managing channel profits

7/28/2019 Managing Channel Profits

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Vol. 27, No. 1, JanuaryFebruary 2008, pp. 5269

issn 0732-2399 eissn 1526-548X 08 2701 0052

informs

doi10.1287/mksc.1070.0332 2008 INFORMS

Managing Channel Profits

Abel P. JeulandGraduate School of Business, University of Chicago, Chicago, Illinois 60637, [email protected]

Steven M. ShuganWarrington College of Business, University of Florida, Gainesville, Florida 32611, [email protected]

Achannel of distribution consists of different channel members each having his own decision variables. How-ever, each channel members decisions do affect the other channel members profits and, as a consequence,actions. A lack of coordination of these decisions can lead to undesirable consequences. For example, in thesimple manufacturer-retailer-consumer channel, uncoordinated and independent channel members decisionsover margins result in a higher price paid by the consumer than if those decisions were coordinated. In addition,the ensuing suboptimal volume leads to lower profits for both the manufacturer and the retailer.

This paper explores the problems inherent in channel coordination. We address the following questions.What is the effect of channel coordination?What causes a lack of coordination in the channel?

How difficult is it to achieve channel coordination?What mechanisms exist which can achieve channel coordination?What are the strengths and weaknesses of these mechanism?What is the role of nonprice variables (e.g., manufacturer advertising, retailer shelf-space) in coordination?Does the lack of coordination affect normative implications from in-store experimentation?Can quantity discounts be a coordination mechanism?Are some marketing practices actually disguised quantity discounts?

We review the literature and present a simple formulation illustrating the roots of the coordination problem.We then derive the form of the quantity discount schedule that results in optimum channel profits.

This article was originally published in Marketing Science, Volume 2, Issue 3, pages 239272, in 1983.

Key words : distribution; profitability; margins; coordinationHistory : This paper was received May 1981 and was with the authors for 4 revisions.

1. IntroductionA channel of distribution consists of different chan-nel members each having his own decision variables.However, each channel members decisions do affectother channel members actions. For example, if aretailer takes an action (e.g., changed shelf location)which causes a decrease in the volume of a par-ticular product, all members in the products chan-nel observe the decreased volume and then react toit. Hence numerous interactions take place betweenchannel decisions. Even if a manufacturer does notobserve a retailers action, the manufacturer may still

respond to that action because the manufacturer doesobserve a change in product volume. This fact illus-trates that the retailer can exercise some control overthe manufacturer. Of course, this is true for all chan-nel members. Each channel member influences otherchannel members decisions. The result is a struc-ture of institutional arrangements that should be ofgreat interest to both researchers and practitioners inmarketing.

This paper addresses the problem of coordinat-ing channel decisions. This problem and its relatedissues have generated considerable research in both

the marketing and economic literature (Bucklin 1966,1970; Cox 1956; Doraiswamy et al. 1979; Douglas1975; Logan 1969; Mattson 1969; McGuire andStaelin 1983a, b; Stasch 1964; Stern and El-Ansary1977; Thomson 1971; Wedding 1952; White 1971;Williamson 1971; Etgar 1974; Zusman and Etgar 1981).First, and not unlike some of the studies just refer-enced, we do not attempt to exhaustively describe thechannel. Instead, we abstract particular channel phe-nomena in order to understand them. Second, witha general demand function, we attempt to analyzeone channel aspect, namely coordination. Third, we

provide a new interpretation for quantity discountswhich are commonly viewed as shifting productionor inventory costs (see Dolan 1978). In fact, we showthat quantity discounts are profitable even with noorder or inventory costs. Fourth, we reinterpret manyprevalent channel phenomena in the light of coordi-nation showing that they may actually be coordinat-ing mechanisms. Finally, we adopt the approach ofeconomic theory building. For example, we assumechannel members are rational, act in their own bestinterests and seek to maximize their respective profits.

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Jeuland and Shugan: Managing Channel ProfitsMarketing Science 27(1), pp. 5269, 2008 INFORMS 53

However, we deviate from the related economic liter-ature in several significant ways. First, we explicitlydeal with nonprice variables (i.e., typical marketingdecision variables like advertising and shelf-space)and their effect on pricing decisions. Second, we shiftour emphasis from the currently popular bargaining

problem back to the central coordination problem.Third, we provide a new justification for quantitydiscounts that is different from the celebrated pricediscrimination explanation given in the economicsliterature. In fact, we show that quantity discountsare profitable even without multiple retailers. Finally,unlike economists who desire to provide social wel-fare implications, our ultimate purpose is to provide asimple model that deals with some important aspectsof the managers decisions. In order to help chan-nel managers, we seek to do more than direct them.A seasoned manager may already know which partic-ular actions work and which do not work. What that

manager really requires is a more thorough under-standing of how the channel functions, i.e., why par-ticular actions work and why others do not. Just as theexperienced engineer gains additional insight fromtheoretical physics, the experienced manager gainsadditional insight from theoretical marketing.

The major objective of this paper is to examine theproblem of channel coordination. We hope to illus-trate the fundamental nature of this problem andhow the failure to recognize it can distort nearly allchannel decisions. We illustrate that the problem isso fundamental that it occurs in the two-member,single manufacturer-single retailer channel known as

the bilateral monopoly in the economics literature.Without the distraction of multiple products, multipleretailers, multiple manufacturers, uncertainty, asym-metric power struggles or institutional constraints,the problem of channel coordination still exists. We,therefore, focus on the simple two-member channelwhich will not distract us from the basic issue ofcoordination to more complex channel phenomena.However, we do extend our analysis to more com-plicated channels such as manufacturer-wholesaler-retailer channels.

In the next section, we start our analysis by for-malizing the relationships and decision variables ofeach channel member in the two-member channel.We resolutely avoid analogies which seek to viewchannel members as agent and principal; or followerand leader. These comparisons put the manufacturerand the retailer in the role of coordinator and coor-dinated, thus avoiding the real problems of coordina-tion such as the motivation for these roles, how theseroles evolve and the stability of these roles. In con-trast to this approach, we construct a symmetric for-mulation where the retailer and the manufacturer areseparate decision-making entitieseach with his own

decision variables (such as his margin) over which hehas control. Our formulation views channel outcomes(such as channel profit) as a function of these separate

but interdependent decisions. In this way, externali-ties which may put a particular channel member in aleadership position become a special case of our anal-

ysis rather than a driving force of the analysis.After formalizing our model in 2, 3 begins ouranalysis of the problem of channel coordination. Weillustrate the mutual incentives for coordination andthe individual disincentives for cooperation. We findeach channel member wants his partner to cooper-ate but does not want to cooperate himself. Withthis problem identified, 4 addresses possible solu-tions together with their strengths and weaknesses.Among the possible solutions discussed are contrac-tual arrangements, implicit understandings and profitsharing. This section then presents the main resultof our papera new mechanism which overcomes

many of the weaknesses of the other mechanisms.However one problem remains. Once coordination isachieved, additional total profits are generated andwe must consider their division. Section 5 brieflyreviews one classical solution to this problem andits implications. Section 6 discusses managerial impli-cations. Section 7 discusses the related research inmarketing. Finally, 8 contains suggestions for futureresearch and 9 gives our conclusions.

2. Formalization of a Simple ChannelAs a first step toward understanding the issues con-cerning the internal functioning of channels of dis-tribution, i.e., the interdependencies between verticalchannel members, we start with a simple structurefor distribution, namely one manufacturer who sellsthe brand under investigation and one retailer whoresells it to consumers. From this simple model, wededuce conclusions that, insofar as our formulationaccurately abstracts an important aspect of reality,are themselves important for management decision-making. We hope future research will examine andovercome the empirical and theoretical limitations ofour analysis. One should note that the structure of thesimple model is directly usable to analyze the case of

a franchise in which a manufacturer sells locally oneproduct exclusively through one retailer. This case isalso studied by McGuire and Staelin (1983a) in thecontext of duopolistic retail competition. For manyactual situations, extensions to the simple model arerequired. Sections 3B and 3C address some of thesegeneralizations.

A. Basic DefinitionsFor the purpose of keeping notations simple, wedenote by capital letters what refers to the manu-facturer and small letters what relates to the retailer.


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Jeuland and Shugan: Managing Channel Profits54 Marketing Science 27(1), pp. 5269, 2008 INFORMS

Some basic notations are:

F f total fixed costs for the manufacturer andretailer, respectively.

C c variable costs of manufacturer and retailer perunit for the product under study.

profit functions of manufacturer and retailer.

Dp consumer demand as a function of retail pricep, dD/dp< 0.

Gg margins of manufacturer and retailer per unit.

B. AssumptionsInitially, we make the following four key assump-tions:

1. A two-member vertical channel.2. A downward sloping retail demand function.3. Certainty over all variables (functions) except

channel member behavior.1

4. Symmetry.

We now discuss each of these assumptions in detail.We will later discuss the sensitivity of our analysis tothese assumptions (see 4H).

A Two-Member Vertical Channel. We initially as-sume the channel has only two membersthe man-ufacturer and the retailer. The manufacturer can sellto multiple retailers but these retailers are not indirect competition. The manufacturer can manufac-ture several brands but he does not sell competing

brands through the same retailer. The retailer cancarry many brands but we consider the profits of onlyone brand. We make these assumptions to enhance

the exposition, augment analytical tractability andemphasize only coordination issues. The extensionsto multiple member vertical channels are straightfor-ward (see 3B). However, extensions to multiple man-ufacturers (and multiple retailers) are complicated byassumptions concerning competition (see 3C) amongmanufacturers (retailers). Nevertheless, coordinationproblems remain (see 3C). Additional extensions to

both multiple manufacturers and multiple retailersare further complicated by the ambiguity surroundingthe definition of a channel and the meaning of chan-nel profits. We leave these other important issues forfuture research and focus our attention on the coordi-nation issue which appears in all of these situations.

A Downward-Sloping Retail Demand Function.We assume the brand demand function is downwardsloping. Our demand function is general in form. Wefurther elaborate on the question of modeling thecompetition that the retailer faces in 2D.

1 The situation is analogous to a chess game where all the rules areknown and each players objective is known (i.e., to win). However,the course of the game remains uncertain.

Certainty Over All Variables (Functions) ExceptChannel Member Behavior. We assume that eachchannel member knows the retail demand function.In our later analysis we also assume that each channelmember knows the retail price. Each channel memberknows the amount of marketing effort he is expend-

ing on the brand. Therefore, each channel membercan infer the marketing effort the other member isexerting on the brand. Finally, we assume that eachchannel member knows the other channel membersvariable costs. However, we later discuss the relax-ation of some of these assumptions (see 4F).

Symmetry. We make no initial assumptions con-cerning channel power or the institutional relation-ship between channel members other than the factit is a vertical relationship. We leave channel powerexogenous to our model and capture it in severalnegotiated constants (see 5). Symmetry allows us

to take an impartial view of the channel. This viewlessens predispositions toward assuming a particularmarket structure when the interesting questions may

be why that structure exists. This unbiased approachis adopted by Gould (1980) who states:

It seems to be that classifying economic agents intothe categories of buyers and sellers is an artificialand potentially misleading way to begin. In a fun-damental sense there are neither buyers nor sellers.simply traders. Each trader is simultaneously a buyerand a seller. The fact that in advanced economies onetrader gives up money in exchange for a good or ser-vice while the other gives up the good or service in

exchange for money should not obscure the basic trad-ing relationship that is involved. It is widely recog-nized in economics that trading occurs because bothparties to the trade realize gains from the transaction.This is important because it means that both partieshave an interest in making a market.

We do not start with the premise that manufac-turer behavior necessarily differs from retailer behav-ior. Hence each channel member is given the samenumber of decision variables, each channel member isassumed to be equally sophisticated, and each chan-nel member is assumed to want to maximize his prof-its. Of course, channel members may have different

costs and different channel functions as well as differ-ent degrees of channel power. This notion of symme-try has been voiced repeatedly in marketing. Bagozzi(1974) and others have stated that marketing is con-cerned with exchange and that both buyer and sellermust benefit if the exchange is to take place.

C. A Simple FormulationWith the preceding notations and assumptions, man-ufacturer profits are given by =GD F and retailerprofits by = gD f so that total channel profits are


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+ = G + gD F f where the channel mar-gin G + g is linked to retail price p by the relationG + g + C+ c = p. The downward-sloping demandfunction, which is a function of retail price, is also afunction of all competitive factors beyond the controlof the channel members. One assumption is to take

these factors as fixed parameters in the function (see2D for more details and extensions). The precedingformulation is perfectly symmetric with respect to themanufacturer and the retailer. Throughout this paper,it will be assumed that the manufacturer has controlover his margin G and the retailer over his margin g.It follows from the preceding formulation that retailprice is the direct result of both the manufacturersdecision on his control variable G and the retailersdecision concerning his control variable g.

D. Some Immediate ExtensionsThe preceding formulation does not recognize that

both the manufacturer and the retailer usually haveother control variables besides G and g. For exam-ple, the manufacturer can modify the quality of hisproduct. Hence, we introduce a second control vari-able Q for the manufacturer. It represents the man-ufacturers opportunity cost due to his effort on theproduct. Consequently, the profit function of the man-ufacturer becomes =GDQ F.

The same situation also exists for the retailer who,in addition to deciding which margin to take, canalso decide how much point-of-sale effort to put intothe product, for example shelf-space. For this reason,we introduce a second control variable s so that the

retailers profit function becomes = gD S f.Given these new variables, the consumer demand

function now has two arguments in addition to p; D=DpQs with D/Q > 0, D/s > 0, 2D/Qs > 0,2D/Q2 < 0, 2D/s2 < 0. Again the extended modelis perfectly symmetric with respect to the manufac-turer and the retailer.

Moreover, if Q denotes product quality, one wouldexpect the manufacturers marginal cost of produc-tion to be a function of Q. Consequently, we willassume C=CQ in the extended formulation. A sim-ilar argument leads to the assumption of retailersmarginal cost to be a function of s so that c= cs. In

the simple formulation C and c are constants.The extended formulation is fairly general in that

(1) the presence of the opportunity cost Q accountsfor the fact that the manufacturers funds competefor optimal allocation, (2) the retailers opportunitycosts s are also incorporated and, (3) the down-ward-sloping demand function reflects the competi-tion faced by the product under study. Concerningassumption (3), and in the practical situation ofoligopolistic competition, the demand for the productis Dpp1 pn where p1 through pn are the prices

of competitive products carried by other retailers. Weassume D/p < 0 and D/pi > 0. In practice, whenthe retailer sets price p, reactions may take place. Thismeans that pi =Rip where Rip is the reaction taken

by product i. Consequently, when the retailer is aleader, demand for the product under study becomes

DpR1pR2pRnp. We assume that the reac-tion functions are well behaved so that

dD

dp=

D

p+

n

i=1

D

pi

Rip

< 0

This condition may be necessary for an equilib-rium with finite prices to existotherwise, economicagents may keep on increasing their prices. An exam-ple of well-behaved reaction functions is developedin the appendix. If there is no immediate reaction, i.e.,Rip pi, then

dD

dp=

D

p< 0

It would thus appear that the downward-slopingdemand assumption is robust whether the retailer isa leader or not.

3. The Economics of Cooperation

A. The Simple ChannelIf a single individual owned the entire channel, per-fect coordination would exist.2 Manufacturer andretailer activities would both be directed by thecommon owner for the common good. The ownerwould seek to maximize the sum of manufacturer andretailer profits, that is, total channel profits. The com-

mon owner would direct each channel member to actconsistently with this objective. We refer to the resultof this overall maximization as the joint maximum.At the joint maximum, + is maximized and chan-nel members have the most profits to divide betweenthem.

The condition necessary for obtaining the joint max-imum that directly involves the manufacturers mar-gin is given by:

+

G=

G+

G= 0 (1)

The joint owner would assign the manufacturer a

margin which satisfies Equation (1). But we know that= gD sf and hence Equation (2) must hold (seeappendix):3

G=

geD

p(2)

2 It would exist given the common owner had perfect informationand the necessary expertise on every aspect (e.g., manufacturingand retailing) of the business.3 In order to enhance the exposition most equations are derived inthe appendix.


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wheree = the absolute price elasticity of demand,e =D/p/D/p.

We know that g, D, and p are positive as wellas the absolute price elasticity e (larger prices implya lower quantity demanded).4 Hence the common

owner would set G and g such that geD/p andtherefore /G are negative. This result indicatesthat the retailer, if he were only interested in his ownprofits, would be unhappy with the margin a com-mon owner would assign to the manufacturer. If theretailer had control over the decision variable G, theretailer would set G such that /G equals zero,thereby maximizing his profits. Of course, without

joint ownership, the retailer would still have no directcontrol over the manufacturers decision variable G.

However, if /G is negative, then for Equa-tion (1) to hold, /G must be positive. This impor-tant implication indicates that at the joint maximum,the manufacturers profits are increasing in G. That is,the manufacturer would be unhappy with G at the

joint maximum and would seek to raise his mar-gin until his profits are maximized. If he were onlyinterested in his own profits, he would seek toraise his margin from the joint maximum margin,denoted G, where /G > 0, to the margin maxi-mizing his independent profits, denoted G, at whichpoint /G= 0.5 The reason why the manufacturercan raise his margin above the margin G that isconsistent with maximization of channel profits and,in the short run, obtain more profit is because the

initial decrease in volume is completely recoveredby the manufacturers higher per unit profit. Themanufacturer does not feel the full volume decrease

because his margin determines only part of the price.The retailer, however, would suffer far more from thedecreased volume than the manufacturer because theretailer loses volume while obtaining no increase inunit profit. Finally, the symmetry of our formulationdictates similar results for g.

The problems occurring with margin determina-tion also appear in other channel decision variables.Again, the channel members acting independently

may not seek to maximize joint profits. For example,

4 Except under very unusual conditions, price elasticities are gener-ally positive.5 Note. At this point we have not yet discussed the simultaneousdetermination of g and G. However, in the appendix, we deriveEquations (3) and (4):

G = g+ c+C eg/e1 (3)

G= g+ c+C/e 1 (4)

Symmetric equations exist for g.

consider product quality. Joint maximization requiresthe condition given by Equation (5) to hold:

+

Q=

Q+

Q= 0 (5)

We know that = gD s f, which yields:6

Q= g

QD= g

D

p

p

Q+

D

Q

(6)

However, it can easily be shown that Equation (5)requires

QD=

D

p

p

Q+

D

Q

to be strictly positive (see appendix). Hence, fromEquation (6), /Q must be strictly positive and, forEquation (5) to hold, /Q must be strictly negative.The manufacturer finds that his profits are currentlydecreasing in Q. He therefore seeks to lower product

quality until /Q equals zero and his profits aremaximized. The manufacturer, who is paying a largershare of the costs for product quality, will thus notseek as high a level of product quality that would

be necessary to maximize channel profits. In the caseof increased product quality, the retailer gains morefrom the increased volume, so the manufacturer seeksa lower level of quality than the retailer. Again, theresult of this action leads to more profits for the man-ufacturer, less profits for the retailer, and less com-

bined profits. Using a symmetric argument, we wouldfind the retailer has similar incentives concerning s.

Summarizing, we find that without joint ownershipand its associated coordination, the manufacturer hasthe power and profit maximizing incentive to raisehis margin above the level at which total channelprofits are maximized. He also has the incentive tolower the product quality below the joint maximumlevel and lower all other promotional decision vari-ables at his disposal. The lack of coordination leads toself-satisfying behavior, which increases the productsprice while lowering its quality. The same is also truefor the retailer. This is why the manufacturer (retailer)should seek cooperation with the retailer (manufac-turer) when he apparently obtains a greater profit in

the short term without cooperation. Otherwise, inde-pendently, both the manufacturer and the retailer willsee the opportunity to gain profits at the expense ofthe other. Each member of the channel, by seeking hisown best profits, reduces the other members profits.These actions eventually create a worse situation for

both.7

6 The notation D/Q should not be confused with D/Q since

D is a function of both Q and pD =DpQsand p =G+ g+CQ+ cs so that p/Q= dC/dQ is different from zero.7 This is the classical prisoners dilemma in game theory.


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It turns out that parts of this analysis were suspectedyears ago (Cournot 1838). The lack of coordination,the associated higher prices paid by consumers andthe subsequent social welfare issues have been dis-cussed in the economics literature (see Machlup andTaber 1960 for a review). However, early economic

research focused on the role of price while subsequentresearch, with a few exceptions (Lindsay 1979), hasemphasized how channel members would bargain forthe increased profits made available by cooperation(for example, Greenhut and Ohta 1979). The bargain-ing problem which we address later in this paper andthe pricing problem are both important. However, theabove development has shown that nonprice factorsare equally important in seeking a suitable mecha-nism for cooperation. Therefore, we will go beyondthe initial work in economics and address how fullchannel cooperation, i.e., involving other marketingmix variables than price could be achieved.

B. Extensions to Multiple Member VerticalChannels

The extension of the previous analysis to multiplemember vertical channels is straightforward. Let ususe subscript j to denote the jth member in the verti-cal channel. Let c denote total channel profits. Then,we know that for the Kmember channel equation, (7)must hold:

cGj

=j

Gj+

k=j

kGj

= 0 for j= 123 K (7)

For channel profits to be maximized, we requirec/Gj = 0 for j= 123 K . But as we havefound in our previous analysis, we now find thatinequality (8) is true:

kGj

=GkeD

p< 0

for k = j for j= 12 K (8)

Hence j/Gj> 0 for all jand the coordination prob-lem exists on every margin in the same directionindicated by our previous analysis. In fact, the coor-dination problem could be worse than before. Intu-itively, coordination is more of a problem becausej/Gj is now the sum of several terms rather than

just one single positive term.

C. Extensions to Retailers Carrying MultipleCompeting Brands

Until now, we have chosen to limit our attention toone brand carried by the retailer. We have done thisto emphasize coordination issues. However, althoughmany issues deserve attention when addressing theproblem of retailers carrying multiple competing

brands, the coordination issue remains. For exam-ple suppose a retailer carries N brands. Then thatretailers profit function is now given by:

=N

i=1

giDip (9)

where

gi = the retailers margin for brand i.p= the price vector for brands carried by the

retailer, i.e., (p1p2 pN, pi is the price forbrand i.

Di= the demand function for brand i.

This retailer is now a member of N vertical chan-nels. For each of the N channel profits to be maxi-mized, we require expressions (10) and (11) to hold:

+i

Gi= 0 for i= 12 N (10)

+i

gi= 0 for i= 12 N (11)

where

i = the profit of manufacturer i=GiDip Fi

Gi = the margin for the manufacturer of brand i.

As before, i/gi < 0 so /gi > 0 because of Equa-tion (11). Hence the retailer will want a larger marginand, thus, coordination problems exist.

4. Mechanisms for Coordination

A. Joint OwnershipIf both channel members agree to cooperate, therewill be more total profit to divide between them.Hence both can gain from cooperation. One methodfor cooperation is to have a centralized decision-maker dictate all channel decisions. This alternativeis possible with joint ownership often called verti-cal integration. Even recently (Klein et al. 1978), jointownership has been proposed again as the best solu-tion. However, in many situations, there are threeimportant problems with vertical integration.

The first problem with vertical integration involvesother products carried by retailers. The retailer (e.g.,grocery store) may carry hundreds and possiblythousands of other products whose variety maydraw many consumers to the retailers establishment,hence, minimizing the consumers cost of shopping.In this common situation, Dp would be drasticallyreduced if retailers were to vertically integrate andcarry only their respective manufacturers products.

A second problem with vertical integration involveslegal constraints. By vertically integrating, overall


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competition may be decreased. From a consumerviewpoint, a coordinated bilateral monopoly may bepreferable to an uncoordinated bilateral monopoly.However, the law prefers a retailer and a manu-facturer who are both in perfect competition to acoordinated bilateral monopoly. The Clayton Act, the

Sherman Antitrust Act, and similar legislation whichpurport to increase competition may prevent jointownership.8

The third, and possibly most important, problemwith vertical integration may be its real ability to pro-vide coordination. In many situations, manufactur-ers and retailers perform specialized functions withassociated economies of scale. Until now, our analy-sis assumed that variable costs, c and C, were fixed.But vertical integration may cause both c and C toincrease. A manufacturer may own production equip-ment, research laboratories, other specialized assetsover which the manufacturer has particular man-

agerial expertise. Similarly, the retailer may haveexpertise at managing his assets such as shoppingcenter property, specialized warehouse equipmentand refrigeration facilities. Hence, when the manu-facturer and retailer are replaced by a centralizeddecision-maker, the latter may not have the know-how to manage both the manufacturing and retail-ing functions equally and efficiently. Thus his costs Cand c would be larger than for managers who spe-cialize in production or retailing.

B. Simple ContractsAn alternative to vertical integration is a legal con-

tract specifying each channel members decision vari-ables. As with vertical integration, channel membersabdicate control over their decision variables. Withvertical integration, this control is relegated to acentralized authority. With a simple contract, thiscontrol is relegated to a legal agreement. For exam-ple, the manufacturer and the retailer might agree tofix their respective margins at G and g by agree-ing to a contract denoted Gg. Obviously, per-fect information is needed to set margins so that theysatisfy the joint channel profit optimality conditionG+ g+C+ c= p.

Unfortunately, following the same reasoning as in3A, one can find that, although both channel mem-bers might agree to such a contract, each could findactions which would make them, in the short run,unilaterally more profitable at the others expense.Moreover, although each channel member can gain

8 The law implicitly assumes that increased numbers of noncollud-ing manufacturers and retailers will benefit consumers. However,if an integrated channel is more efficient, allowing vertical integra-tion may lead to numerous integrated units each in competitionand an even more beneficial consequence for the consumer.

from cooperation, if one member cheats on the agree-ment, the other member may lose more from abiding

by the agreement than having never entered into it.This problem could be mitigated by strict enforce-

ment of the agreement but even with enforcementboth parties would continue to have an incentive

to circumvent the spirit of the contract. A sagaciousmanufacturer might fear that once the retailer hasagreed to the margin contract, the retailer might cir-cumvent the contract by decreasing the shelf-spaceor other promotional effort allocated to the product.This manufacturer might want to prevent this prob-lem by contractually requiring the retailer to buy afixed number of units at a fixed price. This solutionmay be more desirable than contractually specifyingeach retail promotional variable because it leaves theretailer the freedom to optimize shelf-space, productstore location, point-of-purchase displays and otherpromotional methods over which the retailer has

particular expertise. Unfortunately, the wary retailermight avoid such a contract because he fears manu-facturer circumvention with cuts in product quality,leaving the retailer with the burden of selling the con-tracted quantity of a lower quality product. The even-tual, mutually agreeable contract may need to be quitedetailed and, perhaps, quite rigid.

Of course, at this point in our analysis, we haveassumed a world of certainty where the variablesdefined in 2 are known. Hence, cheating and theassociated contract enforcement problems may disap-pear. Even in the real world of uncertainty, enforce-ment costs may still be reasonable and contracts may

be a suitable mechanism for coordination under awide variety of situations. Nevertheless, the rigid-ity of the simple contract remains a serious problem.With a detailed simple contract, neither channel mem-

ber has the freedom to react to temporary externalfactors. Because the contract does not specify rulesof behavior outside the contract point, the resultingcoordination may not be lasting.

C. Implicit Understandings9

We have seen that channel coordination may beachieved by each channel member agreeing to a sim-ple contract Gg. However, one might ask whether

foresighted partners might obtain the benefits of coor-dination without having to sign an explicit contract.Foresighted partners would realize that each part-ner reacts to the other. In other words, each channelmember will develop some expectation concerningthe others reactions to his margin decisions. Conse-quently, each member will factor into his profit max-imizing decision rule what he expects the other will

9 Concerning the issues related to implicit understandings, we ben-efited from the questions of Robert C. Blattberg.


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do. It is reasonable to assume that expectations willdevelop from the observation of the other partnerspast reactions.

It is beyond the scope of the present paper togo into the important issues surrounding implicitunderstandings as just defined. Jeuland and Shugan

(1983b) formalize, in the context of channels of dis-tribution, the notions of expected reaction functions.If the expected behavior matches the actual behav-ior for both the retailer and the manufacturer thennecessary conditions for an equilibrium exist. Theexpected reaction function that matches actual behav-ior is said to be rational. If the expected reactionfunctions match actual behavior for small deviationsaround the equilibrium point then the latter is endur-ing. Jeuland and Shugan (1983b) study simple reac-tion functions and the ensuing modified behavior of

both channel members. They analyze the modifiedprofit maximizing rules that take these expectations

into account. They study the question of whetheran enduring equilibrium exists (existence of ratio-nal expected reactions) and whether resulting channelprofits are higher than at the Cournot-Nash equilib-rium (i.e., the equilibrium when each partner actsindependently and does not recognize that he affectsthe other partners decisions). They also investigatewhether the more sophisticated behavior (i.e., thecase of partners who develop expectations) results inlower profits than with perfectly coordinated behav-ior. Thus implicit understandings (see also Shugan1983) may be useful for channel coordination.10

In general, we might ask what the theory of

games tells us about equilibria for dynamic models.Given the conflict of short term versus long term,i.e., Nash equilibrium versus Pareto optimal coordi-nation, the question of existence of noncooperativemultiperiod equilibria becomes important. Can theseequilibria exist when the payoffs are Pareto optimaleven though the noncooperative equilibria of the sin-gle period model are not Pareto optimal? The reac-tion function approach is older and has been morepopular among researchers dealing with oligopolisticmarket structures. However, the recent approach ofsupergames seems to hold promise for understandinglong-term market competition (see Friedman 1977).

D. Profit SharingThe result of channel coordination can be achieved

by a profit sharing mechanism. Suppose the manu-facturer receives fraction k1 of channel profits plus afixed amount k2 while the retailer receives fraction

10 This research is related to the problem of constructing duopoly oroligopoly models with consistent conjectural variations. This prob-lem has been the object of a series of very recent papers by Laitner(1980), Bresnahan (1981), Perry (1980, 1981), Kamien and Schwartz(1981), Ulph (1981), Boyer and Moreaux (1982a, b).

1 k1 0 < k1 < 1 minus the fixed amount k2 so thatmanufacturer profits and retailer profits are given by:

= k1G+ gD+ k2 F (12)

= 1 k1G+gD k2 f (13)

respectively (k2 positive or negative). We see thatbecause , , and + are all linearly related, theconditions for maximizations of , , and + areall compatible, i.e., all correspond to:

G+ gdD

dp+D= 0 (14)

required for a joint maximum.11 For the time being,we consider the simple formulation where D =Dpand variable costs are constant. The extended formu-lation of 2 is considered in the next section.

If profit sharing does achieve the desirable incen-tive structure for channel coordination, we must still

find a realistic mechanism for implementing profitsharing. Fortunately, quantity discounts provide anexcellent mechanism for profit sharing.

E. Quantity DiscountsA manufacturer who offers the retailer a quantity dis-count varies the price charged to the retailer accordingto the quantity purchased by the retailer. The retailerobtains a discount for purchasing a larger quantityof the product from the manufacturer. The larger thequantity purchased, the lower the per unit costs to theretailer.

Quantity discounts represent a subtle mechanism

for achieving profit sharing. When the manufacturerdoes not offer quantity discounts, the manufacturerobtains a constant profit of G for each additionalunit sold by the retailer. But in order to sell addi-tional units of the product, the retailer must decreasethe retail price, i.e., his margin. Because this effortis totally borne by the retailer, a lower than jointlymaximum volume is obtained. This condition can becorrected by the manufacturer. The manufacturer canshare his profit on the additional unit by giving someof the additional profit to the retailer. He can dothis by reducing the retailers cost for purchasing theadditional unit. That is, the manufacturer can give theretailer a quantity discount. The retailer then has anincentive to sell the additional unit. In fact, the man-ufacturer has the incentive to share additional prof-its until the decrease in price is no longer worth theresulting increased volume. At this point, the com-

bined channel profits are maximized.We know from our discussion of profit sharing

that a quantity discount schedule which would fix

11 This is related to the literature on group decision-making. For adiscussion of some of the issues, see Eliashberg and Winkler (1981).


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the retailers and hence the manufacturers profitsto some fixed linear function of total channel prof-its would lead the channel to maximum profits.The discount would also make individual channelmembers incentives compatible with overall chan-nel profit maximization. As a result, channel mem-

bers would no longer have the incentive to selfishlyoptimize in the short run at the expense of the otherpartner and of total channel profits.

Of course, not every quantity discount schedule hasall the required properties. As stated earlier, the dis-count schedule must link individual channel mem-

ber profits to total profits. Equation (15) illustrates theform that a schedule of this type must take for thesimple model (see appendix):

t= k1pD cC+ k2/D+C (15)

where

k1 k2 are the same constants as in Equations (12)and (13), 1 > k1 > 0,t is the price the retailer pays the manufacturer

for the product t=G+C and p= t+ c+ g,pD= the maximum price which still sells quan-

tity D.12

Given the schedule of Equation (15), the retailersprofit function is

= 1 k1G+gD k2 f

and thus is linearly related to total channel prof-its. Consequently, profit maximizing behavior of the

retailer is congruent with channel profit maximiza-tion. Manufacturer profits are also linearly related toretailer profits and thus, given schedule t, are max-imized when retailer profits and channel profits aremaximized.

We want to emphasize that the manufacturer doesnot impose tD on the retailer. The quantity discountschedule is a result of bilateral negotiations betweenthe parties. The results of the negotiation may or maynot be symmetric (i.e., provide an equal division ofgains). However, each party participates in the sched-ules formulation. The schedule does provide bothmembers the incentive for the manufacturer to supply

the optimal quantity and the incentive for the retailerto demand the optimal quantity. The analysis of thefunction t = tD shows that t is a quantity discountschedule. It is a discount schedule because inequality(16) holds:

dt

dD< 0 (16)

(See the appendix for a proof that this conditionholds.)

12 Mathematically, pD is the inverse of Dp.

Now if we rewrite Equation (15), we obtain:

tD= k1pD+ 1 k1C k1c+k2D

(17)

We realize that schedule t operationalizes simul-taneously a revenue sharing mechanism (the termk1pD, two cost sharing mechanisms (terms 1k1Cand k1c). The last term (term k2/D) correspondsto a fixed payment (independent of quantity) of theretailer to the manufacturer. The determination of k1and k2 will be addressed in the next section. One canalready specify some constraints on k1 and k2 as man-ufacturer and retailer profits must be positive. Theconditions > 0 and > 0 imply:

G+ gD f k1G+gD+ k2 F (18)

As already mentioned, k2 is a fixed payment (side

payment in the terminology of the theory of games)and is not necessary for profit sharing. However, sidepayments are often convenient mechanisms for get-ting around constraints in game theoretic problems(see Owen 1968), which is precisely what inequality(18) specifies.

In order to generalize the discount schedulet= tD for nonprice variables, we apply the generalprinciple of profit sharing to the model given by:

=GDpQsQ F (19)

= gdpQs s F (20)

where

G= tCQ

g= p t cs

Writing = k1G+ gDQ s+ k2 F implies:

t=k1p+1k1

CQ+

Q

D

k1

cs+

s

D

+

k2D

(21)

This expression is similar to Equation (17) and indi-

cates that coordination must involve sharing of man-ufacturer costs by the retailer and reciprocally sharingof retailer costs by the manufacturer. This resultis consistent with the empirical observation of pro-motional allowances (retailer and manufacturer bothshouldering advertising costs) and of manufacturersproviding special displays to their retailers (manufac-turer and retailer sharing distribution costs).

Equation (21) shows that schedule t is a generalvariable price contract and is thus considerably moreflexible than the simple contracts discussed earlier.


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F. The Implementation of Discount SchedulesThe schedule

tD= k1pD+ 1 k1C k1c+ k2/D (22)

is only a function of the quantity ordered, D andthe observable consumer price, p. Implementation ofthe schedule and negotiation of the schedule do notdirectly require complete knowledge of the demandfunction. In other words, to implement the quan-tity discount schedule, the manufacturer and retailermerely agree that the retailer will pay a fraction of theretail price, i.e., k1 p, on top of the agreed upon con-stant 1 k1C k1c. The advantage of this procedureis that it leaves the retailer in charge of his pricing anddoes not rely explicitly on heterogeneity of consumerdemands faced by different retailers. Optimality will

be achieved as the retailer seeks to find the retail pricethat maximizes the retailers profits.

However, in practice, the constant 1

k1C

k1cmay not be known because manufacturer and retailerdo not know each others costs. Furthermore, weexpect that channel members have an incentive toprovide biased information to each other about theirrespective operations when negotiating an agree-ment. For example, if biased costs C and c instead ofthe exact ones are used, the schedule becomes tD=k1pD+ 1 k1 C k1c (assuming no implicit fixedpayment k2). Unless the constant 1 k1 C k1c isequal to 1 k1Ck1c i.e., 1k1 CC = k1c c,schedule t will not lead to optimality. An interestingquestion is whether a somewhat biased schedule may

be better than no schedule at all.Another important issue is the legality or illegality

of quantity discounts. Legally sellers are prevented,under the Robinson Patman Act, from giving differ-ent terms to different resellers in the same resellerclass (discounters, merchandisers, etc.) unless thesereflect corresponding cost differences, distress sales,or a few other special conditions (Kinter, A RobinsonPatman Primer 1970). Thus quantity discounts have

been justified on the basis of cost: it costs less to sup-ply larger than smaller quantities because, in particu-lar, the fixed order and shipment cost can be averagedover a larger volume. There is obviously nothing ille-

gal with justifying the quantity discount by a cost sav-ing argument when it does provide a real cost savings

but in addition serves as a coordination mechanism.However, the implementation of the form of the

quantity discount schedule given by Equation (22)requires more. The form of this schedule shows that adifferent schedule will be needed for retailers whosecosts c are different. It is interesting to note that thisdifference is justified by cost variations across retail-ers and, hence, is in some accord with the spirit of thelaw. Also, as long as retailing costs are homogeneous

within a class of retailers, the same conditions can beoffered to all retailers in a given class. Another inter-esting question is whether a single schedule offered toa group of heterogeneous retailers may be more opti-mal than no schedule at all. Left to future research isthe determination of optimality conditions for a single

schedule offered to a group of retailers characterizedby a distribution of retailing costs c.Another effect of legislation may be the intro-

duction of more complex marketing procedures. Forexample, when quality and shelf-space are taken intoaccount, a more complex cost sharing mechanismthan represented by the constant 1 k1C k1c isneeded as shown by Equation (21). This complex-ity should not necessarily be viewed as a liabilitywhen dealing with the implementation of coordi-nation. In effect, many marketing procedures suchas promotional allowances, cooperative advertising,manufacturer technical service support, manufacturer

supplied promotional materials, retail displays, creditterms, consumer advertising, manufacturer trainingof retail salespeople, full-line supplying, price rebatesand other promotional techniques are different waysin which the manufacturer and retailer can partic-ipate in profit sharing, de facto. These marketingprocedures are quite common and often have theadvantage of being subject to a different interpreta-tion by the courts than quantity discounts. However,the current state of the law is constantly changing and

beyond the scope of this paper.

G. Alternative Uses for Quantity Discounts

Quantity discounts, as we have shown, can be a use-ful tool for achieving channel coordination. However,quantity discounts can be used for more than onepurpose. Several other useful applications have beensuggested for quantity discounts. These explanationsinclude the transfer of inventory/production costs(e.g., see Dolan 1978) and price discrimination (e.g.,see Kinter 1970).

There is no reason why quantity discounts couldnot exist for a variety of purposes. Inventory costtransference, price discrimination and coordinationare all possible usages for quantity discounts. How-ever, an interesting empirical question might be how

often do these different explanations account for thecurrent usage of quantity discounts. Let us con-sider this question by noting the implications of eachexplanation.

Consider the cost justification for quantity dis-counts. In this case, the manufacturer has a highproduction set-up cost or high shipping set-up costand, therefore, the manufacturer prefers to produceor ship the product in large quantities. (High man-ufacturer inventory costs discourage infrequent pro-duction runs.) The manufacturer encourages orders in


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large quantities by offering quantity discounts. Hence,quantity discounts must be justified based on highproduction set-up costs (and a high cost of inventory-ing finished products) or high shipping set-up costs.If quantity discounts reflect a greater savings to theretailer than justified by cost savings to the manufac-

turer, this explanation is not sufficient to justify theexistence of a quantity discount. Moreover, if the fixedcosts of shipping change (e.g., a new type of tank caris developed or a shipping system is automated) orthe cost of inventorying products changes (e.g., heat-ing costs change after an oil embargo or a new ware-house is built), the quantity discount should reflectthose cost changes. Otherwise, again the discount isnot fully justified. Finally, quantity discounts should

be highest directly after production runs when inven-tory costs are highest.

Now consider the price discrimination explanationfor quantity discounts. In this case, the manufacturer

uses quantity discounts in order to charge differentretailers different prices. This action would be prof-itable when retailers who order less are willing topay more for the product. For example, suppose asmall retailer were located in a small town where lit-tle competition exists. That small retailer could makea satisfactory profit on the manufacturers productat a higher retail price than a larger retailer locatedin a large city where intense competition exists. Thelarger retailer would require a lower manufacturerprice before this retailer would be willing to carry theproduct. Hence, the manufacturer charges the largerretailer (who orders a larger quantity because of his

size) less than the smaller retailer (who orders less butwho is willing to pay more per unit).

If quantity discounts exist, price discrimination willnearly always exist. As long as retailers order differ-ent quantities, the retailers will buy at different prices.Almost by definition, quantity discounts imply pricediscrimination. However, our previous example wasmore complex. Price discrimination became profitable

because consumer segments with different demandcurves could be identified by the quantity that theyordered. Hence, the real motivation for quantity dis-counts is to charge price sensitive customers less. This

justification for quantity discounts requires: (1) retail-ers who order less to be less price sensitive, and (2) allretailers be offered the same discount schedule. Thegreater price sensitivity of larger retailers is an empiri-cally testable hypothesis. It would also be necessary todetermine if the magnitude of the quantity discountis justified by the difference in price sensitivity.

In contrast, when quantity discount schedules areused for coordination purposes, we should find thatdifferent schedules would be negotiated with differ-ent retailers. Furthermore, these schedules would dis-appear as retail competition increased, the demand

curve would become flat and the problem of coordi-nation would disappear.

H. Sensitivity to AssumptionsIt is clear that our analysis is more sensitive to someof our four original assumptions. Assumption one, atwo-member vertical channel, was easily relaxed foradditional intermediaries (3B) but less easily relaxedwhen additional horizontal members were considered(3C). Nevertheless, the intuitive motivation for quan-tity discounts remains in far more complex situationsthan the two-member channel. For example, supposethat the retailer seeks to increase his total store vol-ume by using the manufacturers brand as a lossleader. Even in this case, the retailer would still desireas small a manufacturer margin as possible. More-over, the manufacturer would gain even more vol-ume if the retailer margin were negative and larger inabsolute magnitude. The same situation (i.e., retailer

desiring a lower manufacturer margin) would occurif the retailer were keeping a high margin in orderto induce the sale of substitute products offered bythe retailer. Each channel member would still preferthe other to lower his margin and quantity discountscould still be used.

Assumption two, a downward-sloping demandfunction, is critical to our analysis. If the demand func-tion were flat, neither channel member would havecontrol over his margin because the retail price must

be the perfectly competitive price. However, market-ing studies show that this situation seldom occurs.

The relaxation of assumption three, certainty, was

already discussed in 4F so we proceed to examineassumption four, symmetry. Careful examination ofsymmetry shows that in many respects asymmetryis a special case of symmetry (e.g., see Gould 1980,Shugan and Jeuland 1983a).13 However, asymmetricchannel behavior can be very interesting and has beenstudied (McGuire and Staelin 1983b).

5. Divisions of Cooperative Profits:Bargaining in the Channel

A. A Bargaining SolutionIn the previous sections, we have seen that manu-

facturer and retailer cooperation can lead to largertotal profits. We identified several possible solutionsfor achieving this cooperation including a new mech-anism. This new mechanism was a quantity discountprocedure. Unfortunately, solving the cooperationproblem leads to still another problem. We must nowask how the additional profits available through coop-eration are divided. This problem corresponds to the

13 Further discussion of the assumptions is given in Jeuland-Shugan(1983a).


12/19


Figure 1 Profit Division

Manufacturer

profit

Maximum profits line

Retailer profit

2

2

**

**

D

B

F

C

A

E

0

determination of k1 and k2the parameters of thequantity discount schedule.

Figure 1 graphically illustrates the problem of profitdivision. The indeterminacy of the division of channelprofit comes from the identity given by:

+

G

+

g (23)

In other words, any G and g given by a point on theline D E sets both terms in Equation (23) to zero.

If there is no cooperation, the retailer receives profit and the manufacturer receives profit , repre-sented in Figure 1 as point A. However, after coop-eration is achieved, it is possible to reach any profitdivision represented by a point on the line D Egiven by:

+= p cCDp F f (24)

where p is that p which satisfies (see appendix), p=c+Ce/e1. (The simple formulation again is con-sidered here.)

Neither the retailer nor the manufacturer would bewilling to accept less after coordination were achievedthan before it were achieved. Therefore, likely divi-sions of profit will correspond to points on the linesegment BC. The point B corresponds to a solutionwhere the manufacturer receives all the added ben-efits of cooperation. At point C the retailer receivesall of these benefits. Other points on the line segmentBC correspond to solutions where both receivesome benefits.

The question becomes which point on the line seg-ment B C corresponds to the actual negotiatedsolution. This problem is a well-known problem in

bargaining theory and was recognized some time agoin the economics literature. Shumpeter (1954) cites

Cesare Bonesana Marchese di Beccaria as one whoin 1764 anticipated the conclusion of Menger (1871)and Edgeworth (1881). These researchers concludedthat without any further assumptions it is impossibleto determine the division of profits. It took severaldecades for the economics profession to admit this

viewpoint (see Machlup and Taber 1960). However,by making some additional assumptions (e.g., Nash1950), it is possible to determine a profit division.

One common solution obtained by theorists is thatnegotiations should lead to an equal division of theadditional profits made available through coopera-tion. (See, for example, Harsanyi 1956, 1961, 1962,1965, 1966; Nash 1950; or Zeuthen 1930.)

B. Quantity Discounts After NegotiationEquation (17) represented a quantity discount sched-ule which achieves channel coordination. The sched-ule contained two unknown parameters k1 and k2,

respectively. In fact the parameter k1 is the quan-tity discount parameter and k2 is a functional dis-count parameter in the sense that it represents a fixedpayment.

If we assume k2 = 0, and an equal division of addi-tional profits (profits increase by moving away fromthe uncoordinated equilibrium A to F, see Fig-ure 1) we obtain:

k1=F+ 1

2++

++F+f (25)

and the optimal quantity discount is given by:

t= k1pD cC +C (26)

As before, the superscript refers to channel optimumand the superscript to the noncooperative equilib-rium (see derivation of Equation (25) in appendix).

It is important to note that Equations (25) and (26)are a very special case of Equation (17) and only onesolution to the bargaining process. We presented thissolution to provide one example of how k1 may bedetermined. The functional form of the general quan-tity discount schedule (Equation (17)) is independentof how the constants in the quantity discount sched-ules are determined. In fact, k1 will probably neverequal the constant given by Equation (25) and k1 will

depend on many factors external to our formulation.For example, k1 and k2 may depend on the strength ofeach channel members position (e.g., the number ofcompeting retailers), the skill with which each mem-

ber bargains, information held by each bargainer andthe opportunity costs associated with the breakdownin negotiations.14

14 The interested reader may write to the authors for numericalexamples of (26) that illustrate the dependency ofk1 on the startingpoint A. Because of space limitations these examples cannot bereproduced in the paper.


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6. Managerial ImplicationsWe started our analysis by demonstrating the fun-damental nature of the channel coordination prob-lem. We demonstrated that the coordination problemwas a basic problem originating from independentdecision-making and present in even simple chan-

nels. We rederived the classical result that a lack ofcoordination leads to margins which are too highby global channel standards. This classical analysis,once extended to include nonprice variables, allowedus to show that the levels of variables with a posi-tive impact on demand (e.g., product quality) would

be too low by global channel standards. This resulthas immediate implications for empirical researcherswho perform retail experimentation at one of a retailchains stores and then suggest managerial actions

based on experimental outcomes. Our analysis indi-cates that such limited experimentation can lead tomisleading conclusions because experimentation of

this type does not consider channel coordination. Forexample, consider typical competition between tworetailers. Such competition is commonly discussed inthe marketing literature. Suppose that neither retailercan significantly change his market share because theother retailer will match his price decreases. Even-tually, each retailer learns that price cuts yield onlytemporary benefits. In this case, each retailer mightmaintain a price above the price suggested by aretail experiment which does not consider the otherretailers reactions. This conclusion is straightforward.In fact, consultants probably already consider thisproblem.

However, our economic analysis indicates theopposite effect is caused by a vertical channel. In thecase of a vertical channel, the retail experiment willnot suggest a retail price which is below the opti-mum. Instead, the price suggested by the experimentwill be above the optimum channel price. If the chan-nel was properly coordinated, short-term experimen-tation would indicate that the retailers margin should

be raised and that shelf-space should be reduced. Ofcourse, once the retailer permanently implementedthe actions suggested by the experiment, other chan-nel members would react to the decreased volume.The long-term consequence would be a less profitableretailer despite experimental predictions. Moreover,if the channel was not coordinated, the experimentwould indicate levels for price and nonprice variablesthat are optimal only in appearance since actions ini-tiating coordination might lead to even better profits.

Of course, the major implication of our analysisis the identification of quantity discount schedulesand more generally variable price contracts as coor-dinating mechanisms. These schedules allow implicitprofit sharing by allowing channel members to trans-fer the costs of unilateral actions. This result has two

immediate implications. First, quantity discounts pro-vide an improvement over simple contracts whichinclude fixed conditions. By linking the contract toperformance such as quantity ordered for promo-tional spending, the incentive to achieve coordina-tion can be created without the rigidity associated

with fixed requirements. This added flexibility canallow the individual channel members to respond totemporary conditions without breaking the contract.Moreover, even if channel members deviate from thechannel optimum, the quantity discount or variableprice contract provides incentives to return to thechannel optimum. Therefore, variable price contractscreated with quantity discount schedules have addi-tional flexibility and stability not possessed by fixedprice contracts. Second, quantity discounts providea mechanism useful for vertical integration. As wehave already noted, a centralized decision-maker maynot possess all of the skills and information required

to perform all the channel functions. In these case,quantity discount schedules provide a mechanismfor transfer pricing within a firm. The centralizeddecision-maker can provide price schedules ratherthan fixed prices to each channel manager. Again, theindividual manager would retain some freedom to sethis decision variables while still having the incentiveto seek coordination.

7. Related Research in MarketingSeveral concepts underlie our approach to mod-eling channels of distribution. Among them are

(1) profit sharing and incentive compatible coordi-nation mechanisms, and (2) symmetry of the rela-tionship manufacturer-retailer. Concerning item (1),Farley (1964) applied, although he did not explicitlysay so, the same principle to the question of compen-sation of the sales force. If Qiti denotes the salesvolume generated by a salesman if he allocates ti ofhis time to selling product i i = 1 n , and if hisremuneration is a commission rate Bi based on grossmargins Mi (Mi is equal to the selling price minusvariable nonselling cost per unit of product i), thenhis income is given by:

=n

i=1MiBiQiti (27)

wheren

i=1 ti = t, t = total working time of salesman.The contribution to profits of the firm of a salesmanis given by:

=n

i=1

Mi1BiQiti (28)

Farley finds that if Bi = B for all i, then coordina-tion takes place in the sense that total gross revenue


14/19


ni=1 MiQiti is maximized when the salesman maxi-

mizes . It is easy to see that when Bi = B for all i,

= 1B

i

MiQi and = B

i

MiQi (29)

The similarity with our result stops here, however,

as we implement profit sharing in a very differentfashion due to the nature of the problem we address.As far as item (2) is concerned, two recent papers

by McGuire and Staelin (1983) and Zusman and Etgar(1981) are relevant.

The objective of McGuire and Staelin is to inves-tigate the desirability of different channel arrange-ments from the point of view of the manufacturer.Their focus on the manufacturer implies a depar-ture from our symmetric approach. In fact, the majorsource of departure from symmetry is their assump-tion that the retailer does not recognize that he canhave some control over the manufacturer. McGuire

and Staelin assume that the former takes the lattersprice as given. They also assume that the manufac-turer realizes this lack of sophistication on the part ofthe retailer and factors this into his decision rule. Inessence, they assume a follower-leader structure forthe bilateral relationship manufacturer-retailer. Theystudy several cases. One of them is the case of twoproducts competing in the market place and man-ufactured by two different manufacturers who eachdistribute their product through a franchise (see Fig-ure 2). Thus, given that the manufacturer-retailer rela-tionship is that of follower-leader mode, that eachof two retailers carry only one manufacturer prod-

uct (duopolistic market structure with two differenti-ated products), McGuire and Staelin ask the question,should the manufacturer vertically integrate or not?

Figure 2 DuopolyTwo Products Distributed Through Two Franchises

Retailer 1

(Franchise 1)

Retailer 2

(Franchise 2)

Product 2Product 1

Market

Products 1 and 2 offered at prices p1 and p2 in the market place

Manufacturer

of product 1

Manufacturer

of product 2

It is obvious that the coordinated reactions of onechannel to the other as previously discussed is quitedifferent from the follower-leader reaction postulated

by McGuire and Staelin. It is then not surprising thatthe industry equilibrium obtained by McGuire andStaelin is different from the equilibrium of coordi-

nated channels. It is possible to show that the coordi-nated channel equilibrium price is always lower thanthe price obtained for McGuire and Staelins follower-leader scenario so that consumer welfare is superiorfor coordinated channel competition.

Recently, Zusman and Etgar (1981) were inspiredby the theories of bargaining, of risk-sharing, of incen-tive contracting and of the agency relationship.Concerning the bilateral relationship that we study,their solution is based on the following formulation(p. 287) given by:

i =Riqi v

iqi (30)

where i is the retailers profit. Riqi is the net rev-

enue function, i.e., gross revenue net of the retailershandling cost and viqi is the retailers paymentschedule to his partner. The latters profit is given by:

i = viqi ciqi Fi (31)

where ci includes variable production costs, handlingcosts, and costs of delivering to the retailer.

Total profits are i+i =RiCiqi Fi and are max-

imized when the condition dRi/dqi = Ci is satisfied.On the other hand, the retailer will try to maximizehis own profit function i. This gives the condition

dRi/dqi = dvi/dqi. Zusman and Etgar (1981) then givea sufficient condition for the two above conditions to

be compatible, namely the retailers payment sched-ule function is given by:

vi = ciq+ (32)

where is a constant. The implication of this paymentfunction is that profit of the retailer is given by:

i =Riqi ciq (33)

and the profit of his partner is given by:

i = Fi (34)

Thus manufacturer profits are constant and totalprofit variations are equal to retailer profit variations.This exemplifies a clear dissymmetry in their formu-lation of the channel interrelationships. For example,if because of some short-term problem of schedulingof production, the manufacturer only delivers a frac-tion q0 of what the retailer would wish to purchasefrom him, then i = Rq

0 Cq0 and i = Cq0+

Cq0 Fi = Fi. In other words, the manufacturer


15/19


suffers no penalty at all. Consequently, there is somequestion whether a payment schedule function likeviqi can ever be acceptable to the retailer.

In sum, the above examples illustrate that a bodyof research in marketing is emerging that attempts todeal with the question of interdependencies between

institutions. The present paper continues this tradi-tion and focuses on the coordination problem. Themodel recognizes the symmetry of the bilateral rela-tionship and thus clearly links the coordination prob-lem with the bargaining problem.

8. Future ResearchThe simplicity of our formulation has both advan-tages and disadvantages. Among the advantages isthe ability to easily extend the formulation in manydirections. For example, uncertainty in the demandfunction can be considered by allowing the demandfunction to be probabilistic. Channel members thenmaximize expected profit. The manufacturer of anew product may also have more knowledge aboutthe new products demand curve than the retailer,the former having done more research. Uncertaintyabout partners actual costs, CQ and cs may leadto nonoptimal schedules. This problem needs to beresearched further. The effect of competition on thedemand function should be considered further. Theeffect of multiple retailers and manufacturers should

be addressed. The involvement of many economicagents raises questions about the boundary of thechannel. More complex formulations are possible

where the price of the product changes the retailerstotal store volume (across products) or the sales of theretailers other, possibly unrelated, products. Whenthe retailer carries several competing products, hisobjective function is no longer the profit of one brand(its margin times its demand) but the sum of each

brands contribution and a more complex model isneeded.

Finally, in the context of the conflict of short-term versus long-term profit maximizations, dynamicconsiderations need to be explored: Both the reac-tion function approach and supergames might helpresearchers uncover forms of long-term behavior that

insures higher channel profits.

9. Summary and ConclusionsThis paper provides a formulation for describing theinstitutional arrangements present in marketing chan-nels. We started by demonstrating the need for chan-nel coordination. We showed that coordination canlead to results where all channel members receivedlarger profits. However, we saw that this coordina-tion was difficult to achieve because each memberhas an incentive not to cooperate unless all other

members are forced to cooperate. Hence, unless eachmember can be assured of the others cooperation,coordination is not easy to achieve. We discussed sev-eral mechanismscontracts, joint ownership, implicitunderstandingswhich attempt to achieve coordi-nation. We found that profit sharing mechanisms

seem to possess many desirable features. In addi-tion, we found that profit sharing can be implementedwith quantity discounts. We then proceeded to derivethe optimal quantity discount schedule. However,we encountered a classic problemgiven the addi-tional profits made possible through coordination,how should these profits be divided among the chan-nel members? We briefly discussed this problem andmentioned that classical game theory recommends theplausible equal division of additional profits gainedfrom coordination.

Therefore, besides the classical result that channelcoordination is a fundamental problem which occurs

in even the simplest channels and is caused by fun-damental interdependencies in the vertical channelstructure, we come to the following conclusions:

1. Channel coordination problems occur with allmarketing decision variables albeit in different direc-tions. Without coordination, marketing effort will besmaller than optimum (i.e., to maximize channel prof-its). This is a generalization of the result concern-ing margins: without coordination, they will be largerthan optimum (i.e., to maximize channel profits).

2. Achieving channel coordination can be difficult.However, several mechanisms do exist for achievingcoordination.

3. Many channel phenomena (e.g., integration, con-tracts, etc.) may be implicit coordinating mechanisms.

4. Joint ownership and fixed-price contracts areoften inadequate mechanisms for coordination.

5. Quantity discounts can provide an optimalmeans for achieving coordination.

6. Quantity discounts can take the form of othermarketing phenomena such as cooperative advertis-ing or added service levels.

7. Quantity discounts are a method of profitsharing.

8. The channel coordination issue can be separatedfrom the profit division issue. Although, they arerelated decisions.

9. A coordinated channel will make retail marginsand manufacturer margins appear to be too low.

10. Coordination, once achieved, will lead to lowermargins, higher levels of marketing effort, lower retailprices, and larger total channel profits.

AcknowledgmentsThe authors gratefully acknowledge the motivation for thepaper provided by Robert Blattberg. The authors wishto thank Subrata Sen, John Hauser, Richard Staelin, Ram


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Rao, Louis Stern, Jehoshua Eliashberg, and the anonymousreviewers for their many helpful comments.

Appendix

Downward-Sloping Demand Functions When

Competitive Reactions Exist

Given an oligopolistic market environment, the demand forone of the products depends not only on its own price, p,

but also on the n other products prices, pi. Moreover, evenin this case, the assumption of downward-sloping demandfunction is still a reasonable one as long as reaction func-tions pi = Rip satisfy the conditions

D

p+

ni=1

D

pi

dRidp

< 0

For example, let us consider one independent retailerwho sells only one manufacturer product (product 1) andcompetes against one company store owned by a different

manufacturer (product 2). Assume the demand for product iis qi = 1 pi + p j pi, i j= 1 2, j= i (1) (see McGuireand Staelin 1983 and Eliashberg and Jeuland 1982). Assumealso that the management of the company store sets p2 byoptimizing profits, 2 = p2 c2q2, given p1. This leads tothe reaction function

p2p1 =p1 + 1+ c21+

21+

The retailer then faces the demand function

q1 = 1 1+p1 +p2p1

= 1+1+ c21+

21+

2+ 4+2

21+

p1

which like (1) is downward sloping.

Derivation of Equation (2)

= gD f

G= g

D

p

p

G= g

D

p= g

D

p

p

D

D

p

=

geD

p

Note. In the section of the paper using this derivation, weassume g and G are independent decision variables. Hence,dg/dG = 0 and with p = g + G + c + C, we have p/G = 1and D/G= D/p.


+

G= D+ G+g

D

p

p

G=D G+ geD/p = 0

then p G+ge =G+g + c+CGege = 0. Equation (3)follows.

Derivation of Equation (4)/G = DGeD/p= 0 then pGe =G+g+c+CGe = 0.Equation (4) follows.

Proof that /Q in Equation (5) Is Positive

+

Q=

Q+

Q= G

QD 1+ g

QD

= G+ g

QD 1

hence

QD =

D

p

p

Q+

D

Q= 1/G+ g

which is strictly positive, therefore gD/Q and /Qare strictly positive.


+ F= k1++ F+ f + k2

GD= k1p c CD + k2

G= k1p cC + k2/D

and since G= t C

t = k1pD c C + k2/D+C

Derivation of Inequality (16)

dt

dD=

d

dD

k1pD+

k2D+ 1 k1C k1c

=k1D

k2D2

where

D =dD

dp

Because pD is the inverse function of D = Dp, dp/dD =l/D. If k2 0, dt/dD < 0. If k2 < 0, the profit of the manu-facturer must still be positive so that

D= k1p C cD + k2 F > 0

At the channel optimum, p C cD + D = 0 so thatpC c =D/D. Consequently,

D= k1

D2p

Dp

+ k2 F > 0

implies

dtD

dD

=k1

D

p

k2

D2

p


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where

D =dD

dp

p cC=D/D

p cC= p/e

e

1p=

ec+

Cp = c +Ce/e 1

Derivation of Equation (25)From Equation (7),

= k1p cCD F+ k2

hence if

k2 = 0 then = k1p

cCDp F and

= k1++ F+ f F

Equal division of additional profits implies

=

hence,=+

andk1

++ F+ f F=+

Finally,

k1 = ++ F /++ F+ f

Note.

= GDp F

= t

CDp

F

= k1 p cCDp F

= k1 ++ F+ f F

= + as required

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