellng effort only dffers 16

17 among retalers(f L or f H )and not across brands, then outcomes depend on how the brand-specfc values of and are dstrbuted among retalers. For certan confguratons, retalers may sort themselves nto three categores: those who are loyal to brand A, those who are loyal to brand B, and those who provde no brand-specfc sellng effort. 18 Wth two manufacturers competng wth market share dscounts for loyal retalers, the manufacturers profts would be less and some retalers profts would be greater. IV. Welfare Effects To assess the welfare effects of frm s market share dscount, the equlbrum n Proposton 2 may be compared to the outcome where frm s constraned by anttrust or regulaton to charge a unform wholesale prce to all of ts retalers. There are two cases to consder where frm must charge a unform prce. In the hgh-prce case, frm would choose to forgo the benefts of type-l retalers sellng efforts n order to charge a hgh prce and extract as much proft as possble from ts sales to type-h retalers. In ths case, frm s unform prce would be w z as n Proposton 1. In the low-prce case, frm would charge a lower wholesale prce w nduce sellng effort from type-l retalers. To accomplsh ths frm would have to accept reduced profts from type-h retalers, who also would pay the low prce but who would not promote the brand. Whether frm chooses a hgh or low wholesale prce depends on whch of these optons s more proftable. It s the more proftable case (for z to 17

18 a gven set of parameter values) that should be compared to outcomes n Proposton 2 to assess the welfare effects of mposng a unform prcng constrant on the frm. In the hgh-prce case, outcomes would be those ndcated n Proposton 1. In the low-prce case, frm would reduce ts wholesale prce to nduce promotonal actvtes from type-l retalers n spte of lost profts from sales to type-h retalers. Type- L retalers best response to any w ˆ w would be to promote brand because the proft on ncremental sales of the brand would offset or exceed the cost of sellng effort. Type-H retalers would not respond to such a prce by promotng the brand unless f H w z w If frm ntends to nduce sellng effort from only the type-l retalers, the frm would ˆ. charge the wholesale prce ŵ. As a result, every retaler L R would purchase and resell ( )h unts of brand and every retaler j RH would purchase and resell unts. Retal prces would be p 1 z and p0 1 n every market and frms h j profts would be: R h and ( z( ) f )h R L L R fl fl (1 )h and ( z )h j R j j j j H (2) If frm charges a low prce, ts profts are shown n (2). If the frm charges a hgh prce, ts profts are shown n Proposton 1. Comparng frm s profts under these two scenaros ndcates that t s more proftable for the frm to charge a hgh prce where () type-l retalers are small and few compared to type-h retalers, () f L, the type-l retalers cost of promotng brand, s large, () z, the premum -preferrng 18

19 consumers are wllng to pay for the brand, s small, and (v) θ, the fracton of consumers who are susceptble to nfluence, s small. (And conversely for a low prce.) The welfare effects of frm s market share dscount are dfferent dependng on whether a hgh-prce or low-prce equlbrum would arse wth unform wholesale prcng. If constranng frm to charge a unform wholesale prce leads to a hgh-prce equlbrum, then lftng that constrant so the frm could mplement a market share dscount would be a Pareto mprovement. Comparng frms profts n Proposton 1 to those n Proposton 2 ndcates that frm s proft from sales to the type-l retalers would ncrease f t used a market share dscount, but nothng else would change. Because frm captures all of the benefts created by retalers sellng effort, retalers nether gan nor lose from lftng the constrant. Consumer welfare also s unchanged when the constrant s lfted because demands are nelastc. If constranng frm to charge a unform prce leads to a low-prce equlbrum, then lftng that constrant so the frm could mplement a market share dscount would not affect the supply of downstream sellng effort. Ths polcy change would only have redstrbutve effects. Comparng frms profts n (2) to those n Proposton 2 shows that lftng the constrant would smply transfer rents from type-h retalers to frm. In sum, the welfare effects of frm s market share dscount would never mpar market performance. And sometmes t would mprove market performance by nducng effcent downstream sellng effort not otherwse forthcomng. Under the condtons assumed n ths model, the market share dscount offered even by a manufacturer wth a large market share would have at worse an nnocuous effect on welfare. Of course, ths concluson does not apply for a domnant frm who 19

20 uses market share dscounts to nduce downstream actvtes that effectvely shut competng producers out of the market. Ths would happen f competng producers have substantal fxed costs and the domnant frm s prcng reduced ther sales to levels so low that they could not recover those costs (chael D. Whnston). Ths outcome s precluded n the present model by the assumpton that frm s compettors produce wth constant returns to scale and therefore could survve wth arbtrarly low output levels as 1. Under dfferent assumptons about the frms costs, the market share dscounts of a domnant frm mght have sgnfcant exclusonary effects. But ths concern s tempered by knowledge that t s n the nterest of retalers to sustan vulnerable competng producers. Retalers would resst a domnant frm s exclusonary strategy to avod the demse of competng supplers whose presence gves retalers leverage n ther dealngs wth the domnant frm. V. Tered Dscounts The model can be extended to dstrbuton networks wth even more retaler heterogenety. Just as a market share ncentve allows frm to separate retalers who can supply effcent sellng effort from those who cannot, tered market share ncentves may allow further separaton where retalers abltes are more heterogeneous. To llustrate, suppose frm s dstrbuton network ncludes thee types of retalers: types 0, 1, and 2. As before, assume that retaler types and szes are uncorrelated, and that frm does not know the retalers types and szes ex ante. Retaler types are dstngushed as follows. Frst, no retaler k R0 has the ablty to supply sellng effort that would ncrease ts fracton of -preferrng consumers Next,

21 every retaler R1 has the ablty to ncrease the fracton of -preferrng consumers from to 1 by undertakng actvtes that cost fh. 1 Smlarly, every retaler j R2 has the ablty to ncrease the fracton of -preferrng consumers from to 2 for the cost fh. 2 j Suppose these parameters satsfy the followng condtons: 1 0, (3) 2 1 f z, and f z (4) f2 f1 > 2 1 f2 f 1 (1 1 ) (5) (6) Assumpton (3) ndcates that type-2 retalers can ncrease ther fracton of - preferrng consumers more than type-1 retalers. Assumpton (4) ndcates that both type-1 and type-2 retalers can promote brand effcently. Assumpton (5) ndcates that retalers costs ncrease (between types) more than n proporton to the effectveness of ther sellng effort. Better performance, where t s avalable, costs more, but there are dmnshng returns to nvestng n downstream sellng effort. Fnally, assumpton (6) places a bound on the magntude of the dmnshng returns depcted n assumpton (5). Suppose as before that retalers decde whether to supply sellng effort n the second stage of the game. The followng proposton (proof n the Appendx) descrbes 21

22 an equlbrum n whch frm uses tered market share dscounts to nduce sellng efforts from both type-1 and type-2 retalers. Proposton 3: For all feasble values of the model s parameters that satsfy condton (3)-(6), there s a perfect equlbrum n whch frm sets ts wholesale prce equal to f1 w z and offers dscounts of f2 retaler whose brand- share of retal sales s at least 1 or 1 to any retalers whose brand- share of retal sales s at least 2. Retalers prces are p 1 z and p 1, R0 R1 R2. Type-1 and type-2 retalers supply brand-specfc sellng effort and qualfy for the dscounts f1 f2 and 1 2 respectvely. Retalers profts are R h, R R R. Frm s profts from the sale of ( 1)h unts to each retaler R1 are [ z( ) f ]h, ts profts from the 1 1 sale of ( 2)hj unts to each retaler j R2 are [ z( ) f ]h, 2 to j 2 2 j and ts profts from the sale of hk unts to each retaler k R0 are zh. k k Ths proposton dentfes a stuaton where frm can mplement tered market share dscounts to nduce heterogeneous retalers to provde effcent promotonal support for ts brand and to capture all of the rent created by these promotonal actvtes. Notce that type-2 retalers acheve a brand- market share ( 2 ) that s greater than those of other retalers. Also, type-1 retalers brand- market share 22

23 ( ) s greater than type-0 retalers brand- market share. Type-2 retalers also 1 f2 receve a dscount 2 f1 that s greater than the dscount 1 receved by type-1 retalers. Type-0 retalers do not qualfy for a dscount. That s, the retalers who acheve larger brand- market shares get larger dscounts. Ths result holds no matter what the relatve number and sze of retalers of the varous types s. As before, the man consequence of prcng wth market share dscounts s to extract surplus and nduce downstream sellng effort. Aggregate benefts do not decrease and may ncrease, creatng a Pareto mprovement. VI. Examples The ncreased-sellng-effort explanaton for market share dscounts offered n ths paper s not a unversal explanaton for ths practce. But t s a plausble explanaton n some nstances where the practce has been challenged under the anttrust laws. 20 Consder two examples. Cgarette manufacturers Phlp orrs and R. J. Reynolds (RJR) were challenged (ndependently) by groups of wholesale dstrbutors because they offered loyalty rebates to dstrbutors whose cgarette sales acheve certan market share targets. The dstrbutors clamed that the loyalty rebates consttuted prce dscrmnaton n volaton of the Robnson-Patman Act because the largest rebates were beyond the reach of dstrbutors whose busness focused on the sale of dscount cgarette brands. The manufacturers mantaned that ther loyalty programs were desgned to elct stronger customer support for ther cgarette brands from mult-brand dstrbutors. Concludng 23

24 that the companes dscounts were equally and realstcally avalable to all dstrbutors, the tral court dsmssed these cases at the summary judgment stage. 21 The ncreasedsellng-effort explanaton for market share dscounts descrbed n ths paper lends some theoretcal support to the manufacturers clams and to the Crcut Judge s assessment that RJR sought to enlst wholesalers n RJR s marketng efforts by provdng fnancal ncentves to wholesalers wllng to focus on RJR savngs brands (emphass added). 22 ost pharmaceutcal manufacturers offer dscounts on certan prescrpton drugs to hosptals and managed care organzatons that have the ablty to nfluence the prescrbng pattern of physcans (Kenneth G. Elznga and Davd E. lls, and Chrstopher. Snyder and Sara F. Ellson). In some cases these dscounts depend on a specfc drug s fracton of the customer s total usage of drugs n the relevant therapeutc class. Varous retal drug stores challenged these dscounts because, for the most part, these retalers were not equpped to exert as much nfluence over prescrbng patterns as hosptals and managed care organzatons. The manufacturers countered that ther dscounts were desgned to ncentvze those customers who were postoned to nfluence prescrpton patterns. any of the cases n ths sprawlng ltgaton were settled outsde of court. 23 The outcomes of these cases are an ndcaton that U. S. courts have been cautous about readng antcompettve motves nto the use of market share dscounts. 24 Ths paper offers an economc justfcaton for ths cautous treatment of market share dscounts. 24

25 $ Gan from Sellng Effort = θzh p =1+ z w z 0 p =1 = z Cost of Sellng Effort = fh L w ˆ f L = z - λ+ θ 0 λh (λ+ θ)h h Fgure 1 25

26 Appendx Proof of Proposton 2: Suppose frm offers retalers the ndcated prcng menu n stage one. In stage two, no retaler RL RH could charge retal prces that are more proftable than p 1 z and p 1, regardless of whether the frm nvests n sellng efforts. To see ths, notce that no response wth prces p 1 z or p 1 could be optmal for any retaler because such prces could be ncreased wthout changng any consumer s behavor. Next, no response wth prces p 1 z and p 1 could be optmal for any retaler because these prces would elmnate all sales. Prces ths hgh are domnated by p 1 z and p 1. Nor could a response wth p 1 z and p 1 be better than p 1 z and p 1 for any retaler because dvertng -preferrng consumers to an undfferentated brand could produce no more proft. Ths leaves the prces p 1 z and p 1 as the only remanng alternatve to p 1 z and p 1. These prces could not be more proftable than p 1 z and p 1 for any retaler RL RH that nvests n promotonal actvtes because 0 p 1 would elmnate sales of the undfferentated brands wthout ncreasng brand- sales. Nor could p 1 z and p 1 be more proftable than p 1 z and p 1 for any retaler who does not nvest n promotonal actvtes. Any retaler RL RH who does not nvest n promotonal actvtes yet charges the prces p 1 z and p 1 would earn profts of h. If the same retaler charges the prces 26

27 p 1 z and p 1, the frm would sell h unts of brand, and no unts of the undfferentated brands. Because ths qualfes the retaler for frm s dscount, the retaler s proft would be f. (7) R L (1 )h These profts are less than h f f L (1 ) 1 (8) or f f L (1 ). (9) Ths nequalty s satsfed because 1 and because the prevous assumptons that z 1, 1, and f L z jontly mply that f L 1. Thus every retaler charges the retal prces p 1 z and p 1 regardless of whether the frm nvests n promotonal actvtes. Also n stage two, a retaler RL responds to frm s offer by nvestng L fh n sellng effort and sellng ( )h unts of brand. The frm recovers ths cost va the dscount of f L R on each of these unts and earns profts of h. A retaler j RH sells only hj unts of brand and earns profts of 27. The frm does not nvest n sellng effort because the cost fh H j would be greater than the ncremental savngs fh L j R j hj

28 that result from ncreasng brand- sales to ( )h n order to qualfy for the lower j prce. Wth these stage-two responses, frm s profts are [ z( ) f ]h R and zh j R. Ths outcome maxmzes the rent L L j H created by brand and transfers the entre rent upstream to frm. Therefore, the manufacturer s ndcated prcng menu n stage one s an optmal strategy. Proof of Proposton 3: Suppose frm offers retalers the ndcated prcng menu n stage one. In stage two, no retaler R0 R1 R2 could charge retal prces that are more proftable than p 1 z and p 1, regardless of whether the frm nvests n sellng efforts. Reasonng along the same lnes as n the proof of Proposton 2, we only need to nvestgate whether chargng the prces p 1 z and p 1 could be more proftable than p 1 z and p 1 for any retaler R0 R1 R2. Suppose a retaler who nvests nothng n sellng effort charges the prces p 1 z and p 1. Because 0 p 1 would extngush all sales of the undfferentated brands, the retaler would qualfy for ether dscount. Therefore we only need to check to see whether f2 qualfyng for the larger dscount 2 would make these prces more proftable than p 1 z and p 1. Wth the alternatve response, the retaler would sell h unts of f2 brand and nothng else. Because ths qualfes the retaler for the dscount, the frm would earn proft of 28 2

29 R f2 (1 )h. 2 Ths s less proft than h,the frm s proft wth the prces 2 f 2 (1 ). p 1 z and p 1, f (10) Ths nequalty s satsfed for the same reason as nequalty (9) prevously. Ths establshes that no retaler would opt for settng p 1 z and p 1 wthout nvestng n sellng effort. Nor would a retaler j R2 nvest n sellng effort and charge the prces p 1 z and p 1 because ths would only elmnate sales of the undfferentated j j brands wthout ncreasng brand- sales. The fnal thng to check s whether a retaler R1 could make more proft by nvestng n promotonal actvtes and chargng the prces p 1 z and p 1 to f2 dscourage sales of the undfferentated brands and qualfy for the dscount. By respondng n ths way, the retaler would earn proft of: R f2 [( 1 )(1 ) f 1 ]h (11) 2 2 If the same frm provdes sellng effort and charges the prces p 1 z and p 1, ts proft would be h. Thus, provdng sellng effort and chargng the prces p 1 z and p 1 s less proftable f: f2 [( 1 )(1 ) f 1 ]h h (12) 2 29

30 Ths nequalty holds f the model s parameters that satsfy condton (6). Thus chargng the retal prces p 1 z and p 1 n stage two s an optmal response for every retaler R0 R1 R2, regardless of whether the frm nvests n sellng effort. Wth these stage-two responses, frm s profts from the sale of ( 1)h unts to each retaler R1 are [ z( ) f ]h ; ts profts from the sale of ( 2)hj 1 1 unts to each retaler j R2 are [ z( ) f ]h ; and ts profts from the sale of j 2 2 j h k unts to each retaler k R0 are zh. Ths outcome maxmzes the rent k k created by brand and transfers the entre rent upstream to frm. Therefore, the manufacturer s ndcated prcng menu n stage one s an optmal strategy. 30

31 References Blss, Chrstopher, Blss, C. (1988) A Theory of Retal Prcng, Journal of Industral Economcs, 36, pp Carlton, Denns W., and Kenneth Heyer (2008) Approprate Anttrust Polcy Towards Sngle-Frm Conduct, U. S. Department of Justce Economc Analyss Group Dscusson Paper EAG Chae, Sreya, and Paul Hedhues (2004) Buyers Allances for Barganng Power, Journal of Economcs and anagement Strategy, 13, pp Chpty, Tasneem, and Chrstopher. Snyder (1999) Buyer Sze and Barganng Power, Revew of Economcs and Statstcs, 81, pp Elznga, Kenneth G. and Davd E. lls (1997) "The Dstrbuton and Prcng of Prescrpton Drugs," Internatonal Journal of the Economcs of Busness, 4, pp DeGraba, Patrck (2005) Quantty Dscounts from Rsk Averse Sellers, Federal Trade Commsson workng paper no Faella, Ganluca., The Anttrust Assessment of Loyalty Dscounts and Rebates, Journal of Competton Law & Economcs, 4, pp Greenlee, Patrck, Davd Retman (2008) Competng wth Loyalty Dscounts, U. S. Department of Justce Dscusson Paper EAG-04-2 (2004) (2005) Dstngushng Compettve and Exclusonary Uses of Loyalty Dscounts, The Anttrust Bulletn, 50, pp

32 Greenlee, Patrck, Davd Retman and Davd S. Sbley (2004) An Anttrust Analyss of Bundled Loyalty Dscounts, U. S. Department of Justce Dscusson Paper EAG Horn, Henrck, and Asher Wolnsky (1988) Blateral onopoles and Incentves for erger, RAND Journal of Economcs, 19, pp Hovenkamp, Herbert (1998) Anttrust Law: An Analyss of Anttrust Prncples and Ther Applcaton (New York: Aspen Publshers). Inderst, Roman, and Chrstan Wey (2006) Buyer Power and Suppler Incentves, manuscrpt. Klen, Benjamn and urphy, Kevn. (1988) Vertcal Restrants as Contract Enforcement echansms, Journal of Law & Economcs, 31, pp Klen, Benjamn and Andres V. Lerner (2008) The Law and Economcs of Bundled Prcng: LePage s, PeaceHealth, and the Evolvng Anttrust Standard, The Anttrust Bulletn, 53, pp Kobayash, Bruce (2005) The Economcs of Loyalty Dscounts and Anttrust Law n the Unted States, Competton Polcy Internatonal. Kolay, Sreya, Greg Shaffer, and Janusz A. Ordover (2004) All-Unts Dscounts n Retal Contracts, Journal of Economcs & anagement Strategy, 13, pp arvel, Howard P. (1982) Exclusve Dealng, Journal of Law and Economcs, 25, pp arvel, Howard P. and Stephen ccafferty (1984) Resale Prce antenance and Qualty Certfcaton, Rand Journal of Economcs, 15, pp

33 arx, Lesle. and Greg Shaffer (2004) Rent Shftng, Excluson, and arket-share Dscounts, manuscrpt. lls, Davd E., (2007) Quas-Partnershps n Dstrbuton Revew of Industral Organzaton, 31, pp (1995) Why Retalers Sell Prvate Labels, Journal of Economcs and anagement Strategy, 4, pp Nalebuff, Barry (2004) Bundlng as an Entry Barrer, Quarterly Journal of Economcs, 119, pp (2005) Exclusonary Bundlng, The Anttrust Bulletn, 50, pp O, Walter (1971) A Dsneyland Dlemma, Quarterly Journal of Economcs, 85, pp Rubnfeld, Danel L. (2005) 3 s Bundled Rebates: An Economc Perspectve, Unversty of Chcago Law Revew, 72, pp Chrstopher. Snyder and Sara F. Ellson (forthcomng) Countervalng Power n Wholesale Pharmaceutcals, Journal of Industral Economcs. Davd Spector (2005) Loyalty Rebates: An Assessment of Competton concerns and a Proposed Structured Rule of Reason, Competton Polcy Internatonal Telser, Lester G. (1960) Why Would anufacturers Want Far Trade? Journal of Law & Economcs, 3, pp Tom, Wllard K., Davd A. Balto, and Nel W. Avertt (2000) Antcompettve Aspects of arket-share Dscounts and Other Incentves to Exclusve Dealng, Anttrust Law Journal, 67, pp

34 Whnston, chael D. (1990) Tyng, Foreclosure, and Excluson, Amercan Economc Revew, 80, pp The author thanks partcpants n the Bankard Theoretcal Industral Organzaton Workshop at the Unversty of Vrgna, and by Smon Anderson, Kenneth Elznga, axm Engers, Amala ller and a referee, for nsghtful comments. The Bankard Fund for Poltcal Economy at the Unversty of Vrgna provded fnancal support. 2 Other prcng schemes, such as offerng free reflls or free tems after the nth purchase, also condton dscounts on purchase volume or repeat sales. Sreya Kolay, Greg Shaffer, and Janusz. A. Ordover dstngush all-unts dscounts from ncremental dscounts and compare ther effectveness n extractng surplus. 3 Other loyalty programs nvolve mult-product prcng. Bundled dscounts are appled to the sale of two or more goods f buyers purchase one or more or the seller s goods exclusvely, or f the buyer s purchases acheve certan market share targets wth respect to one or more of the goods. 4 For good general dscussons of the relevant anttrust ssues, see the papers by Ganluca Faella, Bruce H. Kobayash, and Davd Spector. 5 Recent promnent cases brought by anttrust authortes nclude LePage s n the U.S. and cheln n Europe. See LePage's Inc. v. 3, 324 F.3d 141 (3d Cr. 2002), cert. dened, 124 S. Ct (2004) and COP/E-2/36.041/PO-cheln (2001). 6 Quantty dscounts are less frequently problematc because they only nvte buyers to purchase addtonal unts to take advantage of a lower prce. The most obvous explanaton for quantty dscounts n ntermedate product markets s that sellers costs of servng buyers may not ncrease n strct proporton wth the quanttes purchased. Also, quantty dscounts may be a prce dscrmnaton tactc (Walter O) or due to sellers rsk-averson (Patrck DeGraba). Other explanatons attrbute quantty dscounts to blateral barganng between a seller and ndependent buyers of varous szes (Suchan Chae and Paul Hedhues, Tasneem Chpty and Chrstopher. Snyder, Henrck Horn and Asher Wolnsky, and Roman Inderst and Chrstan Wey). 7 Bundled dscounts are controversal when offered by domnant frms who sell several goods to the same customers because they may dsadvantage rvals who only sell one or a few of the goods. Some of the anttrust mplcatons of bundled dscounts are examned n Patrck Greenlee, Davd Retman, and Davd S. Sbley, n Barry Nalebuff (2004, 2005), Benjamn Klen and Andres V. Lerner, and n Danel. L. Rubnfeld. 8 Chrstopher Blss dentfes ths captve buyer effect as a contrbutng factor to retalers market power n the sale of specfc goods that are components of bundles (p. 38). 9 Lester G. Telser ntroduced the dea that contractual arrangements between a manufacturer and ts retalers could remedy the downstream moral hazard that prevents the effcent dstrbuton of the manufacturer s goods. Hs analyss nvolved pre-sale servces that retalers provde to help consumers make well-nformed decsons. These servces are valuable to the manufacturer because they ncrease the demand for ts goods. However, provdng these servces entals costs for the retalers that must be shfted upstream to the manufacturer. Telser demonstrated that the manufacturer could overcome free rdng by retalers and nduce valuable pre-sale servces by means of vertcal restrants such as resale prce mantenance or terrtoral restrctons. Howard P. arvel and Stephen ccafferty extended the Telser story to qualty certfcaton servces. Benjamn Klen and Kevn. urphy took ths lne of reasonng beyond free rdng and argued that vertcal restrants are mposed to make retalers comply generally wth ncomplete performance contracts for promotonal servces. 10 Whether a seller s exclusve dealng arrangements wth ts dealers s held to to be llegal depends on how much of the entre market s foreclosed from rvals. Herbert Hovenkamp suggests requrng 34

35 foreclosure of at least 20 percent, and even that number seems rather small.... Even at a hgh foreclosure percentage of, say, 60 percent, we would nsst on a showng that as a result of the exclusve dealng contract [rvals] were havng a dffcult tme fndng adequate outlets for ther product ( 1821). 11 Benjamn Klen and Andres V. Lerner cauton generally that b]ecause competton for dstrbuton often leads to preferred dstrbuton arrangements as part of the normal compettve process, one cannot assume that such contracts are used solely as a way to foreclose rvals (p. 566). 12 Howard P. arvel offered ths explanaton for manufacturers use of exclusve contracts. 13 The assumpton that z<1 means that consumers who prefer brand are wllng to pay at most twce as much for a unt of ths brand. Ths s a plausble assumpton for many dfferentated consumer goods, and the assumpton smplfes some of the paper s results. 14 A smlar result follows f retalers can add value to otherwse undfferentated brands by marketng them as ther own prvate label products (Davd E. lls, 1995). 15 Ths lmtaton of quantty dscounts would not apply f frm could observe ex ante the sze of every retaler. Wth ths nformaton, frm could talor frm-specfc all-unts quantty dscounts or ncremental quantty dscounts that would nduce sellng effort f and only f retalers are type-l. If frm could observe both the sze and type of each retaler ex ante, the screenng functon of the prcng strateges under nvestgaton would be unnecessary. 16 A retaler s outsde opton would be dstrbutng only undfferentated brands and frm s outsde opton would be forfetng ts sales to the retaler and relyng on alternatve dstrbuton channels, f any, to reach the retaler s consumers. 17 Ths result could not be acheved wth a dscount appled only to the ncremental unts purchased by a retaler because frm cannot observe for frm. 18 Competton wth market share dscounts between two manufacturers led to an outcome resemblng ths pattern n the wholesale cgarette example dscussed below. 19 In the alternatve, the cost of supplyng the requste sellng effort for the type-0 retalers s so hgh that the opton s rrelevant. 20 Rent extracton and other knds of effcences may provde better explanatons for the market share dscounts challenged n some other cases where nducng downstream sellng effort dd not appear to be a factor. For nstance, Internatonal Paper offered ts customers a 2.5 percent rebate on purchases of carbonzng tssue f customers purchased at least 25 percent of ther tssue requrements from Internatonal Paper. Larger rebates were offered for even greater percentages. The purpose for these dscounts appears to be rent extracton. Amercan Tara Corporaton v. Internatonal Paper Company, No. 79C1470, 1981 WL (N.D. Ill. July 30, 1981). Brunswck Corporaton, the leadng manufacturer of nboard and stern-drve marne engnes, offered a one percent dscount off ts lst prces to boat bulders who commtted (for one year) to purchase 60 percent of ther marne engnes from Brunswck. The dscount ncreased to two percent for commtments to acheve 70 percent and to three percent for commtments to acheve 80 percent. One ratonale Brunswck offered for ts market share dscounts was that the commtments the dscounts elcted from boat bulders helped the frm reduce producton costs. Concord Boat Corp. v. Brunswck Corp. 207 F. 3d 1039 (8th Cr. 2000). 21 The decson was upheld on appeal. Smth Wholesale Co. v. Phlp orrs USA, Inc., No , 2007 WL (6th Cr. Feb. 27, 2007); Smth Wholesale Co. v. R.J. Reynolds Tobacco Co., No , 2007 WL (6th Cr. Feb. 27, 2007). 22 Smth Wholesale Co. v. R.J. Reynolds Tobacco Co., No , 2007 WL (6th Cr. Feb. 27, 2007), p Brand Name Prescrpton Drugs Anttrust Ltgaton, DL No. 997, U.S.D.C. for N.D. of IL, Eastern Dv. The plantff retalers also clamed that the manufacturers dscounts were the frut of a conspracy. Some of the conspracy charges were tred and the court granted a drected verdct for the manufacturers. The verdct was upheld on appeal. 24 Bruce H. Kobayash reports that courts have generally ruled that above-cost volume dscounts, ncludng those that use market share dscounts and near exclusve thresholds, are lawful and do not volate the anttrust laws (p. 1). 35