Discussion Paper No. 878

HOW DOES DOWNSTREAMFIRMS' EFFICIENCY AFFECTEXCLUSIVE SUPPLY AGREEMENTS?

Hiroshi Kitamura
Noriaki Matsushima
Misato Sato

August 2013
Revised September 2015

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

How Does Downstream Firms’ Efficiency Affect Exclusive
Supply Agreements?∗
Hiroshi Kitamura†

Noriaki Matsushima‡

Misato Sato§

August 4, 2015

Abstract
This study constructs a model to examine anticompetitive exclusive supply contracts that prevent an upstream supplier from selling input to a new downstream firm. With regard to the technology to transform input produced by the supplier, as an entrant becomes increasingly efficient,
its input demand can decrease, and thus, the supplier earns smaller profits when a socially efficient
entry is allowed. Hence, an inefficient incumbent can deter a socially efficient entry through exclusive supply contracts, even in the framework of the Chicago School argument, which comprises asingle seller, buyer, and entrant.

JEL classifications code: L12, L41, L42, C72.
Keywords: Antitrust policy; Entry deterrence; Exclusive supply contracts; Transformational technology.
∗
We especially thank Ricard Gil, Akifumi Ishihara, Lars Persson, Keizo Mizuno, Patrick Rey, David Salant, Mark
Schankerman, and Tommaso Valletti for their insightful comments. We also thank Chiaki Hara, Kazumi Hori, Junichiro
Ishida, Shingo Ishiguro, Atsushi Kajii, Keisuke Kawata, Toshihiro Matsumura, Masaki Nakabayashi, Tatsuhiko Nariu,
Ryoko Oki, Tadashi Sekiguchi, Takashi Shimizu, Katsuya Takii, conference participants at the International Industrial Organization Conference, the European Association for Research in Industrial Economics, and the Japanese Economic Association, and seminar participants at Contract Theory Workshop, Hitotsubashi University, Kwansei Gakuin University, Kyoto
University, and Osaka University for helpful discussions and comments. The second author thanks the warm hospitality
at MOVE, Universitat Autònoma de Barcelona where part of this paper was written and acknowledges financial support
from the “Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation” of JSPS. We gratefully acknowledge financial support from JSPS KAKENHI Grant Numbers 22243022, 24530248, 24730220, 15H03349,
15H05728, and 15K17060, and the program of the Joint Usage/Research Center for ‘Behavioral Economics’ at ISER, Osaka University. The usual disclaimer applies.
†
Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto, Kyoto 603-8555, Japan.
Email: hiroshikitamura@cc.kyoto-su.ac.jp‡
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. Email:nmatsush@iser.osaka-u.ac.jp§
Department of Economics, The George Washington University, 2115 G street, NW Monroe Hall 340 Washington DC
20052, USA. Email: smisato@gwmail.gwu.edu

1Introduction

Among contracts concerned with vertical restraints (e.g., exclusive contracts, loyalty rebates, slotting
fees, resale price maintenance, quantity fixing, and tie-ins),1 exclusive contracts have long been controversial2 because once signed, such contracts can deter efficient entrants. Thus, such contracts seemto be anticompetitive—a view opposed by the Chicago School. For instance, by constructing a modelwith an exclusive contract between an upstream incumbent and a downstream buyer, Posner (1976)
and Bork (1978) argue that the rational buyer does not sign such a contract to deter a more efficiententrant.3 In a rebuttal of the Chicago School argument, post-Chicago economists indicate specific circumstances under which anticompetitive exclusive dealings occur.4 By extending the Chicago School
argument’s single-buyer model to a multiple-buyer model, these studies introduce scale economies,
wherein the entrant needs a certain number of buyers to cover fixed costs (Rasmusen, Ramseyer, andWiley, 1991; Segal and Whinston, 2000a) and competition between the buyers (Simpson and Wickelgren, 2007; Abito and Wright, 2008).
Although these studies investigate cases in which an upstream incumbent makes exclusive offers
to downstream firms, in real business situations, downstream firms offer exclusive supply contracts to
upstream firms. An example of the relationship between an input supplier and final good producer iswhen the U.S. Federal Trade Commission (FTC) stopped a large-scale pharmaceutical company fromenforcing 10-year exclusive supply agreements for an essential ingredient.5 The FTC also exemplified
the relationship between a final goods producer and retailers when it stopped an established toy retailer
from preventing toy manufacturers from selling to warehouse clubs.6 More recently, the Japan Fair
1See, for example, Rey and Tirole (1986), Rey and Vergé (2010), and Asker and Bar-Isaac (2014). See also Rey and
Tirole (2007) and Rey and Vergé (2008) for surveys of vertical restraints.
2
Exclusive dealing agreements take various forms such as exclusive territories and rights (see, for instance, Mathewson
and Winter, 1984; Rey and Stiglitz, 1995; Matsumura, 2003).
3
For discussions on the impact of the Chicago School argument on antitrust policies, see Motta (2004) and Whinston(2006).
4
In an early contribution, Aghion and Bolton (1987) propose a model in which exclusion does not always occur, althoughwhen it does, it is anticompetitive. See also Bernheim and Whinston (1998), who explore market circumstances under which
an exclusive contract excludes rival incumbents.
5
FTC v. Mylan Laboratories, Inc., Cambrex Corporation, Profarmaco S.r.l., and Gyma Laboratories of America, Inc.,
No.X990015-1 (http://www.ftc.gov/os/caselist/x990015ddc.shtm).
6
Toys“R”Us, Inc., v. FTC, No.98-4107 (http://www.ftc.gov/os/adjpro/d9278/toyrus.pdf). Another antitrust case
was The Garment District, Inc., v. Belk Stores Service, Inc., Mathews-Belk Company, Jantzen, Inc., No.85-2362

1

Trade Commission stopped an online gaming company from preventing mobile game developers fromproviding their games through a rival online gaming company.7 Thus, this study aims to ascertain theexistence of anticompetitive exclusive supply contracts that prevent an upstream supplier from selling
inputs to a new downstream entrant.
This study constructs a model of anticompetitive exclusive supply contracts by inverting the vertical relationship in the Chicago School argument. The model comprises an upstream supplier anddownstream incumbent. However, a new downstream firm, which needs input produced by the upstream supplier, arrives as an entrant. The incumbent then offers an exclusive supply contract to the
upstream supplier, as in the standard models for anticompetitive exclusive dealing. If the contract isachieved, then the new entrant cannot enter the market.
In the standard model setting above, we consider an efficiency measure to evaluate the efficiencyof the incumbent and entrant downstream firms. We introduce the measure that the entrant is more
efficient than the incumbent in terms of the transformational technology of an input produced by
the upstream supplier; that is, the entrant demands a smaller quantity of inputs from the supplier toproduce one unit of final product. Thus, in terms of per unit production cost, the entrant is more efficient than the incumbent. The efficiency measure in this study, however, cannot be neglected because
economists have reported significant differences in producer productivity within industries. For example, Syverson (2004) finds large productivity differences even within narrowly defined industries in the
U.S. manufacturing sector. More specifically, using the same measured inputs, he finds that the outputof the plant at the 90th percentile of productivity distribution is almost twice that of the plant at the10th percentile.8 Importantly, the present model differs in not only relation to a market structure where
exclusion occurs, but also the efficiency measure of the incumbent and entrant. Previous studies on
anticompetitive exclusive contracts assume that the (exogenous) marginal cost of an upstream entrant
is lower than that of an upstream incumbent. However, these studies do not consider the efficiency
measure employed in our study, because they focus on entry deterrence in the upstream market.
(https://bulk.resource.org/courts.gov/c/F2/799/799.F2d.905.85-2362.html). See Comanor and Rey (2000) for detailed discussions.
7
See Cease and Desist Order against DeNA Co., Ltd (http://www.jftc.go.jp/en/pressreleases/yearly-2011/jun/individual000427.html.).
8
See Syverson (2011) for details on a related survey.

2

This study shows that when the entrant is efficient in terms of the transformational technology ofan input produced by the upstream supplier, the incumbent and upstream supplier can sign exclusive
supply contracts to deter a socially efficient entry even in the framework of the Chicago School argument, where a single seller, buyer, and entrant exist. More precisely, when the entrant and incumbent
have similar efficiency levels, exclusion never occurs; however, as the entrant’s efficiency increases,
exclusion can occur. To understand our results, consider the impact of a socially efficient entry fromthe viewpoint of the upstream supplier. A socially efficient entry generates downstream competition
and increases the final product output. This increases the demand for input produced by the upstream
supplier and, consequently, its profit. Thus, the demand expansion effect of a socially efficient entry
makes anticompetitive exclusive dealings difficult. However, as the entrant becomes increasingly efficient, it demands a smaller quantity of input produced by the upstream supplier. In addition, such an
entry decreases the market share of the downstream incumbent, which demands a larger quantity of
input produced by the upstream supplier.9 Therefore, as the entrant becomes efficient, its entry does
not lead to a significant increase in the demand for input produced by the upstream supplier; that is, theupstream supplier does not welcome the highly efficient entrant. This induces the upstream supplierto engage in anticompetitive exclusive dealings to deter a socially efficient entry into the downstream
market.
This study also shows that the relationship between the likelihood of exclusion and the entrant’s
efficiency is non-monotonic; that is, exclusion is more (less) likely to occur if the entrant’s efficiency
is at an intermediate (significantly high) level. When the entrant becomes sufficiently efficient, it canmonopolize the downstream market; in other words, the incumbent’s existence does not constrain theentrant’s pricing. Given this significant efficiency difference between the downstream firms, if theentrant’s efficiency increases further, the price of the final products decreases, and this leads to an
expansion of the downstream market, which benefits the upstream supplier. Therefore, exclusion isless likely to occur if the entrant has a significantly high level of efficiency.
In addition, this study shows that exclusion is more likely to occur if the upstream supplier’s
9

If the downstream firms compete in quantity, an improvement in the entrant’s efficiency gradually diminishes the downstream incumbent’s market share. If the downstream firms compete in price and their goods are perfect substitutes, thedownstream incumbent’s market share will be zero, that is, there is a drastic depression in its market share.

3

efficiency is high. The existence of an entrant with more efficient technology than the incumbent
not only decreases demand for input as well as the upstream supplier’s profits but also reduces the
production cost of the upstream supplier, which improves the supplier’s profits. However, this positiveeffect does not work well if the upstream supplier is highly efficient, and therefore, exclusion is more
likely to occur in this case.
Few studies do address anticompetitive exclusive supply contracts, notably, Comanor and Rey(2000) consider a market in which a single upstream supplier, a single downstream incumbent withexternal suppliers, and a single downstream entrant exist.10 They point out that the downstream incumbent’s outside option to buy inputs is a key factor in the emergence of anticompetitive exclusive
supply agreements when each downstream firm offers a purchase (wholesale) price and then the upstream supplier chooses the higher one. Because the outside option diminishes the downstream incumbent’s incentive to offer a higher purchase price, the efficient downstream entrant does not offer ahigher purchase price either. Therefore, the upstream supplier cannot earn higher profits even whena socially efficient downstream entry occurs, which induces the upstream supplier to engage in anticompetitive exclusive dealings. By contrast, the present study does not consider the downstream
incumbent’s outside option but explores how a difference in downstream firms’ technology affects
anticompetitive exclusive supply agreements.
This study is also related to the literature on anticompetitive exclusive dealings to deter upstream
entrants.11 Fumagalli and Motta (2006) propose an extension of Rasmusen, Ramseyer, and Wiley(1991) and Segal and Whinston’s (2000a) model wherein buyers are competing firms.12 They show
10
Recently, by inverting the vertical relationship analyzed by Simpson and Wickelgren (2007) and Abito and Wright(2008), Oki and Yanagawa (2011) show that upstream competition induces upstream suppliers to sign exclusive supply
contracts, forcing upstream suppliers into always earn low profits.
11
Certain studies examine pro-competitive exclusive dealings. Marvel (1982); Besanko and Perry (1993); Segal andWhinston (2000b); de Meza and Selvaggi (2007); and de Fontenay, Gans, and Groves (2010) investigate the role of exclusive
dealings in encouraging non-contractible investments. Chen and Sappington (2011) study the impact of exclusive contracts
on an industry’s R&D and welfare. Fumagalli, Motta, and Rønde (2012) examine the interaction between pro-competitive
and anticompetitive effects and show that the investment promotion effect of exclusive dealing may facilitate anticompetitive
exclusive dealing. In addition, Argenton and Willems (2012) analyze the trade-off between the positive (risk sharing) andnegative (exclusion) effect of exclusive contracts. Calzolari and Denicolò (2013) explore the pro-competitive effects of
exclusive contracts in an adverse selection model, in which differentiated firms compete in non-linear prices. Anothermotivation to consider exclusive dealing is to solve the commitment problem, as suggested by Hart and Tirole (1990), whicharises when a single upstream firm sells to multiple retailers with two-part tariffs under unobservable contracts. See also
O’Brien and Shaffer (1992), McAfee and Schwartz (1994), and Rey and Vergé (2004).
12
Fumagalli and Motta (2008) also show that exclusion with scale economies arises because of coordination failure among4that intense downstream competition reduces the possibility of exclusion. However, Simpson andWickelgren (2007) and Abito and Wright (2008) point out that this result depends on the assumptionthat buyers are undifferentiated Bertrand competitors who need to incur epsilon participation fees tostay active. They show that if buyers are differentiated Bertrand competitors, then intense downstream
competition enhances exclusion even in the presence of epsilon participation fees.13 Wright (2008)
and Argenton (2010) explore the extended models of exclusion with downstream competition where
the incumbent and a potential entrant, respectively, produce a horizontally and vertically differentiatedproduct. Both studies show that the resulting exclusive dealing is anticompetitive.14 Although thesestudies have similar motivations, none of them discusses the possibility of exclusion in the downstream
market.
The remainder of this paper is organized as follows. Section 2 constructs the basic environment of
the model. Section 3 analyzes the case where downstream firms compete in price. Section 4 provides
a discussion and Section 5 offers concluding remarks. In Appendix A, we present the proofs of results
under price competition, and in Appendix B, we analyze the case where downstream firms compete inquantity. Appendix C is an analysis of the case where industry profits are allocated by bargaining.

2

Preliminaries

This section develops the basic environment of the model. In Section 2.1, we explain the basic characteristics of players in the model and in Section 2.2, we introduce the timing of the game. In Section
2.3, we present the design of exclusive supply contracts. For convenience, we consider the relationshipbetween input suppliers and final good producers, although this model is suitable for a more generalapplication; for example, the model can be applied to the relationship between final good producers
buyers even when the incumbent does not have a first-mover advantage in making exclusive offers. Doganoglu and Wright(2010) explore exclusion in the presence of network externalities, an example of scale economies.
13
See also Wright (2009), who corrects Fumagalli and Motta’s (2006) result in the case of two-part tariffs.
14
Kitamura (2010, 2011) also explores the extended model—first, in the presence of multiple entrants, and next, withfinancial constraints. Johnson (2012) extends the models in the presence of adverse selection. Kitamura, Sato, and Arai(2014) explore the model when the incumbent can establish a direct retailer. DeGraba (2013) extends the models where asmall rival that is more efficient at serving some portion of the market can make exclusive offers. These studies show thatthe resulting exclusive dealings are anticompetitive. In contrast, Gratz and Reisinger (2013) show that exclusive contracts
can possibly have pro-competitive effects if downstream firms compete imperfectly and contract breaches are possible.

5and retailers.

2.1

Upstream and downstream markets

The downstream market is composed of an incumbent DI and entrant DE . Each of them produces aunit of final product using an input exclusively produced by an upstream supplier U. For this supplier,the marginal cost is c ≥ 0 and w is the wholesale price of the input offered.
Downstream firms differ in production technology. DI produces a unit of final product using one
unit of input. The transformational technology is denoted by
QI = qI ,where QI (qI ) is the amount of output (input) for DI . The per unit production cost of DI , cI , is denotedbycI = w.

(1)

In contrast, DE produces a unit of final product using k units of input, where k is a positive constant.
The transformational technology is denoted by
QE = qE /k,where QE (qE ) is the amount of output (input) for DE . The per unit production cost of DE , cE , isdenoted bycE = kw.

(2)

Equation (2) implies that DE becomes efficient (that is, the per unit cost of DE decreases) as k decreases. We assume that 0 < k < 1. Comparing (1) with (2) clearly shows that DE is more efficientthan DI in terms of per unit production cost.
There are two interpretations of this assumption. First, between an input supplier and final good
producers, entrant producer DE has the efficient technology that allows it to reduce the use of input or
defective products. Second, between a final good producer and retailers, entrant retailer DE is betterat supply-chain management than the incumbent, because of which it need not hold excess inventories
of final products produced by final good producer U.
6

The efficiency measure of downstream firms in this study differs from those in previous studies on
anticompetitive exclusive dealing. Those previous studies do not focus on differences in the transformational technology of input, because they explore the existence of entry deterrence in the upstream
market. If competitive sectors supply inputs for the upstream firms, the difference in the transformational technology of inputs causes a qualitatively similar difference in their constant marginal costs,
the latter of which is usually assumed in the previous studies, and more importantly, the possibilityof exclusion does not depend on these efficiency measures. In contrast, this study shows that if we
focus on the existence of entry deterrence in the downstream market, the difference in the transformational technology of input produced by the upstream supplier is an important efficiency measure fordownstream firms.15

2.2

Timing of the gameThe timing of the game is as follows (Figure 1). The model consists of four stages. In Stage 1, DI
offers an exclusive supply contract to U. This contract involves some fixed compensation x ≥ 0.
U decides whether to accept this offer. In Stage 2, DE decides whether to enter the downstream
market. We assume that the fixed cost of entry f (> 0) is sufficiently small, such that if DE is active,
it could earn positive profits. In Stage 3, U offers a linear wholesale price of input, w, to the active
downstream firm(s). There are two cases (see Figure 2). If U accepts the exclusive supply offer inStage 1, then it offers input price wa only to DI ; the superscript a indicates that U has accepted theoffer. In contrast, if U rejects the exclusive supply offer in Stage 1, then it offers input price wr to all
active downstream firms; the superscript r indicates that U has rejected the offer. We assume that U
cannot offer different wholesale prices to downstream firms (In Section 4, we discuss the case wheresuch price discrimination is possible.). In Stage 4, active downstream firms order input and compete
in the final market. If an entry arises in Stage 2, then DI and DE compete. DI ’s profit when U accepts(rejects) the exclusive offer is denoted by πaI (πrI ) and U’s profit when it accepts (rejects) the exclusive
offer is denoted by πaU (πrU ).
15

In Section 4.3, we briefly provide the discussion on the efficiency measure of downstream firms.

7

2.3

Design of exclusive supply contracts

Given the equilibrium outcomes in the subgame following Stage 1, we derive the essential conditions
for an exclusive supply contract. For an exclusion equilibrium, the equilibrium transfer x∗ must satisfy
the following two conditions.
First, it must satisfy the individual rationality for DI ; that is, DI must earn higher operating profits
under exclusive dealing, such that
πaI − x ≥ πrI .

(3)

Second, it must satisfy the individual rationality for U; that is, the compensation amount x must
induce U to accept the exclusive supply offer because
x + πaU ≥ πrU .

(4)

From the above conditions, it is easy to see that an exclusion equilibrium exists if and only if
inequalities (3) and (4) hold simultaneously. This is equivalent to the following condition:
πaI + πaU ≥ πrI + πrU .

(5)

Condition (5) implies that for the existence of anticompetitive exclusive supply contracts, we must
examine whether exclusive supply agreements increase the joint profits of DI and U. Therefore, theexistence of exclusion equilibria does not depend on who makes the offer; in other words, the results
do not change even if we allow U to make the exclusive supply offer.

3

Price Competition

This section considers the existence of anticompetitive exclusive dealings to deter the socially efficient
entry of DE when downstream firms are undifferentiated Bertrand competitors. We assume that ageneral demand function Q(p) is continuous and Q0 (p) < 0. Further, we assume that demand from
Di , where i ∈ {I, E}, depends on not only its price but also that of D−i ’s price. The quantity that
consumers demand from Di is Q(pi ) when pi < p−i and 0 when pi > p−i . When pi = p−i , thedownstream firm with the lower per unit production cost supplies the entire quantity Q(pi ).16 For
16

This assumption avoids open-set problems when defining equilibria. See, for example, Abito and Wright (2008).

8

notational convenience, we define p∗ (z) and Π∗ (z) as follows:p∗ (z) ≡ arg max(p − z)Q(p),p(6)Π∗ (z) ≡ (p∗ (z) − z)Q(p∗ (z)),
where z ≥ 0. As often assumed in industrial organization literature, we assume that the second-ordercondition is satisfied.
Assumption 1. The following inequality is satisfied:
2Q0 (p) + (p − z)Q00 (p) < 0.
We first consider the case where U accepts the exclusive offer in Stage 1. In this case, it can supply
only to DI . Given input price wa , DI optimally chooses paI (wa ) = p∗ (wa ) in Stage 4. By anticipating
this pricing, U sets the input price for DI to maximize its profit in Stage 3.
wa = arg max(w − c)Q(p∗ (w)).
w(7)

We assume that the second-order condition is satisfied. Because we have wa > c in the equilibrium,
the equilibrium price level p∗ (wa ) does not maximize the joint profits of DI and U; that is, the double
marginalization problem occurs.
πaI + πaU = (p∗ (wa ) − c)Q(p∗ (wa )) < Π∗ (c).

(8)

Although the entry deterrence allows DI to earn higher operating profits, DI and U cannot maximize
their joint profits owing to the double marginalization problem.
We next consider the case where U rejects the exclusive supply offer in Stage 1. In this case, DE
enters the downstream market in Stage 2. In Stage 4, given the input price wr , the downstream firms
compete in price. DI earns zero profits in this subgame; that is, πrI = 0 for all 0 < k < 1. In addition,
downstream competition leads to two types of equilibria in Stage 4. The undifferentiated Bertrand
competition leads to the following outcomes:
r(i)
r
r
∗
r
r
Case (i) DI offers pr(i)I = w and DE offers pE = w if p (kw ) ≥ w .

9

∗
r
∗
r
r
Case (ii) DI offers pr(ii)= wr and DE offers pr(ii)I
E = p (kw ) if p (kw ) ≤ w .

In Case (i) (if p∗ (kwr ) ≥ wr ), the marginal cost pricing of DI binds the pricing of DE , which leads to
r
∗
r
r
pr(i)
E = w . In Case (ii) (if p (kw ) ≤ w ), the marginal cost pricing of DI does not bind the pricing of∗r
DE , which leads to pr(ii)E = p (kw ).

By anticipating this pricing in Stage 4, U optimally chooses its input price in Stage 3. Notethat for each case, we have a unique interior solution; that is, we have wr(i) ∈ [c, ∞) and wr(ii) ∈[c, ∞). However, each interior solution must satisfy the constraints (wr(i) ∈ [c, p∗ (wr (k))] and wr(ii) ∈[p∗ (wr (k)), ∞)), where wr (k) is the input price satisfyingp∗ (kwr (k)) = wr (k)for each k and is the threshold value at which the mode in Stage 4 changes from Case (i) to Case (ii). In
the rest of this section, we first characterize the properties of each interior solution in the full domain[c, ∞) in Lemmas 1 and 2. We then consider the constraints of each interior solution in Lemma 3 andfinally, characterize the properties of U’s profit in Lemma 4.
From here on, we characterize each interior solution in the full domain [c, ∞). First, in Case (i), U
faces its input demand
r(i)
r
qr(i)
E = kQ(pE ) = kQ(w ).

(9)Given this input demand, U optimally chooses input price wr(i) ≡ arg maxwr k(wr − c)Q(wr ) in Stage
3. With the maximization problem, the profit of U is as follows:πr(i)k(wr − c)Q(wr ) = kΠ∗ (c).
U = max
r
w

(10)

∗
Note that when k = 1, πr(i)U = Π (c), which implies that DE ’s entry allows U to earn profits equivalent

to the maximized value of the joint profits of U and DI . From equations (8) and (10), we identify thefollowing properties.
r(i)Lemma 1. Under the interior solution wr(i) ∈ [c, ∞), πU
has the following properties:

1. πr(i)U is strictly increasing in k but decreasing in c.
∗aa2. As k → 1, πr(i)U → Π (c), which is strictly larger than πI + πU .

10

3. As k → 0, πr(i)U → 0.
Second, in Case (ii), U faces its input demand qr(ii)= kQ(p∗ (kwr )). Given this input demand, U
Esets an input price to maximize its profit in Stage 3:πr(ii)(wr − c)kQ(p∗ (kwr )) = max wQ(p∗ (w)) − kcQ(p∗ (w)) .
U = max
r
w

w

(11)

From equations (7) and (11), we identify the following properties.
Lemma 2. Under the interior solution wr(ii) ∈ [c, ∞), πr(ii)U has the following properties:
1. πr(ii)
U is strictly decreasing in k and c.
r(ii)2. As k → 1, πU→ πaU .
r(ii)
3. For any c ≥ 0, as k → 0, πU→ πaU |c=0 .
a
4. For c = 0, πr(ii)U = πU |c=0 ,where πaU |c=0 is U’s profit level under the standard double marginalization problem when c = 0 (seeequation (7)).
We now characterize these two equilibria on two domains, [c, wr (k)] and [wr (k), ∞). The following
lemma shows that at least one interior solution exists for all 0 < k < 1.
Lemma 3. For Cases (i) and (ii), at least one of the following holds, wr(i) ∈ (c, wr (k)) or wr(ii) ∈(wr (k), ∞).
r(ii)r(i) = wr(ii) = wr (k), we can conclude that one of the aboveBecause we have πr(i)U = πU for w

mentioned interior solutions becomes U’s optimal solution in equilibrium. Therefore, exclusion ispossible regardless of equilibrium type if we haver(ii)πaI + πaU > max πr(i)U , πU .
 r(i) r(ii)The following lemma characterizes the properties of max πU, πU .
r(ii)Lemma 4. max πr(i)has the following properties.
U , πU
11(12)

1. It is strictly decreasing in c.
2. Its functional form is V-shaped with respect to k; that is, there exists a minimized value k0 ∈(0, 1). More precisely, we have
 r(ii)π U
 r(i) r(ii)max πU , πU = πr(i)
U

if 0 < k ≤ k0 ,if k0 < k < 1.

r(ii)Figure 3 summarizes the property of max πr(i)U , πU . Note that the equilibrium outcome whenthe exclusive supply offer is accepted does not depend on k (see equation (8)). Therefore, exclusion ispossible if condition (12) holds for k = k0 .
By combining the above arguments, we have the following proposition:
Proposition 1. Suppose that the downstream firms are undifferentiated Bertrand competitors.
1. For k∗ ≤ k < 1, entry is a unique equilibrium outcome, wherek∗ ≡πaI + πaU.
Π∗ (c)

2. For k < k∗ , the possibility of exclusion depends on the efficiency of U.
(a) When U is sufficiently efficient, 0 ≤ c < c̃, exclusion is possible for 0 < k < k∗ , where c̃ isthe threshold value such that πaU c=0 = πaI + πaU .
(b) When U is not too efficient, c̃ ≤ c, exclusion is possible for 0 < k00 < k < k∗ if there existsaak00 < k∗ that satisfies πr(ii)U = πI + πU .

This proposition implies that the possibility of exclusion depends on not only DE ’s efficiency but
also that of U. To clarify the property of Proposition 1, we show the results in Proposition 1 underlinear demand, Q(p) = (a − p)/b, where a > c and b > 0.
Remark 1. Under linear demand, the exclusion of the highly efficient DE (k < 3/4) occurs if U issufficiently efficient (c < 0.18a is sufficient). More precisely,
1. for 3/4 ≤ k < 1, entry is a unique equilibrium outcome, and12

2. for 0 < k < 3/4, exclusion is a unique equilibrium outcome if U is sufficiently efficient, that is,0 ≤ c < Ĉ(k), where√
6−2Ĉ(k) = √.
(13)
6 − 2k√√Note that ∂Ĉ(k)/∂k > 0, Ĉ(k) → a(3 − 6)/3 ' 0.1835a as k → 0, and Ĉ(k) → 2a(6 − 6)/15 'a0.4734a as k → 3/4.
Figure 4 summarizes the result in Proposition 1 under linear demand. Under linear demand, we have√√k∗ = 3/4, k00 = (2a − (a − c) 6)/2c, and c̃ = (3 − 6)a/3 ' 0.1835a. In Appendix B, we explore
the case where downstream firms compete in quantity and show that exclusion may arise even whenk > 3/4. Note that condition (12) is a sufficient condition. Therefore, there may exist an exclusion
equilibrium even when condition (12) does not hold. Remark 1 shows such a possibility.
The result in Proposition 1 contrasts those in the literature on anticompetitive exclusive dealings.
In the previous literature, as the entrant becomes efficient, firms are unlikely to engage in anticompetitive exclusive dealings. By contrast, in this study, anticompetitive exclusive dealings are likely
to be observed as the entrant becomes efficient. In other words, an exclusive contract works like theLuddites.17
The result in Proposition 1 is derived from the negative relationship between DE ’s efficiency andinput demand. Equation (9) implies that the demand for input decreases as DE becomes efficient (oras k decreases) in Case (i). The socially efficient entry of DE generates two effects. First, DE ’s entry
generates downstream competition and increases the production level of final goods. This expands thedemand for input and increases U’s profit. Second, contrarily, DE ’s entry decreases DI ’s market share
but increases its own market share—note that DE demands a smaller amount of input unlike DI . This
reduces the total input demand, and hence, U’s profit. Therefore, the entry of the highly efficient DE
increases the profit of U only slightly. This allows DI to profitably compensate the upstream supplier’s
profit when such an entry occurs by using its monopoly profits under exclusive dealing.
However, Figure 4 also shows that the relationship between the likelihood of exclusion and DE ’s
efficiency is non-monotonic; that is, exclusion is more (less) likely to be observed for the intermediate
17See, for example, Hobsbawm (1952) and Mokyr (1992).

13

(significantly high) level of DE ’s efficiency. When DE becomes sufficiently efficient, the equilibriumoutcome under entry becomes Case (ii) and DE can monopolize the downstream market. In Case(ii), the existence of DI does not work as a constraint on DE ’s pricing and a further improvementin DE ’s efficiency decreases the price of final products, which then expands the production level ofDE and the input demand. Therefore, as equation (11) implies, for the significantly higher level of
DE ’s efficiency, U welcomes an improvement in DE ’s efficiency. This decreases the possibility ofanticompetitive exclusion.
In addition, note that Figure 4 implies that the possibility of anticompetitive exclusive dealings depends on U’s efficiency: as U becomes inefficient, the possibility of anticompetitive exclusive supply
agreements decreases. Equation (11) implies that in Case (ii), DE ’s efficient transformational technology reduces U’s production cost, which improves the latter’s profit. As U becomes less efficient,
the benefit of such cost reduction increases for U, which decreases the possibility of anticompetitive
exclusive supply agreements.

4

Discussion

This section briefly discusses the wholesale pricing of input and efficiency of downstream firms. Section 4.1 extends the analysis by allowing price discrimination by the upstream supplier. Section 4.2
discusses two-part tariff contracts and the plausibility of employing linear wholesale pricing. Section
4.3 elaborates on the efficiency measure of downstream firms.

4.1

Price discrimination

Thus far, we assumed that U charges downstream firms a uniform price wr . This subsection discusses
how the results in Section 3 change if U is able to discriminate on price when DE enters the downstream market. Then, if U chooses input prices wri for Di , where i ∈ {I, E}, the per unit costs of DI and
DE are denoted by wrI and kwrE .
Consider the case where U rejects the exclusive supply offer in Stage 1 and DE enters the downstream market in Stage 2. In Stage 4, given the input prices set in Stage 3, undifferentiated Bertrand
competition occurs, which leads to monopolization by the downstream firm with a lower per unit cost.

14

In equilibrium, U optimally chooses a pair of input prices (wrI , wrE ), such that wrI = kwrE = p∗ (kc) inStage 3, and earns πrU = (wrE − c)kQ(wrI ) = (p∗ (kc) − kc)Q(p∗ (kc)) = Π∗ (kc). This implies that if
supplier U can discriminate on price, then it can jointly maximize profits with DE and earn all profits
even under linear pricing. In contrast, downstream firms earn zero operating profits. This result implies that price discrimination induces DE not to cover a fixed cost f > 0, and DE does not enter thedownstream market in Stage 2 even when U rejects the exclusive supply offer in Stage 1. Therefore,
when price discrimination is possible, there is a price commitment problem; that is, U is unable toinitially commit to an input price offer that allows DE to cover the fixed cost.18
Proposition 2. Suppose that the downstream firms are undifferentiated Bertrand competitors. When
U is allowed to discriminate on price, exclusion is a unique equilibrium outcome if U cannot commit
to input prices before the entry decision of DE .
To avoid the commitment problem, naturally, U tries to commit to input prices before DE makes
its entry decision. To consider this case, we change the timing of the games as follows. In Stage 2, U
makes input price offers and can commit to these prices. In Stage 3, DE makes its entry decision. We
also assume that the fixed cost of entry f is not too large such that U welcomes the entry of DE .
Assumption 2. The fixed cost of entry satisfies the following condition:
0 < f < Π∗ (kc) − (wa − c)Q(p∗ (wa )).

(14)

If condition (14) does not hold, U does not induce DE to enter the downstream market because it
earns higher profits by trading with DI . Thus, DE does not enter the downstream market.
Note that the timing change does not affect the equilibrium outcomes for the case where U accepts
the exclusive supply offer in Stage 1. However, the difference arises in the case where U rejects the
exclusive supply offer in Stage 1. In Stage 2, U optimally chooses a pair of input prices (wrI , wrE ), suchthat wrI = p∗ (kc) and wrE = wrI /k − f /kQ(wrI ), and earns
πrU = (wrE − c)kQ(wrI ) = (p∗ (kc) − kc)Q(p∗ (kc)) − f = Π∗ (kc) − f.
18
When downstream firms compete in quantity, joint profit maximization is impossible and DE earns a positive profit,
which is lower than that when U employs a uniform price. The result in this section is qualitatively similar to that of thecase in which they compete in quantity.

15

In contrast, downstream firms earn zero profits. By comparing such profits with the joint profit with
DI when U accepts the exclusive supply offer (8), it is easy to see that condition (5) holds for thesufficiently large fixed cost of entry f . For the upper bound value of f in condition (14), U is indifferent
between trading DE with fixed cost compensation and DI without the invitation of DE ; namely, theright-hand side of condition (5) becomes πrI + πrU = Π∗ (kc) − f = (wa − c)Q(p∗ (wa )) = πaU < πaI + πaU .
The last inequality holds because DI earns a positive profit πaI > 0 whenever DE does not exist. Thisimplies that f exists, which simultaneously satisfies conditions (5) and (14).
Proposition 3. Suppose that the downstream firms are undifferentiated Bertrand competitors. In
addition, suppose that U can commit to input prices before the entry decision, such that DE always
enters the market if the exclusive supply offer is rejected. When U is allowed to discriminate on price,
an exclusion equilibrium is possible if the fixed cost of entry is sufficiently large.
1. For 0 < f < f ∗ , entry is a unique equilibrium outcome, wheref ∗ = Π∗ (kc) − (p∗ (wa ) − c)Q(p∗ (wa )).

(15)

2. For f ∗ ≤ f < Π∗ (kc) − (wa − c)Q(p∗ (wa )), exclusion is a unique equilibrium outcome.
Note that for f = f ∗ , the producer surplus in the exclusion outcome and entry outcome coincide;
πaU + πaI + πaE = πrU + πrI + πrE − f ∗ . However, the consumer surplus under the entry outcome isstrictly higher because the entry of DE increases the output of final product Q by solving the double
marginalization problem. Therefore, there exists the fixed cost f (> f ∗ ), under which the entry of DE
is socially efficient but deterred by anticompetitive exclusive supply contracts.
Moreover, note that the exclusion outcome in Proposition 3 can be observed for all 0 < k < 1
and c ≥ 0. Hence, the mechanism for exclusion is different from that in Section 3. The results here
can be explained using the feature of U’s outside option when it rejects the exclusive supply offer.
When U invites DE ’s entry, price discrimination allows U to jointly maximize profits with DE , whichapparently makes exclusion difficult. However, when U trades with DI , instead of inviting DE , linear
pricing prevents U from not only maximizing the joint profits with DI but also extracting all of them.
Hence, even for a large fixed cost of entry, U has an incentive to invite DE , which induces U to earn16lower profits when the exclusive offer is rejected. Therefore, there is a room for DI to profitablycompensate U with the exclusive supply offer for the sufficiently large fixed cost, f .
The results here provide several implications for antitrust agencies. First, when we consider pricediscrimination under an exclusive supply agreement, the possibility of exclusion is sensitive to the
fixed cost. Because price discrimination allows upstream firms to easily extract downstream firms’
operating profits, downstream entry is less likely if an upstream supplier is unable to commit to input
prices. More importantly, even when the upstream supplier can commit to input prices, anticompetitive exclusive supply agreements occur to cover a large fixed cost. Therefore, the model predicts
that exclusive supply agreements are more likely to be observed in industries with large fixed costs,
which supports the finding in Rasmusen, Ramseyer, and Wiley (1991), who show that anticompetitive
exclusive dealing occurs if the entrant faces scale economies.
Second, the results in Proposition 3 regarding smaller fixed costs of entry and the result in Section 3
imply that for a smaller fixed cost, anticompetitive exclusive supply agreements occurs under uniform
pricing and not price discrimination. This provides an important insight that the imposition of uniform
pricing induces the exclusion of an efficient entrant through an exclusive supply contract offered byan inefficient incumbent. That is, a ban on price discrimination, such as the famous Robinson–Patman
Act, can protect smaller or otherwise weaker competitors. We believe that the result confirms themain results in Inderst and Valletti (2009), which shows that the ban on price discrimination in input
markets benefits smaller firms but hurts more efficient, larger downstream firms when downstream
firms engage in cost-reducing activities. Therefore, we conclude that this study shows an alternate
manner in which a ban on input price discrimination harms market environments.

4.2

Two-part tariff and linear wholesale pricing

We assumed that U charges downstream firms linear pricing contracts. We briefly discuss how theresults in Section 4.1 change if U is able to adopt two-part tariffs and make take-it-or-leave-it offers.
Then, we briefly mention the plausibility of employing linear wholesale pricing.
Like discrimination on linear pricing, two-part tariffs allow U to jointly maximize profits with DEand earn all profits when U rejects the exclusive offer. Therefore, a commitment problem still exists.

17

Proposition 4. Suppose that the downstream firms are undifferentiated Bertrand competitors. When U
adopts two-part tariffs and makes take-it-or-leave-it offers, exclusion is a unique equilibrium outcome
if U cannot commit to input prices before the entry decision of DE .
By contrast, suppose that U can overcome the commitment problem. Then, like price discrimination on linear pricing, when U rejects the exclusive supply offer, it earns Π∗ (kc) − f . However,unlike price discrimination on linear pricing, when U accepts the exclusive supply offer, it can jointly
maximize profits with DI and earn all of Π∗ (c), which implies that DI earns nothing even when it
trades with U; namely, condition (14) is changed to
0 < f < Π∗ (kc) − Π∗ (c).

(16)

On comparing conditions (14) and (16), it is easy to see that U does not compensate DE for thelarger fixed cost of entry f when U adopts two-part tariffs and makes take-it-or-leave-it offers. More
importantly, condition (16) can be rewritten as Π∗ (c) = πaI + πaU < πrI + πrU = Π∗ (kc) − f , which implies
that condition (5) never holds. Therefore, an exclusion equilibrium does not exist.
Proposition 5. Suppose that the downstream firms are undifferentiated Bertrand competitors. WhenU adopts two-part tariffs and makes take-it-or-leave-it offers, entry is a unique equilibrium outcome
if U can commit to input prices before the entry decision of DE .
Note that this result highly depends on the assumption that U makes take-it-or-leave-it offers,
which allows U to earn all the joint profits with DI when it trades with DI by not committing to its
contract term. In Appendix C, we explore the case where industry profits are allocated by bargaining
and show that like price discrimination on linear pricing, there exists an exclusion equilibrium evenwhen U can overcome the commitment problem.
From the above discussions, we can conclude that this study is most suitable for a discussion on
the anticompetitiveness of exclusive supply agreements in industries where upstream firms employ
simple linear pricing contracts. This subsection provides real-world examples of such industries. For
example, linear pricing contracts are common in gasoline retailing and shipping industries (Lafontaine
and Slade, 2013), and sometimes, employed in manufacturing industries, although non-linear pricing
18contracts are useful in vertical coordination (Blair and Lafontaine, 2005; Nagle and Hogan, 2005).
Even in terms of franchise contracts, franchisors face several problems in using franchise fees (fixed
payments) as their means of compensation; for instance, the wealth constraints of franchisees andfranchisor opportunism with a lump-sum fee (Blair and Lafontaine, 2005).19 Finally, in the context oflicensing agreements, licenses are often subject to fair, reasonable, and non-discriminatory (FRAND)
commitments, which often require that every licensee be able to choose from the same royalty schedule(Gilbert, 2011). Layne-Farrar and Lerner (2011, p.296) mention that licensees pay the patent pooladministrator either a percentage of their net sales revenue from selling the licensed product or a flatfee per unit sold. Gilbert (2011) also mentions real-world examples of licensing terms subject to
FRAND commitments and linear pricing contracts.20
Furthermore, some economists have empirically found the presence of the double marginalization
problem, which implies that the joint profit maximization is difficult in a real business situation (Parkand Lee, 2002; Gayle, 2013). Therefore, when we apply the model of exclusive contracts to a realbusiness situation, the results for linear pricing that generates the double marginalization problem
cannot be neglected.

4.3

Efficiency measure

We assumed that DE is more efficient than DI in terms of transformational technology of an input
produced by U; that is, DE demands a smaller quantity of inputs from U to produce one unit of final
product. However, as commonly used in the literature, we consider the following efficiency measure
to evaluate the efficiency of downstream firms: DE is more efficient than DI in terms of its per unit
production cost for several inputs, such as labor, which are not produced by U. For example, suppose
downstream firms produce final products using input A that is exclusively supplied by U A at price wA
and input B supplied by competitive sectors at price cB ≥ 0. Then, we can assume that DI produces aunit of final product using one unit of input A and one unit of input B but DE produces a unit of final
19
As also documented in Iyer and Villas-Boas (2003, p.81), in practice, both the magnitude and incidence of two-part tariffs may be insignificant. Milliou, Petrakis, and Vettas (2009) provide a theoretical reason to employ linear pricing contracts.
In addition, Inderst and Valletti (2009) explain real-world examples in which linear pricing contracts are employed.
20
Following these real-world observations, Tarantino (2012) considers standard-setting organizations’ decisions on licensing policy with linear pricing and the standard’s technological specifications.

19

product using one unit of input A and 0 < m < 1 unit of input B:
cI = wA + cB , cE = wA + mcB .
Under this efficiency measure, we can show that DI cannot deter socially efficient entry using an exclusive supply contract (proof of this result can be made available upon request). That is, the difference
in measures to evaluate the downstream firms’ efficiency turns out to be crucial.

5

Concluding Remarks

This study examined anticompetitive exclusive supply agreements focusing on the transformational
technology of inputs. Previous studies have not differentiated between the incumbent and entrants
with regard to the transformational technology of input produced by the upstream supplier, because
they mainly analyzed entry deterrence in upstream markets. However, our study suggests that when
we focus on entry deterrence in downstream markets by considering exclusive supply contracts, thenthe difference in transformational technology of input can be an important market element.
We find that when the incumbent and entrant differ in transformational technology of input produced by the upstream supplier, the downstream incumbent and upstream supplier sign exclusive
supply contracts to deter socially efficient entry, even in the framework of the Chicago School argument, where a single seller, buyer, and entrant exist. In addition, the difference in transformational
technology of input produced by the upstream supplier changes the relationship between the entrant’s
efficiency and possibility of exclusion: anticompetitive exclusive supply agreements are more likely toarise if the entrant’s efficiency is at an intermediate level. These results provide new implications for
antitrust agencies: it is necessary to focus on the efficiency measure when discussing the anticompetitiveness of exclusive supply agreements. It may be possible to measure downstream firms’ efficiency
by checking the defective rate in relationships between an input supplier and final good producer andthe inventory rate in relationships between a final good producer and retailers.
We also find that exclusive supply agreements based on difference in transformational technology
are more likely to arise when upstream firms employ simple linear pricing contracts; price discrimination and two-part tariffs reduce the possibility of anticompetitive exclusive supply agreements. These20

results provide the following implications. First, exclusive supply agreements are more likely to beobserved in industries where linear pricing contracts are employed. Second, a ban on input price discrimination makes exclusion possible because such a ban enforces upstream firms to employ simple
linear pricing contracts.
Finally, we find that even when an upstream supplier adopts price discrimination and two-parttariffs, there remains a possibility of exclusion if the fixed cost of entry is large because these pricing
contracts allow the upstream supplier to easily extract downstream firms’ operating profits. Therefore,
exclusive supply agreements are more likely to be observed in industries where downstream entry
requires large fixed costs.
However, several outstanding concerns require further research. First is this study’s relationshipwith other studies on anticompetitive exclusive dealings. For example, we assume that an upstream
supplier firm is a monopolist. Drawing on the results in Oki and Yanagawa (2011), we predict that
if we add upstream competition to our model, the likelihood of an exclusion equilibrium increases.
Second is the generality of our results. Although the analysis under quantity competition is presented
in terms of parametric examples, the result might be valid in more general settings. We hope this study
facilitates researchers in addressing these issues.

A

Proofs of Results

A.1: Proof of Results under General Demand
A.1.1 Proof of Lemma 3
We show that at least one interior solution exists in the profit maximization problems in Cases (i) and(ii) when the exclusive offer is rejected in Stage 1. For expositional simplicity, we replace wr (k) withw(k), which satisfies (see the last paragraph before Lemma 3)p∗ (kw(k)) = w(k).
The profit maximization problems of U in the two cases are given as
Case (i)max (w − c)kQ(w) s.t. w ∈ [c, w(k)],Case (ii)max (w − c)kQ(p∗ (kw)) s.t. w ∈ [w(k), ∞).

w

w

21

(17)

The first-order conditions are given as
Case (i)H (i) (w) ≡ Q(w) + (w − c)Q0 (w),Case (ii)H (ii) (w) ≡ Q(p∗ (kw)) + (w − c)kQ0 (p∗ (kw))p∗0 (kw).

Note that each maximization problem has a unique interior solution on domain [c, ∞). However, there
exists a possibility of a corner solution, where the problem in Case (i) has an interior solution on
domain [w(k), ∞) and the problem in Case (ii) has an interior solution on domain [c, w(k)]. In suchcases, U’s profit is maximized at the corner, w = w(k). We explore whether the corner solution problem
arises. Note that w(k) is the optimal input price if and only if H (i) (w(k)) > 0 and H (ii) (w(k)) < 0. We
show that the two inequalities do not simultaneously hold. More precisely, we show that H (ii) (w(k)) >0 if H (i) (w(k)) > 0.
Suppose that H (i) (w(k)) > 0, that is,
H (i) (w(k)) = Q(w(k)) + (w(k) − c)Q0 (w(k)) > 0.

(18)

Using equation (17), H (ii) (w(k)) can be rewritten as
H (ii) (w(k)) = Q(w(k)) + (w(k) − c)kQ0 (w(k))p∗0 (kw(k)).

(19)

To explore the above equation’s property, we need to derive p∗0 (z). The first-order condition of the
profit maximization problem (6) becomesQ(p∗ (z)) + (p∗ (z) − z)Q0 (p∗ (z)) = 0.
The total differential of this equation leads top∗0 (z) =Q0 (p∗ (z)).
2Q0 (p∗ (z)) + (p∗ (z) − z)Q00 (p∗ (z))

Using equations (17), (18), (19), and (20), we have the following relationship:
H (ii) (w(k)) > H (ii) (w(k)) − H (i) (w(k))(w(k) − c)Q0 (w(k)){2Q0 (p∗ ) + (p∗ − kw(k))Q00 (p∗ ) − kQ0 (p∗ )}=−2Q0 (p∗ ) + (p∗ − kw(k))Q00 (p∗ )0(w(k) − c)Q (w(k)){kQ0 (p∗ ) + (1 − k)[2Q0 (p∗ ) + p∗ Q00 (p∗ )]}=−> 0,
2Q0 (p∗ ) + (p∗ − kw(k))Q00 (p∗ )
22

(20)

where p∗ ≡ p∗ (kw(k)) = w(k). The last inequality holds because of Q0 (p) < 0 and Assumption 1.
From the above discussion, we have H (ii) (w(k)) > 0 if H (i) (w(k)) > 0. This implies that in Case(ii), an interior solution always exists on domain (w(k), ∞) if in Case (i), the interior solution does notexist on domain [c, w(k)] and the corner solution appears; that is, we always have wr(ii) ∈ (w(k), ∞) if
wr(i) = w(k). This also implies that at least one interior solution exists and there are three possibilities
concerning the optimal input price for U:
1. An interior solution exists only on domain (c, w(k)) in Case (i).
2. An interior solution exists only on domain (w(k), ∞) in Case (ii).
3. Interior solutions exist on domain (c, w(k)) in Case (i) and (w(k), ∞) in Case (ii).
In the first and second case, we have unique interior solutions. In the third case, we need to check
which of the interior solutions is optimal (The method to check this is provided in Section 3.).
Q.E.D.
A.1.2 Proof of Lemma 4
By Lemmas 1 and 2, the first statement in Lemma 4 holds. We prove the second statement. For a
r(i)
r(i)
r(ii)
sufficiently small k (as k → 0), we have πU< πr(ii)
U . However, for k = 1, we have πU > πU .
r(i)0Because πr(ii)U is strictly decreasing in k but πU is strictly increasing in k, there exists k ∈ (0, 1) suchr(ii)that πr(i)U = πU .

Q.E.D.
A.1.3 Proof of Proposition 3
Condition (5) holds if and only if f ≥ f ∗ . From equations (8) and (15), we haveΠ∗ (kc) − (wa − c)Q(p∗ (wa )) − f ∗ = (p∗ (wa ) − c)Q(p∗ (wa )) > 0.
Hence, there exists f > 0 that simultaneously satisfies conditions (5) and (14). Therefore, exclusion isa unique equilibrium outcome for f ∗ ≤ f < Π∗ (kc) − (wa − c)Q(p∗ (wa )).
Q.E.D.
23

A.2 Proof of Results under Linear Demand
A.2.1 Equilibria in subgames after Stage 1
We consider each of the possible subgames after Stage 1. In this appendix, we consider the caseof quantity competition. In A.2.1.1 and in A.2.1.2, we consider cases in which an exclusive offer is
accepted and rejected by the upstream supplier.
A.2.1.1 Exclusive offer is accepted in Stage 1
When the exclusive offer is accepted in Stage 1, the equilibrium demand level for input becomes
qa = QaI =

a−c
.
4b

Before compensation through x, the profits of U and DI are given as
πaU =(a − c)2(a − c)2, πaI =.
8b
16b

A.2.1.2 Exclusive offer is rejected in Stage 1
As we have seen in Section 3, there are two types of equilibria in the subgame after the exclusive offer
is rejected in Stage 1. We first solve each case on the full domain wr ∈ [c, ∞).
Consider Case (i). The profits of U and DI are given as
πr(i)
U =k

(a − c)2, πr(i)I = 0.
4b

Next, we consider Case (ii). Given w, DE chooses the following price.
p∗ (w) =a + kw.
2

The equilibrium input price and price of final product are given as
wr(ii) =a − kc3a + kc, pr(ii)
=
.
E
2k
4

The profits of U and DI are given asπr(ii)U =(a − kc)2, πr(ii)
= 0.
I
8b
24

We now determine the optimal input price for supplier U. For 0 < k ≤ 1/2, we always have
r(i)
r(i)
r(ii)
πU
< πr(ii)
U . In contrast, for 1/2 < k < 1, we have πU < πU if c > Ć(k), where√a(k − 2k(1 − k))Ć(k) =,k(2 − k)and where ∂Ć(k)/∂k > 0, Ć(1/2) = 0, and Ć(1) = 1.
Finally, we examine whether input prices in each equilibrium satisfy the definition of each case.
We first check Case (i). For 0 < k < 1, we have p∗ (wr(i) ) > wr(i) if c < C̆(k), whereC̆(k) =ka,2−kwhere ∂C̆(k)/∂k > 0, C̆(0) = 0, and C̆ A (1) = 1. Because we have√a( 2k − k)(1 − k)C̆(k) − Ć(k) =>0k(2 − k)r(i)r(ii)
for all 0 < k < 1, whenever we have πU> πU, the equilibrium input price in Case (i) satisfies
r(ii)
r(i)
r(ii) . For 2/3 < k < 1,
pr(i)E = w . We next check Case (ii). For 0 < k < 2/3, we always have pE < wr(ii) if c < C̀(k) where
we have pr(ii)E <w

C̀(k) =a(3k − 2),k(2 − k)and where ∂C̀(k)/∂k > 0, C̀(2/3) = 0, and C̀(1) = 1. Because we have√a(2 − 2k)(1 − k)>0Ć(k) − C̀(k) =k(2 − k)r(i)r(ii)
for all 2/3 < k < 1, whenever we have πU< πU, the equilibrium input price in Case (ii) satisfies
r(ii) . Therefore, for all 0 < k ≤ 1/2, we have the equilibrium in Case (ii). On the other hand,pr(ii)
E < w

for 1/2 < k < 1, we have the equilibrium in Case (i) (Case (ii)) if c ≤ Ć(k) (c > Ć(k)).
A.2.2 Proof of Remark 1
If the equilibrium outcomes in Case (i) arise on the equilibrium path when the exclusive supply offer
is rejected, condition (7) holds for k < 3/4. In contrast, if the equilibrium outcomes in Case (ii) ariseon the equilibrium path, condition (7) holds for 0 ≤ c < Ĉ(k).
Q.E.D.
25

B

Quantity Competition

B.1: Results
This appendix considers the existence of anticompetitive exclusive dealings to deter the socially efficient entry of DE when downstream firms compete in quantity. In this appendix, we use linear demand;
that is, the inverse demand for the final product P(Q) is given by a simple linear function we use in
Remark 1:
P(Q) = a − bQ,
where Q is the output of the final product supplied by downstream firms and where a > c and b > 0.
The following proposition shows that exclusion is possible not only under price competition but under
Cournot competition as well.
Proposition B.1. Suppose that the downstream firms compete in quantity. Then, there can be an
exclusion equilibrium as DE becomes efficient (that is, k < k̂), where k̂ ' 0.921543. More precisely,
1. for k̂ ≤ k < 1, entry is a unique equilibrium outcome, and
2. for 0 < k < k̂, exclusion is a unique equilibrium outcome if U is sufficiently efficient, that is,0 ≤ c < C(k) and

p
  3
2 + 3k − 7 +2 (−4k4 − 12k3 + 31k2 − 26k + 10)

27(1
−
k)
a
2k
+
3k







(2k − 1)(14k − 13)(k2 − k + 1)
C(k) = if c < Ċ(k),






 Ĉ(k)if c ≥ Ċ(k).

(21)

where Ĉ(k) is in (13) andĊ(k) =

pa k2 − k + 1 − 3(1 − k)2 (k2 − k + 1)
(2 − k)(k2 − k + 1)

.

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Note that ∂Ċ(k)/∂k > 0, Ċ(k) → 0 as k → 1/2, and Ċ(k) → 1 as k → 1 and that ∂C(k)/∂k < (≥)0 for√
k > (≤)K̇(cA ), C(k) → a(3 − 6)/3 ' 0.1835a as k → 0, and C(k) → 0 as k → k̂.
Figure 5 summarizes the result in Proposition B.1. On comparing Figures 4 and 5, we observea notable difference that the possibility of anticompetitive exclusion under Cournot competition is26

higher; that is, exclusion may arise even when k > 3/4. This result follows from the difference in the
degree of demand expansion between the two types of competition. Compared with undifferentiatedBertrand competition, DE ’s entry under Cournot competition leads to smaller demand expansion because it partially solves the double marginalization problem. Therefore, DE ’s entry leads to a smaller
increase in U’s profit.
In addition, when both downstream firms produce a positive amount of final products (for c <Ċ(k)), the possibility of anticompetitive exclusion increases as DE becomes efficient. Under undifferentiated Bertrand competition, the production level of DI is always zero and it does not depend on
the degree of DE ’s efficiency. By contrast, under Cournot competition, the production level of DI is
positive, and more importantly, an improvement in DE ’s efficiency gradually reduces the productionlevel of DI that demands a large amount of input. This additional effect leads to further reduction ofdemand for input and, thus, increases the benefit of exclusion.

B.2: Proof of Proposition B.1
We consider each of the possible subgames after Stage 1. Note that when the exclusive offer is acceptedby U, equilibrium outcomes coincide with the case of price competition in Appendix A.2.1.1. Bycontrast, when U rejects the exclusive supply offer, DE enters the downstream market and U deals
with DI and DE . Given w, the quantities supplied by the downstream firms are given asa − (2 − k)wa, if w ≤
,


r
3b
2−k
qI (w) = 

a



if w ≥,
 0,2−k
a + (1 − 2k)wa, if w ≤
,



3b
2
−
k
r
qE (w) = 
a − kwa
,
if w ≥,2b2−kAnticipating the outcome, U sets its w to maximize its profit.
max (w − c)(qI (w) + kqE (w)).
wFirst, for w ≤ a/(2 − k), we derive the “local” optimal input price. The maximization problem is27

given as
max (w − c)wa − (2 − k)w
a + (1 − 2k)w
+k
3b
3b

This leads towr =!
s.t. w ≤a.
2−k(1 + k)a + 2(1 − k + k2 )c.
4(1 − k + k2 )This is an interior solution if and only ifc≤

2 − 5k + 5k2.
2(2 − 3k + 3k2 − k3 )The profits of U and DI are given asπrU =(a(1 + k) − 2c(k2 − k + 1))2(a(5k2 − 5k + 2) − 2c(2 − k)(k2 − k + 1))2
r
,
π
=
.
I
24b(k2 − k + 1)
144b(k2 − k + 1)

Second, for w ≥ a/(2 − k), we derive the “local” optimal input price. The maximization problem
is given as
max (w − c)kw

a − kwas.t. w ≥.
2b
2−kThis leads towr =a + kc.
2kThis is an interior solution if and only ifc≥3k − 2.
k(2 − k)The profits of U and DI are given asπrU =(a − kc)2, πrI = 0.
8b

For any c ∈ [0, a) such that
3k − 22 − 5k + 5k2≤c≤,k(2 − k)2(2 − 3k + 3k2 − k3 )two local optimal input prices exist. We now determine the price that is better for U. The first input
price leads to higher profits for U if and only if c < Ċ(k) (see (22)). Therefore, if c < Ċ(k), the optimal

28

input price is the first wr , and then, both DI and DE are active. Otherwise, it is the second wr , andthen, only DE is active.
We explore whether an exclusion equilibrium exists by examining whether the inequality in (5)holds. Substituting the result in the previous subsection with the inequality in (5), we have the condition 0 < c < C̄(k) (see (21)) in Proposition B.1. Therefore, an exclusion equilibrium exists for0 ≤ c < C(k).
Q.E.D.

C

Industry profits allocated by bargaining

C.1: Results
This appendix extends Section 4.2’s model analysis to the case in which the industry profit in Stage
3 is allocated by a random-proposer bargaining model introduced in Fumagalli, Motta, and Rønde(2012). The bargaining procedure in this appendix is as follows. With probability β ∈ (0, 1), U makes
a two-part tariff contract, and with probability 1 − β, active downstream firms make two-part tariff
contracts. In this setting, Section 4.2’s model can be interpreted as a special case of β = 1.
We first consider the case in which the exclusive supply offer is accepted in Stage 1. In Stage 3,
with probability β, U makes a two-part tariff contract, and U earns Π∗ (c) while DI earns nothing. By
contrast, with probability 1 − β, DI makes the two-part tariff contract, and DI earns Π∗ (c) while U
earns nothing. As a result, the firms’ equilibrium profits, excluding the fixed compensation x, are
πaU = βΠ∗ (c), πaI = (1 − β)Π∗ (c).

(23)

We next consider the case in which the exclusive supply offer is rejected in Stage 1 and then, DE
enters the downstream market in Stage 2. In Stage 3, with probability β, U makes a two-part tariff
contract and earns Π∗ (kc), while DI and DE earn nothing. By contrast, with probability 1 − β, DI and
DE compete in two-part tariff contracts. DE earns Π∗ (kc) − Π∗ (c) and U earns Π∗ (c), while DI earns
nothing. As a result, the equilibrium firms’ profits are given as follows:
πrU = βΠ∗ (kc) + (1 − β)Π∗ (c), πrI = 0, πrE = (1 − β)(Π∗ (kc) − Π∗ (c)).
29

(24)

We now consider a commitment problem by U. From (24), it is easy to see that unlike Section
4.2, DE earns positive profits in Stage 3, which mitigates the commitment problem. However, there
still exists the commitment problem for the larger fixed cost of entry.
Proposition C.1. Suppose that the downstream firms are undifferentiated Bertrand competitors. Suppose also that firms adopt two-part tariffs and the bargaining procedure follows a random-proposermodel. When U cannot commit to input prices before DE ’s entry decision, exclusion is possible if the
fixed cost of entry is not too small.
1. For 0 < f ≤ (1 − β)(Π∗ (kc) − Π∗ (c)), entry is a unique equilibrium outcome.
2. For (1 − β)(Π∗ (kc) − Π∗ (c)) < f , exclusion is a unique equilibrium outcome.
Similar to Section 4, to avoid the commitment problem, assume that U can commit to two-parttariff contracts before DE makes its entry decision. We also assume that the fixed cost of entry satisfies
the following condition.
Assumption 3. The fixed cost of entry is not too large, such that U welcomes the entry of DE :(1 − β)(Π∗ (kc) − Π∗ (c)) < f < Π∗ (kc) − βΠ∗ (c).

(25)

If the first inequality of (25) does not hold, then DE always enters the downstream market regardless of commitment. If the second inequality of (25) does not hold, then the entry of DE is notprofitable for U and U does not induce DE to enter the downstream market.
When U rejects the exclusive supply offer in Stage 1, in Stage 2, U optimally chooses two-parttariff contracts, such that πrU = Π∗ (kc) − f and πrI = πrE = 0. This profit allocation is equivalent to
Section 4.2. The crucial difference from Section 4.2 arises when U decides the trading partner after
the exclusive supply offer is rejected in Stage 1. U prefers the entry of DE for Π∗ (kc) − f > βΠ∗ (c),which can be rewritten as the second inequality of (25). By comparing (16) and (25), it is easy to seethat when U does not have full bargaining power, it prefers the entry of DE even for the larger fixed
cost of entry. Hence, there exists f that simultaneously satisfies conditions (5) and (25).

30

Proposition C.2. Suppose that the downstream firms are undifferentiated Bertrand competitors. In
addition, suppose that U can commit to input prices before the entry decision, such that DE always
enters the market if the exclusive supply offer is rejected. When firms adopt two-part tariffs and thebargaining procedure follows a random-proposer model, an exclusion equilibrium is possible if the
fixed cost of entry is sufficiently large.
1. For (1 − β)(Π∗ (kc) − Π∗ (c)) < f < f 0 , entry is a unique equilibrium outcome, wheref 0 = Π∗ (kc) − Π∗ (c).

(26)

2. For f 0 ≤ f < Π∗ (kc) − βΠ∗ (c), exclusion is a unique equilibrium outcome.

C.2: Proof of Proposition C.2
Condition (5) holds if and only if f ≥ f 0 . We show that f 0 satisfies condition (25). From equations(23) and (26), U welcomes the entry of DE when the exclusive supply offer is rejected if and only ifΠ∗ (kc) − f 0 − βΠ∗ (c) = (1 − β)Π∗ (c) > 0,
which implies that the second inequality of (25) holds. By contrast, from equations (24) and (26), DE
cannot enter the downstream market in the absence of commitment if and only if
f 0 − (1 − β)(Π∗ (kc) − Π∗ (c)) = β(Π∗ (kc) − Π∗ (c)) > 0,
which implies that the first inequality of (25) holds. Hence, there exist f > 0, which simultaneously
satisfies conditions (5) and (25). Therefore, exclusion is a unique equilibrium outcome for f 0 ≤ f <Π∗ (kc) − βΠ∗ (c).

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Stage 1

Stage 2

Stage 3

Stage 4DI makes an
exclusive offer.

DE makes
entry decision.

U makes input
price offers.

Active downstream firms
order the input andcompete.

U decides.

Figure 1: Time line

When U accepts exclusive offers

When U rejects exclusive offers

U

U

DI
DI

Contracting Party

DE
Figure 2: Wholesale price offers in Stage 3

37

DE


r(ii)
Figure 3: Properties of max πr(i)U , πU38

Figure 4: Results of Proposition 1 under linear demand (a = 1)

Figure 5: Results of Proposition B.1 (a = 1)39