The Role of Price Floor in a Differentiated Product Retail Market

Transcription

1 Economc Analyss & Polcy, Vol. 40 No. 3, DECEMBER 2010 The Role of Prce Floor n a Dfferentated Product Retal Market Barna Bakó 1 Faculty of Economcs, Corvnus Unversty of Budapest Fovám tér 8, Budapest, 1093, Hungary (Emal: barna.bako@un-corvnus.hu) Abstract: The ablty of a manufacturer to enhance competton among ts retalers by mposng a prce floor was recently ntroduced n the lterature. The purpose of ths artcle s to revst ths ant-collusve explanaton of the retal prce mantenance n a more general model n whch we ntroduce asymmetrc retalers. We fnd that a manufacturer can amplfy the retal market s competton by mposng a prce floor when retalers sell dfferentated products. Ths result contradcts the prevalng concept of retal prce mantenance. I. Introducton Prce restrctons are undoubtedly among those practces that are more severely treated by anttrust authortes than any other vertcal restrant, however there s a trend towards a more flexble atttude. 2 Yet, retal prce mantenance (RPM) and prce floors are often consdered per se llegal. 3,4 In a recent artcle, Overvest (2010) has argued that a monopolst manufacturer may n fact be able to ncrease ts proft mposng prce floor because ths makes downstream market colluson less proftable. In essence, f retalers nteract n an nfnte number of tmes they may form a cartel whch causes the tradtonal double margnalzaton problem to the manufacturer. By mposng a prce floor the producer may destablze the cartel whch ncreases ts proft. The argument s potentally an mportant one because t supports the avalable emprcal evdences, whch has contradcted the pro-colluson theory of the prce mantenance. However, the result s crucally based on a specal model, the nfntely repeated Bertrand game wth homogeneous good, n whch the core problem of double margnalzaton does not arse when retalers can not collude. Ths s not the case when we ntroduce dfferentated products. Everyday 1 I would lke to thank the anonymous referee for the valuable comments and suggestons, whch led to substantal mprovements n the paper. I gratefully acknowledge fnancal support from the Hungaran Competton Authorty. 2 The US Supreme Court recently revsted the per se ban of the prce fxng and replaced a nearly 100 year old precedent by adoptng a rule of reason standard for analyzng resale prce mantenance, see Leegn Creatve Leather Products, Inc. v. PSKS, Inc, 551 U.S. 877, 127 S. Ct.2705 (2007). 3 Throughout ths analyss the mnmum resale prce and the prce floor terms are used synonymously. 4 For a broad overvew of the effects of the RPM, see Overstreet (1983). 363

2 The Role of Prce Floor n a Dfferentated Product Retal Market observatons suggest that frms expend consderable efforts to dfferentate the products they sell from the products of ther compettors. As a result, we should consder the ncentve for prce floor and the mpact of t n an ndustry n whch retalers add extra value to the product they sell. In ths artcle we reconsder the Overvest (2010) model and the downstream market s descrbed by a Bertrand duopoly model wth dfferentated products. We show that a proft maxmzng manufacturer sellng ts product through dfferentated Bertrand frms has the ncentve to mpose a prce floor on ts product to destablze a potental tact colluson and ncrease competton among retalers. The ntuton behnd ths result s that retalers fnd the devaton from a cartel agreement more proftable or less costly n the presence of a prce floor than wthout t, and so, a cartel whch would be stable n the absence of a prce mantenance can be unstable when manufacturer ntroduces a prce floor. Thus, a retal prce mantenance can boost competton among retalers whch ncreases the manufacturer s proft. Furthermore, we prove that a prce floor beng ntroduced to destablze a retaler cartel s a decreasng functon of the product dfferentaton. II. The Model We assume the followng set-up. A monopolst manufacturer sells ts product to fnal consumers through two asymmetrc retalers. The margnal costs of producton are c. The retalers have no addtonal costs n obtanng the products from the manufacturer. Demands are gven by D (p, p j ) = α - p +βp j (1) where {,j} = {A,B} wth α > 0 and (β (0,1). We nterpret parameter β as the degree of product dfferentaton between fnal products, for β close to 1 retalers sell close substtutes, whle for β close to 0 they supply to almost ndependent markets. The tmng of the game s as follows. Frst, the manufacturer sets ts wholesale prce p w and possbly a prce floor p f. 5 Second, retalers observe the wholesale prce and compete n Bertrand-fashon or they are engaged n tact colluson n the market stage where the retalers nteract repeatedly many tmes wthout knowng the exact tmng of the endng stage of the game. Here some remarks need to be made. Frstly, we suppose that the retalers are not aware of the endng of the game, however they know the probablty of the stage game whch s gong to be the last one and ths probablty (l р) does not vary durng the tme. Furthermore, we suppose that frms use a common dscount factor of (δ 0; 1).and each retaler can observe and remember the hstory of the game. These nformaton consttute common knowledge to the frms. Frms maxmze ther dscounted pay-offs. We solve the model usng backward nducton. The retalers one stage proft maxmzaton problem can be gven by 364 * maxπ = ( p p ) D ( p, p ),j=a,b j (2) p w j 5 Note, that here we assume lnear prces, a contract specfyng a payment T (q ) = p w q from retaler to manufacturer.

3 Barna Bakó Ths yelds the equlbrum prces and profts of the stage game =A,B. (3) * [ α (1 β ) pw ] π = 2 (2 β ) 2 Thus, the manufacturer s problem can be gven by =A,B. (4) max p w π m = ( pw c)[d ( p * ) + D j ( p j * )](1+δρ +δ 2 ρ ) (5) Hence, the manufacturer sets a wholesale prce (6) whch yelds equlbrum profts π * 1 [α (1 β)c] 2 m = 1 δρ 2(1 β)(2 β) (7) =A,B. (8) However, ths does not necessarly consttute an equlbrum where retalers are able to coordnate a tact colluson on the monopoly prce. By colludng, each retaler earns a stage proft ) (9) where,j=a,b, j. (10) Yet, the retalers may not be able to coordnate on the monopoly prce. When the devaton from the cartel prce at any stage s proftable the colluson may not be stable. Supposng trgger strateges beng used by retalers devaton s not proftable f and only f > or δρ> (11) Therefore, the manufacturer sets pw regardng to (6) f δρ Ñ θ C and obtans the proft equal to (7). On the other hand, when the retalers can collude, the manufacturer s problem bols down to (12) 365

4 The Role of Prce Floor n a Dfferentated Product Retal Market where p m ( = A,B) s gven by (10), whch yelds proft equal to. These profts are always smaller than the proft gven by (7), f β < 1. A possble soluton to solve the problem caused by double margnalzaton s to mpose a prce floor p f. Ths may lead to a less stable cartel by makng the devaton from the cartel agreement less costly. Under a prce floor retalers commt themselves not to charge a prce lower than p f. We assume that the manufacturer s able to enforce such a contract. A tact colluson s feasble f and only f the followng condton s satsfed > (13) for every =A,B ( j), where The rght-hand sde of the above condton s ncreasng n p f f δρ > θ C * m and p f ( p w, p ) where р * w s gven by (6) and p m = max{p m, p m j}, where p m s gven by (10). It s easy to show that for a proft maxmzng manufacturer a prce floor equal to p m always domnates any prce floor bgger then p m, moreover a prce floor smaller than р * w can not destablze a cartel whch s feasble next to р * w. Thus to destablze a cartel a reasonable prce floor to choose s the smallest p f whch stll volates condton (13). The manufacturer s problem can be gven by. s.t. whch yelds (14) (15) (16) (17) 366

5 Barna Bakó Hence, f retalers can engage n a tact colluson a manufacturer wll mpose a prce floor to f * destablze the cartel f and only f ts proft next to a prce floor ( π m ) s hgher than ts proft * wthout a prce mantenance ( π ), that s, when m > The above nequalty holds f β < 1 whch s the case by assumpton. Thus, as n the case of symmetrc retalers (see Overvest (2010)), a manufacturer s always better off by ntroducng a prce floor for ts product when retalers have the ncentve to engage n tact colluson. Ths result s summarzed n the followng Proposton 2.1 If δρ Ñ θ c the retalers compete n Bertrand fashon and set the prces gven by (3). The manufacturer sets p w such that É m s maxmzed. If δρ > θ c the retalers would engage n tact colluson but the manufacturer prevents ths collusve behavor by mposng a prce floor. The manufacturer sets a prce floor gven by (15), whch s hgher than the wholesale prce. Retalers acqure postve profts, the manufacturer gans from nducng a prce floor. What drves ths concluson s the fact that retalers can proft from colluson f the frms are patent enough, whch has a negatve effect on the manufacturer s proft. Accordngly, the manufacturer has an ncentve to prevent a cartel n the retal market. One way to do ths s to mpose a prce floor. Havng a closer look at the optmal prce floor mposed by the manufacturer we can examne how t s affected by the degree of product dfferentaton. Takng the frst dervatve of the expresson (15) wth respect to β yelds (18) whch s strctly postve whenever δρ > θ c. Ths yelds the followng Proposton 2.2 The optmal prce floor s decreasng n the degree of product dfferentaton. So, a β close to 1 requres a relatvely hgher prce floor than a β close to zero. To understand the reason why a manufacturer ntroduces a hgher prce floor n the case of less dfferentated products, let us consder the case when retalers sell close substtutes. When sellng close substtutes, symmetrc retalers earn zero proft wthout colluson and have a strong ncentve to sustan a tact colluson. Therefore, to prevent the cartel a manufacturer has to mpose a prce floor whch s hgh enough to make the retalers devaton from the cartel agreement proftable. On the other hand when products are almost ndependent, that s, when β s close to zero, the cartel becomes harder to sustan and as a result a smaller prce floor can make the cartel unstable. 367

6 The Role of Prce Floor n a Dfferentated Product Retal Market III. Concluson The purpose of ths paper s to show that a manufacturer has an ncentve to mpose a prce floor to enhance competton and not colluson as the prevalng lterature states. In contrary t demonstrates that the prce floor may bear an ant-colluson effect. The noton was ntroduced by Overvest (2010) n a specal model based on a homogenous Bertrand competton. In ths artcle we showed that the man result remans vald even f we suppose dfferentated products. Avalable emprcal results (see Jullen and Rey (2008), Cooper et al. (2005) and Overstreet (1983)) suggest that after a prce floor s beng mposed by a manufacturer the prces fall n the market whch should be plausble after the model presented n ths artcle. References Cooper, J.C., L.M. Froeb, D. O Bren, and G.M. Vta (2005). Vertcal Anttrust Polcy as a Problem of Inference, Federal Trade Commsson. Jullen, B. and P. Rey (2008). Resale prce mantenance and colluson, RAND Journal of Economcs. 38: Overstreet, T.R., Jr. (1983). Resale Prce Mantenance: Economc Theores and Emprcal Evdence, Bureau of Economcs Staff Report, Federal Trade Commsson. Overvest, B.M. (2010). A note on colluson and resale prce mantenance, European Journal of Law and Economcs. Avalable on the web: accessed May 27,