Role of Bargaining in Marketing Channel Games of Quality Choice and Profit Share

Transcription

1 Workng Paper Seres FSWP Role of Barganng n Marketng Channel Games of Qualty Choce and Proft Share Phlppe Bontems* Toulouse School of Economcs (GREMAQ, INRA and IDEI) Trtha Dhar Sauder School of Busness, Unversty of Brtsh Columba Jean-Paul Chavas Unversty of Wsconsn-Madson Food System Research Group Unversty of Wsconsn-Madson December 2007 *emal: bontems@toulouse.nra.fr; Malng Address: Manufacture des Tabacs, Ale Jean-Jacques Laffont, 21, allée de Brenne, TOULOUSE, FRANCE Correspondng Author; emal: trtha.dhar@sauder.ubc.ca; Malng Address: 2053 Man Mall, Vancouver, BC V6T1Z2 Canada emal: jchavas@wsc.edu; Address: Taylor Hall, 427 Lorch Street, Unversty of Wsconsn, Madson, WI 53706, USA

2 Role of Barganng n Marketng Channel Games of Qualty Choce and Pro t Share Abstract: Snce the 1980s, ncreased concentratons across marketng channels have changed barganng relatonshps between retalers and manufacturers both n North Amerca and n Europe. At the same tme contract mechansms wthn the marketng channels have become more complex and prvate label market share have grown rapdly. Ths paper rst nvestgates the mplcatons of barganng between manufacturers and retalers. The analyss apples to an arbtrary number of manufacturers and retalers, and holds under general technology and product d erentaton condtons, assumng that each retaler acts as a monopolst on ts own market. Under Nash barganng, we show that two wdely used types of contracts (quantty forcng contracts and two-part-tar contracts) are su cent to obtan e cency n the channel condtonnally on products spec catons but mportantly generate a d erent sharng of surplus. We then nvestgate the mplcatons for non cooperatve qualty choces made before the barganng stage. We examne how the barganng power of retalers and manufacturers a ect the quantty, prcng and qualty decsons. Ths provdes useful nsghts nto the changng relatonshps between manufacturers and retalers. Our analyss helps explan the recent growth of prvate labels, exclusve products for retalers desgned by natonal brand manufacturers, the growng use of sde payments and other emergng trade practces. Key-words: Barganng, Buyer power, Qualty choce, Prvate Labels, marketng channel. JEL class caton numbers: L12, L42, M3 2

3 1 Introducton Wth the advent of powerful retalers and manufacturers n d erent marketng channels understandng the ntrcaces of channel relatonshps s becomng more and more mportant. Increase n concentratons and market powers of channel players have also led to ncrease n tensons and trade skrmshes between supplers and retalers. Recent skrmshes and tense negotaton between Apple and musc producers s an example. 1 These rsng strategc tensons between manufacturers and retalers have rased questons about the relatve power of channel members and ts mplcaton on market outcomes. In ths paper our goal s to explore the role of cost structures of supplers and qualty provsons by the channel players n the negotated equlbrum outcomes, wth mplcatons for consumers, retalers and manufacturers. Ths paper s also motvated by the growng polcy concerns regardng the rse n barganng power of retalers both n Europe and n North Amerca (e.g., see Inderst and Wey, 2004; Innes and Hamlton, 2006)), wth mplcatons for qualty choces and economc e cency n the marketng channel. So, n ths paper we try to address the followng three crtcal emergng questons: [1] How s total channel pro t shared between channel members gven shftng barganng powers from manufacturers to retalers? For example, questons are beng asked whether retalers may be drvng manufacturers to bankruptcy by demandng more and more of the channel pro t from the supplers. Our approach here addresses ths queston n the context of a general barganng model nvolvng multple retalers and manufacturers. [2] What are the crtcal drvers of negotaton between powerful channel players? Here our focus wll be on the role of producton costs n the negotaton process between channel players. The reason for ths focus s that t s not obvous why powerful retalers lke WalMart 1 "Unversal n Dspute wth Apple over Tunes" New York Tmes July 2 nd

4 are so obsessed about the cost structure of ther supplers. It s also alleged that ncrease n retal market power may be leadng to a race to the bottom by a relentless push for supplers to reduce ther cost. Retalers are demandng more nformaton from manufacturers n terms of ther cost and plant structures. 2 For example, to become a suppler from Chna, WalMart requres supplers to provde detaled nformaton on ther manufacturng process, numbers of workers employed and also ther supply hstory to WalMart s compettors. From the perspectve of marketng and supply chan management, t s not clear how shftng focus from cost of procurement to cost structures of the supplers help powerful retalers. If WalMart s purely nterested n gettng the lowest wholesale prce, then such obsesson wth the cost structures of ts suppler s somewhat ba ng. Surely, a few decades back when mom and pop retalers domnated the world, they also wanted the lowest prce avalable from ther supplers but they hardly bothered about the cost structures of ther supplers. [3] After explorng characterstcs of the barganng outcomes we then ask another mportant and crtcal queston: what wll be the nature of the equlbrum n terms of qualty of products gven rsng barganng power of retalers and ncreasng market share of prvate labels n most marketng channels? Ths s mportant n terms of consumer welfare. Does the overall qualty of products n the marketng channel ncrease or decrease due to shftng market power n the marketng channel? And how does ths a ect consumer welfare? Choce of qualty ssue s also related wth the recent growth of prvate labels n the marketng channel (Inderst and Sha er, 2007; Sha er, 2005; Avenel and Caprce, 2006). Indeed, n the case of prvate label, the choce of qualty s typcally made by the retaler (Sayman, Hoch and Raju, 2002). In ths context, we explore the qualty choce equlbrums to provde nsghts nto the lnks between qualty choce and prvate labels. Regonally Europeans and North Amercan retalers sgn cantly dverge n terms of pr- 2 Ths s exempl ed by Walmart s focus on supplers cost structures. See the dscusson n the followng two documenteres: "Is Wal-Mart Good for Amerca" (produced by Frontlne PBS) and "The Age of Wal-Mart - Insde Amerca s Most Powerful Company," (Produced by CNBC). 4

5 vate label strateges (Cotterll, 1997). Accordng to Cotterll, powerful retalers n Europe (such as Carrefour n Europe) have reled more on the prvate labels to grow ther busness compared to some of the US counterparts (such as Wal-Mart). On average, Hoch et al. (2002) found that n 86 % of the 225 categores sold n ther large sample of retal outlets prvate label share had trended upward at 1% pont per year durng the perod , whle natonal brand share stagnated. And accordng to Stener (2004) ths upward trend n overall prvate label dollar share contnued from n all three classes of retalers (Prvate Label Manufacturers Assocaton, 2001) and n supermarkets and drug chans. The prvate label s dollar market share n these three classes of retalers for the 52 weeks endng August 12, 2000 was 14.4%, and prvate label s volume market share had reached 28.1% (Prvate Label Magazne, 2000). The ncreasng mportance of prvate labels s a ectng the relatonshp between supplers and retalers. Even for branded products more and more qualty on the store shelves are negotated rather than taken as gven by the retalers. For example, recently HP and Best Buy n the US market has ntroduced an exclusve laptop for Best Buy stores whose qualty was determned through negotatons. 3 Smlarly WalMart s nsstence on qualty has led to ntroducton of store brands by leadng natonal brand manufacturers lke: Starter sneakers by Nke, Levs Strauss jeans by Levs Inc., Slce carbonated soft drnks by Peps. 4 To address these questons, ths paper develops an analytcal model of a marketng channel that reles on a two-stage game, where qualty choces are made non-cooperatvely n the rst stage, and n the second stage blateral barganng between pars of manufacturers and retalers determne pro t maxmzng quantty and prcng. The analyss apples to an arbtrary number of manufacturers and retalers, and holds under general technology and product d erentaton condtons. We focus however on the case where each retaler s ndependent and acts as a monopoly on ts nal market. Ths s a reassonable assumpton as Slade (1995) 3 How HP Reclamed Its PC Lead Over Dell (Wall Street Journal, June 4 th, 2007). 4 For some nterestng and detaled dscussons on how Wal-Mart n uenced qualty choces for branded products: Fast Company Magazne ( 5

6 argued that n the emprcal settngs retalers do not compete drectly wth each other for a gven product or product category on prce. Note that ths assumpton does not rule out the possblty of non-prce competton. Ths assumpton has been also retaned n recent lteraure to explore the mpacts of ncreasng buyer power (see e.g. Inderst and Wey (2003), Inderst and Sha er (2007), Inderst and Wey (2005)). By abstractng away from downstream prce competton allows us to focus on how the equlbrum qualtes and shares of surplus depend on barganng power, technologes, and demands spec caton. We rst show that, two smple and often used forms of contracts, namely quantty forcng contracts (hereafter QF) wth xed transfer payments and two-part tar contracts (hereafter TPT) (whch allow for slottng fees and other forms of sde payments), are su cent to reach e cency from the channel s perspectve. 5 However, the nature of contracts has an n uence on the sharng of total surplus n the channel. In partcular, when all blateral barganng takes place over TPT wth retalers holdng the rght to order any quanttes they need, the latter are able to extract more surplus from manufacturers than under QF contracts. The ndngs of ths paper also shed lghts on how the changng barganng power of retalers and manufacturers a ect the quantty and prcng. We provde ratonale for the excessve focus of powerful retalers on the cost structures of the supplers. We show how nformaton on the cost structure of the supplers become crtcal as the barganng power of the retalers ncrease to optmze retal pro ts. Also, our analyss provdes useful nsghts on the role of qualty choce decsons on market outcomes. It shows why under d erent barganng condtons and decson processes t may not be possble for channel ntermedares to agree on qualty choces. By endogenzng the qualty choce process, we provde nsghts nto the role of prvate labels, exclusve deals between retalers and natonal brand manufacturers, the growng use of slottng fees and other forms of sde payments (e.g., trade and 5 If there s competton between retalers on the same market, then the complexty of contracts needed to reach e cency nsde the channel rases. For nstance, consder the case of a monopolst suppler dealng wth two competng retalers. If manufacturer has all the barganng power, publc two-part tar s ental e cency. Ths contrasts wth the opposte stuaton where retalers have all the barganng power. Indeed, Marx and Sha er (2005) have shown that publc two-part tar s s no longer su cent and Rey et al. (2006) have shown that three-part-tar s contngent on the market structure (exclusvty or common agency) are needed. 6

7 promotonal allowances), the choce of retal contracts, and other emergng trade practces n market channels. The paper s organzed as follows. The model s presented n secton 2. We provde the equlbrum soluton to the barganng game n secton 3. Secton 4 presents the analyss of payment schemes, wth a focus on the role of contract type, barganng power, role of cost structures of the manufacturers. The qualty choce ssues are nvestgated n secton 5. Secton 6 presents smulaton results llustratng our analyss. Fnally, secton 7 concludes. 2 The Model The model nvolves a two-stage game. The qualty decsons are made n a rst stage. And n the second stage each retaler and each manufacturer usng blateral negotaton decdes on quanttes and payments for products. Usng backward nducton, we start wth the analyss of stage-two decsons. For modelng purpose, t wll be convenent to assume that all negotatons are smultaneous and to use an asymmetrc Nash barganng approach. 6 However, our analyss can stll apply n stuatons where each barganng sesson nvolves an teratve process. Then our model would represent the outcome of ths process. 7 As such, we beleve that our nvestgaton can provde a good approxmaton of the actual barganng takng place between retalers and manufacturers. 8 Furthermore, each retaler s a local monopoly n the market t s operatng, whch means that consumers compare prces wthn a store but not across stores. It also means that t s stll possble to have non-prce competton among retalers. However, manufacturers compete wth each other wthn a retal chan. Retalers also compete when barganng wth a common provder. 9 6 To model smultaneous negotatons between manufacturers and retalers, we assume that each manufacturer employs I sale agents and each retaler employs J buyers. Each sale agent negotates ndependently wth hs correspondng buyer whle antcpatng frutful outcomes n all other negotatons. 7 An example s the teratve barganng scheme proposed by Zeuthen (1930). As shown by Harsany (1977), the Zeuthen teratve scheme converges to the Nash barganng outcome. 8 The CNBC produced documentary mentoned n secton 1 provdes useful nsghts nto the negotaton process at Wal-Mart. 9 The model can be mod ed to ncorporate non-prce competton between retalers, but ths wll sgn - 7

8 To provde nsghts nto negotaton/barganng outcomes n a marketng channel we rst need to decde on the on desgn of the contracts. We consder two types of contracts: () Quantty forcng contracts (QF) where, for gven qualty, each retaler and each manufacturer bargan over a par of quanttes and payments. If expressed per unt bass ths types of contracts are observatonally equvalent to wholesale prce contracts. In other words, our paper do take nto account wholesale prcng contracts provded the contracts are negotated. And () Two-part Tar (TPT) whch s the most wdely used form of non-lnear prcng mechansm. In ths case, agan for a gven qualty, each retaler and each manufacturer bargan over a xed transfer payment and a wholesale prce. We assume that a retaler keeps the rght to order any desred quantty. Ths type of contracts can lead to slottng allowances now wdely used n marketng channels. Note that TPT contract as presented does not rule out the possbltes of n knd (.e. non-monetzed) sde payments between retalers and manufacturers lke sharng nformaton on consumer demand, nventores etc. We present our analyss under both types of contracts. A number of results and nsghts hold under both types of contracts. Such results are presented rst. For example, both contracts elmnate double margnalzaton problems n the marketng channel. In the absence of drect externaltes between retalers and/or manufacturers, t follows that quantty choces are the monopoly outcomes on each ndependent markets. The man d erence between the two contracts s that the two-part tar outcome leaves more exblty to retalers than the quantty forcng contracts n stuatons of barganng falure. As we wll see, ths a ects the relatve barganng poston of retalers versus manufacturers as well as the dstrbuton of pro t and hence the qualty choces at the second stage. In partcular, we wll consder qualty choces that can be made ether by manufacturers n the case of branded products or by retalers n the case of store brands or prvate labels. cantly decrease analytcal tractablty of the paper wthout addng much to the focus of our analyss. 8

9 2.1 Assumptons and notatons We consder a set I of n retalers that buy goods from a set J of m manufacturers. Retalers wll be denoted by 2 I = f1; 2; :::ng and manufacturers by j 2 J = f1; 2; ::::; mg. The quantty of the products purchased by the -th retaler from the j-th manufacturer s denoted by the vector q j 0. The goods q j have qualty attrbutes denoted by the vector j. The -th retaler also pays the amount T j to the j-th manufacturer. The vector q = fq j : j 2 Jg denotes all quanttes bought (and sold on ts nal market) by the -th retaler wth products characterstcs = f j : j 2 Jg, and the vector q j = fq j : 2 Ig denotes all quanttes produced by the j-th manufacturer wth products characterstcs j = f j : 2 Ig. Also, we let q = fq j : 2 I; j 2 Jg and = f j : 2 I; j 2 Jg. The -th retaler faces the followng prce-dependent demand for q j : p j = P j (q ; ) for 2 I; j 2 J: For smplcty we normalze retalers retalng cost to be zero. It means that the only costs pad by retalers are the costs of procurng products from the manufacturers. The pro t made by the -th retaler s then gven by: = R (q ; ) X T j : (1) j2j where R (q ; ) = P j2j P j(q ; )q j denotes the -th retaler s revenue. The pro t made by the j-th manufacturer s: j = X T j C j (q j ; j ); (2) 2I where C j (q j ; j ) s the cost of producton for the j-th manufacturer. Aggregate pro t s gven by: (q; ) = X X R (q ; ) C j (q j ; j ): (3) 2I Throughout, we assume that (q; ) s concave n (q; ). Also, we assume that R (q ; ) depends on the attrbute j only when q j 6= 0; 2 I; and that C j (q j ; j ) depends on j only when q j 6= 0; j 2 J. j2j 9

10 As dscussed above, two types of contracts are nvestgated: quantty forcng and two-part tar contracts. In the quantty forcng (QF) contracts between the -th retaler and the j-th manufacturer, the nstruments are the quanttes q j and the payments T j, 2 I; j 2 J: Under two-part tar, we have T j = F j + w j q j, where w j s the vector of wholesale prces for q j sold to the -th retaler by the j-th manufacturer, and F j s the xed payment made by the -th retaler to the j-th manufacturer, 2 I; j 2 J. 10 In the two-part tar (TPT) contracts between the -th retaler and the j-th manufacturer, the nstruments are the prces w j and the xed payments F j, 2 I; j 2 J. 3 Barganng Equlbrum Startng wth stage two, consder the decsons about quanttes and payments made among retalers and manufacturers, condtonal on qualty. Assume that the blateral barganng between the -th retaler and the j-th manufacturer s represented by the followng asymmetrc Nash barganng game: maxf j ln( j ) + j ln( j j)g (4) where j agent, j > 0 s the barganng weght for the -th agent when barganng wth the j-th s the threat pont for the -th agent when barganng wth the j-th agent, and the barganng weghts are normalzed such that j + j = 1; 2 I; j 2 J: The threat ponts j and j represent pro ts obtaned when negotatons fal between agents and j. As dscussed below, the characterzaton of the threat ponts n general depends on the nature of the contracts. Blateral Nash barganng beng a cooperatve game, t mples that decsons are made so as to maxmze the total channel pro t + j made by the j-th manufacturer and the -th retaler. As we wll show here that n our context wth ndrect externaltes between players, ths s consstent wth choosng quanttes q so as to maxmze aggregate pro t (q; ): 10 In our notaton, w jq j denotes the nner product of the two vectors w j and q j, wth w jq j beng the total varable payment made by the -th retaler to the j-th manufacturer. 10

11 Proposton 1 Under blateral barganng represented by the asymmetrc Nash barganng game (4), for a gven qualty, the optmum quantty choce s q () 2 arg max q0 f(q; )g, where (q; ) s aggregate pro t gven n (3). Ths result apples to quantty-forcng contracts as well as two-part tar s where the prces are w ( ) (q (); )=@q ; 2 I. Proof: See appendx A. Proposton 1 mples that, condtonal on qualty, the barganng outcome wll lead to monopoly outputs. By maxmzng aggregate pro t, ths elmnates any double margnalzaton problems n the marketng channel. Note the generalty of ths result: t allows for an arbtrary number of manufacturers, an arbtrary number of retalers, a general technology, and arbtrary possbltes of substtuton among products wthn a retal chan. And ths result apples to QF as well as TPT contracts (wth wholesal prce w ( ) (q (); )=@q ; 2 I n the case of TPT contracts). Next we derve the generalzed pro t sharng rule under the Nash barganng soluton: Proposton 2 Under blateral barganng represented by the asymmetrc Nash barganng game (4), retaler and manufacturer j s pro ts are equal to ther threat pont pro t plus a weghted share of the jont barganng gan ( j j j ): = j + j j j j ; 2 I; (5) and j = j + j j j j ; j 2 J; (6) where j = + j s the jont pro t of the -th retaler and the j-th manufacturer. Proof: Usng the de ntons of and j gven n (1) and (2), note that the objectve functon n (4) s d erentable and strctly concave n T j (or F j under two-part tar s). For retaler and manufacturer j, the assocated rst-order condton for a maxmum s j j + j j j = 0 (7) 11

12 Rewrtng (7) and usng the normalzaton rule j + j = 1 gve the desred results. Proposton 2 show that each agent s pro t depends on both the level of threat pont pro ts ( j, j ) and on the value of the barganng parameter j = 1 j. The threat pont pro ts re ect avalable outsde optons n the case of negotaton falure. And the barganng parameters 0 s represent relatve barganng sklls. Proposton 2 mples that agents wth hgh threat ponts and good negotatng sklls wll grab a large porton of total pro t. Alternatvely, agents wth low threat ponts and low barganng sklls wll obtan only a small porton of total pro t. In general, small stores can be expected to have fewer resources, more lmted optons and thus lower threat ponts. In other words, n a world of e cent mega-retalers, some small retalers may stll be able to do well provded that they have good negotatng sklls. 4 Threat Ponts, Cost and Payment Schemes The results obtaned above apply for quantty-forcng as well as two-part tar contracts. And they apply for generc threat ponts. We now nvestgate how threat ponts, condtonal on qualty, can vary wth the type of contracts, wth mplcatons for payment schemes and the dstrbuton of pro ts. 4.1 The case of Quantty Forcng (QF) Contracts Under QF contracts between the -th retaler and the j-th manufacturer, decsons are made about quanttes q j and payments T j ; 2 I; j 2 J: Consder that a barganng falure between the -th retaler and the j-th manufacturer corresponds to q j = 0 and T j = 0. In addton, under blateral barganng falure between the -th and j-th agent and QF contracts, we assume that the quanttes chosen wth other agents fq lk : l 2 I; k 2 J; (l; k) 6= (; j)g and the payments nvolvng other agents ft lk : l 2 I; k 2 J; (l; k) 6= (; j)g reman una ected by the (; j)-th barganng falure. In ths context, denote the revenue of the -th retaler when t does not contract wth the j-th manufacturer by R j = R (q j ; ) where q j = fq k : k 2 12

13 J; q j = 0g. Smlarly, de ne C j ths mples that R j become: and and C j = C j (qj ; j ) where qj = fq lj : l 2 I; q j = 0g. Note that do not depend on q j. The threat ponts under QF contracts j j QF = R j jj QF = X l2in T lj X k2jnj T k ; 2 I; (8) C j ; j 2 J; (9) evaluated at fqlk () : l 2 I; k 2 J; (l; k) 6= (; j)g, where Jnj = fk : k 2 J; k 6= jg, In = fk : k 2 I; k 6= g. Under an (; j)-th barganng falure, treatng ft lk : l 2 I; k 2 J; (l; k) 6= (; j)g as xed and usng equatons (1), (2) and (5) yeld the followng result: Proposton 3 Under QF contracts, the payment T j can be expressed as a functon of ncremental cost to the j-th manufacturer, C j Cj, and ncremental revenue from the -th retaler, R : R j T j = 1 j R R j + j C j Cj ; 2 I; j 2 J: (10) Equaton (10) shows how the barganng weghts s a ect the transfer payments T. If the -th retaler has lttle barganng power whle negotatng wth the j-th manufacturer ( j ' 0), then T j ' R of the ncremental revenue (R R j. Ths means that the j-th manufacturer wll receve all the bene ts R j ) obtaned from sellng ts product to the -th retaler. However, the j-th manufacturer wll face the entre ncremental cost (C j hand, f retaler has all the barganng power ( j ' 1); then T j ' C j Cj ). On the other Cj. Ths means that the j-th manufacturer wll be totally compensated for the ncremental cost (C j C j ) of sellng ts product to the -th retaler. But the -th retaler wll keep the entre ncremental revenue (R R j ). In ntermedate stuatons where j 2 (0; 1), then ncremental cost and ncremental revenue wll be shared between manufacturers and retalers, wth a sharng rule that depends on ther relatve barganng sklls (as represented by j ). Usng equatons (1), (2) and (10), the pro ts under QF contracts can be expressed as follows: 13

14 Proposton 4 Under QF contracts, the -th retaler s pro t s j QF = R X (1 j )(R R j j2j and the j-th manufacturer s pro t s j j QF = X 2I (1 j ) R ) X j2j j R j + X j C j 2I C j Cj Cj ; 2 I; (11) C j ; j 2 J: (12) Proposton 4 provdes useful nsghts nto the relatonshps between manufacturers and retalers. Gven j 2 (0; 1), equaton (11) mples that the pro t of the -th retaler j QF s postvely related to the threat revenue R j, and negatvely related to the ncremental costs C j. Notng =@R j QF = 1 Pj2J (1 j ) = 1 P j2j j, the e ect of C j revenue R on s depends on the relatve barganng weghts: t s postve (negatve) when P j2j j < (>)1. Smlarly, equaton (12) mples that the pro t of the j-th retaler j j QF s negatvely related to the threat cost Cj, and postvely related to the ncremental revenue R. Notng j =@C j j QF = P 2I j 1, the e ect of cost C j on j s depend R j on the relatve barganng weghts: t s postve (negatve) when P 2I j > (<)1. Proposton (4) dent es the role of barganng power among agents under QF contracts. To llustrate, consder the case where the -th retaler s a poor negotator wth P j2j (1 j ) > 1. Ths corresponds to a stuaton where the j s tend to be small. Then any ncrease n R wll have a negatve mpact on pro t j QF. Intutvely, a declne n the negotatng power of the -th retaler s assocated wth manufacturers extractng more of any ncreased revenue. In such cases, perversely, the -th retaler would bene t from a strategy that reduces ts revenue R. In the extreme case of a very weak retaler (or very strong manufacturers), we have j ' 0 for all j. Then, equaton (11) mples that the -th retaler s pro t becomes j QF ' R P j2j (R R j ). In such a stuaton, pro t j QF depends only on the revenue patterns, and the cost of manufacturng ceases to play a role n determnng the -th retaler s pro t. Alternatvely, consder the case where the j-th manufacturer s a poor negotator wth P 2I j > 1. Ths corresponds to a stuaton where the j s tend to be large (or equvalently 14

15 the j s tend to be small). Then any decrease n C j wll have a negatve mpact on pro t j j QF. Intutvely, a declne n the negotatng power of the j-th manufacturer s assocated wth retalers extractng more of the reduced cost. In such cases, perversely, the j-th manufacturer would bene t from a strategy that ncreases ts cost C j. In the extreme case where the -th retaler has very strong barganng power, we have j ' 1 for all j. Then, from equaton (11), the -th retaler s pro t becomes j QF ' R Pj2J C j. Ths mples that the -th retaler wth hgh negotatng power pays the manufacturers only the C j ncremental cost P j2j (C j C j ). The present analyss can help explan why powerful retalers lke WalMart are so senstve about every aspects of costs of producton. Wth better negotatng power and hgh threat ponts, they can extract all the surplus from the marketng channel and pay ther supplers only the ncremental cost of producton. In ths context, growth n retal pro t comes n large part from squeezng the costs of the supplers. Also, usng equaton (12), note that j ' 1 for all mples that the j-th manufacturer s pro t becomes j j QF = P 2I C j C j. Thus, n the presence of powerful retalers, pro t j j QF depends only on the manufacturng cost, and patterns of revenue cease to play a role n determnng manufacturers pro t. Note that f the retalers only provde for the ncremental cost of producton then they have major ncentves ether to push supplers to buld larger plants or look for supplers wth more atter average cost functons. Also, because of the mportance of the cost structures of the supplers, retalers have ncentves to ask supplers to relocate to cheaper locatons wth larger plants thereby leadng to the phenomenon of race to the bottom. The qualtatve results presented here also hold under TPT contract, as t wll be clear n the next secton. 4.2 The Case of Two-Part Tar s (TPT) C j Under TPT contracts, the payments made by the -th retaler to the j-th manufacturer take the form T j = F j + w j q j ; 2 I; j 2 J: Agan, consder that a barganng falure between the -th retaler and the j-th manufacturer corresponds to q j = 0 and F j = 0 15

16 (mplyng that T j = 0). Under blateral barganng between the -th and j-th agent and TPT contracts, we assume that the prces facng other agents fw lk : l 2 I; k 2 J; (l; k) 6= (; j)g and the xed payments nvolvng other agents ff lk : l 2 I; k 2 J; (l; k) 6= (; j)g reman una ected by the (; j)-th barganng falure. To compare, QF contracts keep the payments ft lk : l 2 I; k 2 J; (l; k) 6= (; j)g and quanttes fq lk : l 2 I; k 2 J; (l; k) 6= (; j)g constant when the -th and j-th agents fal to reach an agreement. In contrast, TPT contracts keep the xed payments ff lk : l 2 I; k 2 J; (l; k) 6= (; j)g and the prces fw lk : l 2 I; k 2 J; (l; k) 6= (; j)g constant. But barganng falure under TPT allows some adjustments n the quanttes fq lk : l 2 I; k 2 J; (l; k) 6= (; j)g and ths a ects threat ponts and pro t sharng. We assume that these quantty adjustments are decded by the retalers. Implctly, ths means that, under contract falure, the retalers make decsons that reman consstent wth ther own nterest. In other words, for gven prces w, each retaler retans the rght to choose the quanttes to order from manufacturers and keeps on behavng as a pro t maxmzer when blateral negotatons fal. In the context of an (; j)-th barganng falure, agan de ne R j = R (q j ; ) where q j = fq k : k 2 J; q j = 0g. From Proposton 1, let TPT prces be w () (q (); )=@q ; 2 I, where q () 2 arg max q0 f(q; )g. Ths mples that ql () 2 arg max q l 0fR l (q l ; l ) P j2j w lj ()q ljg for l 2 In. For gven prces w (), t means that, under TPT contracts, the quantty decsons nvolvng "other retalers" (besdes the -th one) reman una ected by an (; j)-th barganng falure. However, wth retalers behavng as pro t maxmzers, when negotatons fal wth the j-th manufacturer, the -th retaler s decsons become ^q j () 2 arg max fr j q j 0 X k2jnj w k ()q kg; 2 I: In general ^q j k () 6= q k (), mplyng quantty adjustments for q k; k 2 Jnj. Under TPT 16

17 contracts, the threat-pont pro t for the -th retaler s thus de ned as: j j X T P T = max fr j wk ()q X kg F k ; q j 0 = ^R j X k2jnj k2jnj w k ()^q j k () X k2jnj k2jnj F k ; 2 I; (13) where ^R j = R (^q j (); ) s R j evaluated at ^q j (). A comparson of equatons (8) and (13) shows that the threat ponts d er between QF and TPT contracts. Intutvely, TPT contracts gve the retalers the rghts to choose the quanttes ordered and sold to consumers. As dscussed below, ths added exblty n procurement gves an advantage to the retalers under TPT contracts (compared to QF contracts). Next, consder the case of manufacturers n the context of an (; j)-th barganng falure. As just dscussed, under TPT prces w () (q (); )=@q ; 2 I, the quantty decsons nvolvng "other retalers" reman una ected when the -th retaler fals to agree wth the j-th manufacturer. Ths mples that q lj = qlj () for l 2 In and j 2 J wth or wthout barganng falure. Thus n case of barganng falure wth the -th retaler, the j-th manufacturer produces q j = 0. But t also produces the same quanttes fqlj () : l 2 Ing that t would have produced under a successful negotaton. Note that ths s the same threat-pont characterzaton obtaned under QF contracts and gven by j j QF n equaton (9). It follows that, under TPT, the threat pont pro t for the j-th manufacturer s: jj T P T = X l2in [F lj + w lj q lj ] C j ; (14) evaluated at fwlk () : l 2 I; k 2 J; (l; k) 6= (; j)g and fq lk () : l 2 I; k 2 J; (l; k) 6= (; j)g, where C j = C j (qj ; j ) and qj = fq kj : k 2 I; q j = 0g; j 2 J. Under an (; j)-th barganng falure, treatng ff lk : l 2 I; k 2 J; (l; k) 6= (; j)g as xed, and usng equatons (1), (2) and (5) yeld the followng result. Proposton 5 Under TPT contracts where w () (q (); )=@q ; 2 I, the payment 17

18 from the -th retaler to the j-th manufacturer s: F j + wj()q j = 1 j R X + 1 j evaluated at q = q (). k2jnj j ^R + j C j h w k ()(^q j k () Cj ; q k) (15) Comparng the payment scheme (15) under TPT contracts wth the payment scheme (10) under QF contract s nstructve. The rst term n (15) s smlar to the rst term n (15): they both nvolve a weghted change n the -th retaler s revenue assocated wth negotaton falure wth the j-th manufacturer. However, ^R j n (15) d ers from R j n equaton (10). As dscussed above, the former allows for quantty adjustments that are not present n the latter. The second terms n (15) and (10) are dentcal. They measure the e ect of a negotaton falure wth the -th retaler on the j-th manufacturer s cost. Fnally, the thrd term n (15) does not appear n (10). Snce the second terms are dentcal, the d erences n payments between TPT and QF contracts are due entrely to the rst and thrd terms n (15). To examne these d erences, note that equaton (13) mples ^R j X k2jnj wk ()^q j k () R j X k2jnj w k ()q k: (16) Combnng equatons (10), (15) and (16) gves the followng result. Proposton 6 The payments made by the -th retaler to the j-th manufacturer satsfy F j + w j()q j T j ; (17) mplyng that the -th retaler tends to pay less under TPT than under QF contracts. Proposton 6 shows that retalers tend to be better o under TPT than under QF contracts. Ths s a very general result whch apples under general technology, barganng sklls and market condtons. Ths result s ntutve. Whle QF contracts keep quanttes constant under barganng falure, TPT gves some exblty to the retalers n adjustng quanttes when negotaton fals. Ths exblty a ects ther threat ponts and ther payment schemes. 18

19 Usng equatons (1), (2) and (15) yelds the followng results under TPT contract. Proposton 7 Under TPT contracts, the -th retaler s pro t s j T P T = R X X (1 j )(R j2j X j2j k2jnj ^R j ) (1 j )w k () ^q j k X and the j-th manufacturer s pro t s j j T P T = X (1 j ) j R ^R + X j C j 2I 2I + X X (1 j )w k () ^q j k q k 2I k2jnj j2j j C j q k ; 2 I; Cj Cj C j ; j 2 J: (18) (19) The TPT results stated n Proposton 7 are smlar to those obtaned n Proposton 4 under QF contracts, except for two mportant d erences. Frst, the revenue term R j under QF contract s replaced by ^R j under TPT. Second, the term P k2jnj (1 j )w k () ^q j k q k s present under TPT but not under a QF contract. As dscussed above, both d erences re ect the fact that, compared to QF contracts, TPT gves some addtonal exblty for retalers to adjust quanttes under barganng falure. Except for these two d erences, smlar results are obtaned. Agan, equatons (18) and (19) show how the dstrbuton of barganng power among agents a ects the dstrbuton of pro t n the marketng channel. Next, we explore the e ects of the type of contract on manufacturers and retalers pro ts. These pro ts are de ned n equatons (11) and (12) under QF contracts and n equaton (18) and (19) under TPT. Usng equatons (1), (2), and (17), we obtan the followng result. Proposton 8 The pro ts made by retalers and manufacturers satsfy j T P T j QF ; 2 I; and j j T P T j j QF ; j 2 J: 19

20 Proposton 8 shows that TPT contracts tend to bene t retalers at the expense of manufacturers. As dscussed above, ths re ects the fact that retalers gan added exblty usng TPT when negotatons fal. Ths tends to ncrease ther threat ponts and mprove ther poston n clamng a larger share of pro t. Fnally, n the context of TPT contracts, we explore the determnants of the xed payments F j. When postve, these payments nvolve retalers payng manufacturers a xed amount of money. But when negatve, they are xed payments from manufacturers to retalers. As such, when negatve, F j represents slottng fees. Such slottng fees have become more commonly used over the last few years. Ths rases the ssue: what are the determnants of slottng fees? And when are they lkely to arse? In general, the xed fees F j are determned as gven n equaton (15). Ths shows that the determnants of the F j s can be complex: they depend on the cost and revenue structure and on the dstrbuton of barganng power. Here, we look for su cent condtons under whch we can determne the sgn of F j. Proposton 9 Su cent condtons for a slottng fee, F j < 0, between the -th retaler and the j-th manufacturer are: () the ncremental average revenue [R (kq j ) j ^R ]=k s ncreasng n k (where k s a postve scalar representng a proportonal rescalng of q j ), and () P 2I Pk2Jnj w k ()(^q j k q k ) 0, evaluated at q = q (): Proof: Usng (13) and at the optmum, we have, j = R ^R j F j wj ()q j + P 2I Pk2Jnj w k ^q () j k q k. Snce j 0, and usng w j () =@q j, t follows that R ^R j [@R =@q j ] q j + P 2I Pk2Jnj w k () ^q j k q k F j. Note that the ncremental average revenue [R (kq j ) R ^R j j ^R ]=k beng ncreasng n the scalar k > 0 mples that [@R =@q j ] q j < 0 (evaluated at k = 1). Ths gves the desred results. Proposton 9 presents su cent condtons for slottng fees to arse between the -th retaler and the j-th manufacturer, wth F j < 0. These condtons are that the ncremental av- 20

21 erage revenue [R (kq j ) j ^R ]=k s ncreasng n k, and that P 2I Pk2Jnj w k ()(^q j k q k ) 0. Condton () re ects local economes of scale n retal sales. It s sats ed when a proportonal ncrease n q j generates a more than proportonal ncrease n ncremental revenue j [R ^R ]: Ths could happen n stuatons where consumer response exhbt "mnmum thresholds" wth respect to quanttes q j. Condton () means that settng q j = 0 tends to decrease the demand for other products sold by the j-th retaler fq k : k 2 Jnjg,.e. that q j and fq k : k 2 Jnjg behave as complements. Ths complementarty relatonshp can nduce the j-th manufacturer to pay a xed fee to the -th retaler. In other words, Proposton 9 states that slottng fees are lkely to arse when local economes of scale n retal sales exsts wth respect to q j, and when the commodtes q j tends to be complement wth other products sold by the -th retaler. These results appear to be new. They provde valuable nsghts about scenaros where slottng fees are expected to arse. 5 Product postonng So far, we have nvestgated the second stage barganng process over product quanttes and payments among manufacturers and retalers, condtonally on qualty attrbutes. In ths secton, we nvestgate the rst stage alternatve decson rules related to the qualty choces/attrbutes de nng product postonng n the marketng channel. In ths paper, we consder cases where products are vertcally d erentated. Note that n the case of costless horzontal d erentaton product postonng becomes trval. So, n rest of the analyss an ncrease n wll mply mprovement n product qualty. 5.1 Optmal product postonng from the total channel perspectve For reference, we start by analyzng the optmal product postonng from the total channel perspectve as a benchmark case to whch we wll compare manufacturers and retalers qualtes choces. From proposton 1, the total channel pro t can be wrtten as () = (q (); ), where (q; ) s de ned n equaton (3) and q () 2 arg max q0 f(q; )g s 21

22 the monopoly quanttes condtonal on. Let A represent the feasble set for, 2 A. Therefore, the monopoly qualty choces are consstent wth the pro t maxmzng problem: 2 arg max 2A f ()g: (20) Lettng q = q ( ), ths can be alternatvely wrtten as ( ; q ) 2 arg max 2A;q0 f(; q)g: 5.2 Optmal postonng n a two-stage game We focus our attenton on two cases: () the case where each manufacturer chooses the qualty of the products t produces; and () the case where retalers make the qualty choce smlar to the most cases of qualty choce for prvate labels. In ether case, we nvestgate how changes n the relatve barganng power of market partcpants a ects qualty choces. Ths analyss wll provde us nsghts nto how changes n barganng power and who makes the qualty choce decsons wll mpact market outcomes and socal welfare. Case () corresponds to stuatons where manufacturers choose the product type/qualty. We focus our attenton on the stuaton where the qualty produced by each manufacturer s unform for all retalers. 11 Thus, for the j-th manufacturer, we assume that j = j ; 2 I. Let the feasble set for j be A j ; j 2 J. Usng equaton (6), the qualty choce made by the j-th manufacturer for j s gven by the optmzaton problem m j ( I j ; Jnj ) 2 arg max j2a j f X 2I j + j B j ( ) g; (21) where = f j : j 2 Jg, B j ( ) = [ (q ( ); )+ j (qj ( ); j ) j j ] s the barganng gan obtaned jontly by the -th retaler and j-th manufacturer, I j = f j : 2 Ig and Jnj = f k : k 2 Jnjg. Equaton (21) de nes m j (I j ; Jnj ) as the reacton functon representng the j-th manufacturer s decson for j condtonal on the barganng weghts I j and on other qualty decsons Jnj. Case () corresponds to the stuaton where retalers make the qualty choce. For the -th retaler, usng equaton (5), ths means that the choce of j s made as follows 11 The case where each manufacturer sells d erent product qualtes to d erent retalers s presented n Appendx B. 22

23 r j( j ; In;Jnj) 2 arg max j 2A j f j + j B j()g; (22) where B j () = [ (q (); )+ j (qj (); j) j j ] s the barganng gan obtaned jontly by the -th retaler and j-th manufacturer, and In;Jnj = f lk : l 2 In; k 2 Jnjg: Equaton (22) de nes r j (j ; In;Jnj) as the reacton functon representng the -th retaler s decson for j condtonal on the barganng weght j and on other qualty decsons In;Jnj. Equatons (21) and (22) d er from equaton (20). Ths mples that the non-cooperatve qualty decsons made at stage one n general d er from the optmal product postonng gven n (20). Ths s because the j-th manufacturer does not nternalze all the e ects of ts qualty decson. Two sets of factors play a role. Frst, n general, the threat ponts j and j depend on the qualty choce j. To see that, t su ces to note that, under blateral barganng falure, both C j and C j depend on j (through q j ) under ether a QF contract or a TPT contract. Second, equatons (21) and (22) mply that the relatve barganng weght 0 s play a role n the qualty decson. Equatons (21) and (22) also d er from each other. Ths shows that the qualty decsons depend on who makes these decsons. There are two reasons for ths d erence. Frst, whle m j (I j ; Jnj ) n (21) depends on the barganng weghts of the j-th manufacturer wth respect to all retalers I j = f j : 2 Ig, note that r j (j ; In;Jnj) n (22) depends only on the barganng weght j spec c to the -th retaler. Second, the strategc e ects nvolved n qualty choces d er n (21) versus (22). Indeed, whle m j (I j ; Jnj ) n (21) depends on Jnj, r j (j ; In;Jnj) n (22) depends In;Jnj, re ectng our assumpton that the qualty produced by each manufacturer (n case ()) s unform for all retalers. The market determnaton of product qualty s analyzed n detals below, wth a focus on two ssues: 1/ the role of changng barganng power; and 2/ the e ects of control on product postonng. 23

24 5.2.1 Optmal postonng from the manufacturer s perspectve When each manufacturer chooses product qualty that s unform across all retalers, equaton (21) provdes the relevant characterzaton of the qualty choce j ; j 2 J. In ths context, the strategc e ects of Jnj on m j n m j (I j ; Jnj ) are relevant. De ne the qualtes k and j to be m-strategc substtutes (m-strategc complements) when m j (I j ; Jnj ) s decreasng (ncreasng) n k ; k 2 Jnj. For smplcty, we lmt our dscusson to the case where j s a scalar and where the optmzaton problem (21) has a unque nteror soluton. In ths context, the next proposton nvestgates the e ects of changng relatve barganng power (as captured by the 0 s) on product postonng. Proposton 10 Assume that the manufacturers choose qualty accordng to (21): Then, ceters parbus, () an ncrease n j mples a decrease (ncrease) n qualty j j( j > 0 (< 0); 2 I; () an ncrease n k mples a decrease (ncrease) n qualty j k ( k > 0 (< 0); k 2 Jnj; k (substtutes). > 0 (< 0) when k and j are m-strategc complements Proof: Gven j = 1 j and assumng d erentablty, applyng comparatve statcs analyss to (21) m j = j( j g: (23) Thus, a ceters parbus ncrease n j tends to ncrease (decrease) m j j( j s negatve (postve). Ths yelds result (). Note from (21) that a ceters parbus change n k (or equvalently (1 k )) has no drect mpact on m j when k 2 Jnj. Under d erentablty and for k 2 Jnj, t follows that the mpact of k on j reduces to ts strategc m k k Usng (23), ths yelds result (). 24

25 Proposton 10 shows the mpact of barganng weghts on the j-th manufacturer s qualty decson j. Result () states that ncreasng the barganng power of any retaler relatve to the j-th manufacturer (through an ncrease n j ) mples a decrease (ncrease) n qualty j j( j s postve (negatve), 2 I. Ths dent es the role of the barganng gan B j ( ) and ts propertes wth respect to a change n j. However, note that, n general, the e ects of j on B j ( : ) can be complex: they depend on the propertes of manufacturng cost C j, revenue R, as well as the threat ponts j and j. They wll be further evaluated below. Result () shows the e ect on j (the qualty produced by the j-th manufacturer) of a change n the barganng power of retalers wth respect to other manufacturers (as measured by k, k 2 Jnj). It states that the qualty produced by the j-th manufacturer decreases (ncreases) wth a rse n k k ( k > 0 (< 0); k 2 Jnj: Agan, ths dent es the role of the barganng gan B j ( ) and ts propertes wth respect to a change n j. It also shows the role of strategc behavor, as captured by the strategc e k. For example, n the case where ncreasng qualty contrbutes to ncreasng the barganng gan B k ( ) (.e., k( k > 0), then a rse n the barganng power of retalers wth respect to the k-th manufacturer (as measured by k ; k 2 Jnj) mples an ncrease (decrease) n the qualty j chosen by the j-th manufacturer when k and j are m-strategc substtutes (complements). Ths llustrates the e ects of strategc behavor on product postonng Optmal postonng from the retaler s perspectve We now turn our attenton to the case where the qualty choce s made by retalers n the rst stage of the game. Ths re ects the changng role of retalers over the last few years. In partcular, ths s motvated by the growng mportance of large retalers n product postonng. Equaton (22) provdes the relevant characterzaton of the qualty choce for ths analyss. In ths context, the strategc e ects of In;Jnj on r j n r j (j ; In;Jnj) are relevant. 12 The case where manufacturers o er d erent product qualty to d erent retalers gves smlar qualtatve results. Ths case s presented n Appendx A. 25

26 De ne the qualtes j and lk to be r-strategc substtutes (r-strategc complements) when r j (j ; In;Jnj) s decreasng (ncreasng) n lk ; l 2 In; k 2 Jnj. For smplcty, we lmt our dscusson to the case where j s a scalar and where the optmzaton problem (22) has a unque nteror soluton. In ths context, the next proposton nvestgates the e ects of changng relatve barganng power (as captured by the 0 s) on product postonng. Proposton 11 Assume that the -th retaler chooses qualty j accordng to (22). Then, ceters parbus, () an ncrease n j mples an ncrease (decrease) n qualty j j( j > 0 (< 0); 2 I; j 2 J; () an ncrease n k l 0); l 2 In; k 2 Jnj; lk (substtutes). mples an ncrease (decrease) n qualty j lk ( lk > 0 (< > 0 (< 0) when j and lk are r-strategc complements Proof: Assumng d erentablty, applyng comparatve statcs analyss to (22) r j = j g: (24) Thus, a ceters parbus ncrease n j tends to ncrease (decrease) r j j s postve (negatve). Ths yelds result (). Note from (22) that a ceters parbus change n k l has no drect mpact on r j when l 2 In; k 2 Jnj. Under d erentablty and for l 2 In; k 2 Jnj, t follows that the mpact of k l ths yelds result (). on j reduces to ts strategc r r k l : Usng (24), Proposton 11 shows the mpact of barganng weghts on the qualty decson j made by the -th retaler for products obtaned from the j-th manufacturer. Result () states that ncreasng the barganng power of the -th retaler relatve to the j-th manufacturer (through an ncrease n j ) mples an ncrease (decrease) n qualty j j postve (negatve), 2 I; j 2 J. Agan, ths dent es the role of the barganng gan B j () and ts propertes wth respect to changes n j. s 26

27 Result () shows the e ect on j (the qualty chosen by the -th retaler for products obtaned from the j-th manufacturer) of a change n the relatve barganng power of other retalers and manufacturers (as measured by k l, l 2 In; k 2 Jnj). It states that the qualty j ncreases (decreases) wth a rse n k l lk ( lk > 0 (< 0); l 2 In; k 2 Jnj: Agan, ths dent es the role of the barganng gan B j () and ts propertes wth respect to a change n j. It also shows the role of strategc behavor, as captured by the strategc e lk. For example, n the case where ncreasng qualty contrbutes to ncreasng the barganng gan B lk () (.e., lk > 0), then a rse n the barganng power of the l-th retaler wth respect to the k-th manufacturer (as measured by k l ; l 2 In; k 2 Jnj) mples a decrease (ncrease) n the qualty j when lk and j are r-strategc substtutes (complements). Comparng the results stated n Propostons 10 and 11 s nstructve. In partcular, result () of each proposton shows that changng the barganng weght j tends to have opposte e ects on the qualty choce j dependng on who has control of the qualty decson and product postonng. For example, n the case where ncreasng qualty tends to ncrease the barganng gan B j, then a rse n the barganng power of the -th retaler (as measured by j ) would decrease product qualty j when the qualty decson s made by the j-th manufacturer, but t would ncrease product qualty j when the qualty decson s made by the -th retaler. Ths shows the presence of mportant trade-o s between barganng power, control, and qualty management. Further exploratons of these tradeo s are presented next. 6 Barganng Outcomes usng Smulaton Gven the complexty of qualty choces, ths secton explores the determnants of product qualty n a marketng channel usng smulaton technques. We consder qualty choces n the context of a vertcally d erentated product market. 13 To keep the analyss tractable, we smulate a market wth two retalers and two manufacturers wth manufacturer A producng 13 Note that, under purely horzontally d erentated products where the cost of d erentaton s zero, the choce of qualty s trval. 27