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This paper uses the framework of aggregation and separation that Lee Fennell develops in Slices and Lumps to discuss two fundamental questions of antitrust policy. First, how far does the lumpiness of trading partners dictate the limits of antitrust policy? Second, what does antitrust miss under the common practice of lumping price, consumer welfare, and allocative efficiency together? Discussion of these questions is clarified and sharpened by the vocabulary of Fennell’s framework.
The framework of aggregation and division that Lee Fennell develops
in Slices and Lumps is both elegant and encompassing. Through the simple
device of questioning how ideas and individuals are grouped together, or
split apart, Fennell is able to explain and challenge concepts from diverse
areas of law. While few subjects would not benefit from the clarity of this
approach, the framework developed in Slices and Lumps strikes me as es-
pecially tailored to the study of antitrust law.
The importance of aggregation and division in modern antitrust policy
cannot be overstated. Illegal acts of collusion are defined by the agreement
of separate competitors to join together in acting as though they were a
single firm in a collusive scheme. Tying arrangements are only potentially
anticompetitive when the tying and tied products could be sliced apart and
purchased separately. Anticompetitive concerns with mergers arise from
the economic aggregation of separate competitors into a single entity. The
inability of a parent company to collude with its wholly owned subsidiary
reflects a unity of economic interest that is masked by the formal slicing
of institutions at the boundaries of their incorporation.
The identification of relevant markets in antitrust analysis is an exercise
solely defined by aggregation and division. As I have recently argued in
another context, relevant markets in antitrust have little to do with lay con-
cepts of industry, markets, or lines of trade. Rather, the modern and eco-
nomically defensible concept of an antitrust relevant market is a cross sec-
tion of trade in which a hypothesized competitive injury could potentially
occur. This functional definition requires care to avoid both overinclusive
and underinclusive market concepts. By aggregating up too much trade,
an overinclusive market may mask potential competitive harm by includ-
ing too many competitors in the mix and thus overstating the existence of
* Working paper for the 2019 Slices and Lumps symposium at the University of Chicago.
Contact the author at
constraining competitive influences. On the other hand, by slicing trade
too thinly, an underinclusive market may either overstate potential harm
by omitting important sources of competition, or understate it, by obscur-
ing broader patterns of interdependence and potential anticompetitive co-
ordination among competitors.
Though any of these examples (and many more) could be productively
developed within Fennell’s framework, I use the remainder of this short
essay to consider two questions of a somewhat more fundamental nature.
First, how far does the lumpiness of trading partners go in dictating the
limits of antitrust policy? Second, what does antitrust miss under the now
common practice of lumping together price effects, consumer welfare, to-
tal welfare, and other concerns? Discussion of these questions is clarified
and sharpened by reliance on Fennell’s framework.
Imagine all voluntary exchange as taking place somewhere on a two-
dimensional grid defined by the number of potential trading partners on
either side of the transaction. Though these dimensions are in principle
continuous, we can for expositional simplicity limit our discussion to the
four discrete cases identified in Table 1, below.
Table 1. Buyer/Seller Numerosity and Related Economic Theories
One way to understand Fennell’s flexible concept of lumpiness is in
terms of market concentration. A small number of potential sellers consti-
tutes a lumpy supply side of the market. Consumers have only a few lumpy
options when seeking to complete a transaction. By contrast, a large num-
ber of potential sellers constitutes a smooth supply side. The same idea
Large # Buyers
Small # Buyers
Large # Sellers
Classical Price Theory
Small # Sellers
Bargaining Theory
applies on the buyer side of the market. As the following discussion ex-
plains, this type of lumpiness delimits much of the scope of antitrust law,
and also highlights a disquieting conceptual weakness at its core.
Start with the top-left quadrant of Table 1. This situation reflects a trans-
action that could take place between any pair of a large number of potential
buyers and sellers. All else equal, antitrust policy has little to contribute
here. Simply put, trade in this setting usually works well enough on its
The reasoning comes directly from classical economic theory. In classic
price theory models, a single commodity is traded between a large number
of potential buyers and sellers. Assuming away certain externalities and
transaction costs, economic theory predicts that market-clearing prices
will maximize allocative efficiency in this setting. This is a strong claim,
but empirical studies seem to bear it out.
A nice illustration is a “pit market” experiment described by Charles
Holt, in which a large numbers of buyers and sellers are cast into a trading
pit to try to organically find and negotiate trades. The process is noisy and
chaotic as the student subjects in the experiment rush around the trading
pit trying to find willing trading partners. Yet even with minimal infor-
mation about market conditions, and with little time to find and negotiate
trades, subjects in this experiment often achieve results surprisingly close
to the efficiency predictions of perfect competition.
The point is that, for all their artificial properties, textbook models of
perfect competition appear to be quite robust, at least when there are many
potential trading partners on both sides of a transaction. Problems only
emergeand antitrust policy only becomes importantwhen lumps form
on either the buyer or seller side of an exchange.
Start with a lumpy seller side: the bottom-left quadrant of Table 1. In
monopoly and oligopoly models, trade takes place between a large number
of potential buyers and a small number of potential sellers. A mature liter-
ature in industrial organization economics predicts that trade in this setting
will not generally exhibit the allocative efficiency of perfect competition.
Often, but not always, lumpy sellers will seek to maximize their profits by
driving prices above the allocatively efficient level. Compared to a perfect
competition benchmark, sellers do better, buyers do worse, and overall so-
cial welfare declines.
Roughly the same holds true when the lumps form on the buyer side of
a transaction. In the top-right quadrant of Table 1, a large number of po-
tential sellers attempt to trade with a small number of potential buyers. The
efficiency implications of monopsony and oligopsony models are the mir-
ror image of monopoly and oligopoly. Here, the lumpy buyers will often,
though not always, seek to pad their wallets by driving prices down below
the allocatively efficient level. Compared to a perfect competition bench-
mark, buyers do better, sellers do worse, and overall social welfare again
Traditional antitrust policy is largely preoccupied with these two forms
of trade (the anti-diagonal of Table 1). Among other things, antitrust law
can often be interpreted as protecting the smoother side of a transaction
against the lumpier side. Thus, the efforts of a small number of oligopolists
to collude may be illegal under Section 1 of the Sherman Act. Actions that
would further increase trading lumpiness by driving a competitor from the
market may be illegal under Section 2 of the Sherman Act. Mergers that
enhance or exploit certain forms of lumpiness may be illegal under Section
7 of the Clayton Act.
More could be said about antitrust policy in the three quadrants dis-
cussed so far, but I would rather shift focus to the fourth category of trade.
The often overlooked lower-right quadrant of Table 1 involves exchange
between small numbers of potential buyers and sellers. In the limit, this
category of trade converges to negotiated exchange between a single buyer
and a single seller: a condition sometimes termedbilateral monopolyin
the law and economics literature. The question raised by discussion so far
is what role, if any, antitrust policy should play in this quadrant.
The answer is complicated by the uncertain economics of this form of
trade. In the extreme case of individual negotiation and bilateral monop-
oly, simple bargaining models can rationalize any division of the benefit
of trade that does not make either the buyer or seller worse off than if the
transaction had not occurred at all. Put another way, there is no clear pre-
diction about the division of buyer and seller surplus in the lower-right
quadrant. Allocatively efficient exchange can occur at any of an infinite
number of potential “prices” in this setting. But does allocatively efficient
exchange occur at all?
Again, the answer is uncertain. Most basic bargaining models predict
that mutually beneficial exchanges will occur wherever feasible. But this
turns out to be empirically doubtful. Impasse and failed exchange are often
observed in experimental research on bilateral bargainingat least when
it takes place between individuals. Indeed, the holdout problem, the sub-
ject of much concern in law and economics, is at root an empirical predic-
tion that beneficial exchange may not take place at all if it must be nego-
tiated between a small number of potential trading partners.
Backing away from the extreme of individual negotiation, the situation
becomes less opaque in some forms of auctioned exchange, though many
of the uncertainties of trade between few potential trading partners remain.
An adequate treatment of action economics is impossible in the space of
this essay. For present purposes, it suffices to note that auction prices can
depend on factors such as differences in relative valuations, auction rules,
and the number of bidders. Outcome efficiency is similarly complicated,
potentially depending on information availability, auction rules, and bid-
der strategies, among other things.
The economic complexity and uncertainty of trade between small num-
bers of potential trading partners is substantial. At least for now, economic
theory simply has more that it confidently can say about the properties of
trade in aggregate (the first three quadrants of Table 1) than it has to say
about the properties of specific instances of trade between small numbers
of potential trading partners (the fourth quadrant of Table 1). But where
does this leave antitrust in the lower-right quadrant?
There are plausible arguments that antitrust has little to offer here. First,
in contrast to the bottom-left and top-right quadrants, there may be no
asymmetry of lumpiness to create a disadvantaged side of the transaction
in need of protection. Indeed, roughly equal lumpiness might protect each
side of an exchange against attempted exercises of market power by the
other. This thinking has motivated calls for relaxed antitrust enforcement
in the literature, at least where market power would be exercised against a
single entity, if at all. The treatment of “powerful buyers” as a mitigating
factor in competitive effects analysis in the current Merger Guidelines
evinces similar thinking. Second, as will be discussed in greater detail in
the next section, allocative inefficiency does not necessarily follow from
surplus appropriation in this setting, suppressing at least one of the tradi-
tional justifications for antitrust intervention.
But there are also plausible arguments that antitrust is indeed needed in
the bottom-right quadrant of Table 1. First, and foremost, there is no prin-
cipled reason to think that traditional antitrust injuries cannot occur in
transactions involving only a few potential trading partners. The Merger
Guidelines identify mergers of competing bidders as a possible source of
anticompetitive harm. And mergers affecting only a small number of buy-
ers are sometimes opposed by the federal agencies. A recent example is
the Federal Trade Commission’s move to prevent Staples from acquiring
Office Depot on grounds that this merger would weaken the negotiation
posture of large business-to-business buyers of office supplies. To the ex-
tent that antitrust law already protects the negotiation posture of large cor-
porate entities as they negotiate multi-million-dollar supply contracts, it
may already reach far into the bottom-right quadrant of Table 1.
Second, the empirical evidence on bargaining failure may suggest an
alternative and independent basis for opposing extreme lumpiness under
antitrust law. Past a certain point, a reduction in the number of potential
trading partners may lead to allocative inefficiency simply as a result of
an increased likelihood of bargaining impasse and failed exchange. This
is admittedly not a traditional basis for antitrust enforcement, but it tracks
the underlying concern of allocative efficiency and total welfare theories
of antitrust policy, and it probably deserves at least some consideration in
the context of heavily concentrated markets.
The point of this discussion is not to suggest that antitrust policy must
take any specific course of action in situations like the lower-right quad-
rant of Table 1. Neither economics nor antitrust law are mature enough to
recommend or exclude any approach as a bright-line rule. But trade be-
tween small numbers of potential trading partners is a common and im-
portant form of commerce, and clearer antitrust policy in this area is some-
thing to which we might aspire in years to come.
While much more could be said about the four quadrants of Table 1 and
how lumps in trading partners influence antitrust policy, I now turn to how
the framework of Slices and Lumps facilitates discussion of another latent
issue in modern antitrust: imprecision in the fundamental goals of antitrust
Many antitrust textbooks start by comparing equilibrium outcomes in
models of perfect competition and single-price monopoly, roughly paral-
leling some of this essay’s earlier discussion. Takeaways from the usual
textbook treatment also track aspects of earlier discussion. Relative to the
many small sellers that make up the supply curve in a model of perfect
competition, a monopolist internalizes the effect of each incremental price
reduction on all units sold. This gives the monopolist a profit motive to
raise the price of a good or service above the competitive level.
In the typical comparison, the consequences for consumers and society
provide a number of related justifications for antitrust policy. The market
price is higher under monopoly than under perfect competition. Some con-
sumers pay the higher monopoly price, and their benefit of trade is reduced
in exact proportion to the enhanced profit margin of the monopolist. Other
would-be consumers are unwilling or unable to trade at the higher monop-
oly price. Their failure to obtain the goods or service leads to a lower total
quantity of trade, and also implies an allocative inefficiency. The goods or
service could have been supplied to these would-be consumersas proven
by their ability to buy it at the lower perfect-competition priceand be-
cause the profit maximizing behavior of the monopolist obstructs these
trades, it necessarily deprives society of beneficial transactions.
In this textbook treatment of the evils of monopoly, price correlates with
many variables. Price and output are directly linked. There is a single price
that determines the quantity traded (and vice versa). For the same reason,
price correlates with allocative efficiency. Any price above (or below) the
competitive price implies fewer trades than would have occurred under
competitive pricing, which in turn implies an inefficient allocation of re-
sources. If the market price deviates in any way from the equilibrium price
in perfect competition, then some feasible and beneficial exchanges are
bound to remain unrealized.
Finally, many texts and antitrust scholars draw an additional correlation
between consumer welfare and total welfare in this setting. In the textbook
comparison of single-price monopoly with perfect competition, the reduc-
tion in consumer welfare is brought about by a higher-than-competitive
monopoly price. This monopoly price prevents some beneficial trades
from occurringan allocative inefficiency. And this allocative ineffi-
ciency (combined with a welfare neutral redistribution of the gain of trade
among those who continue to trade) implies a net reduction in society’s
overall gains from trade, reducing total welfare. So consumer welfare and
total welfare are linked as well.
This chain of inferences, linking reductions in consumer welfare to re-
ductions in total welfare, may help to explain Robert Bork’s infamous con-
flation of the two concepts in the Antitrust Paradox. Bork’s conflation,
and some underlying uncertainty about the differences, may help explain
the willingness of many judges to lump together the concepts of price el-
evation, output reduction, consumer welfare reduction, and total welfare
reduction. Finally, the authoritative language of some judicial opinions has
undoubtedly allowed (if not compelled) some practitioners and scholars to
adopt this same imprecision in treating these different ideas as though they
were basically interchangeable in practice.
But there is a problem with lumping these ideas together too freely. The
chain of inferences that links price to output and consumer welfare to total
welfare does not generalize to many settings more complicated than the
simplistic comparison in which it is often presented. For one thing, the
baseline of perfect competition is rarely, if ever, the appropriate bench-
mark for measuring competitive injury. Almost always, the baseline for
assessing a challenged act is itself an imperfectly competitive status quo.
Moreover, the removal of a single assumption throws the entire chain of
inference into doubt.
The critical assumption is that a firm with market power sets a single
per-unit price for the good or service it provides. In perfect competition,
this assumption aligns with intuition. When fiercely competitive price-tak-
ing agents sit on either side of a commodity exchange, it is hard to imagine
anything other than a single per-unit price emerging as the market equilib-
rium. But monopolists are not price takers. And unless some external force
prevents it, the monopolist’s power to set prices will generally include the
power to set different prices for different transactions. This raises an obvi-
ous question: what does the comparison to perfect competition, or any ap-
propriate baseline, look like if the monopolist does not charge a single per-
unit price?
The answer depends on what pricing model the monopolist adopts
and there are many possibilities. To take one extreme, suppose the monop-
olist charges each customer a customized price. In a model of perfect price
discrimination, the seller is assumed to be able to accurately predict the
willingness-to-pay of every consumer and to be able to prevent arbitrage
by technical or legal constraints (foreclosing resale among consumers). A
monopolist in such a position could charge each consumer the most that
this person would possibly pay for the quantity of the good or service being
traded. The effect is complete appropriation of consumer welfare by the
monopolist: the value of trade to all consumers is driven down to almost
nothing. But the effect is also complete preservation of the allocative effi-
ciency of perfect competition. The monopolist has a strong profit motive
to make sure that every last efficient trade occurs in this setting, so the
total quantity traded is the same for perfect price discrimination as it is for
perfect competition, and total welfare is the same as well. In short, the
effect of perfect price discrimination is to completely unlink changes in
consumer welfare from changes in total welfare.
As another example, a monopolist may engage in imperfect price dis-
crimination, setting different prices in different geographic locations or
selling products in different quantity or quality brackets. These strategies
increase the monopolist’s profits, but their implications for consumer and
total welfare are ambiguous. Often, this type of imperfect price discrimi-
nation will make one group of consumers better off than if the monopolist
had set a single price while simultaneously making another group of con-
sumers worse off. The effect on consumer welfare then turns on the phil-
osophically difficult question of how different groups of consumers should
be sliced or aggregated in computing changes in consumer welfare. Total
welfare presents fewer conceptual challenges but is no less ambiguous, in
that it may be higher or lower than under single price monopoly depending
on how much each of the different groups of consumers gains and loses
under the imperfect price discrimination scheme. Comparisons to perfect
competition are more or less extreme than under the comparison to single-
price monopoly, depending on the same considerations.
Other pricing schemes present their own complications. There are other
types of price discrimination that a monopolist may pursue. There are also
the various pricing strategies now studied in the growing economic litera-
ture on nonlinear pricing: things like quantity discounts, peak-load pricing,
two-part tariffs, various forms of bundling, among others. And as noted
earlier in this essay, individual negotiation and auctioned exchange present
further complicationsat the most extreme, decoupling prices from effi-
ciency implications over substantial bands of exchange.
The point of this discussion is not to suggest that any particular pricing
scheme is good or bad in the abstract. It is also not to suggest that antitrust
law cannot handle cases involving nonlinear pricing. The point is simply
to highlight the dubious theoretical basis for lumping changes in price,
consumer welfare, allocative efficiency, and total welfare together as
though they were equivalent in every case. They are not. And the problems
inherent in treating them as equivalent are substantial.
For one thing, the uncritical lumping of these concepts stunts the growth
of antitrust policy. There are reasoned arguments for why antitrust should
focus on consumer welfare just as there are arguments for why it should
focus on total welfare. There are reasons to direct attention to price effects
just as there are reasons to let price take a second seat to efficiency. These
options, and the tradeoffs between them, are needlessly obscured by the
common practice of lumping together all these concerns.
Another problem arising from the conflation of concepts like consumer
welfare and total welfare is that it confuses articulation of the principles
upon which cases are being decided. In the recent Supreme Court decision
of Ohio v. American Express, for example, did the majority really mean
what it said in defining market power as “the ability to raise price profita-
bly by restricting output”? If so, then it would seem to be motivated by
concern for allocative efficiency and total welfarenot consumer welfare
as it elsewhere suggests. If not, then it confuses readers with a mistaken
lumping of allocative efficiency and consumer welfare. In the other direc-
tion, when the Eleventh Circuit passed down the important rule that to de-
fend a merger on efficiency grounds any cost savings needed tobenefit
competition and, hence, consumers,” did the court really mean to articulate
a pure consumer welfare standard for merger review? Or was it simply and
mistakenly assuming that anything which reduced consumer welfare al-
ways reduced total welfare as well?
Finally, the imprecise lumping together of different objectives frustrates
basic antitrust analysis. As Steven Salop has observed, the antitrust analy-
sis of harm to competitors differs substantially between the consumer wel-
fare and total welfare standards. Inefficient allocations of output between
the members of a cartel may similarly invite harsher treatment under a total
welfare norm of antitrust than under the consumer welfare standard. More
generally, imprecision about what norms define anticompetitive harm and
procompetitive injury complicates the day-to-day weighing of competitive
effects, as required in many merger cases, for example. The comparison
of competitive costs and benefits is a difficult exercise under the best of
circumstances. And when combined with confusion about what counts as
a harm or benefitthe predictable result of routine conflation of different
antitrust policy objectivesthe difficulty and unpredictability of the exer-
cise can simply expand beyond control.
All these problems arise from the assumption that changes in price, con-
sumer welfare, allocative efficiency, and total welfare always (or almost
always) move together in simplistic ways. This is not a sound assumption,
but even if it was, the uncritical lumping together of conceptually different
policy objectives would remain both unwarranted and counterproductive
to modern antitrust practice. Antitrust law would be well-served by a more
conscious slicing apart of its different objectives in scholarship, opinions,
and advocacy. Helpfully, this exercise is not only invited by the framework
Fennell develops in Slices and Lumps but facilitated by it as well.
ResearchGate has not been able to resolve any citations for this publication.
American Express, 138 S. Sct. at 2290
  • E G See
See, e.g., American Express, 138 S. Sct. at 2290; Leegin Creative Leather Prod., Inc. v. PSKS, Inc., 551 U.S. 877, 906 (2007).