ISSN (Print) 0473-453X

Discussion Paper No. 1127

ISSN (Online) 2435-0982

LEASE OR SALE:WHEN
A DURABLE GOODS MONOPOLISTCAN CHOOSE
SUPPLY CHAIN’S OPENNESS
Hiroshi Kitamura
Noriaki Matsushima
Misato Sato

March 2021

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

Lease or sale: When a durable goods monopolist canchoose supply chain’s openness∗
Hiroshi Kitamura†

Noriaki Matsushima‡

Misato Sato§

March 30, 2021

Abstract
We construct a two-period model of the supply chain’s openness in a durable goods
market by introducing two marketing modes: leasing and selling. Given a marketing
mode, at the beginning of the first period, an incumbent supplier and the downstream
monopolist choose one of the trading modes: (i) a two-period exclusive supply chainor (ii) an open supply chain, allowing the downstream monopolist to trade with anefficient supplier in the second period. We show that the downstream monopolist always
chooses the open supply chain in the leasing mode, although the exclusive supply chain
is attainable in the selling mode if the incumbent supplier’s efficiency is high. Moreover,when we allow the downstream monopolist to choose the marketing mode endogenously
before the first period, it chooses the selling mode if the incumbent supplier’s efficiency
is low; otherwise, it chooses the leasing mode. Regardless of the chosen marketing
mode, the open supply chain always occurs on the equilibrium path, implying that the
recent advancement of ICT to enhance leasing may discourage choosing the exclusive
supply chain.

JEL classification codes: L12, L41, L42, C72.
Keywords: Durable goods; Exclusive dealing; Vertical relation; Antitrust policy.

∗

We gratefully acknowledge the financial support from JSPS KAKENHI grant numbers JP15H05728,
JP17H00984, JP17K13729, JP18H00847, JP18K01593, JP19H01483, JP20H05631 and JP20K13485, The
Japan Center for Economic Research, and the program of the Joint Usage/Research Center for “Behavioral
Economics” at the ISER, Osaka University. 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§
Graduate School 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

1

Introduction

The recent advancement of information technology allows consumers to share durable goods
with others. In daily life, we observe that the lease markets of those products flourish.
Mobike, a Chinese-oriented bike-sharing operator, is a typical example to foster the leasemarket of bicycles. Mobike sets many parking slots of bicycles in cities, and customers easily
search the locations of those parking slots through their mobile phones. Moreover, Toyota,
a famous car manufacturer, has launched an automated car-lease service through customers’
mobile phones.1
Along with the recent change of the technological environment, we also need to consider
how those manufacturers form vertical relations with their suppliers in light of the researchachievement on the relation between the property of durable goods and vertical chains (e.g.,
Desai, Koenigsberg, and Purohit, 2004; Arya and Mittendorf, 2006). In particular, we areinterested in the openness of the supply chain in durable goods markets because researchers
have emphasized the importance of supply chain management in many contexts (the exclusiveness of keiretsu in the Japanese automobile industry (e.g., Aoki and Lennerfors, 2013),
channel coordination (e.g., Jeuland and Shugan, 1983; Coughlan, 1985, Gupta and Loulou,
1998; Gupta, 2008)).
As a flip side of supply chain openness, our argument is also on the discussion of exclusive
contracts. In reality, we commonly observe exclusive contracts, currently regarded as lawful
agreements, in many markets for durable goods such as industrial machinery/equipment
and electronic and electric equipment (Heide, Dutta, and Bergen, 1998).2 Moreover, we
1

See the official announcement “Toyota Launches “Toyota Share” Car-Sharing Service and “Chokunori”
Toyota Rent-a-Car Service for the Future Mobility Society in Japan” Toyota Motor Corporation, October28, 2019 (https://global.toyota/en/newsroom/corporate/30300778.html.
2

See also Mollgaard and Lorentzen (2004), who explore exclusive dealing in Eastern Europe’s car component industry.
Moreover, in the aviation industry, the Boeing Company andAirbus sometimes award exclusivity to one or two jet engine makers over the others.
See“GE Unit Lands Exclusive Boeing Pact For Developing Commercial Jet Engine” The Wall Street

1have also observed anticompetitive exclusive contracts in the market for durable goods suchas aluminum (the United States of America v. Aluminum Co. of America in the U.S.,
1945.), furniture (Paramount Bed Case in Japan, 1998), artificial teeth (the United States ofAmerica. v. Dentsply International, INC., in the U.S., 2005), and CPU (Intel Case in the
U.S., 2005).3
Despite these observations, most of the existing studies on exclusive contracts focus on
perishable goods markets. More importantly, none of the studies focus on the relationshipbetween the marketing mode and the likelihood of exclusive dealing. Therefore, this study
aims to ascertain how the marketing mode affects the supply chain’s openness, contributing
to the literature on supply chain management and competition policy.
Using the framework in Kitamura, Matsushima, and Sato (2021), we construct a twoperiod model in which an incumbent supplier makes an exclusive offer to a downstream
durable goods monopolist to deter the future entry of a more efficient entrant supplier. We
use the demand system in Purohit (1995) to explore the downstream monopolist’s marketing
mode choice, leasing or selling. By endogenizing the marketing mode choice, we explore
whether an incumbent supplier and a downstream durable goods monopolist choose one of
the trading modes, exclusive or open supply chain.
We first investigate the trading mode choice, exclusive or open supply chain, in eachof the two marketing modes. We show that the incumbent supplier and the downstream
durable goods monopolist choose the open supply chain in the leasing mode. Conversely,
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).
3

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/); Blairand Sokol (2015); 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.

2they choose the exclusive supply chain in the selling mode if this supplier’s efficiency is nothigh, similar to Kitamura, Matsushima, and Sato (2021). To understand those results, consider the effect of an efficient supplier’s future entry. As in the Chicago School argumentin the 1970s (Posner, 1976; Bork, 1978), the entry into the upstream market benefits thedownstream monopolist, restraining the incumbent supplier from offering an acceptable exclusive contract to the downstream monopolist. However, in the selling mode, an efficiency
improvement in the future exacerbates the time inconsistency problem in the durable goods
market, reducing the contracting party’s joint profit. Such a problem is significant when
the incumbent supplier’s efficiency is high because the expected wholesale price in the subsequent period matches the incumbent supplier’s marginal cost in the open supply chain.
In this case, the incumbent supplier and the downstream monopolist establish the exclusive
supply chain, which mitigates the time inconsistency problem. Conversely, the time inconsistency problem does not exist in the leasing mode; the efficiency gain from the efficient
supplier’s entry becomes a dominant effect. Thus, the downstream monopolist chooses theopen supply chain.
We next endogenize the downstream monopolist’s marketing mode choice. The downstream monopolist chooses the leasing mode if the incumbent supplier’s efficiency is high;otherwise, it chooses the selling mode. For the marketing mode decision, choosing the leasing mode has two benefits: (i) eliminating the time inconsistency problem and (ii) using a
final product twice. However, the twice use of final products also has a negative effect ofboosting the initial wholesale price in the leasing mode, which becomes significant when theincumbent supplier’s efficiency is low because the initial wholesale price becomes considerably high. Besides, the time inconsistency problem is not significant in the selling mode when
the incumbent supplier’s efficiency is low. Therefore, the downstream monopolist chooses
the selling mode if the incumbent supplier’s efficiency is low.
The results here provide several important implications for the vertical relationship in3

the advanced information society. The recent progress of information and communication
technology allows a firm to lease its durable goods to consumers more easily. First, fromthe viewpoint of marketing strategy, such technological progress does not necessarily facilitate leasing; we can observe both selling and leasing in the advanced information society.
Second, from a supply chain management perspective, the technological change to enhanceleasing may affect supply chain openness; the vertical relationship is less likely to establish
the exclusive supply chain. Finally, from the standpoint of competition policy, the technological change that facilitates leasing may reduce the achievement of anticompetitive exclusive
dealing in the upstream market for durable goods.
This study contributes to the literature on anticompetitive exclusive contracts that prevent a potential entrant’s socially efficient entry. The literature starts from the Chicago
School argument in the 1970s (Posner, 1976; Bork, 1978). They claim that rational economic agents never sign exclusive contracts for anticompetitive purposes. In rebuttals of
this view, researchers show that welfare decreasing exclusion is achievable by focusing on
scale economies (Rasmusen, Ramseyer, and Wiley, 1991; Segal and Whinston, 2000) anddownstream competition (Fumagalli and Motta, 2006; Simpson and Wickelgren, 2007).4
Existing models in the literature assume perishable goods markets. A companion work in
Kitamura, Matsushima, and Sato (2021) is an exception that considers durable goods markets in the context of exclusive contracts when the downstream durable goods monopolist
sells its product but does not lease it. Here, we provide a follow-up framework to clarify
whether the marketing mode is crucial to attaining exclusive contracts in durable goods
markets.
The remainder of this paper is as follows: Section 2 constructs the model. Section 3
analyzes the trading mode choices in the leasing mode, whereas Section 4 provides the results
4

Other key factors of exclusion are a penalty for breach of contract (Aghion and Bolton, 1987) andthe structure of the upstream market (Yong, 1996; Farrell, 2005; Fumagalli, Motta, and Persson, 2009;
Fumagalli, Motta, and Rønde, 2012; Kitamura, Matsushima, and Sato, 2017, 2018).

4

on the trading modes in the selling mode. Section 5 introduces the analysis of marketing
mode decisions. Section 6 offers concluding remarks. Appendix A provides the equilibriumoutcomes in the selling mode. Appendix B presents the proof of Proposition 3.

2

Preliminary

We employ the framework of Kitamura, Matsushima, and Sato (2021), by introducing thedemand system in Purohit (1995). The precise explanation for the modeling, including thejustification of assumptions, is provided in Kitamura, Matsushima, and Sato (2021).

2.1

Market environment

We consider a two-period model with a downstream durable goods monopolist D, an incumbent input supplier UI , and an entrant input supplier UE . There is a common discount factorρ ∈ (0, 1) for all players who are active in two periods. The demand system follows that inPurohit (1995) (see also Bulow, 1982; Purohit and Staelin, 1994). We explain the detail ofthe demand system in the subsequent section. Our terminology to describe downstream andupstream players differs from that in Purohit (1995).5
D launches a durable good that endures for two periods. It needs one unit of input toproduce one unit of durable goods. D incurs per unit wholesale price to procure its inputs.
Except for the procurement cost, D does not incur any cost. We consider two marketing
modes: (i) D leases the durable good to final consumers; (ii) it sells the goods to final
consumers. The durable good is perfectly durable in the two-period model, and there is aperfectly competitive second-hand market in the selling mode.
In the upstream market, only UI exists at the beginning of period 1, although UE has achance to enter the market at the beginning of period 2. UI and UE produce an identical5

He refers to upstream and downstream players as a supplier (or a monopolist) and a retailer, although
we refer to them as a supplier(s) and a monopolist. We focus on the downstream durable goods monopolist.

5input with the constant marginal costs cI and cE (0 ≤ cE < cI ). We assume that thedifference between cE and cI is not large such that the existence of UI restricts the pricingof UE .
Consumers are forward-looking and rational. Taking into account the current price ofthe durable good, each consumer expects its future price. The expectations of consumers
form consumers’ willingness to pay for the durable good.
Timing In period 0, D chooses one of the marketing modes, leasing or selling. In period
1, only UI exists in the upstream market. Period 1 consists of three stages. In period 1.1,
UI makes a two-period exclusive offer to D, with fixed compensation x ≥ 0. The exclusive
offer does not contain the term of wholesale prices as in the related papers.6 Given theoffer with the compensation x, D determines whether to accept it. If D accepts the offer,
it immediately receives x. Let ω ∈ {a, r} be the result in period 1.1, where the script “a”(“r”) represents that D accepts (rejects) the offer of the exclusive contract. In period 1.2,
UI offers a linear wholesale price to D. In period 1.3, D orders the input and markets the
final good to consumers.7
At the beginning of period 2, UE has a chance to enter the upstream market if D does
not accept the exclusive offer in period 1. Period 2 contains three stages. In period 2.1, UE
determines whether to enter the market if possible.8 We assume that UE ’s fixed entry cost
6

If contracting parties cannot describe concrete product characteristics in advance, commitment totrading terms is difficult in the stage of making exclusive offers (Rasmusen, Ramseyer, and Wiley, 1991;
Segal and Whinston, 2000).
7

In the leasing mode, this study’s analytical procedure differs from that of the rental case in Purohit(1995,§3.2). In Purohit (1995,§3.2), first, he solves the optimal quantities of the downstream firm in periods
1 and 2. Second, considering the quantities that depend on the first- and second-period wholesale prices, hederives the optimal wholesale prices in periods 1 and 2. The procedure implies that the upstream suppliercan commit to the second-period wholesale price at the beginning of the game in the rental case.
8

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

6

is sufficiently small such that UE can earn positive profits. In period 2.2, active suppliers
offer linear wholesale prices to D. When UE has entered, UI and UE become competitors ofhomogeneous input. We assume that if their trading terms are equally attractive for D, theefficient supplier UE supplies its input to D. In period 2.3, D orders the input and markets
the final good to consumers.
ωωLet πi|t(i ∈ {I, E}) be Ui ’s profit in period t in case ω ∈ {a, r}. Also, let πD|tbeω
ω
D’s profit in period t in case ω ∈ {a, r}. The objectives of UI and D are πI|1
+ ρπI|2
and
ω
ω
ω
πD|1
+ ρπD|2
respectively. The objective of UE is ρπE|2, when it enters in period 2.

2.2

Design of exclusive contracts

Exclusion is achievable if and only if the equilibrium compensation x∗ must satisfy thefollowing two conditions simultaneously.
First, D must gain from the exclusive contract. That is,
a
a
r
r
r
r
a
a
πD|1
+ x∗ + ρπD|2≥ πD|1+ ρπD|2or x∗ ≥ πD|1
+ ρπD|2− (πD|1+ ρπD|2).

(1)

Second, UI must also gain from the exclusive contract. That is,
a
a
r
r
a
a
r
r
πI|1
+ ρπI|2− x∗ ≥ πI|1
+ ρπI|2or x∗ ≤ πI|1
+ ρπI|2− (πI|1+ ρπI|2).

(2)

From the two conditions, an exclusion equilibrium exists if and only if the inequalities in(1) and (2) simultaneously hold. The condition is equivalent to the following inequality:
a
a
a
a
r
r
r
r
πI|1
+ ρπI|2+ πD|1+ ρπD|2≥ πI|1+ ρπI|2+ πD|1+ ρπD|2.

(3)

Condition (3) implies that an exclusion equilibrium is attainable if such an exclusive contract
increases the two-period joint profits of UI and D. It is sufficient to focus on the two-period
joint profits of UI and D.

7

3

Leasing

This section considers the situation in which D chooses the leasing mode in stage 0. It
produces q1 units of the good in period 1 and q2 units of the good in period 2. Because of
the no depreciation assumption, D can lease q1 + q2 units of the goods in period 2. Following
the formulation in Purohit (1995,§3.2), we set the lease prices of the good in periods 1 and2, l1 and l2 , as follows:
l1 = α − βq1 ,l2 = α − β(q1 + q2 ),where α and β are positive constants. To simplify the exposition, we assume that cI is not
too large:
Assumption 1.
cI <(3 + ρ)α.
3 + 2ρ

(4)

Condition (4) simplifies the exposition of the results but does not change the property of theresults.9
From now on, we solve the game by backward induction. We consider D’s optimal
production level in period 2.3, given the linear wholesale price w2 . Considering the constraint
q2 ≥ 0, D chooses q2 to maximize the second period profit:q2∗ (w2 , q1 ) ≡ argmax l2 (q1 + q2 ) − w2 q2 .
q2 ≥0

The profit maximization problem leads to α − 2βq1 − w2 if w ≤ α − 2βq ,21∗
2βq2 (w2 , q1 ) =0
if w2 ≥ α − 2βq1 ,2
 (α − βq )q + (α − 2βq1 − w2 ) if w ≤ α − 2βq ,
1
1
2
1
∗
πD|2
(w2 , q1 ) =4β(α − βq1 )q1
if w2 ≥ α − 2βq1 .
9The results in which (4) does not hold is available upon request.

8(5)

In the following subsections, we consider two trading modes: an exclusive supply chain andan open supply chain.

3.1

Exclusive supply chain

In this case, UI is the upstream monopolist in both periods.
In period 2.2, anticipating D’s reaction (5), UI chooses w2 to maximize its second period
profit:w2a∗ (q1 ) ≡ argmax (w2 − cI )q2∗ (w2 , q1 ).
w2 ≥cI

The profit maximization problem leads to α + cI − 2βq1
if βq1 ≤ (α − cI )/2,a∗w2 (q1 ) =2 cif βq1 ≥ (α − cI )/2.
I

From (5) and (6), given q1 , we obtain the production level in period 2 α − cI − 2βq1 if βq ≤ (α − c )/2,
1
I
a∗
4β
q2 (q1 ) =0
if βq1 ≥ (α − cI )/2.

(6)

(7)

In period 2.1, nothing happens due to the achievement of the exclusive contract.
In period 1.3, given that UI offers w1 , D chooses q1 to maximize the overall profit
q1a∗ (w1 ) ≡ argmax (a − βq1 − w1 )q1
q1+ρ(α − β(q1 + q2a∗ (q1 )))(q1 + q2a∗ (q1 )) − ρw2a∗ (q1 )q2a∗ (q1 ).
The profit maximization problem leads to(4 + 3ρ)α + ρcI − 4w1
if w1 ≥ (1 + ρ)cI ,
2β(4 + 3ρ)a∗q1 (w1 ) =(1 + ρ)α − w1
if w1 ≤ (1 + ρ)cI .
2β(1 + ρ)

From (6), (7), and (8), we obtain w2a∗ (q1a∗ (w1 )) and q2a∗ (q1a∗ (w1 )) respectively: 2w1 + (2 + ρ)cI if w ≥ (1 + ρ)c ,
1
I
a∗ a∗
4 + 3ρ
w2 (q1 (w1 )) =cI
if w1 ≤ (1 + ρ)cI ,
9

(8)


 w1 − (1 + ρ)cIa∗ a∗β(4 + 3ρ)q2 (q1 (w1 )) =0

if w1 ≥ (1 + ρ)cI ,if w1 ≤ (1 + ρ)cI .

In period 1.2, by anticipating this reaction, UI chooses w1 to maximize its overall profits:
w1a∗ ≡ argmax (w1 − cI )q1a∗ (w1 ) + ρ(w2a∗ (q1a∗ (w1 )) − cI )q2a∗ (q1a∗ (w1 )).
w1

The profit maximization problem leads to(4 + 3ρ)2 α + (16 + 8ρ − 5ρ2 )cI16(2 + ρ)w1a∗ =(1 + ρ)cI(1 + ρ)α + cI2

(4 + 3ρ)α,4 + 7ρ
(1 + ρ)α(4 + 3ρ)α≤ cI ≤,
if
4 + 7ρ
1 + 2ρ
(1 + ρ)αif≤ cI .
1 + 2ρ

if cI ≤

(9)

The resulting profits, excluding the fixed compensation x∗ , are summarized as follows.
(4 + 3ρ)2 α2 − 2(16 + 8ρ + 5ρ2 )αcI + (16 − 8ρ + 17ρ2 )c2I64β(2 + ρ)
(4 + 3ρ)α
if cI ≤,
4 + 7ρ
a∗a∗(10)
πI|1 + ρπI|2 =(4 + 3ρ)α(1 + ρ)αρ(α − cI )cI
if≤ cI ≤,

2β
4 + 7ρ
1 + 2ρ
(1 + ρ)α((1 + ρ)α − cI )2
if≤ cI .
8β(1 + ρ)
1 + 2ρ
(64 + 144ρ + 92ρ2 + 19ρ3 )α2
256β(2 + ρ)2





2(64 + 80ρ + 28ρ2 + 7ρ3 )αcI

 −


256β(2 + ρ)2(4 + 3ρ)α(64 + 16ρ + 28ρ2 + 43ρ3 )c2Ia∗a∗
if cI ≤,+
πD|1
+ ρπD|2=(11)
2
256β(2 + ρ)
4 + 7ρ
(1 + ρ)(α − cI )2(4 + 3ρ)α(1 + ρ)α


if
≤
c
≤
,

I


4β
4 + 7ρ
1 + 2ρ
((1 + ρ)α − cI )2(1 + ρ)αif≤ cI .
16β(1 + ρ)
1 + 2ρ

3.2

Open supply chain

In this case, competition in the upstream market occurs in period 2.2, which differs from theprevious case.
10

In period 2.2, the wholesale price becomes w2r∗ = cI because of the upstream competition(we have assumed that UE is not so efficient such that it cannot be an upstream monopolist
without any constraint on its pricing). UI earns nothing in period 2.
From (5) and w2r∗ = cI , D chooses the following production level in period 2: α − cI − 2βq1 if βq ≤ (α − c )/2,
1
I
r∗
2β
q2 (q1 ) =0
if βq1 ≥ (α − cI )/2.

(12)

In period 1.3, given that UI sets w1 , D chooses q1 to maximize its overall profits:
q1r∗ (w1 ) ≡ argmax (a − βq1 − w1 )q1
q1+ρ(α − β(q1 + q2r∗ (q1 )))(q1 + q2r∗ (q1 )) − ρcI q2r∗ (q1 ).
The profit maximization problem leads to
α + ρcI − w1
if w1 ≥ (1 + ρ)cI ,
2βr∗q1 (w1 ) =(1 + ρ)α − w1
if w1 ≤ (1 + ρ)cI .

2β(1 + ρ)
From (12) and (13), we obtain q2r∗ (q1r∗ (w1 )): w1 − (1 + ρ)cIr∗ r∗
2β
q2 (q1 (w1 )) =

0

(13)

if w1 ≥ (1 + ρ)cI ,if w1 ≤ (1 + ρ)cI .

In period 1.2, by anticipating this reaction, UI chooses w1 to maximize its overall profits:
w1r∗ ≡ argmax (w1 − cI )q1r∗ (w1 ).
w1The profit maximization problem leads toα + (1 + ρ)cI




2



w1r∗ =(1 + ρ)cI(1 + ρ)α + cI
2

if cI ≤α,1+ρα(1 + ρ)α≤ cI ≤,1+ρ
1 + 2ρ
(1 + ρ)αif≤ cI .
1 + 2ρ

if

11

(14)

UI ’s profit is(α − (1 − ρ)cI )2α
if cI ≤
,


8β
1+ρ


 ρ(α − c )cα
(1 + ρ)α
I I
r∗
r∗
πI|1
+ ρπI|2=if≤ cI ≤,
2β
1+ρ
1 + 2ρ
(1 + ρ)α((1 + ρ)α − cI )2
if≤ cI .
8β(1 + ρ)
1 + 2ρ

(15)

Also, D’s profit is(1 + 4ρ)α2 − 2(1 + 3ρ)αcI + (1 + ρ)2 c2I
α


if
c
≤
,
I


16β
1
+
ρ



 (1 + ρ)(α − c )2α
(1 + ρ)αIr∗r∗
πD|1 + ρπD|2 =if≤ cI ≤,
4β
1+ρ
1 + 2ρ
(1 + ρ)α((1 + ρ)α − cI )2
if≤ cI .
16β(1 + ρ)
1 + 2ρ

3.3(16)

Comparison

Using (10), (11), (15) and (16), we check whether condition (3) holds to explore the existence
a∗
a∗
a∗
a∗
of an exclusion equilibrium. By calculating the difference between πI|1
+ ρπI|2+ πD|1+ ρπD|2r∗r∗r∗r∗
and πI|1+ ρπI|2+ πD|1+ ρπD|2, we obtain the following proposition:

Proposition 1. In the leasing mode, UI and D do not choose an exclusive supply chain.
Under the exclusive supply chain, anticipating the higher wholesale price in period 2, D
needs to produce more in period 1 than in the open case. In fact, from (8) and (13), we
find that q1a∗ (w1 ) > q1r∗ (w1 ) holds if and only if w1 ≥ (1 + ρ)cI , which is the necessary andsufficient condition that the second-period production level is positive in both the exclusive
supply chain and the open supply chain.10 However, the monopoly power of UI under the
exclusive supply chain partially offsets the stronger incentive of D to produce more in period
1. Actually, w1a∗ in (9) is larger than w1r∗ in (14) if and only if cI < (4 + 3ρ)α/(4 + 7ρ), whichis the necessary and sufficient condition that the second-period production level is positive10

If w1 ≤ (1 + ρ)cI , q1a∗ (w1 ) = q1r∗ (w1 ) always holds.

12under the exclusive supply chain.11 As a result, the overall activity under the exclusion
supply chain is lower than that in the open supply chain, preventing UI from making an
acceptable exclusive offer to D.

4

Selling

This section considers the situation in which D chooses the selling mode in stage 0. It
produces q1 units of the good in period 1 and q2 units of the good in period 2. In contrast
to the leasing mode, D sells q2 units of the goods in period 2. By considering consumers’intertemporal purchase decision, we set the selling prices of the good in periods 1 and 2, p1
and p2 , where
p1 = l1 + ρp2 , p2 = l2 .
This marketing mode is similar to Kitamura, Matsushima, and Sato (2021). Here, we briefly
introduce the results. See Appendix A for a precise derivation procedure of each trading
mode’s equilibrium outcomes D chooses the selling mode.
Under the exclusive supply chain, the profits of UI and D, excluding the fixed compensation x∗ , are((128 + 184ρ + 67ρ2 )α − (128 + 56ρ − 5ρ2 )cI )((8 + 3ρ)α − (8 − 5ρ)cI )128β(8 + 5ρ)2
(17)((24 + 17ρ)α − (24 + 25ρ)cI )2+ρ,
128β(8 + 5ρ)2((8 + 7ρ)α − (8 − ρ)cI )((8 + 3ρ)α − (8 − 5ρ)cI )
aS
aS
πD|1
+ ρπD|2=128β(8 + 5ρ)(18)((24 + 17ρ)α − (24 + 25ρ)cI )2+ρ,
256β(8 + 5ρ)2aSaS=
+ ρπI|2πI|1and the equilibrium wholesale price in period 1 is(128 + 184ρ + 67ρ2 )α + (128 + 104ρ + 5ρ2 )cI
aS
,
w1 =
32(8 + 5ρ)11

If cI ≥ (4 + 3ρ)α/(4 + 7ρ), w1a∗ = w1r∗ always holds.

13

(19)

where the script “aS” represents accepting an exclusive offer in the selling mode.
Conversely, under the open supply chain, the profits of UI and D are(α − (1 − ρ)cI )2,2β(4 + ρ)((2 + 4ρ + ρ2 )α − (2 + 2ρ + ρ2 )cI )(α − (1 − ρ)cI )
rS
rS
πD|1
+ ρπD|2=2β(4 + ρ)2((3 + ρ)α − (3 + 2ρ)cI )2+ρ,
4β(4 + ρ)2
and the equilibrium wholesale price in period 1 becomes
rS
rS
πI|1
+ ρπI|2=

w1rS =

α + (1 + ρ)cI
,
2

(20)

(21)

(22)

where the script “rS” represents rejecting an exclusive offer in the selling mode.
Using (17), (18), (20) and (21), we check whether condition (3) holds to explore theaS
aS
existence of an exclusion equilibrium. By calculating the difference between πI|1
+ ρπI|2
+
aS
aS
rS
rS
rS
rS
πD|1
+ ρπD|2and πI|1+ ρπI|2+ πD|1+ ρπD|2, we obtain the following proposition:

Proposition 2. In the selling mode, UI and D choose an exclusive supply chain ifp
768 + ρ 768 − 1156ρ − 865ρ2 − 8(8 + 5ρ) (4 + ρ)(208 + 133ρ)α.
cI ≤768 + ρ(512 − 6820ρ − 4425ρ2 )(23)

The efficiency improvement through the entry in period 2 exacerbates the time inconsistency problem due to the expected retail price reduction in period 2. The negative effect of
the second-period entry facilitates establishing an exclusive supply chain. More importantly,
the entry’s negative impact is significant when cI is small because the expected wholesale
price in period 2 is w2rS = cI due to the upstream competition in period 2. Therefore, whencI is small, the entry of UE is harmful to UI and D; they establish the exclusive supply chain,
which deters efficient future entry in the upstream market.

5

Leasing versus Selling

Using the above results, we now explore which marketing mode D chooses in period 0 andwhich trading mode UI and D establish in period 1. By considering D’s profit, we obtain14

the following proposition:
Proposition 3. If D chooses one of the marketing modes, leasing or selling, it chooses
selling if and only if√
3 + 2ρ − ρ 4 + ρα.
cI ≥3 + 3ρ − ρ2(24)

On the equilibrium path, UI and D always choose an open supply chain for any level of cI .
Note that if (24) holds, (23) never holds; namely, the open supply chain always occurs
when D chooses the selling mode. Conversely, if (24) does not hold, the open supply chain
and leasing are chosen. Therefore, this proposition implies that the exclusive supply chain
does not appear if we consider D’s choice of the marketing modes.
Choosing the leasing mode eliminates the time inconsistency problem and allows D to
use a final product twice. Those two effects are the benefits of choosing the leasing mode.
However, the comparison between (19) and (22) implies that the first-period wholesale pricein the leasing mode is higher than that in the selling mode for the higher marginal cost of
UI (i.e., w1r∗ > w1rS holds for cI > α/(1 + ρ)). The higher wholesale price stems from thetwice leases of final products made in period 1. Moreover, the time inconsistency problem
becomes not significant in the selling mode as cI increases. Thus, when UI is sufficiently
inefficient, the negative effect of choosing the leasing mode becomes the dominant effect, andD chooses the selling mode and the open supply chain.12

6

Conclusion

This study constructs a two-period model in which an incumbent supplier and a downstream
durable goods monopolist choose the supply chain’s openness by focusing on the downstream
monopolist’s marketing mode choice between leasing and selling. Under the open supply
chain, an efficient supplier’s entry occurs in the second period. Using the demand system in
12

The threshold value in (24) is larger than α/(1 + ρ).

15

Purohit (1995), we first explore how the incumbent supplier and the downstream monopolist
determine the supply chain’s openness in each marketing mode. We then endogenize thedownstream monopolist’s marketing mode decision to investigate the relationship between
the marketing mode and the supply chain’s openness.
We show that in the leasing mode, the initially existing players choose an open supply
chain, which allows the downstream monopolist to trade with the efficient entrant supplierin the future. Conversely, in the selling mode, the incumbent supplier and the downstream
monopolist can establish a two-period exclusive supply chain to deter the efficient future entry
if the incumbent supplier’s efficiency is high; otherwise, they choose the open supply chain.
More importantly, if we allow the downstream monopolist to choose one of the marketing
modes endogenously, it chooses the selling mode if the incumbent supplier’s efficiency is low;otherwise, the downstream monopolist chooses the leasing mode. Although the downstream
monopolist chooses one of the marketing modes depending on the incumbent supplier’s
efficiency level, it always chooses the open supply chain on the equilibrium path.
The findings here provide several important implications. First, from the viewpointof marketing strategy, the recent progress of information and communication technology,
allowing a firm to lease its durable goods to consumers more easily, does not necessarily
facilitate leasing. Second, from a perspective of supply chain management, the technologicalchange to enhance leasing may affect the supply chain’s openness; the vertical relationship isless likely to establish the exclusive supply chain in the advanced information society. Finally,
from the competition policy perspective, as leasing spreads throughout society, the vertical
relationship is less likely to engage in exclusive dealing for an anticompetitive purpose.
Despite these contributions, several concerns are requiring future works. First, we haveassumed that the trading term between the downstream monopolist and a supplier follows alinear wholesale price contract. We can consider another trading term based on a two-parttariff contract. Second, there is concern about the generality of our results. Although the16analysis depends on a specific demand system, we could extend it to more general settings.
We hope this study will assist future research in applying the model to these situations.

17A

Equilibrium Outcomes under SellingThis appendix considers the situation in which D chooses the selling mode in stage 0. For
the sake of convenience in solving the game by backward induction, we consider D’s optimal
production level in period 2.3, given w2 . D chooses q2 to maximize the second period profit:
q2S (w2 , q1 ) ≡ argmax (p2 − w2 )q2 .
q2 ≥0

The profit maximization problem leads toα − βq1 − w2,2βq2S (w2 , q1 ) =S
πD|2(w2 , q1 ) =(25)(α − βq1 − w2 )2.
4β

In the following subsections, we consider two trading modes: an exclusive supply chain andan open supply chain.

A.1

Exclusive supply chain

In this case, UI is the upstream monopolist in both periods.
In period 2.2, anticipating D’s reaction (25), UI chooses w2 to maximize its second period
profit:w2aS (q1 ) ≡ argmax (w2 − cI )q2S (w2 , q1 ).
w2 ≥cI

The profit maximization problem leads to
w2aS (q1 ) =α + cI − βq1
.
2

(26)

From (25) and (26), given q1 , we obtain the production level in period 2
q2aS (q1 ) =α − cI − βq1,
4βwhich leads to the following price in period 2
paS
2 (q1 ) =3α + cI − 3βq1
.
4β
18

(27)

In period 2.1, nothing happens due to the achievement of the exclusive contract.
In period 1.3, given that UI offers w1 , D chooses q1 to maximize the overall profit
aS
aS
aS
q1aS (w1 ) ≡ argmax (a − βq1 + ρpaS
2 (q1 ) − w1 )q1 + ρ(p2 (q1 ) − w2 (q1 ))q2 (q1 ).
q1

The profit maximization problem leads to
q1aS (w1 ) =(8 + 5ρ)α + 3ρcI − 8w1.
(16 + 11ρ)β(28)

From (26), (27), and (28), we obtain w2aS (q1aS (w1 )) and q2aS (q1aS (w1 )) respectively:
w2aS (q1aS (w1 )) =(4 + 3ρ)α + 4(2 + ρ)cI + 4w1,(16 + 11ρ)βq2aS (q1aS (w1 )) =(4 + 3ρ)α − (8 + 7ρ)cI + 4w1.
2(16 + 11ρ)βIn period 1.2, by anticipating this reaction, UI chooses w1 to maximize its overall profits:
w1aS ≡ argmax (w1 − cI )q1aS (w1 ) + ρ(w2aS (q1aS (w1 )) − cI )q2aS (q1aS (w1 )).
w1

The profit maximization problem leads to (19). The resulting profits of UI and D, excluding
the fixed compensation, are (17) and (18).

A.2Open supply chain

In this case, competition in the upstream market occurs in period 2.2, which differs from theprevious case.
In period 2.2, the wholesale price becomes w2rS = cI because of the upstream competition.
UI earns nothing in period 2. From (25) and w2rS = cI , given q1 , D chooses the following
production level in period 2:
q2rS (q1 ) =α − cI − βq1.
2βwhich leads to the following price in period 2
prS
2 (q1 ) =α + cI − βq1.
2β19In period 2.1, UE enters the upstream market.
In period 1.3, given that UI sets w1 , D chooses q1 to maximize its overall profits:
rS
rS
q1rS (w1 ) ≡ argmax (a − βq1 + ρprS
2 (q1 ) − w1 )q1 + ρ(p2 (q1 ) − cI )q2 (q1 ).
q1

The profit maximization problem leads to
q1rS (w1 ) =2(α + ρcI − w1 ).
(4 + ρ)βIn period 1.2, by anticipating this reaction, UI chooses w1 to maximize its overall profits:
w1rS ≡ argmax (w1 − cI )q1rS (w1 ).
w1The profit maximization problem leads to (22). The resulting profits of UI and D are (20)and (21).

B

Proof of Proposition 3

The leasing mode has three cases: (i) cI ≤ α/(1 + ρ), (ii) α/(1 + ρ) ≤ cI ≤ (1 + ρ)α/(1 + 2ρ),(iii) (1 + ρ)α/(1 + 2ρ) ≤ cI . The threshold value of Proposition 2 in the selling mode, (23), isalways lower than α/(1 + ρ). Therefore, we consider four cases: (I) cI ≤ α/(1 + ρ) and (23)holds, (II) cI ≤ α/(1 + ρ) and (23) does not hold, (III) α/(1 + ρ) ≤ cI ≤ (1 + ρ)α/(1 + 2ρ),(IV) (1 + ρ)α/(1 + 2ρ) ≤ cI < 3(1 + ρ)α/(3 + 2ρ).
For case (I) (cI ≤ α/(1 + ρ) and (23) holds), the exclusive supply chain is chosen in
the selling mode. In this case, the highest profit of D, including the fixed compensation x∗ ,
aS
rS
rS
aS
aS
aS
+ ρπI|2). By comparing the highest profit of D with− (πI|1+ ρπI|2+ πD|1+ πD|2
becomes πI|1r∗r∗
+ ρπD|2
in the leasing mode, we have
πD|1
aS
aS
aS
aS
rS
rS
r∗
r∗
πI|1
+ ρπI|2+ πD|1+ πD|2− (πI|1+ ρπI|2) − (πD|1+ ρπD|2)=−

ρ(λ1 α2 − 2λ2 αcI + λ3 c2I ),256β(4 + ρ)(8 + 5ρ)2

which is negative for any cI , where λ1 ≡ (256 + 256ρ + 244ρ2 + 121ρ3 ), λ2 ≡ (256 − 512ρ +276ρ2 + 465ρ3 ), and λ3 ≡ (256 − 1280ρ + 5684ρ2 + 4905ρ3 + 400ρ4 ). Thus, in case (I), D
always chooses the leasing mode.
20

For case (II) (cI ≤ α/(1 + ρ) and (23) does not hold), the open supply chain is chosen
rS
rS
r∗
r∗
in the selling mode. We compare πD|1
+ ρπD|2
in the selling mode with πD|1
+ ρπD|2
in theleasing mode.
rS
rS
r∗
r∗
πD|1
+ ρπD|2− (πD|1+ ρπD|2)=−

ρ(α − (1 − ρ)cI )2 ),16β(4 + ρ)

which is negative for any cI . Hence, in case (II), D always chooses the leasing mode.
For case (III) (α/(1 + ρ) ≤ cI ≤ (1 + ρ)α/(1 + 2ρ)), the open supply chain is chosen in the
rS
rS
r∗
r∗
selling mode. We compare πD|1
+ ρπD|2
in the selling mode with πD|1
+ ρπD|2
in the leasingmode.
(3 + ρ)α2 − 2(3 + 2ρ)αcI + (3 + 3ρ − ρ2 )c2I,
4β(4 + ρ)√
which is positive if and only if cI ≥ (3 + 2ρ − ρ 4 + ρ)α/(3 + 3ρ − ρ2 ) as in (24). Thus, in
rS
rS
r∗
r∗
+ ρπD|2− (πD|1+ ρπD|2)=−
πD|1

this case, D chooses the selling mode if (24) holds; otherwise it chooses the leasing mode.
For case (IV) ((1 + ρ)α/(1 + 2ρ) ≤ cI < 3(1 + ρ)α/(3 + 2ρ)), the open supply chain is
rS
rS
r∗
r∗
chosen in the selling mode. We compare πD|1
+ ρπD|2
in the selling mode with πD|1
+ ρπD|2

in the leasing mode.
rS
rS
r∗
r∗
πD|1
+ρπD|2−(πD|1+ρπD|2)=(1 + ρ)(11 + 3ρ)α2 − 2(1 + ρ)(11 + 4ρ)αcI + (11 + 16ρ + 8ρ2 )c2I,
16β(1 + ρ)(4 + ρ)

which is positive for any cI (≥ (1 + ρ)α/(1 + 2ρ)). Thus, in case (IV), D always chooses theselling mode.

Q.E.D.

References
Aghion, P., and Bolton, P., 1987. Contracts as a Barrier to Entry. American Economic Review 77(3), 388–401.
Aoki, K., and Lennerfors, T.T., 2013. Whither Japanese Keiretsu? The Transformation of
Vertical Keiretsu in Toyota, Nissan and Honda 1991-2011. Asia Pacific Business Review 19(1), 70–84.
21

Arya, A., and Mittendorf, B., 2006. Benefits of Channel Discord in the Sale of Durable Goods.
Marketing Science 25(1), 91–96.
Blair, D., and Sokol, D.D., 2015. The Oxford Handbook of International Antitrust Economics
Volume 2. Oxford: Oxford University Press.
Bork, R.H., 1978. The Antitrust Paradox: A Policy at War with Itself. New York: Basic
Books.
Bulow, J., 1982. Durable-Goods Monopolists. Journal of Political Economy 90(2), 314–332.
Bulow, J., 1986. An Economic Theory of Planned Obsolescence. Quarterly Journal of Economics 101(4), 729–750.
Coase, R., 1972. Durability and Monopoly. Journal of Law and Economics 15(1), 143–149.
Coughlan, A.T., 1985. Competition and Cooperation in Marketing Channel Choice: Theory
and Application. Marketing Science 4(2), 110–129.
Desai, P.S., Koenigsberg, O., and Purohit, D., 2004. Strategic Decentralization and Channel Coordination. Quantitative Marketing and Economics 2(1), 5–22.
Farrell, J., 2005. Deconstructing Chicago on Exclusive Dealing. Antitrust Bulletin 50, 465–
480.
Fumagalli, C., and Motta, M., 2006. Exclusive Dealing and Entry, when Buyers Compete.
American Economic Review 96(3), 785–795.
Fumagalli, C., Motta, M., and Persson, L., 2009. On the Anticompetitive Effect of Exclusive Dealing when Entry by Merger is Possible. Journal of Industrial Economics 57(4),785–811.

22

Fumagalli, C., Motta, M., and Rønde, T., 2012. Exclusive Dealing: Investment Promotion
may Facilitate Inefficient Foreclosure. Journal of Industrial Economics 60(4), 599–
608.
Gupta, S., 2008. Channel Structure with Knowledge Spillovers. Marketing Science 27(2),247–261.
Gupta, S., and Loulou, R., 1998. Process Innovation, Product Differentiation, and Channel
Structure: Strategic Incentives in a Duopoly. Marketing Science 17(4), 301–316.
Heide, J.B., Dutta, S., and Bergen, M., 1998. Exclusive Dealing and Business Efficiency: Evidence from Industry Practice. Journal of Law and Economics 41(2), 387–408.
Jeuland, A.P., and Shugan, S.M., 1983. Managing Channel Profits. Marketing Science 2(3),239–272.
Kitamura, H., Matsushima, N., and Sato, M., 2017. Exclusive Contracts and Bargaining Power.
Economics Letters 151, 1–3.
Kitamura, H., Matsushima, N., and Sato, M., 2018. Exclusive Contracts with Complementary Inputs. International Journal of Industrial Organization 56, 145–167.
Kitamura, H., Matsushima, N., and Sato, M., 2021. Which is Better for Durable Goods Producers, Exclusive or Open Supply Chain? ISER Discussion Paper No.1115, Available
at SSRN: https://dx.doi.org/10.2139/ssrn.3773927.
Mollgaard, H.P., and Lorentzen, J., 2004. Exclusive Safeguards and Technology Transfer:
Subcontracting Agreements in Eastern Europe’s Car Component Industry. European
Journal of Law and Economics 17(1), 41–71.
Posner, R.A., 1976. Antitrust Law: An Economic Perspective. Chicago: University of Chicago
Press.
23

Purohit, D., 1995. Marketing Channels and the Durable Goods Monopolist: Renting versus
Selling Reconsidered. Journal of Economics & Management Strategy 4(1), 69–84.
Purohit, D., and Staelin, R., 1994. Rentals, Sales, and Buybacks: Managing Secondary Distribution Channels. Journal of Marketing Research 31, 325–338.
Rasmusen, E.B., Ramseyer, J.M., and Wiley Jr., J.S., 1991. Naked Exclusion. American Economic Review 81(5), 1137–1145.
Segal, I.R., and Whinston, M.D., 2000. Naked Exclusion: Comment. American Economic
Review 90(1), 296–309.
Simpson, J., and Wickelgren, A.L., 2007. Naked Exclusion, Efficient Breach, and Downstream
Competition. American Economic Review 97(4), 1305–1320.
Yong, J.S., 1996. Excluding Capacity-Constrained Entrants through Exclusive Dealing: Theory and an Application to Ocean Shipping. Journal of Industrial Economics 44(2),115–129.

24