Quasi-Partnerships in Distribution

David E. Mills Department of Economics

P.O. Box 400182 University of Virginia

Charlottesville, VA 22904-4182 434.924.3061 (phone)

434.924.7659 (fax) mills@virginia.edu

August 2007

Key Words: Bargaining, Distribution, Market Share Discounts, Vertically Differentiation

Abstract

This paper concerns the sale of a vertically differentiated good by a manufacturer to retailers that have market power when reselling to consumers. The contractual relationships between the manufacturer and individual retailers are characterized as “quasi-partnerships,” reflecting the ongoing and multi-dimensional nature of such relationships. Contractual terms are predicted by the Nash bargaining solution and are distinguished from those in an ordinary bilateral monopoly because they make allowance for competing, vertically differentiated brands. The model predicts that differences in retailers’ ability to promote the manufacturer’s brand induce prices that vary systematically with the manufacturer’s market share of retailers’ sales.

1

I. Introduction

Much of the sales activity in distribution channels occurs between buyers and

sellers who, because of their size or product differentiation, have some degree of market

power. For example, Business Week reported in 2003 that Wal-Mart, the world’s largest

retailer, was responsible for 24 percent of Del Monte Foods’ sales and 23 percent each of

Clorox’s and Revlon’s cosmetics sales.1 Del Monte, Clorox, and Revlon are themselves

major competitors in their respective markets. The relationships between buyers and

sellers like these are complex and ongoing. Sellers hire specialized account managers to

manage their relationships with large buyers, and the buyers hire specialists to work the

other side of the relationship. Wal-Mart’s “vendor partnerships” with its suppliers are

well known for exchanging real-time scanning data and coordinating inventory levels and

delivery schedules, among other involvements.2

Many such relationships in the distribution sector (and elsewhere) involve implicit

commitments based on trust and cooperation as well as explicit commitments. These

relationships do not conform to the assumptions of single price monopoly, monopsony, or

oligopoly models with arms-length transactions. Noll (2005, p. 603) suggests that a

useful way to characterize continuing, encompassing relationships might be to assume a

buyer and a seller “negotiate a long-term contract that specifies both price and quantity.”

The impetus for building multi-dimensional relationships is the compelling interest that

buyers and sellers have in reaching mutually beneficial contracts that extract as much

1 www.businessweek.com:/print/magazine/content/03_40/b3852001_mz001.htm, October 6, 2003

2 As an illustration, Grean and Shaw (2002) chronicle the evolution of the partnership that exists between

Procter & Gamble and Wal-Mart.

2

surplus as possible from the buyers’ downstream customers. In modeling buyer-seller

relationships, Whinston (2006, p. 139) calls the “bilateral contracting principle” the

expectation that when two parties to an exchange are contracting in isolation under

conditions of complete information, “they will reach an agreement that maximizes their

joint payoff.”3

This paper applies Whinston’s principle to a specific hypothetical situation that is

representative of a wider class of situations in the distribution sector. The specific

situation considered is the sale of a vertically differentiated good by a manufacturer to

one or more retailers. The manufacturer has market power when selling to retailers that

stems from product differentiation. The retailers have market power when reselling to

consumers that stems from their size, location, or other distinguishing characteristics.4

The paper uses the Nash bargaining solution to predict the terms of the contract

negotiated by a buyer and the seller, and characterizes their contractual relationships as

“quasi-partnerships.” These contracts are distinguished from those that achieve the

vertically integrated outcome in an ordinary bilateral monopoly because they make

allowance for competing, vertically differentiated brands.

3 The insight that buyers and sellers with market power might achieve a vertically integrated solution is

invoked by Bernheim and Whinston (1998), Chipty and Snyder (1999), Matthewson and Winter (1987),

and Tirole (1988), among many others. Blair and Harrison (1993) discuss the idea’s antecedents in early

economic theory.

4 Similar circumstances include, among others, intermediate product markets where buyers use the product

to produce another good or service, and markets where buyers are distributors or dealers who resell the

product to retailers. Vertical differentiation means consumers have common ordinal preferences among

competing products.

3

Differences in retailers’ sizes, consumer populations, and abilities to promote the

quasi-partner’s brand affect the terms of the equilibrium contracts. While retailers’ prices

may vary systematically with quantities sold in some circumstances, the most distinctive

prediction of the model is that differences in retailers’ ability to promote mean that those

prices vary systematically with the quasi-partner’s market share of the retailers’ sales.

While induced promotion of the quasi-partner’s brand may reduce the sales of competing

brands, those brands are not totally foreclosed because their inclusion increases the

surplus that the quasi-partners can extract from the vertical structure.

The analysis in this paper does not disprove the possibility that, under certain

conditions, dominant buyers and sellers might partner to exclude competing sellers. But

it does suggest that quasi-partnerships between the firms may have pro-competitive

consequences.

II. A Model of Distribution

1. Homogeneous Goods

Consider a homogeneous consumer good produced by perfectly competitive

manufacturers. These firms have no fixed costs and constant marginal costs. With no

further loss in generality, assume marginal costs are zero. The good is sold to retailers

who have market power when reselling the good to consumers. A representative

retailer’s market power is due to the firm’s size, location, or other distinguishing

characteristic. In the case of grocery stores and mass merchandisers, some degree of

market power is also due to consumers’ shopping for bundles of goods instead of single

items. Shopping for bundles conserves shopping costs, but it reduces consumers’ in-store

4

demand elasticities for specific components of the bundle.5 Assume that the retailer’s

variable cost of handling and reselling a unit of the good is constant and zero.

A representative consumer's utility is θ – p0, where θ is a consumer-specific taste

parameter and p0 is the retailer’s price. Consumers’ taste parameters θ are uniformly

distributed on [0, 1]. A consumer buys a single unit of the good if the retailer’s price is

less than its reservation price θ. Otherwise, the consumer buys nothing and receives zero

utility. Where the retailer has a continuum [0, h] of consumers, these assumptions imply

that the retailer’s inverse demand for the good is

r(q0) = 1 – q0/h , (1)

where q0 is the total number of units sold. The retailer cannot observe consumers’ taste

parameters and cannot price discriminate among consumers.

In equilibrium, with competition among the manufacturers, the good is sold to the

retailer for a wholesale price of zero. Maximizing profit, the retailer buys q0 = h/2 units

and resells them for a retail price of p0 =1/2.

2. A Differentiated Brand

Now suppose manufacturer M’s brand is differentiated from others in ways that

some, but not all, consumers discern or value. Let M’s product differentiation costs be

fixed. This cost must be incurred regardless of whether the present retailer carries the

firm’s brand and regardless of how many units it buys. A fraction φ of the retailer’s

consumers prefer brand M to others, where 0 < φ < 1. The M-preferring consumers are

5 Bliss (1988, p. 38) identifies this “captive buyer” effect as a contributing factor to retailers’ market power

in the sale of specific goods.

5

indifferent among the undifferentiated brands. The remaining consumers are indifferent

among all brands including brand M. As before, consumers’ reservation prices for the

undifferentiated brands are θ and are uniformly distributed on [0, 1]. An M-preferring

consumer with a reservation price of θ for the undifferentiated brands has a reservation

price of βθ for brand M, where β > 1.

The retailer’s brand M unit sales qM and its unit sales of the undifferentiated

brands q0 depend on the firm’s retail prices pM and p0. The demand functions facing the

retailer are derived as follows, beginning with the M-preferring consumers: Were it not

for the brand M option, the inverse demand for undifferentiated brands on the part of the

retailer’s φh M-preferring consumers would be

r0(q0) = 1 - q0/φh, for 0 < q0 < φh . (2)

Similarly, were it not for the undifferentiated brand option, the inverse demand for brand

M on the part of those consumers would be

rM(qM) = β -β qM/φh, for 0 < qM < φh . (3)

To derive the M-preferring consumer’s demands with both goods available,

consider several possibilities. First, if p0 ≥ 1, then no consumer would purchase an

undifferentiated brand. The result is the same if p0 ≥ pM , since every consumer would

buy either brand M or nothing with these prices. On the other hand, if pM > p0 + β - 1,

then every consumer would buy either an undifferentiated brand or nothing and qM would

be zero. Together, these conditions mean that positive sales of both brands only occur if

retail prices satisfy:

p0 < 1 and p0 < pM < p0 + β - 1 . (4)

6

Where retail prices satisfy inequalities (4), the quantities demanded by M-

preferring consumers are found by simultaneously solving:

rM(qM) - pM = r0(qM) - p0 , and (5a)

r0(qM + q0) – p0 = 0 . (5b)

Equation (5a) identifies the margin between choosing brand M and choosing an

undifferentiated brand. Equation (5b) identifies the margin between choosing an

undifferentiated brand and choosing not to purchase the good. M-preferring consumers

with the highest values of θ will buy brand M since they are willing to pay a higher

premium for brand M than others. Those with lower values of θ will buy an

undifferentiated brand or nothing. Substituting equations (2) and (3) into equations (5a)

and (5b), and solving, gives the M-preferring consumers’ demand functions for prices

that satisfy inequalities (4):

fM(pM, p0) = φh[1 - (pM – p0)/(β - 1)] , and (6)

gM(pM, p0) = φh[(pM – p0)/(β - 1) – p0] . (7)

With prices that satisfy inequalities (4), the retailer’s non-M-preferring consumers

would not buy units of brand M. This means that equation (6) is the retailer’s total

demand for brand M. The demand for undifferentiated brands on the part of the (1-φ)h

non-M-preferring consumers is found using equation (1):

g0(pM, p0) = h(1 - φ) (1 – p0) . (8)

3. Bargaining Equilibrium

Although there are other manufacturers of the good in the picture, the relationship

between firm M and the retailer is much like a bilateral monopoly. Under certain

7

conditions, this setup would be susceptible to the double marginalization distortion.

There are several things aside from bargaining that one or both of the firms might do to

avoid or mitigate this distortion. These include the use of lump sum payments or other

forms of nonlinear pricing.6 Also, the retailer might introduce its own private label or

proprietary brand to compete with the seller’s brand.7 But let us suppose that the firms

face no barriers to negotiation so that Whinston’s bilateral contracting principle applies.

Assume further that the outcome of negotiations is given by the Nash bargaining solution.

This outcome consists of contractual terms (qM, T), where T is the retailer’s total payment

to M in exchange for qM units of the brand.8

The Nash bargaining solution in this market is achieved by setting the retail prices

pM and p0 at values that maximize the firms’ joint profits:

pMfM(pM, p0) + p0gM( pM, p0) + p0g0( pM, p0). (9)

The retail prices that maximize this expression are:

6 Tirole (1988).

7 Mills (1995).

8 Formally, the firms play a standard bargaining game with alternating offers. Assume that the firms have

equal “bargaining power” and complete information about the parameters h, φ, and β. At time 1, firm M

proposes a set of contractual terms to the retailer that would determine both the size and the division of the

firms’ joint profits. The retailer agrees to accept those terms or else refuses and, at time 2, counteroffers a

different set of terms. Firm M then either agrees to accept the retailer’s offer or else counteroffers at time

3, and so on. If an agreement is reached at time t, then each firm’s profit is discounted by the factor δ t < 1.

For sufficiently “quick” responses, δ → 1, and the perfect equilibrium of this game has the firms

immediately agreeing to terms that equally divide the maximum gains from trade. A full discussion of

equilibria in bargaining games with alternating offers and complete information is found in Sutton (1986)

or in Osborne and Rubinstein (1990). The seminal paper in this literature is Rubinstein (1982).

8

= β/2 and = 1/2. (10) *Mp *

0p

Unit sales at these prices are:

= φh/2 and = (1 - φ)h/2, (11) *Mq *

0q

and maximized joint profits are

π* = (h/4)(1-φ+βφ) . (12)

The outcome represented by equations (10) – (12) is derived from demands that

assume that the retailer has positive sales of both brand M and the undifferentiated

brands. To see that selling both goods is more profitable than the alternatives, first

suppose that the retailer only sells undifferentiated brands. The retailer’s demand

function for these brands would be the inverse of equation (1), and its profit-maximizing

price would be p0 = 1/2. Charging this price for the undifferentiated brands, the quasi-

partners’ joint profits would be π = h/4, which is less than π* as seen by comparing this

outcome with equation (12).

Next, suppose that the retailer only sells brand M. The retailer’s demand for

brand M in this instance would be the sum of M-preferring consumers’ demand for that

brand and non-M-preferring consumers’ demand for the undifferentiated brands, since

these consumers are unwilling to pay a premium for brand M. To find this sum, equation

(3) is inverted and added to equation (8). The joint profit-maximizing price of brand M

here would be ))1((2 φβφ

β−+

=Mp . Charging this price, the firms’ joint profits would

be ))1((4 φβφ

βπ−+

=h , which is also less than π* for admissible values of φ and β. To

9

maximize joint profits, the retailer must set prices as in equation (10) and sell the

quantities in equation (11).

The distribution of profits with Nash bargaining depends on the firms’

“disagreement payoffs” – the profit that each is assured if no agreement is reached. If an

agreement were not reached, the retailer would sell only undifferentiated brands.

Charging p0 = 1/2, the retailer’s profit would be h/4. These profits, made available by

the presence of the undifferentiated brands, provide a safety net for the retailer that

strengthens its bargaining position. Firm M has no comparable safety net in the retailer’s

market, so its profit in this market would be 0 if an agreement with the retailer were not

reached.9 If we use these profit levels and equation (12), the maximum gains from trade

for the two firms are

π* - h/4 = φh(β - 1)/4 . (13)

Where the bargaining power of the firms is equal, the Nash bargaining solution

divides these gains equally. The equilibrium contract between the firms is depicted in:

Proposition 1: Nash bargaining with symmetry and complete information

about h, φ, and β produces an equilibrium contract for the sale of

units of brand M for a payment of T* =φh(β -1)/8. Retail prices and unit

sales in this equilibrium are , and .

*Mq

*Mp *

0p , *Mq *

0q

9 The brand M monopolist may sell its brand in many other markets, but none of those prices or profits is

affected by the outcomes in the game in question. Similarly, although the retailer may sell many other

goods, none of these prices or profits is affected either. There is no linkage on either the demand or supply

side among the markets. What happens in other markets is independent of what happens in the

representative retailer’s market.

10

Proposition 1 indicates that the quasi-partners extract and divide all of the profit

that is latent in their vertical structure (on the assumption that the retailer cannot price

discriminate among consumers). The retailer’s profit, which hinges on that firm’s retail

monopoly on all brands in its market, is h/4 + T*. Firm M’s profit, which hinges on that

firm’s manufacturing monopoly on brand M, is T*.

This contract also can also be expressed in terms of a fixed quantity and a

wholesale price w* = (β-1)/4. Since β >1, the retailer’s gross margin ( - w*)/ =

(β+1)/2β on brand M is less than the gross margin on the undifferentiated brands (

0)/ = 1. This relationship is consistent with the evidence presented in Mills (1995, p.

522), and elsewhere, that retail gross margins on private label products generally are

larger than retail gross margins for national brands of the same good.

*Mq

*Mp *

Mp

*0p –

*0p

Demand equations (6) – (8) indicate that Proposition 1 depicts a separating

equilibrium among consumers. At the prices ( , ), no M-preferring consumer buys

an undifferentiated brand, and no non-M-preferring consumer buys brand M. Half of the

M-preferring consumers buy brand M, and half of the non-M-preferring consumers buy

undifferentiated brands. The remaining halves of both groups do not buy the good even

though they have positive reservation prices. This is the only source of allocative

inefficiency in equilibrium because no reallocation among consumers of the goods sold

could increase total welfare. The exercise of market power does not always lead to an

efficient distribution of the goods actually sold, as it does here. For instance, third degree

price discrimination denies goods to some consumers whose willingness to pay is greater

than the willingness to pay of other consumers who buy the product at a low price.

*Mp *

0p

11

Even though consumers collectively weakly prefer brand M, the availability of

undifferentiated brands increases the quasi-partners’ profits because it gives them two

control variables for extracting consumers’ surplus: pM and p0.. Undifferentiated brands

create some of the rents captured by firm M and the retailer, but competition among the

producers of the undifferentiated brands prevents those firms from capturing any of it. 10

Suppose a quasi-partnership relationship along these lines develops independently

between firm M and several or many retailers, each with market power due to its location

or some other product differentiation considerations. Since each retailer’s demand

depends on firm-specific values of β, φ, and h, each retailer’s contract with firm M sets

firm-specific values of and T*. If firm M contracts with retailers who are only

distinguished from each other by their size h, values of vary proportionately with h,

but the wholesale price w* is the same for all of the contracts. Wholesale prices also are

the same if retailers serve consumer populations with different fractions of M-preferring

consumers φ. However, if the M-preferring consumers served by different retailers’ place

different premia β on brand M, this would lead to contracts with different wholesale

prices w*.

*Mq

*Mq

There are other reasons why wholesale prices might differ if additional aspects of

the relationship between the firms were brought into the model. For instance, the

bargaining power of the firms might not be equal. Suppose retailers’ bargaining power in

their relationships with firm M were an increasing function of their size h. Without going

into details, this would mean that the Nash bargaining solution would assign a greater

10 The availability of the undifferentiated brands also bolsters the strength of the retailer’s bargaining

position because without them, its disagreement payoff would fall to zero.

12

fraction of the gains from trade to a “large” retailer than to a “small” retailer, other things

equal. In this instance, M’s pricing would incorporate implicit quantity discounts because

large retailers would pay lower wholesale prices than would small retailers.

Another aspect of the relationship between the firms that can be brought into the

model is promotional support for brand M. Suppose the retailer has the ability to

influence the fraction of its consumers who prefer brand M by undertaking brand-specific

selling effort to alter marginal consumers’ preference for firm M’s brand. As seen below,

inducing retailers’ selling effort may involve contracts that incorporate implicit market

share discounts.

III. Inducing Retail Selling Effort

1. A Representative Retailer

Suppose that the fraction of the representative retailer’s consumers who prefer

brand M in the previous setup is not exogenous but rather depends on the retailer’s brand-

specific selling effort. Specifically, suppose that if the retailer “merchandises” brand M

in its store, the fraction of consumers11 who prefer that brand increases from φ to φ + ∆,

where ∆ < 1 - φ. In general terms, retail merchandising involves in-store promotional

activities that convey potentially useful brand-specific information or service to

consumers.12 Once they receive this information or service, some consumers come to

prefer brand M where they did not before. The retailer’s merchandising activity has no

11 The M-preferring consumers’ reservation prices for brand M remain uniformly distributed on [0, β].

12 This assumes that there is no better or less costly way for firm M to convey the relevant information or

provide the relevant service to consumers than by invoking retail merchandising.

13

effect on other consumers. Those who preferred brand M before they were exposed to

the retailer’s selling effort continue to do so, and a fraction 1 - φ - ∆ of consumers remain

indifferent among the brands in spite of the retailer’s selling effort on behalf of M.

An example of this kind of promotional activity would be a sporting goods store

that features a particular brand of fly fishing gear by displaying the brand prominently or

emphasizing the brand’s distinguishing characteristics in sales presentations. Another

would be a building supply store that calls building contractors’ attention to the merits of

particular brands of roofing materials or plumbing fixtures.13

Let the cost to the retailer of merchandising brand M be hτ, an amount that is in

proportion to the retailer’s size h. Whether merchandising would increase the firms’ joint

profits depends on the parameters φ, β, and τ. To exclude the uninteresting case where

merchandising is not economic, assume that:

τ < ∆(β -1)/4 . (A1)

Proceeding as before, if the retailer merchandises, the firms’ joint profits are:

pMfM(pM, p0) + p0gM( pM, p0) + p0g0( pM, p0) – hτ,

where φ + ∆ replaces φ in demand functions (6) – (8). The prices that maximize this

expression are ( , ) and the numbers of units sold are: *Mp *

0p

= (φ + ∆)h/2 and = (1 - φ - ∆)h/2 . (11a) **Mq **

0q

Maximized joint profits are:

π** = (h/4)(1-φ - ∆ +βφ + β∆) - hτ , (12a)

13 An “upstream” example would be a wine distributor that devotes more effort to promoting sales of a

particular winery’s wines than to promoting the sales of other wineries.

14

so that maximum gains from trade for the two firms are:

π** - h/4 = (φ + ∆)h(β - 1)/4 - hτ . (14)

Assumption (A1) implies that these gains from trade exceed those in equation (13) where

there is no merchandising effort.

Where the bargaining power of the firms is equal, the Nash bargaining solution

divides these gains equally as depicted in:

Proposition 2: With assumption (A1), Nash bargaining with symmetry and

complete information about h, φ, β, and τ produces an equilibrium contract for

the sale of units of brand M for a payment of T** = (φ + ∆)h(β -1)/8 - hτ**Mq /2.

Retail prices and unit sales in this equilibrium are , , and *Mp *

0p , **Mq **

0q .

The main differences between this equilibrium and the one in Proposition 1 are

that the retailer’s market share of brand M sales increases from φ to (φ + ∆) and the

wholesale price decreases from w* to w** = (β-1)/4 - τ /(φ + ∆). The latter difference is

the result of the manufacturer absorbing half of the retailer’s merchandising cost.14 The

contract in Proposition 2 induces selling effort on the part of the retailer, and extracts and

divides all of the incremental profit that merchandising brings to the quasi-partnership.

When compared to the outcome in Proposition 1, where no retailer services are induced,

this outcome incorporates an implicit market share discount.15

14 When multiplied by the (φ + ∆)h /2 units of brand M sold, the “discount”τ /(φ + ∆) equals hτ /2.

15 While this model uses Nash bargaining to show how induced merchandising may cause prices that vary

with market shares, bargaining models have also been use to explain quantity discounts. Chipty and

Snyder (1999) show that production scale economies may lower prices for large buyers in vertical

structures similar to those examined here. McAfee and Schwartz (1994) and Horn and Wolinsky (1988)

15

The welfare effects of inducing retail selling effort in this model are positive.

Both quasi-partners make more profit in the Proposition 2 outcome than in the

Proposition 1 outcome. But this does not come at consumers’ expense. In fact,

consumers who “switch” from an undifferentiated brand to brand M are better off

because of the information conveyed or service provided by the retailer. While the

retailer’s merchandising reduces unit sales of undifferentiated brands, these brands are

not excluded from the retailer’s market. Even in their diminished role, the availability of

these brands creates rent that the quasi-partners are able to capture.

2. Heterogeneous Retailers

Firm M may contract with retailers whose merchandising productivity differs. In

this case, M’s contracts with these retailers may differ as well. Suppose that firm M

distributes its brand to retailers in T markets, indexed i = 1, 2, . . T, where each retailer

shares a common value of β and φ, but whose (exogenous) merchandising skills and sizes

are reflected in firm-specific values of τi, ∆ i and hi. Assume that retailers’ merchandising

skills satisfy:

∆ 1 > 0, and ∆ i > ∆ i-1, for i = 2, . . . T (A2)

τ1 > 0, and τi / ∆ i >τi-1 / ∆ i-1, for i = 2, . . . T (A3)

τi < ∆ i(β- 1)/4, for i = 1, . . . T . (A4)

Assumption (A2) orders retailers by their merchandising effectiveness. Higher indexed

retailers are able to induce a preference for brand M in a greater fraction of their

show that quantity discounts may arise in multilateral bargaining between an upstream monopolist and

competing downstream customers.

16

consumers. Together, assumptions (A2) - (A4) imply that every retailer is capable of

rendering value-added retail services, that the merchandising programs of higher indexed

retailers are more costly, and that these costs increase more than in proportion to their

effectiveness in inducing a preference for brand M. This means that while better

performance costs more, there are diminishing returns to investing in promotional

activity. Nothing is assumed about the relationship, if any, between the sizes hi and

merchandising skills of retailers.

If firm M negotiates contracts with each retailer, the terms of those contracts are

depicted in Proposition 2, where firm-specific values of τi, ∆ i and hi are substituted (these

values satisfy all previous assumptions made aboutτ, ∆, and h). Under these contracts,

retail prices are ( , ) in every market, and unit sales vary from one market to

another. Brand M’s market shares are (φ + ∆

*Mp *

0p

i) for i = 1, 2, . . T, and retailers’ wholesale

prices are:

= (β - 1)/4 -τ*iw i/(φ + ∆ i), for i = 1, 2, . . . T . (15)

With assumptions (A2) and (A3), these prices vary inversely with the market share

performance of retailers. The most proficient merchandisers (larger i) achieve greater

brand M market shares and pay lower prices to offset partially the merchandising costs

they incur.

Unless retailers’ hi values are highly correlated with their ∆ i values, brand M

market shares and bear no relation to the size of retailers.*iw 16 The lower prices go to

16 Once again, this would not hold if, instead of symmetry, retailer bargaining power were an increasing

function of firm size.

17

the most proficient merchandisers regardless of whether they are large or small. This

holds even though a retailer’s merchandising cost hiτi is in direct proportion to its size.

Since, under Proposition 2, firm M’s contractual terms vary among heterogeneous

retailers, the outcomes predicted by this model could not be replicated if firm M were

constrained by public policy to sell to every retailer on the same terms. Even if M could

negotiate retailer-specific fixed quantities, there is no uniform wholesale price that the

firm could charge that would not harm market performance as compared to the quasi-

partnership arrangements in Proposition 2. Constrained to charge a uniform wholesale

price, firm M’s and the retailers’ profits in at least T – 1 markets would be reduced, and

the consumers in those markets who value the brand-specific information or services that

retailers might provide would be worse off.17 No firm and no consumer would be better

off in a same-price-for-all environment.

IV. Exclusion and Antitrust

While the model discussed here is highly stylized, it sheds light on quasi-

partnerships that may arise in distribution channels where there is market power on both

sides of the transaction. The model highlights the role of upstream competitors who lack

market power, and it explores the effects of inducing downstream services in support of

the upstream partner’s brand. It is natural to ask whether the quasi-partnerships

represented by these equilibrium contracts have exclusionary effects on upstream

competitors.

17 This claim would be weakened if the regulatory environment that imposed uniform prices permitted side

payments.

18

Without establishing a benchmark for sales quantities and market shares in a

regulatory environment that precludes arrangements like those depicted in Propositions 1

and 2, it is impossible to predict the extent of foreclosure of competing sellers, if any,

caused by the arrangements. Nevertheless, it is not in the joint interest of the bargaining

parties to squeeze competing sellers out of the market altogether. Some distribution of

competing brands adds a second control variable to facilitate the quasi-partners’

extraction of consumers’ surplus, even though competition precludes competing sellers

from participating in the capture.

When quasi-partnerships between buyers and a dominant seller induce

downstream services, their effect is to increase sales of the dominant seller’s brand at the

expense of competing brands, as seen by comparing Propositions 1 and 2. Yet even here

competing sellers are not completely excluded from the market.

There is an important qualification to the limited foreclosure predicted by the

quasi-partnerships described in this paper. This qualification stems from the assumption,

maintained throughout the analysis, that production of the undifferentiated brands lacks

significant scale economies. Suppose, contrary to previous assumption, that such scale

economies exist. This would mean that competing sellers could not survive by producing

small quantities.18 If the minimum efficient size of those firms is sufficiently large,

compared to the volume sought by buyers, then some, or in extreme cases all, of those

firms might exit rather than produce at a loss. Whether the dominant seller and its

partners would prefer complete foreclosure or dominant-firm market shares that are less

than those in Propositions 1 and 2 depends on how constraining the competing sellers’

18 See Whinston (1990).

19

scale economics are.19 Suffice it to say that for the analysis in this paper to apply, some

competing sellers must be able to remain in the market.

To the extent the quasi-partnership arrangements portrayed in this paper have

material exclusionary effects, those effects may be assessed under a “rule of reason” in

much the same way as are exclusive dealing arrangements in the U.S. Exclusive dealing

arrangements have both potentially pro-competitive and potentially anticompetitive

effects.

On the pro-competitive side, it is widely acknowledged that by giving the retailer

a greater stake in the fortunes of the manufacturer, an exclusivity arrangement focuses the

retailer’s selling effort on the manufacturer’s goods. Scherer (1980, p. 586) wrote “for

manufacturers, exclusive dealing arrangements are often appealing because they ensure

that their products will be merchandised with maximum energy and enthusiasm.” 20

Marvel (1982) argued that a manufacturer might require exclusivity to protect the

investment it makes in its retailers by preventing their using that investment in the service

of competing sellers. Without exclusive dealing, the manufacturer would be less inclined

to make those investments, and distribution would be less efficient. Klein and Murphy

(1988) view exclusive dealing arrangements (and vertical restraints generally), in

19 Of course retailers are likely to resist accepting contracts that lead to the complete withdrawal of

competing sellers since that withdrawal would drive their own disagreement payoffs to zero and weaken

their bargaining positions with firm M.

20 The staff of the Federal Trade Commission (2001, p. 6) recognized that exclusive dealing contracts

“may lead retailers to become usefully committed to making a particular product a success in the

marketplace, and they may not be harmful to competition as long as other retailers remain available for

other manufacturers to use in reaching the market.”

20

conjunction with the threat of manufacturer termination, as enforcement mechanisms to

induce dealer performance endeavors that are noncontractible.21

On the anticompetitive side, several mechanisms have been identified where a

dominant seller might profitably use exclusive dealing contracts to foreclose rivals and

harm consumers. Aghion and Bolton (1987) showed that long-term requirements

contracts between an incumbent seller and its buyers might limit entry (or prevent re-

entry) by rival sellers. Rasmusen, Ramseyer, and Wiley (1991) showed that a dominant

firm might use exclusive dealing to exploit a coordination problem among retailers and

deprive smaller rivals or entrants of sufficient sales to remain viable. Bernheim and

Whinston (1998, p. 67) showed that exclusive dealing contracts might prevent the most

efficient configuration of vertical relationships among suppliers and dealers by

“extracting rents from markets other than the ones in which they are employed.”22

The various theories of exclusive dealing arrangements, and their disparate

implications for market performance, provide the economic basis for applying a rule of

reason analysis to exclusive dealing, as U.S. courts have done since the Supreme Court’s

21 The views of Bork (1978) and Posner (1976) of exclusive dealing arrangements are that manufacturers

would only seek exclusive dealing requirements in circumstances that assure an improvement in market

performance. The argument is that exclusivity could not be imposed on retailers except on terms that

compensate them for profits forgone when they accept the exclusivity requirement. Thus constrained,

manufacturers would not impose exclusivity unless those requirements are profitable because they have

efficiency effects.

22 A common thread in these mechanisms is that, by imposing exclusivity, a dominant seller raises its

rivals’ costs by denying them sufficient sales to reach the minimum efficient size.

21

1961 Tampa Electric decision.23 Insofar as foreclosure is an issue with the quasi-

partnerships described in this paper, those arrangements may be assessed in a similar

fashion.

23 Tampa Electric Co. v. Nashville Coal Co., 365 U.S. 320 (1961).

22

Acknowledgements

The author thanks participants in the Bankard Theoretical Industrial Organization

Workshop at the University of Virginia, Simon Anderson, Kenneth Elzinga, Maxim

Engers, Amalia Miller, Larry White, and referees for valuable comments.

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