BUYER POWER AND INDUSTRY STRUCTURE
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)
[email protected]
February 10, 2010
1
Abstract
This paper investigates the exercise of market power by a large buyer who emerges via growth,
merger, or group purchasing. It explores the efficiency and redistributive effects of such an
event when a competitive fringe of small buyers remains in the market. Terms of trade,
including those for small buyers, depend on structural conditions on the supply side of the
market and the nature of interactions between the newly emerged dominant buyer and suppliers.
Predicted aggregate welfare effects have implications for antitrust.
Key Words
Antitrust, Buyer Power, Dominant Buyer, Waterbed Effect
2
I. Introduction
Large, powerful buyers can be found in many markets. Examples include health plans, in
their dealings with physicians or hospitals; producers of food and beverage ingredients, in their
dealings with agricultural commodity growers; aircraft manufacturers, in their dealings with
aircraft engine manufacturers; and hospital group purchasing organizations, in their dealings with
the suppliers of health care products. When a large buyer exercises market power to influence
the terms of trade with its suppliers, the firm is said to possess “buyer power.” This term applies
to a variety of situations.1 A uniquely large buyer may emerge by growth or merger. Or the
large buyer may be a cooperative association of small buyers, such as a group purchasing
organization or even a buyer cartel.
The starting point for this paper’s analysis is an input or intermediate product market with
many small buyers who are not direct downstream competitors.2 Next a dominant buyer
emerges in the market because one of the buyers grows large in relation to the rest, or because a
significant number of buyers merge or form a group purchasing organization. The dominant
buyer exercises its market power to obtain favorable terms from sellers. But this conduct may
affect sellers’ terms to the remaining buyers. The dominant buyer’s effects on prices, quantities
and welfare depend on structural conditions on the supply side of the market and on the
interactions between the dominant buyer and suppliers.
If the good is produced by a perfectly competitive industry with infinitely elastic supply,
then a dominant buyer cannot influence the good’s price. But if industry supply is upward
1
Inderst and Shaffer (2008, p. 1612) define buyer power as “the ability of buyers to obtain advantageous terms of
trade from their suppliers”. Similarly, Noll (2005, p. 589) defines it as “the circumstance in which the demand side
of a market is sufficiently concentrated that buyers can exercise market power over sellers”.
2
The model also applies to retail distribution where buyers are retailers and where the dominant buyer does not
compete in the same geographic market as other retailers.
3
sloping, the dominant buyer can induce a lower price by reducing its demands. In this scenario,
the low price that the dominant buyer forces on sellers becomes the market price, so the welfare
effect of the dominant buyer’s emergence is positive for all buyers. The welfare effect on
suppliers is negative, and the aggregate welfare effect is negative as well because unit sales
decrease. The dominant buyer’s emergence creates a dead weight loss.
Outcomes are different for buyers who purchase an input or intermediate product from a
monopolist or the supplier of a strongly differentiated good. This is because a dominant buyer
may negotiate terms of trade that do not apply to small buyers. In what follows, the dominant
buyer’s dealings with the seller are modeled as a Nash bargaining game. With this, the
emergence of a dominant buyer has no effect on small buyers if the seller has constant marginal
costs. But if the seller has increasing marginal costs, Nash bargaining creates a “waterbed
effect” on prices: The dominant buyer pays a lower price than if it were a passive price-taker and
the remaining price-taking buyers pay a higher price. In this scenario, the welfare effect of the
dominant buyer’s emergence is negative for non-dominant buyers, but aggregate welfare may
increase or decrease. The likelihood that a dominant buyer increases aggregate welfare is greater
where the supplier’s marginal costs do not increase rapidly and where the small buyer segment is
small.
The predicted effects on aggregate welfare have implications for antitrust. Buyers who
purchase inputs or intermediate products from suppliers in a competitive market should be
prohibited from merging or forming group purchasing organizations solely to create a dominant
buyer. If the input or intermediate product is sold by a monopolist, however, the formation of a
dominant buyer should not be prohibited in every instance. Leniency may be warranted if
market conditions portend a positive effect on aggregate welfare.
4
II. Competitive Sellers
Consider a homogeneous good that is produced and sold in a perfectly competitive
industry. Let the industry’s increasing and continuously differentiable supply function be
y = S( p ) for p > p . There are many buyers, each of whose demand for the good is decreasing
and continuously differentiable on the interval ( 0, p ) , where p < p . Aggregate
demand y = D( p ) is decreasing and continuously differentiable on the same interval, so the
competitive price and output level ( pc , yc ) are uniquely determined by yc = D( pc ) = S( pc ) , with
yc > 0 and pc ∈ ( p, p ) .
Now suppose that a group of small, independent buyers merge to form a single dominant
buyer whose demand x = f ( p ) is decreasing and continuously differentiable on the
interval ( 0, p ) . In the alternative, the dominant buyer may be a group purchasing organization
consisting of independent buyers whose combined demand is f ( p ) .3 In either case, the
remaining independent buyers’ aggregate demand is y = g( p ) , where g( p ) ≡ D( p ) − f ( p ) .
These assumptions imply that f ( pc ) > 0 and g( pc ) > 0 .
If the dominant buyer is large enough in relation to the rest, it is plausible that the firm’s
size and prominence give it some influence over prices in the market. Indeed acquiring this
influence may be the raison d’être of the dominant buyer. A buyer such as this is unlikely to
exhibit the passive, price-taking behavior of atomistic buyers in a competitive market.
To focus on the immediate welfare effects of a dominant buyer, assume that this firm
does not compete directly with other buyers in a downstream market. (Whether non-dominant
3
For convenience, the dominant buyer will be referred to as a “firm” even if it is a group purchasing organization.
5
buyers compete with each other downstream is immaterial.) This assumption applies to several
scenarios. The good may be an intermediate product where buyers are producers of unrelated or
strongly differentiated final goods. Or the good may be a locally produced intermediate product
that is purchased by local producers of a final good that is sold in a global market in which even
the dominant buyer has no market power. Finally, non-dominant buyers may be dealers or
retailers who distribute the good in different marketing channels or at different locations than
does the dominant buyer. In none of these scenarios is a small buyer’s demand for the good
dependent on the price paid by the dominant buyer.
This model is an exact demand-side analogy of the familiar “dominant firm” model that
has a uniquely large seller in a market with many small sellers. In that model, the dominant
seller chooses a price to maximize its own profit on the presumption that small, competing
sellers are passive price-takers (e.g., Stigler, 1965). This exercise of market power sustains a
price that is higher than the competitive price. In the dominant buyer case, a large buyer uses its
price-setting ability to impose a lower than competitive price (Blair and Harrison, 1993). The
dominant buyer’s ability to impose such a price stems from the firm’s ability to reduce
significantly the total quantity demanded at any price.4
To see how a dominant buyer affects outcomes in the industry, note that the residual
supply of the good available to the dominant buyer is x = S( p ) − g( p ) . This quantity is positive
4
This paper emphasizes the effects of group purchasing organizations that are formed to exercise monopsony
power. Other papers have emphasized the ability of group purchasing organizations to exploit nonlinear pricing or
vertical restraints. Marvel and Yang (2008, p. 1091) show that a buying group may form to elicit discounts from
competing suppliers and “extract attractive prices from suppliers not through enhanced bargaining power, but rather
through their ability to obtain [nonlinear] tariffs that pit suppliers against one another effectively”. In a model that is
an extension of O’Brien and Shaffer’s (1997) analysis of interactions between a monopsonist and a duopoly, Dana
(2006) shows that buying groups may organize in order to win discounts from duopolists by committing to purchase
exclusively from the supplier who offers the lower price.
6
for any price greater than p , where p ∈ ( p, pc ) is defined by S( p ) = g( p ) .5 For any price less
than or equal to p , the residual supply is zero because producers would not even supply enough
output to meet the demands of the small buyers. The dominant buyer’s residual supply function
is increasing and continuously differentiable on the interval ( p, p ) . By the inverse function
theorem, this function may be inverted to give a function p = σ ( x ) that is increasing and
continuously differentiable on the interval ( 0,S( p )) . Accordingly, the dominant buyer may
purchase any quantity x ∈ ( 0,S( p )) of the good for a total cost of σ ( x ) ⋅ x .
The dominant firm’s inverse demand function p = f −1 ( x ) is decreasing and continuously
differentiable on the interval ( 0 , f ( 0 )) . The firm’s surplus from acquiring x units is
∫
x
0
f −1 ( z )dz − σ ( x ) ⋅ x . To maximize this surplus, the dominant buyer purchases x* units,
where x* uniquely satisfies the first-order condition:
σ ( x*) + σ '( x*) ⋅ x* = f −1 ( x*) .
(1)
The firm pays the price p* ≡ σ ( x*) for these units. At this price, the remaining buyers purchase
y* ≡ g( p*) units.
The main effects of the dominant buyer’s emergence are summarized in:6
Proposition 1: p* < pc , x* < f(pc ), y* > g(pc ) and x* +y* < yc .
The dominant buyer causes a price decrease by withholding purchases to support the lower price.
This means that the dominant buyer purchases fewer units than if the firm acted as a passive
price-taking buyer. The remaining buyers are passive beneficiaries of the dominant buyer’s
5
6
The existence of a unique p is assured by previous assumptions about S( p ) and g( p ) .
Proofs of the propositions are in the Appendix.
7
market power because they buy more units of the good at a lower price than before the dominant
buyer emerged.
The welfare effect of an emerging dominant buyer is positive for every buyer in the
market. For producers, the welfare effect is negative because total output falls; they sell fewer
units at a lower price. The aggregate welfare effect is negative because the producers’ loss
exceeds the buyers’ gain. With perfectly competitive suppliers, the emergence of a dominant
buyer creates dead-weight loss in the market.
The predictions in Proposition 1 hinge on the assumption that the industry supply
function is increasing. The price effects are smaller the more elastic is S( p ) . If the industry
supply function is infinitely elastic, a dominant buyer would have no impact on market outcomes
because it could not force a lower price on sellers by purchasing fewer units. There would be no
“power buyer” incentive for buyers to merge or form group purchasing organizations if supply is
infinitely elastic. Profitably exercising market power on the buyers’ side of the market requires a
less-than-infinitely elastic industry supply.
III. A Single Seller
Now consider a good produced and sold by a monopolist. In the alternative, the good
may be produced and sold by a single firm in an industry with several firms whose products are
strongly differentiated. The seller’s cost function C( y ) is increasing and continuously
differentiable with C''( y ) ≥ 0 for all y > 0 . Aggregate demand y = D( p ) is the same as before,7
and may be inverted to give p = D −1 ( y ) for all y ∈ ( 0,D( 0 )) . The seller’s profit function is
7
If the good is a differentiated product, D( p ) depends on the prices of competing “brands,” although cross price
elasticities are assumed to be small. This dependence is suppressed in the notation.
8
π ( y ) = D −1 ( y ) ⋅ y − C( y ) . The firm’s profit-maximizing output level ym is given by π '( ym ) = 0 ,
and its price by pm ≡ D −1 ( ym ) . Call the seller’s resulting profit π m ≡ π ( ym ) .
As before, suppose that a group of buyers merge to form a single dominant buyer or
organize a group purchasing organization with demand x = f ( p ) . The combined demand of the
remaining buyers is y = g( p ) . An example of a dominant buyer and a single seller might be a
health plan (the buyer) and a regional hospital (the seller) where the health plan purchases
hospital services for a large fraction of the patients who reside in the region served exclusively
by the hospital. Another example might be an airline (the buyer) and an airport (the seller)
where there are no other nearby airports and where the airline accounts for a significant fraction
of the airport’s fees and lease payments for flight-related services. The emergence of a dominant
buyer in this situation has different effects on market outcomes than with competitive suppliers.
In particular, seller competition no longer prevents an outcome in which the dominant buyer
pays a different price than others.
The relationship between the dominant buyer and the seller resembles a bilateral
monopoly. Since this arrangement can be vulnerable to the double marginalization distortion,
the firms have strong incentives to reach mutually beneficial terms of trade to extract as much
surplus as possible from their transaction.8 Assume that the dominant buyer and the seller
negotiate a contract in a bilateral bargaining game instead of an arrangement where the buyer
chooses a quantity after the seller sets the price. In market structures where there is both a buyer
and a seller with market power, and where the firms contract in isolation under conditions of
8
Inderst and Shaffer (2008) distinguish market structures where firms interact via a “market interface” versus a
“bargaining interface.” In the former, impersonal market forces set prices. In the latter, prices are set in bilateral
bargaining between individual buyers and sellers.
9
complete information, Whinston’s (2006, p. 139) “bilateral contracting principle” predicts that
the firms “will reach an agreement that maximizes their joint payoff”.9
In accordance with this principle, the dominant buyer and the seller negotiate a contract
that maximizes the sum of the dominant buyer’s surplus and the seller’s profit. The market
structure assumed here is distinguished from a bilateral monopoly because there is a competitive
fringe of small buyers. Although they are passive, the latent surplus of these buyers affects
bilateral negotiations between the dominant buyer and the seller. It is natural to assume that the
firms’ contract reflects endogenous effects on the seller’s profit from sales to its remaining
buyers. Let the terms of the contract between the firms be those predicted by the Nash
bargaining solution.
The dominant buyer and the seller negotiate a contract for x units of the good and a total
payment of T. This contract anticipates sales of y units to small buyers at the price g −1 ( y ) .
With Nash bargaining, the output levels ( ˆx, ˆy ) are those that maximize:
x
M ( x, y ) = ∫ f −1 ( z )dz + g −1 ( y ) ⋅ y − C( x + y ) .
0
(2)
The division of M ( xˆ , yˆ ) between the dominant buyer and the seller is achieved by the dominant
buyer’s payment T̂ . With Nash bargaining, T̂ depends on each firm’s bargaining power and
their outside options: the firms’ payoffs should an agreement not be reached.
9
The insight that buyers and sellers with market power can achieve the vertically integrated solution is invoked by
Bernheim and Whinston (1998), Chipty and Snyder (1999), Mathewson and Winter (1987), Campbell (2007), and
Tirole (1988), among many others. Blair and Harrison (1993) discuss the idea’s antecedents in early economic
theory. Baker, Farrell, and Shapiro (2008) are less sanguine about the generality of the vertically integrated solution
because of obstacles raised by asymmetric information and incomplete contracts.
10
Assume that if the firms failed to reach an agreement, the seller would charge the
price pm to all buyers and the dominant buyer would purchase f ( pm ) units. With this, the seller’s
profit would be π m and the dominant buyer’s surplus would be:
vm ≡ ∫
xm
0
f −1 ( x )dx − pm ⋅ xm .
(3)
Based on these outside options, the firms’ joint gain from bilateral bargaining is:
M ( xˆ , yˆ ) − π m − vm .
(4)
Let α ∈ ( 0,1 ) designate the bargaining power of the dominant buyer and 1 − α the
bargaining power of the seller. The Nash bargaining solution predicts that the contract between
the firms fixes T̂ so that the dominant buyer retains the fraction α of expression (4) and the seller
gets the rest. This division implies that the seller’s profit π̂ , the dominant buyer’s surplus v̂ , and
the payment T̂ are jointly determined by:
πˆ = ˆp y ⋅ ˆy + Tˆ − C( ˆx + ˆy )
x̂
v̂ = ∫ f −1 ( x )dx − Tˆ
0
.
(5)
Tˆ = ( 1 − α ) ⋅ ( πˆ + vˆ − π m − vm )
Under the contract ( ˆx,Tˆ ) , the dominant buyer pays the seller an effective price
of p̂x ≡ Tˆ x̂ . The main effects of the dominant buyer’s emergence are:
⎛=⎞
⎛=⎞
⎧= ⎫
Proposition 2: If C'' ⎨ ⎬ 0 , then pˆ x < pm ⎜ ⎟ pˆ y , xˆ > f(pm ), yˆ ⎜ ⎟ g(pm ) and xˆ + yˆ > ym .
⎩> ⎭
⎝<⎠
⎝<⎠
The first result to notice is that the contract between the seller and the dominant buyer
calls for a lower price and more output than if the buyer had instead acted as a passive pricetaker. The second result to notice is that the dominant buyer’s emergence increases total unit
11
sales in the market. The final result to notice is that the dominant buyer’s impact on small
buyers depends on the seller’s costs.
Small buyers are unaffected by the dominant buyer’s emergence if the seller has constant
marginal costs. But if the seller’s marginal costs are increasing, the dominant buyer creates a
waterbed effect on prices. That is, the price paid by small buyers increases while the dominant
buyer’s price decreases. By negotiating superior terms with the seller, the dominant buyer
secures a lower effective price than pm . But this precipitates a higher price than pm for small
buyers. In effect, the dominant buyer wrests a “discount” from the seller. But this discount
triggers a price increase for remaining small buyers because supplying more output to the
dominant buyer increases the incremental cost of supplying the rest.
The source of the waterbed effect in this model is the seller’s increasing marginal costs.
This pricing phenomenon arises for different reasons in some other models. Inderst and Valletti
(2006) identify a waterbed effect that stems from the fixed costs that buyers may bear if they
search for or switch to a backup source for the seller’s good, or if they integrate upstream to
produce the good themselves. In that model, a seller must offer a lower price to a large buyer
than to small buyers to induce the large buyer to forgo alternatives. Majumdar (2005)
demonstrates a waterbed effect in a model with two suppliers who have decreasing marginal
costs. In that model, a large buyer elicits a low price by inviting bids to become its sole supplier.
Once the large buyer selects a sole supplier, competition between the suppliers for sales to the
remaining buyers supports a higher price than the large buyer pays. Mathewson and Winter
(1996) show that if a group of independent buyers in a monopolistically competitive market form
a group purchasing organization to negotiate exclusive contracts with a subset of the suppliers,
they will pay lower prices than do outside buyers. Scale economies of one kind or another play a
12
role in each of these models. But in the present analysis, the waterbed effect is caused by
diseconomies of scale.
The only price or quantity in Proposition 2 that depends on the relative bargaining power
of the seller and the dominant buyer is pˆ x . The quantities x̂ and ˆy and the small buyers’
price p̂ y are not affected by a change in α . The dominant buyer’s payment T̂ varies inversely
with α , so the effective price pˆ x paid by that buyer decreases as its bargaining power increases.10
The payment T̂ is bounded above and below as follows: First,
limTˆ < ˆx ⋅ pm ,
α →0
(6)
because v̂ would be less than vm if the dominant buyer paid an effective price of pm for
x̂ > f ( pm ) units of the good. This would be unacceptable to the dominant buyer. Also,
limTˆ > ˆx ⋅ f −1 ( ˆx ),
α →1
(7)
because π̂ would be less than π m if the dominant buyer paid an effective price of f −1 ( ˆx ) for
x̂ units of the good. An effective price this low would award the entire incremental surplus
created by increasing x to the dominant buyer while reducing the seller’s profit from sales to the
small buyers. This would be unacceptable to the seller. These bounds on T̂ mean that the
dominant buyer’s effective price is never as high as pm and never as low as f −1 ( ˆx ) .
While the welfare effect of a dominant buyer on small buyers is positive when there are
many sellers, the same does not hold when there is a single seller with market power. With a
single seller, the welfare effect on the seller and on those buyers who grow, merge, or organize is
10
Inderst and Shaffer (2008) provide an extensive discussion of factors that affect the value of firms’ outside options
and comparative bargaining power in bilateral negotiations between buyers and sellers with market power.
13
positive; but the welfare effect on the remaining buyers is non-positive. This is because small
buyers cannot free ride on the advantageous terms negotiated by the dominant buyer when there
is a single seller. If the seller’s marginal costs are constant, the dominant buyer has no effect on
small buyers. In this instance the aggregate welfare effect of the dominant buyer is positive
because the contract between the dominant buyer and the seller reduces dead weight loss. But if
the seller’s marginal costs are increasing, the welfare effect on small buyers is negative because
of the waterbed effect on prices. Even if small buyers are losers when the dominant buyer
emerges, the aggregate welfare effect of the dominant buyer still may be positive. This occurs if
the small buyer segment is small relative to the dominant buyer,11 or if C''( y ) is sufficiently
small. Either condition would make the loss incurred by small buyers less than the gain jointly
captured by the dominant buyer and the seller.
Proposition 2 applies where the dominant buyer and the seller negotiate an efficient
contract. But most of the price and quantity relationships predicted in the Proposition apply
more generally. Suppose that there are obstacles to efficient contracting between the firms,
which causes them to strike a bargain ( x,T ) that is suboptimal in the sense that their joint payoff
is less than M ( xˆ , yˆ ) .12 Any such contract would be mutually beneficial to the dominant buyer
and the seller.
A mutually beneficial contract ( x ,T ) between the dominant buyer and the seller is one
that has:
π ( x ) ≥ π m and v( x ) ≥ vm , with at least one strict inequality,
11
(8)
At the limit, if there were no small buyers, this would be an instance of bilateral monopoly/monopsony, and any
negotiated outcome between the two parties must improve the welfare of both parties and thus improve aggregate
welfare.
12
See Baker, Farrell, and Shapiro (2008) for a discussion that challenges the feasibility of efficient contracting in
these kinds of commercial relationships.
14
where
h( x ) ≡ arg max[ M ( x, y )] ,
(9)
y
and where π ( x ),v( x ), and T( x ) jointly satisfy:
π ( x ) = g −1 ( h( x ))h( x ) + T( x ) − C( x + h( x ))
x
v( x ) = ∫ f −1 ( z )dz − T( x )
.
0
(10)
T( x ) = ( 1 − α ) ⋅ ( π ( x ) + v( x ) − π m − vm )
Under such a contract, the dominant buyer pays an effective price px = T( x ) / x , and the
monopolist charges small buyers the price p y = g −1 ( h( x )) .
Any mutually advantageous contract between the seller and an emergent dominant buyer
has the following effects:
⎧= ⎫
⎛=⎞
Proposition 3: If C'' ⎨ ⎬ 0 , then px < pm ⎜ ⎟ p y , x > f(pm ) and
⎩> ⎭
⎝<⎠
⎛=⎞
y ⎜ ⎟ g(pm ) for any contract
⎝<⎠
(x,T(x)) that satisfies (8).
This Proposition indicates that if the seller has constant marginal costs, any mutually beneficial
bargain that a seller strikes with a dominant buyer leaves small buyers untouched. The aggregate
welfare effect of the dominant buyer’s emergence in this instance is positive because the contract
reduces dead weight loss. If the seller’s marginal costs are increasing, the Proposition indicates
that any mutually beneficial contract between the two firms brings on a higher price and fewer
unit sales for small buyers. The size of the waterbed effect, and the sign of the effect on
aggregate welfare, depends on the terms of the contract, the relative size of the small buyer
segment, and the magnitude of C''(y) .
15
IV. Policy Implications
In recent years, several Federal Trade Commission conferences and reports have studied
potential antitrust problems related to the purchasing practices of dominant firms in industries as
diverse as e-commerce, health care, and petroleum.13 There is general recognition that the
exercise of market power on the demand side of a market may create allocative inefficiency that
is similar to market power on the supply side. Because the effects of monopsony and monopoly
“are basically the same,” Noll (2005) argues that antitrust policy “should be symmetrical” (p.
623). The relevance of antitrust for monopsony was underlined recently by the Supreme Court’s
decision in Weyerhaeuser Co. v. Ross-Simmons Hardwood Lumber Co., Inc., 549 U.S. 312
(2007).14
The analysis in this paper suggests that the emergence of dominant buyers is problematic
in some circumstances but not all.15 Insofar as antitrust is guided by the goal of promoting
economic efficiency, input and intermediate product buyers should be prohibited from merging
or forming group purchasing organizations to achieve dominance when purchasing from
suppliers in a competitive market. But the correct prescription is less clear-cut when the
dominant buyer’s trading partner is a seller with market power. If the seller has constant
marginal costs, the emergence of a dominant buyer is socially beneficial and does not harm small
13
Noll (2005) summarizes these studies and reviews the implications of “buyer power” for antitrust policy.
In Weyerhaeuser the plaintiff (a small buyer) claimed that the defendant (a large buyer) bid prices up so as to
impose losses on the plaintiff; i.e., the behavior was allegedly predatory. In the present analysis, the dominant
buyer’s conduct reduces its own price but may raise the price that small buyers pay because of the seller’s
diseconomies of scale.
15
The notion that the “countervailing power” of a dominant buyer can subdue the market power of a large seller and
improve market performance has a long history, beginning with Galbraith (1952, 1954). Galbraith’s main
hypothesis was that the “countervailing power” of a dominant retailer lowers retail prices. Chen (2003), Dobson and
Waterson (1997), and von Ungen-Sternberg (1996) each have found specialized structural conditions and other
features of retail markets that support this hypothesis. The mechanisms and qualifications that they identify are
different, but all of them rely on vigorous competition among retailers to transfer benefits downstream to consumers.
The analysis in this paper indicates that countervailing power may pit the interests of one class of buyers against
another, whether or not it improves market performance.
14
16
buyers. An event like this does not call for antitrust intervention. However, if the seller has
increasing marginal costs, the dominant buyer’s emergence may or may not be socially
beneficial. This is because the dominant buyer’s emergence creates a waterbed effect that
reduces the welfare of small buyers. If the effect on the small buyer segment is sufficiently
large, intervention to prohibit a merger or the formation of a group purchasing organization to
achieve dominance would be warranted. The two factors that raise a red flag for antitrust under
this scenario are if the seller has significant diseconomies of scale and if the size of the buyer
segment left to absorb the waterbed effect is relatively large.
These conclusions must be qualified by two considerations. The first qualification is that
some dominant buyers may not be created by growth or by the merger or group purchasing of a
large number of small buyers. Some may be created when two oligopsonists merge who already
are large enough to exert some influence over their terms of sale with the seller. With this kind
of merger, some of the gains unlocked by mutually advantageous contracts between a dominant
buyer and the seller may already have been captured. This reduces the incremental welfare
gains, if any, that would arise if the buyers merged.
Also, the analysis and conclusions in this paper do not account for distortions, if any, that
may arise if the dominant buyer competes downstream with the small buyers. Where this
happens, small competitors incur a cost disadvantage because of the waterbed effect. If there is
downstream competition (e.g., buyers are competing retailers), this disadvantage might create a
vicious cycle where upstream market power confers a downstream cost advantage that bolsters
downstream market power. This, in turn, amplifies the firm’s upstream market power, and so on
(Dobson and Inderst, 2008). In extreme cases, it is possible that this chain of events might
culminate in the exclusion of downstream rivals, or deterrence of downstream entrants.
17
Appendix
Proof of Proposition 1:
Recall that f −1 ( x ) is decreasing on ( 0 , f ( 0 )) . To show that x* < f ( pc ) , it is sufficient to
show that the dominant firm’s incremental surplus would be negative if the firm purchased
f ( pc ) units. When purchasing x units, the dominant firm’s incremental surplus is:
d ⎡ x −1
f ( z )dz − σ ( x ) ⋅ x ⎤ = f −1 ( x ) − σ ( x ) − σ '( x ) ⋅ x .
⎦⎥
dx ⎣⎢ ∫0
(11)
Evaluating the r.h.s. of this expression at x = f ( pc ) gives:
pc − σ ( f ( pc )) − σ '( f ( pc )) ⋅ f ( pc ) .
(12)
Next, inverting both sides of f ( pc ) = S( pc ) − g( pc ) gives:
σ ( f ( pc )) = pc .
(13)
Substituting (13) into (12) simplifies (12) to −σ '( f ( pc )) ⋅ f ( pc ) , which is negative. This
establishes that x* < f ( pc ) .
It follows from x* < f ( pc ) that σ ( x*) < σ ( f ( pc )) and hence that p* < pc . Further,
because p* < pc and g'( p ) < 0 , we have y* = g( p*) > g( pc ) . Finally,
S( p*) < S( pc ) ,
because p* < pc and S '( p ) > 0 . Inequality (14) implies that x* + y* < yc .■
18
(14)
Proof of Proposition 2:
Without a dominant buyer, those buyers who otherwise merge would purchase
f ( pm ) units of the good, and the remaining buyers would purchase g( pm ) units. These
quantities satisfy:
df −1 ( f ( pm ))
= C'( f ( pm ) + g( pm ))
dx
.
dg −1 ( g( pm ))
−1
g ( g( pm )) + g( pm ) ⋅
= C'( f ( pm ) + g( pm ))
dy
f −1 ( f ( pm )) + f ( pm ) ⋅
(15)
The first order conditions for maximizing M ( x, y ) are:
f −1 ( ˆx ) = C'( ˆx + ˆy ) and g −1 ( ˆy ) + ˆy ⋅
dg −1 ( ˆy )
= C'( ˆx + ˆy ) .
dy
(16)
Suppose ˆx + ˆy ≤ ym . Because C''( ⋅ ) ≥ 0 , this relationship would imply:
C'( ˆx + ˆy ) ≤ C'( ym ) .
(17)
Because f −1 ( x ) and g −1 ( y ) are decreasing, and because ym = f ( pm ) + g( pm ) , (15) - (17) imply
that x̂ > f ( pm ) and ŷ ≥ g( pm ) . This establishes a contradiction and shows that:
ˆx + ˆy > ym .
(18)
⎧=⎫
⎧=⎫
C'( ˆx + ˆy ) ⎨ ⎬ C'( f ( pm ) + g( pm )) if C'' ⎨ ⎬ 0 .
⎩>⎭
⎩>⎭
(19)
Next, (18) implies that:
Equations (15) and (16) together with (19) imply that:
⎧=⎫
⎧=⎫
ŷ ⎨ ⎬ g( pm ) if C'' ⎨ ⎬ 0 .
⎩>⎭
⎩<⎭
Because g( ⋅ ) is decreasing, (20) implies that:
19
(20)
⎧=⎫
⎧=⎫
pˆ y ⎨ ⎬ pm if C'' ⎨ ⎬ 0 .
⎩>⎭
⎩>⎭
(21)
Together with (18), (20) also establishes that x̂ > f ( pm ) . Finally pˆ x < pm because the dominant
buyer would prefer ( pm , f ( pm )) to ( p,xˆ ) for any p ≥ pm .■
Proof of Proposition 3:
For (8) to hold, it is straightforward that x > f ( pm ) . This inequality implies that
px < pm because otherwise v( x ) < vm , which contradicts (8). For any x , (9) requires
that y = h( x ) must satisfy:
g −1 ( y ) + y ⋅
dg −1 ( y )
= C'( x + y ) .
dy
(22)
⎛= ⎞
⎛= ⎞
⎧=⎫
With x > f ( pm ) , equation (22) implies that pm ⎜ ⎟ p y and y ⎜ ⎟ g(pm ) if C'' ⎨ ⎬ 0 because
⎝<⎠
⎝ <⎠
⎩>⎭
g( p ) is decreasing.■
20
Acknowledgements
The author thanks the General Editor, two referees, Simon Anderson, Federico Ciliberto,
Kenneth Elzinga, Maxim Engers, and Nathan Larson for helpful comments, and the Bankard
Fund for Political Economy at the University of Virginia for financial support.
21
References
Baker, J. B., J. Farrell, and C. Shapiro (2008). Merger to Monopoly to Serve a Single Buyer:
Comment. Antitrust Law Journal, 75, 637-646
Bernheim, B. D. and M. D. Whinston (1998). Exclusive Dealing. Journal of Political Economy,
106, 64-103
Blair, Roger D. and Jeffrey L. Harrison (1993). Monopsony: Antitrust Law and Economics.
(Princeton: Princeton University Press)
Campbell, T. (2007). Bilateral Monopoly in Mergers. Antitrust Law Journal, 74, 521-536
Chen, Z. (2003). Dominant Retailers and the Countervailing-Power Hypothesis. RAND Journal
of Economics, 34, 612-625
Chipty, T., and C. M. Snyder (1999). Buyer Size and Bargaining Power. Review of Economics
and Statistics, 81, 326-340
Dana, J. (2006). Buyer Groups as Strategic Commitments. Retrieved February 10, 2010, from
The Center for the Study of Industrial Organization at Northwestern University Web site:
http://www.wcas.northwestern.edu/csio/Papers/2005/CSIO-WP-0067.pdf
Dobson, P. W. and Inderst, R. (2008). The Waterbed Effect: Where Buying and Selling Power
Come Together. Wisconsin Law Review, 2008, 331-357
Dobson, P. W. and M. Waterson (1997). Countervailing Power and Consumer Prices. The
Economic Journal, 107, 418-430
Galbraith, J. K. (1952). American Capitalism: The Concept of Countervailing Power. (Boston:
Houghton Mifflin)
____________ (1954). Countervailing Power. American Economic Review, 44, 1-6
Inderst, R. and G. Shaffer (2008). Buyer Power in Merger Control. (In W. D. Collins (ed.),
Issues in Competition Law and Policy, Vol. II (pp. 1611-1635). Chicago: American Bar
Association.)
Inderst, R. and T.M. Valletti (2009). Price Discrimination in Input Markets. RAND Journal of
Economics, 40, 1-19
Majumdar, A. (2005). Waterbed Effects and Buyer Mergers. Retrieved February 10, 2010, from
ESRC Centre for Competition Policy at University of East Anglia Web site:
http://www.uea.ac.uk/polopoly_fs/1.104475!ccp05-7.pdf
22
Marvel, H. P., and H. Yang (2008). Group Purchasing, Nonlinear Tariffs, and Oligopoly.
International Journal of Industrial Organization, 26, 1090-1105
Mathewson, G. F., and R. A. Winter (1987). The Competitive Effects of Vertical Agreements:
Comment. American Economic Review, 77, 1037-1062
________ (1996). Buyer Groups. International Journal of Industrial Organization, 15, 137-164
Noll, R. G. (2005). “Buyer Power” and Economic Policy. Antitrust Law Journal, 72, 589-624
O’Brien, D. P. and G. Shaffer (1997). Nonlinear Supply Contracts, Exclusive Dealing, and
Equilibrium Market Foreclosure. Journal of Economics & Management Strategy, 6, 755-785
Stigler, G. J. (1965). The Dominant Firm and the Inverted Umbrella. Journal of Law and
Economics, 8, 167-172
Tirole, J. (1988). The Theory of Industrial Organization. (Cambridge: MIT Press)
von Ungen-Sternberg, T. (1996). Countervailing Power Revisited. International Journal of
Industrial Organization, 14, 507-520
Whinston, M. D. (2006). Lectures on Antitrust Economics. (Cambridge: MIT Press)
23