Which is Better for Durable Goods Producers, Exclusive or Open∗
Supply Chain?
Hiroshi Kitamura†

Noriaki Matsushima‡

Misato Sato§

Abstract
Recent developments in information communication technology (ICT) seemingly
facilitate supply chains’ openness because such progress allows downstream firms to findalternative trading partners more easily. Following this recent trend, we develop a twoperiod durable goods market with a general demand setting by introducing an entrant
supplier in the second period to explore the supply chain problem of a downstream
durable goods monopolist. The monopolist chooses one of the following trading modesin the first period: an exclusive supply chain with an incumbent supplier or an open
supply chain, which allows the monopolist to trade with a new efficient entrant in thesecond period. The predicted retail price reduction in the second period dampens the
profitability of the original firms. An efficient entrant’s entry magnifies such a pricereduction, causing a further reduction of original firms’ joint profits. In equilibrium,
the downstream monopolist chooses the exclusive supply chain to escape further pricereductions, although it anticipates efficient entry. This finding implies that downstream
durable goods producers may have strong incentives to develop an exclusive supply
chain even when recent ICT developments facilitate those producers to find efficient
suppliers in the future.

JEL classification codes: L12, L41, L42, D43.
Keywords: Durable goods; Exclusive supply chain; Vertical relation; Antitrust policy.
Running head: Exclusive or Open Supply Chain∗

An earlier version of this paper is entitled “Exclusive Contracts in Durable Goods Markets.” We havebenefited from many constructive comments from the Co-Editor and anonymous referees. We thank Keisuke
Hattori, Akifumi Ishihara, Hirokazu Ishise, Hiroshi Kinokuni, Gordon Klein, Inés Macho-Stadler, Chrysovalantou Milliou, Tomomichi Mizuno, Takeshi Murooka, as well as the conference participants at the 3rd
Asia-Pacific Industrial Organisation Conference (The University of Melbourne), EARIE 2019 (Universitat
Pompeu Fabra), XXXIV Jornadas de Economı́a Industrial (Universidad Complutense de Madrid), Japan Association for Applied Economics, Spring Meeting (Nanzan University), and Japanese Economic Association,
Autumn Meeting (Kobe University), and seminar participants at Osaka University (ISER and OSIPP) and
Summer Workshop on Economic Theory (Otaru Chamber of Commerce & Industry). We gratefully acknowledge the financial support from JSPS KAKENHI grant numbers JP15H05728, JP17H00984, JP17K13729,
JP18H00847, JP18K01593, JP19H01483, JP20H01507, JP20H05631, and JP21K01452, The Japan Center
for Economic Research, and the program of the Joint Usage/Research Center for “Behavioral Economics” at
the ISER, Osaka University. Although Matsushima serves as a member of the Competition Policy ResearchCenter (CPRC) at Japan Fair Trade Commission (JFTC), our paper does not reflect the views of JFTC.
The usual disclaimer applies.
†
Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto-City 603-8555,
Japan. E-mail: hiroshikitamura@cc.kyoto-su.ac.jp‡
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047,
Japan. E-mail: nmatsush@iser.osaka-u.ac.jp§
Faculty of Humanities and Social Sciences, Okayama University, Tsushima-naka 3-1-1, Kita-Ku,
Okayama 700-8530, Japan. E-mail: msato@okayama-u.ac.jp

Which is Better for Durable Goods Producers,
Exclusive or Open Supply Chain?
Abstract
Recent developments in information communication technology (ICT) seemingly
facilitate supply chains’ openness because such progress allows downstream firms to findalternative trading partners more easily. Following this recent trend, we develop a twoperiod durable goods market with a general demand setting by introducing an entrant
supplier in the second period to explore the supply chain problem of a downstream
durable goods monopolist. The monopolist chooses one of the following trading modesin the first period: an exclusive supply chain with an incumbent supplier or an open
supply chain, which allows the monopolist to trade with a new efficient entrant in thesecond period. The predicted retail price reduction in the second period dampens the
profitability of the original firms. An efficient entrant’s entry magnifies such a pricereduction, causing a further reduction of original firms’ joint profits. In equilibrium,
the downstream monopolist chooses the exclusive supply chain to escape further pricereductions, although it anticipates efficient entry. This finding implies that downstream
durable goods producers may have strong incentives to develop an exclusive supply
chain even when recent ICT developments facilitate those producers to find efficient
suppliers in the future.

JEL classification codes: L12, L41, L42, D43.
Keywords: Durable goods; Exclusive supply chain; Vertical relation; Antitrust policy.
Running head: Exclusive or Open Supply Chain

1

Introduction

We commonly observe an exclusive supply chain in many markets for durable goods, including industrial machinery/equipment and electronic and electric equipment (Heide, Dutta,
and Bergen, 1998),1 although the recent progress of information communication technology(ICT) helps firms find new trading partners worldwide, which affects the organizational formation of firms in various ways (Granot and Sošić, 2005; World Bank, 2009, Chapter 6;
Bloom et al., 2014). The exclusive supply chain in the smartphone processor market is atypical example.2 Apple, for instance, has selected an exclusive supply chain with Taiwan
Semiconductor Manufacturing Company (TSMC) for Apple’s processors.3 The argument of
supply chain openness is also related to the discussion on exclusive contracts in the context
of competition policy (see the earlier discussions of Posner, 1976 and Bork, 1978). In reality, we have observed anticompetitive exclusive contracts in the market for durable goods
such as aluminum (the United States of America v. Aluminum Co. of America in the US,1945), furniture (Paramount Bed Case in Japan, 1998), artificial teeth (the United Statesof America v. Dentsply International, Inc., in the US, 2005), and CPUs (Intel Case in the1

See also Mollgaard and Lorentzen (2004), who explore exclusive dealings in the Eastern European carcomponent industry. Moreover, in the aviation industry, Boeing Company and Airbus sometimes award
exclusivity to one or two jet engine makers over other makers. See “GE Unit Lands Exclusive Boeing Pact
For Developing Commercial Jet Engine” The Wall Street Journal, July 8, 1999 (https://www.wsj.com/
articles/SB931391538252682453), and “Airbus selects Rolls-Royce Trent 7000 as exclusive engine for the
A330neo” Rolls-Royce, July 14, 2014 (https://www.rolls-royce.com/media/press-releases/yr-2014/
140714-a330neo.aspx).
2

For the case of Qualcomm’s exclusive supply chain with Samsung, see “Samsung beats TSMC to win
new Qualcomm order to make mobile chips” The Korea Economic Daily, October 6, 2020 (https://www.
kedglobal.com/newsView/ked202010100034).
3

See “Taiwan’s TSMC to continue as Apple’s exclusive A-series chip supplier: reports” Taiwan News,
October 13, 2018 (https://www.taiwannews.com.tw/en/news/3551431). Moreover, in the gaming industry, AMD is the exclusive supplier of CPUs for video-game consoles such as Microsoft Xbox One, Nintendo
Wii U, and Sony PlayStation 4. See “Build Your Dream. A Unique Approach to Engineering.” AMD,(https://www.amd.com/en/products/semi-custom-solutions).

1

US, 2005).4 Despite these observations, previous studies on exclusive vertical chains andexclusive contracts investigate only perishable goods markets. In this study, to contribute tosupply chain management and competition policy, we consider the problem of an exclusive
supply chain in durable goods markets.
We consider a two-period durable goods market, as in Bulow (1986), Denicolò and Garella(1999), and Desai, Koenigsberg, and Purohit (2004), by introducing the entrant supplier inthe second period. We explore the situation in which a downstream durable goods monopolist
chooses one of two trading modes in the first period: (i) a two-period exclusive supply chain
with an existing incumbent supplier, or (ii) an open supply chain, which causes competition
between the incumbent and a potential supplier.5 We investigate whether the incumbent
supplier and the downstream firm sign a two-period exclusive contract in the first period. To
do so, we combine the model framework of durable goods markets (Bulow, 1986; Denicolò andGarella, 1999; Desai, Koenigsberg, and Purohit, 2004) with the scenario of entry deterrence
through exclusive contracts in the Chicago School argument (Posner, 1976; Bork, 1978).
By introducing two-part tariffs as in Desai, Koenigsberg, and Purohit (2004), we showthat exclusion is a unique equilibrium outcome in a general demand setting; in other words,
the durability of products induces a downstream firm to choose an exclusive supply chain.
As in the Chicago School framework, second-period entry generates upstream competition,
which allows the downstream firm to procure inputs at a lower wholesale price in the second
period. Thus, exclusion seems difficult. However, in durable goods markets, a retail price4

For each case, see the United States of America v. Aluminum Co. of America, 148 F.2d 416(1945, https://law.justia.com/cases/federal/appellate-courts/F2/148/416/1503668/); Blair and
Sokol (2015); the United States of America v. Dentsply International, Inc., 399 F.3d (2005, https://www.
leagle.com/decision/2005580399f3d1811565); Advanced Micro Devices, Inc., a Delaware corporation,
and AMD International Sales & Services, Ltd., a Delaware corporation, v. Intel Corporation, a Delaware corporation, and Intel Kabushiki Kaisha, a Japanese corporation, Civil Action No. 05-441-JJF (2005, https://www.amd.com/system/files/amd-intel-full-complaint.pdf, respectively.
5

There are many papers on the problem of channel coordination under the rapid development of information technology (see, for instance, the issue of showrooming in Kuksov and Liao (2018) and the papers inthe section ‘Related Literature’ in their article).

2

reduction through upstream competition in the second period makes some final consumers
refrain from purchasing in the first period, leading to a low retail price and low joint profits forthe contracting party in the first period. That is, second-period upstream entry exacerbates
the intertemporal pricing problem in the downstream market. Because exclusive contracts
can mitigate such a pricing problem, the contracting party can enjoy higher joint profits
in the first period. Therefore, the incumbent supplier can profitably make a two-period
exclusive offer to the downstream firm in durable goods markets in the first period.
The findings in this study provide important predictions for information societies and theopenness of supply chains. Recent developments in ICT seemingly facilitate the opennessof supply chains because such progress allows downstream firms to find alternative trading
partners more easily. However, our findings imply that such a view does not necessarily
remain valid in durable goods markets; downstream durable goods producers may choose todevelop an exclusive supply chain even when efficient suppliers appear in the future.6
Because the exclusive contract in this study is a tool to deter the entry of efficient entrants
in the future, this study is suitable for a situation where a local firm faces the threat of entryof highly efficient multinational firms.7 Several key retailers accepted exclusive distributionagreements with Vist, a Russian personal computer maker, although those retailers expectedentry by multinational computer makers such as Compaq, IBM, and Hewlett-Packard (Dawar
and Frost, 1999). In such a case, multinational firms usually spend some time entering themarkets after the news of their entry (Bao and Chen, 2018). Such news in the media
allows every economic agent to predict future entry and reconsider their trading networks,
both of which are necessary for this study’s exclusion mechanism. Therefore, the exclusion
6

Our focus is also related to the exclusiveness of keiretsu in the Japanese automobile industry (e.g., Aoki
and Lennerfors, 2013) and channel coordination (e.g., Jeuland and Shugan, 1983; Coughlan, 1985; Gupta
and Loulou, 1998; Gupta, 2008).
7

Note that multinational firms usually have high productivity, and they are more efficient than domestic
firms (Helpman, Melitz, and Yeaple, 2004; Kimura and Kiyota, 2006).

3

mechanism can apply to such situations. In Section 5, we introduce several examples of
exclusive supply chains in detail and consider the linkage with the results in this study.
The exclusion mechanism in our study also provides an important implication for competition policy. The Chicago School argument, which introduces the impossibility of exclusive
contracts for anticompetitive reasons, does not necessarily apply to durable goods markets.
Our study’s exclusion mechanism arises from the nature of a durable goods monopolist, initially argued by Coase (1972).8 Moreover, the exclusion outcomes in our study are derived
under a general demand setting. The Supplementary Appendix shows that exclusion outcomes are attainable under the general demand setting even when efficiency improvements
reduce the incumbent supplier’s marginal cost in the second period and even when the efficient supplier exists in the first period. The appendix also shows that exclusion outcomesare achievable under a linear demand system in various extended settings. Hence, we canapply the findings to diverse real-world exclusive supply chains in durable goods markets.
The remainder of this paper is organized as follows. Section 2 provides the literature
review. Section 3 constructs the model. Section 4 analyzes the existence of exclusion outcomes under two-part tariffs. Section 5 extends the model and discusses the relevance of thisstudy to real-world examples. Section 6 offers concluding remarks. Appendix A provides
the proofs of the results.

2

Literature Review

This study is related to the literature on entry deterrence in durable goods markets.9 Bycomparing selling with renting, Bucovetsky and Chilton (1986) show that a durable goods
8

For a model analysis of the Coase conjecture, see Stokey (1981), Bulow (1982), Gul, Sonnenschein, andWilson (1986), and Hart and Tirole (1988).
9

Several studies analyze firms’ strategies to deter future entry in the perishable goods market because ofcost uncertainty (Milgrom and Roberts, 1982), quality uncertainty (Schmalensee, 1982), and switching costs(Klemperer, 1987).

4monopolist may choose selling to deter future entry. Bulow (1986) also shows that a durable
goods monopolist has an incentive to increase durability to prevent future entry from theviewpoint of planned obsolescence. These studies focus on how vertically integrated durable
goods monopolists influence the demand for future entrants. By contrast, this study discusses entry deterrence by an upstream firm that trades with a downstream durable goods
monopolist by focusing on exclusive contracts.
The market environment in our model is also related to those in which consumers havemulti-period opportunities to purchase final products. In those models, Besanko and Winston (1990) and Dudine, Hendel, and Lizzeri (2006) discuss storable goods markets, andCoase (1972), Bulow (1982, 1986), Denicolò and Garella (1999), Bruce, Desai, and Staelin(2006), Agrawal et al. (2012), and Gilbert, Randhawa, and Sun (2014) investigate durable
goods markets. Our paper contributes to the research stream on those product markets withvertical supply chains (storable goods markets (Desai, Koenigsberg, and Purohit, 2010; Lin,
Parlaktürk, Swaminathan, 2018; Kabul and Parlaktürk, 2019), leasing versus selling (Purohit, 1995; Desai and Purohit, 1999; Bhaskaran and Gilbert, 2009, 2015), and secondary
markets (Shulman and Coughlan, 2007; Oraiopoulos, Ferguson, and Toktay, 2012)).
In particular, the model formulation of our paper has links to the models of durable goods
markets concerning vertical channel coordination (Desai, Koenigsberg, and Purohit, 2004;
Arya and Mittendorf, 2006; Su and Zhang, 2008; Bhaskaran and Gilbert, 2009, 2015; Yang,2012; Gümüş, Ray, and Yin, 2013; Ramanan and Bhargava, 2014). Desai, Koenigsberg, andPurohit (2004) employ two-period durable goods monopoly models with a separate retailchannel to discuss the effect of commitment on the vertical trading term. They show thatthe commitment to the vertical contract overcomes the Coase problem, leading to a higher
profit for the monopoly manufacturer. Arya and Mittendorf (2006) consider a multi-period
durable goods monopoly market. The monopolist determines if it separates its input sector
to overcome the Coase problem. The trading term between the input and retail sectors is a5

linear wholesale price. They show the possibility that vertical separation by the monopolist
occurs in equilibrium.10 In line with the discussions by Desai, Koenigsberg, and Purohit(2004) and Arya and Mittendorf (2006), Su and Zhang (2008) investigate a newsvendor
problem with demand uncertainty to discuss channel coordination. Bhaskaran and Gilbert(2009, 2015) follow Bulow (1982) to investigate the durability choice by a monopoly manufacturer under four scenarios ((i) centralized or decentralized channel and (ii) selling or leasing).
Gümüş, Ray, and Yin (2013) discuss return policy under demand uncertainty in decentralized durable goods markets. The authors of those papers do not address the openness of the
supply chain in durable goods markets, which is the primary topic of our article.
Our paper contributes to the literature on how to mitigate future price reduction in
dynamic models.11 Recently, for instance, Deb and Said (2015) discuss the monopolist’s
optimal mechanisms in a two-period model and show that it manipulates the timing ofcontracting to mitigate the negative effect of price reduction in period 2. Dilmé and Li(2019) consider a finite period model with high- and low-valuation consumers and show thatmanaging the monopolist’s limited product stock can induce high-valuation consumers to
buy at regular prices. The key factors of mitigating future price reduction in those papers
differ from ours (exclusive dealing).
This study is also related to the literature on anticompetitive exclusive contracts that
deter the socially efficient entry of a potential entrant.12 The literature on anticompetitive
exclusive contracts starts from the Chicago School argument in the 1970s (Posner, 1976;
10

Yang (2012) extends Arya and Mittendorf (2006) to downstream oligopoly. Ramanan and Bhargava(2014) also employ the framework of Arya and Mittendorf (2006) to discuss consumers’ uncertainty on theirvaluations of the product.
11

Hörner and Samuelson (2011) and Chen (2012) investigate optimal pricing strategies under multi-period
sales opportunities. They do not emphasize a seller’s specific (non-price) manipulation to mitigate future
price reduction.
12

Several studies focus on the fact that active firms may compete for exclusivity and explore the welfare
effect (Mathewson and Winter, 1987; O’Brien and Shaffer, 1997; Bernheim and Whinston, 1998). Recently,
Calzolari and Denicolò (2013, 2015) introduced asymmetric information in this literature.

6

Bork, 1978). Using a simple setting, they point out that rational economic agents neversign exclusive contracts for anticompetitive reasons if we consider all members’ participation constraints in the contracting party.13 In rebuttal to the Chicago School, post-Chicago
economists find that rational economic agents agree with exclusive contracts for anticompetitive reasons in certain market environments.14 Some papers extend a single-buyer modelin the Chicago School argument to a multiple-buyer model. For instance, the entrant needsa certain number of buyers to cover its fixed costs (Rasmusen, Ramseyer, and Wiley, 1991;
Segal and Whinston, 2000b), and buyers compete in downstream markets (Simpson andWickelgren, 2007; Abito and Wright, 2008).15 In these studies, negative externalities exist; signing exclusive contracts reduces the possibility of entry under scale economies, andupstream entry reduces industry profits in the presence of downstream competition.16 Furthermore, in the framework of a single downstream firm, several studies point out that theintensity of upstream competition plays a crucial role in the Chicago School argument.17
They show that the exclusion result is attainable in the cases where the incumbent sets
liquidated damages for the case of entry (Aghion and Bolton, 1987), where the entrant is
13

For the analysis of the impact of this argument on antitrust policies, see Motta (2004), Whinston (2006),
and Fumagalli, Motta, and Calcagno (2018).
14

Post Chicago School economists also explore the market environment in which exclusive contracts encourage the relationship-specific investment in vertical relationships (e.g., Marvel, 1982; Masten and Snyder,
1993; Segal and Whinston, 2000a; de Meza and Servaggi, 2007).
15

In the literature on exclusion with downstream competition, Fumagalli and Motta (2006) show that theexistence of participation fees to remain active in the downstream market plays a crucial role in exclusion
if buyers are undifferentiated Bertrand competitors. See also Wright (2009), who reconsiders the result of
Fumagalli and Motta (2006) in the case of two-part tariffs.
16

For the extended model of exclusion with scale economies, see Miklós-Thal and Shaffer (2016), Stefanadis(2016), Choi and Stefanadis (2018), and Chen and Shaffer (2014, 2019). By contrast, for extended models of
exclusion with downstream competition, see Wright (2008), Argenton (2010), Kitamura (2010), and DeGraba(2013), who show the anticompetitiveness of the realized exclusive contracts. Gratz and Reisinger (2013)
show procompetitive effects if downstream firms compete imperfectly and contract breaches are possible.
17

For another mechanism of anticompetitive exclusive dealing, see Fumagalli, Motta, and Rønde (2012),
who focus on the incumbent’s relationship-specific investments. See also Kitamura, Matsushima, and Sato(2018), who focus on a complementary input supplier with market power.

7

capacity constrained (Yong, 1996), where upstream firms compete à la Cournot (Farrell,2005), and where upstream firms can merge (Fumagalli, Motta, and Persson, 2009).18 To
the best of our knowledge, existing papers in this literature consider only perishable goods
markets. Thus, we construct the model here to clarify that the exclusion mechanism inthis study depends on the nature of durable goods markets; exclusion occurs because of thenegative externality that future entry reduces current industry profits.

3

Model

We consider a two-period model with a common discount factor δ ∈ (0, 1) for all players.
There is a final good that is perfectly durable; that is, the final good produced and used inperiod 1 can be used in period 2, without depreciation.
Consumers There is a unit mass of consumers, each of whom buys at most one unit of
the final good. Let v ∈ [0, v̄] be a type of consumer’s willingness to pay, which is stationary
for all periods and whose distribution depends on F (v), where F ′ (v) > 0 for all v ∈ [0, v̄),F (0) = 0, and F (v̄) = 1.19 If a type v consumer purchases the final good at pt in periodt(= 1, 2), the consumer’s gross lifetime discounted surplus evaluated in period 1 becomesu = δ t−1 (v − pt ).
Denicolò and Garella (1999) use a similar formulation to discuss a durable goods market.20
In period 2, a consumer type v, who does not purchase the final good in period 1,
18

See also Kitamura, Matsushima, and Sato (2017), who show that anticompetitive exclusive dealing canoccur if the downstream buyer bargains with suppliers sequentially.
19

In the Supplementary Appendix, we introduce the analysis under linear demand in which F (v) = v tocheck various situations such as linear wholesale pricing and vertical product differentiation.
20

Alternatively, we can consider the setting in which v represents a value of per period use; the surplus ofconsumer type v is (1 + δ)v − p1 for the purchase in period 1, while it is δ(v − p2 ) for the purchase in period
2. In the Supplementary Appendix, we explore such a setting under linear demand and derive exclusion
results.

8

purchases the final good if and only if the consumer surplus is nonnegative, i.e., v − p2 ≥ 0.
By rationally predicting p2 , the consumer purchases the final good in period 1 if and only ifv − p1 ≥ δ(v − p2 ). The indifferent consumer type v1 is defined by v1 − p1 = δ(v1 − p2 ). Let
q1 be the mass of consumers purchasing in period 1. By definition, we have q1 = 1 − F (v1 ).
Then, by using these two equations, we have the static inverse demand in period 1:
P1 (q1 , p2 ) ≡ (1 − δ)F −1 (1 − q1 ) + δp2 .
P1 (q1 , p2 ) has the following properties:∂P1 (q1 , p2 )1−δ∂P1 (q1 , p2 )
=− ′
< 0,
= δ > 0.
∂q1
F (1 − q1 )∂p2
Firms The upstream market consists of an incumbent supplier UI and an entrant supplier
UE . UI and UE produce an identical input but differ in terms of cost efficiency. The constantmarginal costs of UI and UE are cI (< v̄) and cE ∈ [0, cI ), respectively. To guarantee thatsome consumers prefer to purchase the final good in period 1 (q1 > 0), we assume that thedifference in suppliers’ marginal costs is not too large.21 Each supplier offers a two-part tariff,which consists of a linear wholesale price w and an upfront fixed fee ψ, to the downstream
market if it is active.
The downstream market is composed of a downstream monopolist D. This modelingstrategy clarifies the role of durable goods; namely, the prevention of efficient entry occurs
even in the absence of scale economies and downstream competition, both of which require
more than one downstream firm. D transforms one unit of the input into one unit of the final
good, which is durable. To simplify the analysis, we assume that the cost of transformationis zero. Thus, if D faces a wholesale price wt in period t, its per-unit production cost inperiod t becomes wt . We assume that all firms cannot commit to future prices and that
there is no possibility of renting products. There is no resale market for simplicity.
21

In Section 4.4, we extend the model to the case in which the difference in the efficiency is too large andno consumer purchases the final good in period 1 when UE ’s entry is anticipated.

9

Timing The timing of the game is as follows (see Figure 1). In period 1, only UI exists
in the upstream market.22 This may be because of a patent right, superior technology,
efficient marketing, or an industry protection policy. Period 1 consists of three stages. In
period 1.1, UI offers a two-period exclusive contract to D, with fixed compensation x ≥ 0.23
Following the standard literature on naked exclusion, we assume that the exclusive offer
does not contain the term of wholesale prices.24 After observing the exclusive contract, Ddecides whether to accept the exclusive contract. D immediately receives x if it accepts thecontract. In period 1.2, UI offers a two-part tariff contract to D. In period 1.3, D orders the
input and sells the final good to consumers.
At the beginning of period 2, UE appears in the upstream market if D rejects the exclusive
contract in period 1.1. Period 2 consists of three stages. In period 2.1, UE decides whether
to enter the market if UE appears.25 We assume that the fixed entry cost is sufficiently small
such that UE can earn positive profits; namely, UE always enters the upstream market if
D rejects the exclusive contract in period 1.1. In period 2.2, active suppliers offer two-parttariff contracts to D. For the case of UE ’s entry, UI and UE become homogeneous Bertrand
competitors. We assume that if they charge the same input price, the efficient supplier,UE , supplies its input to D. In period 2.3, D orders the input and sells the final good to
consumers.
22This assumption simplifies the analysis. In the Supplementary Appendix, we consider the case in which
both UI and UE exist in the upstream market at the beginning of period 1. We obtain exclusion outcomeseven in such a setting. Section 5.1 introduces a brief summary of the results in the extensions.
23

In Section 4.3, we show that for the existence of exclusion outcomes, it does not matter whether UI or
D makes exclusive offers.
24

If UI is able to credibly commit to the trading terms after achieving the two-period exclusive contract, UI
can eliminate the time-inconsistency problem by committing to a prohibitively high second-period wholesale
price, facilitating signing the exclusive contract. Moreover, in the naked exclusion literature, it is known that
if the incumbent can commit to wholesale prices, then the possibility of anticompetitive exclusive dealing isenhanced. See Yong (1999) and Appendix B of Fumagalli and Motta (2006).
25

The result does not change if we consider the possibility that UI makes exclusive offers in period 2 if
its exclusive offer in period 1 is rejected. In such a case, the Chicago School argument can be applied; UI
cannot make exclusive offers to profitably compensate D in period 2.

10

We use the superscripts “a” and “r” to indicate the acceptance and the rejection of theω
exclusive contract by D in period 1.1. Then, πi|t(i ∈ {I, E}) is Ui ’s profit in period t whenω
D’s decision in period 1.1 is ω ∈ {a, r}. Likewise, πD|t
is D’s profit in period t.
ωWe assume that UI and D maximize the present discounted value of their profits πI|1
+
ω
ω
ω
r
δπI|2
and πD|1+ δπD|2
respectively, while UE maximizes the second-period profits πE|2
forthe case of entry.
[Figure 1 about here.]

4

Analysis

We characterize the properties of subgame perfect Nash equilibria by solving the game using
backward induction. Starting from the game in period 2, we explore the equilibrium outcomesin the subgame after D’s decision in period 1.1. We then explore the contractual decision inperiod 1.1 to examine the existence of exclusion outcomes.

4.1

Period 2

Let v2 denote the indifferent consumer in period 2, which satisfies v2 − p2 = 0. By defining
q2 as the mass of consumers purchasing in period 2, the sum of the production level in both
periods becomes q1 + q2 = 1 − F (v2 ). From these two equations, we obtain the residual
inverse demand function in period 2 given q1 :P2 (q2 |q1 ) ≡ F −1 (1 − q1 − q2 ).
For notational convenience, we define q2∗ (q1 , z), P2∗ (q1 , z), and Π∗2 (q1 , z) as follows:q2∗ (q1 , z) ≡ argmax (P2 (q2 |q1 ) − z)q2 ,q2 ≥0

P2∗ (q1 , z) ≡ P2 (q2∗ (q1 , z)|q1 ),Π∗2 (q1 , z) ≡ (P2∗ (q1 , z) − z)q2∗ (q1 , z), where 0 ≤ z < P2 (0|q1 ).
11(1)

In period 2.3, given the two-part tariff contract (w2 , ψ2 ), D chooses q2∗ (q1 , w2) to maximize
its second-period profit, which leads to the equilibrium price P2∗(q1 , w2 ). D earns Π∗2 (q1 , w2 )−ψ2 . The following lemma summarizes the properties of q2∗ (q1 , w2 ), P2∗ (q1 , w2 ), and Π∗2 (q1 , w2 ).
Lemma 1. q2∗ (q1 , w2 ), P2∗ (q1 , w2 ), and Π∗2 (q1 , w2 ) have the following properties:∂q2∗ (q1 , w2 )∂P2∗ (q1 , w2)∂Π∗2 (q1 , w2 )
< 0,
> 0,
< 0.
∂w2
∂w2
∂q1
Proof. See Appendix A.1.
In period 2.2, the supplier(s) considers (consider) the profit maximization problem(s),given q1 . First, we discuss the case in which D accepts the exclusive contract in period 1.1.
Second, we explore the case in which D rejects the exclusive contract in period 1.1. Finally,
we compare both cases.
Exclusive supply chain When D accepts the exclusive contract (chooses the exclusive
supply chain), only UI exists in the upstream market in period 2. In period 2.2, UI offers theaatrading term, (w2|I, ψ2|I) = (cI , Π∗2 (q1 , w2 )). D accepts this trading term, and the resulting

profits of UI and D are given byaa
πI|2= Π∗2 (q1 , cI ), πD|2
= 0.

The realized price in period 2 is pa2 = P2∗ (q1 , cI ).
Open supply chain When D rejects the exclusive contract (chooses the open supply
chain), UE enters the upstream market in period 2.1 anticipating positive profits. In period
2.2, the upstream competition between UI and UE induces UI to offer the best trading term,
r
r
(w2|I
, ψ2|I) = (cI , 0), which allows D to earn Π∗2 (q1 , cI ). Anticipating this trading term byrr) = (cE , Π∗2 (q1 , cE ) −UI , UE needs to leave Π∗2 (q1 , cI ) for D and therefore sets (w2|E, ψ2|EΠ∗2 (q1 , cI )). D accepts this trading term, and the resulting profits of D, UI , and UE are
r
r
r
πD|2
= Π∗2 (q1 , cI ), πI|2
= 0, πE|2= Π∗2 (q1 , cE ) − Π∗2 (q1 , cI ).

12

The realized price in period 2 is pr2 = P2∗ (q1 , cE ).
Comparison Finally, we compare the above outcomes in period 2 given q1 . For the pairof UI and D, their joint profit under the exclusive supply chain is the same as that under
the open supply chain. The difference between these two cases appears in the realized prices
in period 2. Using the results in Lemma 1, we have the following property:
Lemma 2. Given q1 , the realized price under the exclusive supply chain is higher than that
under the open supply chain: P2∗ (q1 , cI ) > P2∗ (q1 , cE ) always holds.
The lower realized price in period 2 under the open supply chain follows from the efficiencyof UE .

4.2

Period 1

Anticipating the outcome in period 2, D determines q1 given the trading term (w1 , ψ1 ) inperiod 1.3.
We use P1 (q1 |cI ) ≡ P1 (q1 , P2∗ (q1 , cI )) and P1 (q1 |cE ) ≡ P1 (q1 , P2∗ (q1 , cE )) to express thestatic inverse demand functions under the exclusive supply chain and the open supply chain
in period 1, respectively. Using the properties of ∂P1 (q1 , p2 )/∂p2 > 0 and Lemma 2, the two
inverse demands in period 1 have the following property:
Lemma 3. The static inverse demand in period 1 under the exclusive supply chain is always
strictly larger than that under the open supply chain; i.e., P1 (q1 |cI ) > P1 (q1 |cE ) holds forany q1 .
The result in Lemma 3 implies that the exclusive supply chain allows D to face larger
consumer demand than the open supply chain, which can be explained by the intertemporalexternal effect of entry in period 2. Under the open supply chain, the entry of UE occurs inperiod 2, allowing consumers to purchase the final good at a low price in period 2. Such a13

low price in period 2 induces some consumers to refrain from purchasing in period 1. Hence,the consumer demand in period 1 under the open supply chain becomes smaller than that
under the exclusive supply chain. In other words, the contracting party suffers from thesmall consumer demand in period 1 under the open supply chain.
In the rest of this subsection, we derive the equilibrium outcomes in the cases of the
exclusive supply chain and the open supply chain, separately.
Exclusive supply chain We derive the equilibrium outcome starting from D’s profit
maximization problem in period 1.3. When the exclusive supply chain is chosen in perioda1.1, D anticipates that it earns zero profit in period 2; namely, πD|2
= 0. Then, given

the two-part tariff contract (w1 , ψ1 ), which is offered by UI in period 1.2, D chooses the
production level q1a (w1 ) to maximize its overall profits in period 1.3:
q1a (w1 ) ≡ argmax (P1 (q1 |cI ) − w1 )q1 − ψ1 .

(2)

q1 ≥0

The first-order condition of the maximization problem in (2) isP1 (q1a (w1 )|cI ) − w1 +∂P1 (q1a (w1 )|cI ) a
q1 (w1 ) = 0.
∂q1

(3)

a
We now consider UI ’s profit maximization problem in period 1.2. By anticipating πI|2=Π∗2 (q1a (w1 ), cI ), UI ’s overall profits become(w1a , ψ1a ) ≡ argmax (w1 − cI )q1a (w1 ) + ψ1 + δΠ∗2 (q1a (w1 ), cI ).
w1 ,ψ1

UI determines the highest ψ1 such that D prefers accepting (w1 , ψ1 ) to declining it; that is,ψ1 = (P1 (q1a (w1 )|cI ) − w1 )q1a (w1 ). Under this two-part tariff contract, D’s overall profits areaazero; πD|1
+ δπD|2= 0. Then, UI ’s profit maximization problem is rewritten as

w1a ≡ argmax (P1 (q1a (w1 )|cI ) − cI )q1a (w1 ) + δΠ∗2 (q1a (w1 ), cI ).

(4)

w1

The first-order condition of the maximization problem in (4) is∂P1 (q1a (w1a )|cI ) a a∂Π∗2 (q1a (w1a ), cI ) a ′ aaa(P1 (q1 (w1 )|cI ) − cI ) +q1 (w1 ) + δ
q1 (w1 ) = 0.
∂q1
∂q1
14

(5)

Using the first-order conditions in (3) and (5), we obtain the following:
w1a = cI − δ∂Π∗2 (q1a (w1a ), cI ).
∂q1

From Lemma 1, we have ∂Π∗2 (q1a (w1a ), cI )/∂q1 < 0, which implies that w1a > cI holds. The
following proposition summarizes the discussion.
Proposition 1. When an exclusive supply chain is chosen for both periods, the equilibrium
wholesale price in period 1 is strictly higher than the marginal cost of UI ; that is, w1a > cI .
Proof. The above discussion is based on q1a ′ (w1a ) < 0. The proof of q1a ′ (w1a ) < 0 is provided
in Appendix A.2.
This proposition is a generalization of Desai, Koenigsberg, and Purohit (2004) in thatthe demand system in our paper is a general form. Under the exclusive supply chain, Dchooses the first-period production level without considering the profit in period 2 because
it anticipates that it earns nothing in period 2. To control D’s behavior in period 1, UI sets
w1a > cI to fulfill the overall joint profit maximization of UI and D.
Note that the realized production level in period 1, q1a (w1a ), is the same as q1∗ , which isthe solution of the following maximization problem:q1∗ ≡ argmax (P1 (q1 |cI ) − cI )q1 + δΠ∗2 (q1 , cI ).
q1 ≥0This means that UI indirectly controls q1 through its wholesale price, w1 , to maximize theoverall joint profits of UI and D. As a result, the overall joint profits of UI and D become
a
a
a
a
πI|1
+ δπI|2+ πD|1+ δπD|2= (P1 (q1∗ |cI ) − cI )q1∗ + δΠ∗2 (q1∗ , cI ).

(6)

Open supply chain When the open supply chain is chosen in period 1.1, D anticipates itr= Π∗2 (q1 , cI ) in period 2. Then, given the two-part tariff contract (w1 , ψ1 ), whichearns πD|215

is offered by UI in period 1.2, D chooses the production level q1r (w1 ) to maximize its overallprofits in period 1.3:
q1r (w1 ) ≡ argmax (P1 (q1 |cE ) − w1 )q1 − ψ1 + δΠ∗2 (q1 , cI ).

(7)

q1 ≥0

The first-order condition of the maximization problem in (7) is
P1 (q1r (w1 )|cE ) − w1 +∂Π∗ (q r (w1 ), cI )∂P1 (q1r (w1 )|cE ) r
q1 (w1 ) + δ 2 1
= 0.
∂q1
∂q1

(8)

By anticipating this reaction, UI ’s profit maximization problem in period 1.2 becomes(w1r , ψ1r ) ≡ argmax (w1 − cI )q1r (w1 ) + ψ1 .
w1 ,ψ1

Note that under the open supply chain, D can earn δΠ∗2 (0, cI ) in period 2 through the competition between UI and UE if it rejects the two-part tariff contract (w1 , ψ1 ). UI determines
the highest ψ1 such that D prefers accepting (w1 , ψ1 ) to declining it; the optimal level of
upfront fixed payment satisfies ψ1 = (P1 (q1r (w1 )|cI ) − w1 )q1r (w1 ) + δΠ∗2 (q1 , cI ) − δΠ∗2 (0, cI ).
Under this two-part tariff contract, UI cannot extract all the overall joint profits of UI and D;rr
unlike the exclusive supply chain, D earns positive overall profits, πD|1
+ δπD|2= δΠ∗2 (0, cI ).

Then, UI ’s profit maximization problem is rewritten as
w1r ≡ argmax (P1 (q1r (w1 )|cE ) − cI )q1r (w1 ) + δΠ∗2 (q1r (w1 ), cI ) − δΠ∗2 (0, cI ).

(9)

w1

The first-order condition of the maximization problem in (9) is∂P1 (q1r (w1r )|cE ) r r∂Π∗ (q r (w r ), cI )(P1 (q1r (w1r )|cE ) − cI ) +q1 (w1 ) + δ 2 1 1
∂q1
∂q1



q1r ′ (w1r ) = 0.

Using the first-order conditions in (8) and (10), we obtain the following:
w1r = cI .
The following proposition summarizes the discussion.
16

(10)

Proposition 2. When UE enters the upstream market in period 2, the equilibrium linear
wholesale price in period 1 equals the marginal cost of UI ; that is, w1r = cI .
Proof. The above discussion is based on q1r ′ (w1r ) < 0. The precise proof of q1r ′ (w1r ) < 0 isprovided in Appendix A.3.
Under the open supply chain, from (8) and (10), we find that D’s maximization problemaligns with UI ’s if and only if UI sets w1r = cI as in the standard two-part tariff pricing.
Note that the realized production level in period 1, q1r (w1r ), is the same as q1∗∗ , which isthe solution of the following maximization problem:
q1∗∗ ≡ argmax (P1 (q1 |cE ) − cI )q1 + δΠ∗2 (q1 , cI ).
q1 ≥0

Thus, the overall joint profits of UI and D become
r
r
r
r
πI|1
+ δπI|2+ πD|1+ δπD|2= (P1 (q1∗∗ |cE ) − cI )q1∗∗ + δΠ∗2 (q1∗∗ , cI ).

4.3

(11)

Exclusive contracts

For an exclusion equilibrium to exist, the equilibrium transfer x∗ must simultaneously satisfy
the following two conditions.
First, the exclusive contract must satisfy individual rationality for D:
a
a
r
r
r
r
a
a
).
+ δπD|2− (πD|1+ δπD|2or x∗ ≥ πD|1
+ x∗ + δπD|2≥ πD|1+ δπD|2
πD|1(12)

Second, the exclusive contract must satisfy individual rationality for UI :
a
a
r
r
a
a
r
r
πI|1
+ δπI|2− x∗ ≥ πI|1
+ δπI|2or x∗ ≤ πI|1
+ δπI|2− (πI|1+ δπI|2).

(13)

From the above conditions, it is evident that an exclusion equilibrium exists if and only if
inequalities (12) and (13) simultaneously hold. This is equivalent to the following condition:
a
a
a
a
r
r
r
r
πI|1
+ δπI|2+ πD|1+ δπD|2≥ πI|1+ δπI|2+ πD|1+ δπD|2
.

17

(14)

Condition (14) implies that anticompetitive exclusive contracts are attained if exclusive
contracts increase the overall joint profits of UI and D. The condition also implies thatwhether UI or D makes an exclusive offer does not affect the existence of exclusion outcomes.
Comparison We finally examine the contractual decision in period 1.1. We compare
equations (6) and (11): the overall joint profits in the two trading modes. For q1 , the overall
joint profits in period 1 under the exclusive supply chain areΠa (q1 ) ≡ (P1 (q1 |cI ) − cI )q1 + δΠ∗2 (q1 , cI ),(15)

while those under the open supply chain areΠr (q1 ) ≡ (P1 (q1 |cE ) − cI )q1 + δΠ∗2 (q1 , cI ).

(16)

The only difference between Πa (q1 ) and Πr (q1 ) is in the static inverse demand in period
1, P1 (q1 |·). From Lemma 3, we have P1 (q1 |cI ) > P1 (q1 |cE ) for any q1 , which implies thatΠa (q1 ) > Πr (q1 ) holds for all q1 . Recall that, under the two modes, UI indirectly controls
q1 through its wholesale price, w1 . Therefore, under the exclusive supply chain, by setting
w1 = w1a , UI achieves the overall joint profits, Πa (q1∗ ), which are strictly higher than thoseunder the open supply chain, Πr (q1∗∗ ); that is, condition (14) always holds.
Theorem 1. In durable goods markets, UI and D choose an exclusive supply chain for any
cI , cE , and δ if D produces the positive production level in period 1 when consumers predict
UE ’s entry in period 2.
Theorem 1 implies that if at least some consumers purchase final goods in period 1 under
the open supply chain, the two-period exclusive supply chain, which deters the entry of an
efficient entrant in period 2, is always established in durable goods markets. This result canbe explained by the intertemporal negative externality in durable goods markets. In durable
goods markets, future entry intertemporally affects the current market outcome. Efficient18

entry in period 2 discourages final consumers from purchasing final goods in period 1 because
they predict that entry leads to a future price reduction. Such a property prevents thecontracting party from choosing the optimal pair of prices (p1 , p2 ) to maximize overall joint
profits under the open supply chain. In other words, using the two-part tariff contract, UI
can indirectly control the pair of prices to achieve overall joint profit maximization under the
exclusive supply chain, whereas it cannot control the prices in period 2 because of the entryof UE under the open supply chain. Therefore, although consumers benefit from future entry,
such entry is harmful to the contracting party; namely, in durable goods markets, rational
economic agents choose the exclusive supply chain, which deters efficient future entry.
In addition, from the viewpoint of competition policy, the findings here provide a new
insight for anticompetitive exclusive contracts. If we modify our model to the case of perishable goods markets, the modified model coincides with the framework of the Chicago School
argument; exclusive contracts cannot deter the entry of an efficient entrant. Theorem 1
implies that the Chicago School argument cannot be applied to durable goods markets; thenature of durable goods markets allows the inefficient incumbent supplier to deter efficient
future entry thorough anticompetitive exclusive contracts.26

4.4

Highly efficient entrant

Thus far, we have explored the case in which at least some consumers purchase final goods
in period 1. However, if UE is sufficiently efficient, the inverse demand in period 1, P1 (q1 |cE ),becomes so small that no consumer purchases final goods in period 1 under the open supply
chain; that is, q1r = 0. In this case, the overall joint profits in period 1 under the open supply
chain are Πr (0) = δΠ∗2 (0, cI ). From (15) and (16), we haveΠa (q1∗ ) > Πa (0) = Πr (0),26

In the Supplementary Appendix, we compare the social surpluses under the exclusive supply chain andthe open supply chain, by introducing linear demand. We show that the exclusive supply chain to deter theefficient entrant is always undesirable from the viewpoint of social surplus.

19

which implies that the exclusive supply chain leads to higher overall joint profits of UI andD than the open supply chain even when UE is highly efficient.
Theorem 2. In durable goods markets, UI and D choose an exclusive supply chain for any
cI , cE , and δ even if D does not produce the positive production level in period 1 when
consumers expect UE ’s entry in period 2.
The results in Theorems 1 and 2 imply that in durable goods markets, the exclusive
supply chain is always established regardless of the difference in cost efficiency. Note thatthe results in this study depend on the assumption that upstream suppliers can adopt twopart tariffs. In the Supplementary Appendix, we extend the model of linear demand to thecase of linear wholesale pricing. We show that in contrast to the case of two-part tariffs,
linear wholesale pricing does not lead to exclusion outcomes for a high discount factor. The
major difference between the two types of wholesale pricing is the existence of a double
marginalization problem, which is often observed for the case of linear wholesale pricing.
When the exclusive supply chain is chosen, the double marginalization problem occurs forboth periods, which reduces the overall joint profits of UI and D under the exclusive supply
chain. By contrast, when the open supply chain is chosen, efficient entry in period 2 canmitigate such a problem; D can earn considerably high profits in period 2. If the discountfactor is high, this effect becomes dominant and thus, the open supply chain is chosen in theequilibrium.

5

Discussion

This section briefly introduces extensions and discusses some real-world exclusive supply
chains.

20

5.1

Extensions

We briefly introduce two extensions. We first introduce the case in which UI ’s marginal
cost decreases in period 2 because of efficiency improvement. We then introduce the case inwhich UE exists at the beginning of period 1.
Future efficiency improvement In Section 1 of the Supplementary Appendix, we extend
the analysis in Section 4 to the case in which the second-period marginal cost of UI becomesĉ ∈ (cE , cI ) because of efficiency improvements. We show that UI and D always choose theexclusive supply chain even in the extended setting. The result implies that the mechanismof exclusive dealing carries through as long as UI remains less efficient than UE even after
UI ’s efficiency improvements.
When UE appears in period 1 In Section 2 of the Supplementary Appendix, we extend
the analysis in Section 4 to the case in which both UI and UE exist at the beginning of
period 1. In this setting, we obtain the following results: (i) if only UI can offer an exclusive
contract to D, UI and D always choose an exclusive supply chain, (ii) if only UE can offer an
exclusive contract to D, UE and D are always indifferent between an exclusive supply chain
and an open supply chain, and (iii) if both UI and UE can offer exclusive contracts to D, UE
and D always choose an exclusive supply chain.
The findings in these extended settings confirm the robustness of the exclusion mechanismin this study; the exclusive supply chain can be chosen even when all suppliers are existing
firms. In durable goods markets, the inefficient supplier always has an incentive to exclude
the efficient supplier. The efficient supplier chooses an exclusive supply chain with thedownstream firm to protect the upstream market against the exclusive offer by an inefficient
supplier.

21

5.2

Real-world examples of exclusive supply chains

We briefly discuss the relevance of the exclusive supply chain in this study to real-world
examples. We commonly observe exclusive supply chains in markets for durable goods. For
example, manufacturers of personal computers and digital cameras often choose exclusive
supply chains to procure inputs such as CPUs and sensors.27 Moreover, camcorder and automotive manufacturers have established exclusive supply chains with retailers and distributors(Shepard, 1993, Nurski and Verboven, 2016).
The following two features play an essential role in the mechanism of exclusion: (i) the
price decline of durable goods and (ii) consumers who are aware of the existence of exclusive
supply chains.28 We consider each feature below.
We first consider the price decline of each durable good. In all the above exclusive supply
chains, there is a consistent pattern of price declines over time following product introduction.
For example, Lou, Pretice, and Yin (2012) investigate a dynamic demand model using dataon the US digital camera market. Their estimation results on the supply side show thatmarkups decline over time, suggesting that price declines occur because of intertemporal
price discrimination or increased competition between durable-goods producers. See also
Copeland and Shapiro (2016) for the personal computer market, Gowrisankaran and Rysman(2012) for the camcorder market, and Copeland (2014) for the automobile market.
We next consider the possibility that consumers know of the existence of exclusive supply
chains. First, for input supply, magazines and webpages for personal computer users and27

In the last paragraph of this section, we provide examples of exclusive supply chains for these products.

28

In Section 4, we consider the situation in which the exclusive contract is used to deter entry by efficient
suppliers in the future. Such a situation is suitable for the case of Vist in the Introduction. However, ofcourse, there exists a situation in which the exclusive contract is used to exclude existing suppliers, andthe efficient supplier may exclude the inefficient supplier by constructing the exclusive supply chain. The
results of extended analyses, introduced in Section 5.1, imply that the exclusive supply chain is attainable
even when all firms exist in period 1 and all existing suppliers can use exclusive contracts to exclude theirrivals. Moreover, the efficient supplier wins the exclusive-offer competition in the extended model. Thus,
our exclusion mechanism can apply to the wide range of real-world examples here.

22

camera users convey the CPU information of personal computers and the sensor information of digital cameras, allowing consumers to understand the supply chain environment for
those durable goods. For example, web news often presents information about the future
supply chain of CPUs for Apple’s products such as iPhone, iPad, and Mac.29 Second, auto
dealers usually specialize in vehicles produced by a particular automaker in many countries. Furthermore, in Japan, the retail stores engaged in exclusive dealing agreements withthe manufacturer and exclusively sold household appliances, including camcorders (Shepard,1993). These business practices are usually known facts; thus, consumers are aware of theexistence of exclusive supply chains.

6

Conclusion

This study has explored a supply chain problem in durable goods markets. We consider thesituation in which a downstream durable goods monopolist chooses one of two trading modes:(i) an exclusive supply chain with an existing incumbent supplier, or (ii) an open supply
chain, which causes competition between the existing incumbent supplier and a potential
supplier in the future. The problem is also related to the discussion of anticompetitive
exclusive contracts. Therefore, this study contributes to the literature in terms of bothsupply chain management and competition policy. Extending the static framework of the
Chicago School argument to a two-period durable goods model without price commitment,
we show that the downstream durable goods monopolist chooses the exclusive supply chain
by signing long-term exclusive contracts; the potential entrant cannot enter the upstream
29

See “TSMC to be only supplier of Apple A13 chips in 2019” Digitimes, October 11, 2018(https://www.digitimes.com/news/a20181011PD215.html and “TSMC to kick off 3nm chip production in 2H22 for Apple devices” Digitimes, August 11, 2021 (https://www.digitimes.com/
news/a20210811PD214.html).
For digital cameras, there exist web pages introducing the input information.
See, for example, “List of all Nikon DSLR cameras and their sensor manufacturer/designer” Nikon Rumors, December 16, 2015 (https://nikonrumors.com/2015/12/16/
list-of-all-nikon-dslr-cameras-and-their-sensor-manufacturerdesigner.aspx/).

23

market even when it is efficient. This study’s exclusion mechanism is explained by thetime-inconsistency problem (Coase, 1972).
The results here could explain why some vertical relations are too stable, which results
in inefficiency. In the literature on business and management, long-standing organizationties cause lower incentives for opportunistic behavior (Williamson, 1975), information search(Uzzi, 1997), and necessary restructuring (Ernst and Bamford, 2005). Such organizations areless likely to search for new partners and capabilities and instead pursue existing businesspractices, resulting in a decrease in benefits within interorganizational ties or a negative
impact on organization performance (Uzzi, 1997; Goerzen, 2007; Poppo, Zhou, and Zenger,2008).30 In our model, the downstream firm has an incentive to sign a two-period contract
with the incumbent supplier, even by anticipating the appearance of a new efficient supplierin the near future. The resulting outcome leads to inefficiency of the vertical chain. Thus,
although the advancement of informatization and globalization seemingly expands the open
supply chain, these business environment changes may have a smaller impact on the opennessof vertical relations in durable goods markets.
Our result has new policy implications for antitrust agencies; the Chicago School argument, which is based on static perishable goods markets, is not necessarily applicable todurable goods markets. Because of the nature of durable goods, rational economic agentscan engage in anticompetitive exclusive contracts to exclude the efficient entrant in the future even under the simplest setting in which exclusion never occurs in static perishable
goods markets. When we discuss the anticompetitiveness of exclusive contracts, we need toconsider the durability of final goods in the market in which exclusion occurs. Otherwise, we
may overestimate the Chicago School argument, which may lead to misleading predictions.
30

In addition, as those organizations accumulate relationship-specific experiences, such organizational
inertia becomes stronger, and the partners share relationship-specific routines (Kim, Oh, and Swaminathan,2006). Moreover, the specificity and efficiency of a relationship-specific investment may discourage thedownstream firm from switching to a new trading partner (Kitamura, Miyaoka, and Sato, 2016).

24

Despite these contributions, there remain some issues requiring future research. First,
we predict that the exclusion results are more likely to be observed if we introduce productdurability into the other models of anticompetitive exclusive dealing based on perishable
goods in the literature. Second, for the analysis in this study, we restrict our attention toa particular industry structure—a single potential entrant supplier—for clarity, but we cancertainly assume multiple entrant suppliers. As in Kitamura (2010), if we assume multiple
entrants, the competition between entrants induces the downstream firm to earn higher
profits under the open supply chain, which enables us to predict that the exclusive supply
chain may not be chosen if multiple entrants are sufficiently efficient. Thus, extensions andapplications of our model can help researchers and policy makers address similar real-world
issues.

A

Proofs of the results

A.1

Proof of Lemma 1

In this proof, we often use q2∗ ≡ q2∗ (q1 , w2 ) for notational simplicity. We first explore theproperty of ∂q2∗ (q1 , w2 )/∂w2 . For z = w2 , the first-order condition of D’s profit maximization
problem (1) becomes
P2 (q2∗ |q1 ) − w2 +∂P2 (q2∗ |q1 ) ∗q2 = 0.
∂q2(17)

The second-order condition of the maximization problem in (1) leads to
2∂P2 (q2∗ |q1 ) ∂ 2 P2 (q2∗ |q1 ) ∗q2 < 0.
+∂q2∂q22

Note that P2 (q2 |q1 ) has the following property:∂P2 (q2 |q1 )
1∂P2 (q2 |q1 )
=
=− ′
< 0.
∂q1
∂q2
F (1 − q1 − q2 )(18)Then, using (17), the implicit function theorem shows that1
dq2∗
= ∂P (q∗ |q ) ∂ 2 P (q∗ |q ) < 0.
2 2 1
dw2
q2∗
2 2 2 1 +
2
∂q2

∂q2

25

(19)

Hence, we have ∂q2∗ (q1 , w2 )/∂w2 < 0. We next consider the property of ∂P2∗ (q1 , w2 )/∂w2 .
Using (18) and (19), partial differentiation leads to∂P2 (q2∗ (q1 , w2 )|q1 )∂P (q2∗ |q1 ) ∂q2∗ (q1 , w2 )∂P2∗ (q1 , w2 )
=
=
> 0.
∂w2
∂w2
∂q2
∂w2
Finally, we examine the property of Π∗2 (q1 , w2 ). Using (18) and (17), we have∂Π∗2 (q1 , w2)∂P2 (q2∗ |q1 ) ∗=q2 < 0.
∂q1∂q1
Q.E.D.

A.2

Proof of Proposition 1

We only show that q1a ′ (w1 ) < 0 holds. The second-order condition of D’s profit maximization
problem (2) leads to
2∂P1 (q1a (w1 )|cI ) ∂ 2 P1 (q1a (w1 )|cI ) a
q1 (w1 ) < 0.
+
∂q1
∂q12

Using (3), the implicit function theorem shows thatdq1a1
= ∂P1 (qa (w1 )|c ) ∂ 2 P1 (qa (w1 )|c )
< 0.
I
I
1
1
dw1
+
2
q1a (w1 )
2
∂q1

∂q1

Q.E.D.

A.3

Proof of Proposition 2

We only show that q1r ′ (w1 ) < 0 holds. The second-order condition of the maximization
problem in (7) leads to2∂ 2 Π∗2 (q1r (w1 ), cI )∂P1 (q1r (w1 )|cE ) ∂ 2 P1 (q1r (w1 )|cE ) r
+
q
(w
)
+
δ
< 0.
1
1
∂q1
∂q12
∂q12

Using (8), the implicit function theorem shows that
dq1r
1
< 0.
= ∂P1 (qr (w1 )|c ) ∂ 2 P1 (qr (w1 )|c )∂ 2 Π∗ (q r (w ),c )
I
I
1
1
dw1
+
2
q1r (w1 ) + δ 2 1 2 1 I
2
∂q1

∂q1

∂q1

Q.E.D.
26

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