Outsourcing without Cost Advantages

Chrysovalantou Milliou�

April 2019Preliminary Draft

Abstract

We study outsourcing to an external supplier without a cost advantage in input pro-

duction. We show that the supplier can pro�tably induce outsourcing by two competing

vertically integrated �rms through the use of two-part tari¤s. This occurs although out-

sourcing generates cost asymmetry and deteriorates the competitive position of one of its

customers. We also show that the presence of an otherwise redundant input producer in

the market can be welfare-increasing.

Keywords: strategic outsourcing; make-or-buy; two-part tari¤s; common supplier; raise

rivals�cost

JEL classi�cation: D43; L11; L21; L22; L23

�Department of International and European Economic Studies, Athens University of Economics and Busi-ness, e-mail: cmilliou@aueb.gr. I would like to thank Konstantinos Papadopoulos for his contribution in earlierstages of this paper. I am grateful to John Asker and Michael H. Riordan for their useful suggestions. I wouldalso like to thank Aaron Barkley, Andrea Fosfuri, Massimo Motta, Lambros Pechlivanos, Emmanuel Petrakis,Patrick Rey, Konstantinos Serfes, seminar participants at Columbia University, and conference participantsat IIOC in Boston for their comments. Full responsibility for all shortcomings is mine.

1 Introduction

In today�s world, it is rare to �nd a �rm that does not outsource at least a part of its pro-

duction.1 The most obvious and extensively studied motive for outsourcing is cost-reduction,

typically due to the external supplier�s lower input production cost.2 This is consistent with

many instances of outsourcing to suppliers located in countries with lower labor or material

costs, such as China and India.3 Not all �rms, however, outsource to suppliers with lower

production costs. Boeing, for example, outsources the production of a signi�cant percentage

of its aircraft fuselage to a Japanese consortium, although neither labor costs nor other costs

in the Japanese aircraft industry are known to be lower than in the US.4 In fact, wages in

Japan as well as in several other countries where key Boeing suppliers hang their hats, such

as Germany and France, are high. Furthermore, with the cost advantages of suppliers from

countries in Asia to which �rms traditionally o¤shore steadily deteriorating, more and more

US �rms nowadays opt for reshoring and domestic outsourcing.5 Therefore, they procure

inputs from suppliers that have access to similar production factors as them.

The widespread use of outsourcing is accompanied by the emergence of large input sup-

pliers �contract manufacturers �that often act as common suppliers of competing �rms.6

For instance, Pratt & Whitney and GE Aviation both source jet engine components from

Ishikawajima Harima Heavy Industries, Apple and Samsung procure ceramic capacitors from

Murata, Mercedes-Benz and BMW outsource car assembly to Magna, Cisco and HP outsource

the design engineering of their network hardware to Jabil.

In this paper, we explore �rms� incentives to outsource to a common supplier without

a cost advantage in input production. We abstract from the cost-reduction rationale of

outsourcing in order to focus on the role of vertical contracting. We examine how vertical

contracting, and in particular, the contract type used in outsourcing arrangements and the

timing of contracting a¤ect the emerging input production pattern and its e¢ ciency.

To do so, we consider a framework in which two �rms produce substitute goods using

1For information on the extent of outsourcing, see e.g., outsourcing reports by Statista.2Another well recognized motive for outsourcing is �rms�intention to focus on their core activities, such

as product design, innovation, and marketing.3This is documented in a number of empirical studies and surveys on outsourcing, see e.g., National

Academy on Engineering (2008), Deloitte (2016).4The consortium includes Mitsubishi Heavy Industries, Kawasaki Heavy Industries and Fuji Heavy Indus-

tries. For more details, see Chen (2011).5This phenomenon is mainly due to increases in local wages in China and India as well as increases in

transportation costs and/or tari¤s on imports from these countries. For evidence of this trend, see e.g.,Pearce (2014), Why �Nearshoring�Is Replacing �Outsourcing�, The Wall Street Journal (June 4, 2014), LocalOutsourcing on Rise in US, The Economic Times (August 4, 2012), Outsourcing and O¤shoring: Here, Thereand Everywhere (special report), The Economist (January 19, 2013), and �Made in China� Isn�t so CheapAnymore and that could Spell Headache for Beijing, CNBC (February 27, 2017).

6 In the electronics sector, the Chinese Foxconn is the world�s largest contract manufacturer with serving�rms such as Apple, Sony, and Dell. Its net pro�ts in 2017 totaled $138.7 billion. In the same sector, theCanadian contract manufacturer Celestica reported $22.1 million net pro�ts in 2014. In the biotechnologysector, the pro�ts of Freudenberg Medical, a US contract manufacturer, exceeded $1 million in 2016.

2

an input that they source from a monopolistic external supplier or produce in-house at the

same cost as the external supplier. The supplier makes sequential two-part tari¤ o¤ers to

the �rms that compete in the market in quantities. Two-part tari¤s, as we discuss shortly,

are commonly used in vertical transactions. When a �rm accepts the supplier�s o¤er, it

outsources.

In equilibrium, both �rms outsource to the external supplier without cost advantage. The

emergence of outsourcing hinges on the supplier�s ability to manipulate the input cost of its

customers and generate cost asymmetry between them. Two-part tari¤s grant such �exibility;

they allow the supplier to charge a wholesale price in order to favor or not a customer and,

in turn, use the �xed fee to recuperate or compensate. In equilibrium, the supplier sets a

positive mark-up to the �rm with which it trades �rst, while it subsidizes the second �rm.

This happens because the supplier can enhance the aggressiveness of the �rm with which

its trades second more e¤ectively. In fact, it transforms the latter into a Stackelberg leader.

Therefore, the supplier, through its contract o¤ers, can induce and does induce outsourcing.

Interestingly, the supplier serves the �rst �rm not in order to enjoy higher input demand,

but to increase the pro�ts that it makes from its sales to the second �rm. While Industry

pro�ts would be maximized if the �rst �rm was fully foreclosed from the market, the supplier

chooses not to foreclose it. This is not because it is unable to commit that it will not

behave opportunistically, but because the second �rm has an outside option �the in-house

production capability �which foreclosure would reinforce it. Stated di¤erently, the external

supplier takes into account both the rent generation e¤ects and the distributional e¤ects of

vertical contracting.

The ability and the incentives of the supplier to induce outsourcing are contract de-

pendent. As we show, when wholesale price contracts are used, outsourcing coincides with

insourcing and is unpro�table for a supplier without a cost advantage. Without the �xed

fees, the supplier cannot cause downstream cost asymmetry and generate rents for itself.

Outsourcing with two-part tari¤s is bene�cial for consumers and welfare. This conclusion

is not driven by the production technology of the external supplier. It is driven exclusively

by vertical contracting, and in particular, by the subsidization, via the wholesale price, that

a �rm enjoys under outsourcing, which results in a lower �nal price. Interestingly, thus, the

presence of large contract manufacturers, even when they are redundant and not cost-superior

than original brand manufacturers, can be socially e¢ cient.

Extending our analysis, we show that when the external supplier can choose the contract

type, it opts for two-part tari¤s rather than for wholesale price contracts since, as mentioned

above, rent generation and extraction is impossible with wholesale prices contracts. On this

basis, we provide justi�cation for the contract type used in our main model. We also provide

justi�cation for sequential transactions; we show that the supplier prefers to trade sequentially

with its potential customers to avoid the opportunism problem that arises when trading occurs

3

simultaneously. Interestingly, outsourcing by both �rms also arises when �rms compete in

prices. However, under price competition, outsourcing is driven by collusion motives, and

hurts welfare.

The structure of the rest of the paper is as follows. In Section 2, we review the related

literature. In Section 3, we describe our main model and present the benchmark case in which

outsourcing is absent. In Section 4, we introduce outsourcing and explore its implications

and incentives. In Section 5, we study what happens when wholesale price contracts are used.

In Section 6, we explore the case of simultaneous trade. In Section 7, we discuss a number

of further extensions of our model, and in Section 8 we conclude.

2 Literature review

Various �elds, including industrial organization, operational management, and marketing,

study outsourcing.7 Many papers explore its cost-saving motives (e.g., Lewis and Sappington,

1989, van Mieghem, 1999, Cachon and Harker, 2002, Shy and Stenbacka, 2003). Others focus

on strategic explanations. Yet, even the latter, when they study outsourcing to a common

supplier (e.g., Buehler and Haucap, 2006, Gilbert et al., 2006, Arya et al. 2008, Feng and

Lu, 2012), assume that the supplier enjoys a cost advantage in input production; otherwise,

outsourcing does not emerge.8 ;9 In addition, they assume that trading between the supplier

and its customers is with wholesale price contracts. As we discuss below, the wholesale price

contracts assumption does not have support in the vertical contracting literature. Moreover,

it lacks wide support in empirical studies which conclude that in various industry sectors, such

as in the US yogurt market and in the bottled water market in France, two-part tari¤s are used

(e.g., Villas-Boas, 2007, Bonnet and Dubois, 2010 and 2015). To the best of our knowledge,

our paper along with Feng and Lu (2013) are the only ones that examine outsourcing with

two-part tari¤s. In Feng and Lu (2013), though, the supplier has a cost advantage. We

show how a supplier without a cost advantage can use two-part tari¤s in such a way as to

pro�tably induce outsourcing.10 Doing so, we complement existing motives for outsourcing

as well as we provide an explanation for outsourcing to suppliers that do not have superior

7 In economics, a large branch of the literature, starting with Coase (1937), focuses on �rm�s boundariesand points out that asset speci�city and contract incompleteness contribute to the expansion of boundaries,thereby restrict outsourcing (e.g., Grossman and Hart, 1986, Grossman and Helpman, 2002).

8Exceptions include Liu and Tyagi (2011) and Colombo and Scrimitore (2018), which consider a supplierwithout a lower cost, but have a di¤erent focus than our paper. They focus on the role of product positionand of strategic delegation respectively.

9There exist also strategic explanations for outsourcing in environments with multiple suppliers and/or avertically integrated supplier (e.g., Chen et al, 2004, Chen et al, 2011, Bakaouka and Milliou, 2018, Colomboand Scrimitore, 2018).10 In this sense, our paper is also related to contributions by e.g., Bonanno and Vickers (1988) and Jansen

(2003), which explore how two-part tari¤s can induce vertical separation (outsourcing) in place of verticalintegration (in-house production). These contributions, however, focus on settings with exclusive - specializedinput suppliers rather than with a common supplier.

4

input production technologies and for the increasing phenomenon of domestic outsourcing in

the US.

The two closest papers to our work are those of Arya et al. (2008) and Buehler and

Haucap (2008). Although these papers, similarly to our paper, allow for sequential trading

by a common supplier, the strategic explanations that they provide di¤er signi�cantly from

ours. Arya et al. (2008) argue that the �rst �rm opts for outsourcing to alter the supplier�s

vested interests in its rival and, in turn, raise its rivals�cost. We show that via outsourcing the

�rst �rm raises its own cost even more than its rivals�cost, and in fact, it makes a loss without

its compensation with the �xed fee. Hence, in contrast to Arya et al. (2008), in our paper

outsourcing is driven by the ability of the supplier to generate rents for itself through vertical

contracting. Buehler and Haucap (2006), using a reduced-form model, argue that �rms opt

for outsourcing to bene�t from the softening competition that results from the exogenously

assumed higher and uniform wholesale prices. We argue, instead, that outsourcing arises

even though it places one of the �rms in a worse competitive position, decreases the �nal

price, and increases welfare.

Our paper is also related to the literature on supply chain coordination - vertical con-

tracting. This literature studies the e¢ ciency of contracts types in various environments,

including when a monopolist input supplier transacts with multiple competing �rms (e.g.,

McAfee and Schwartz, 1994, Cachon and Lariviere, 2005, Gilbert et al., 2006, Taylor, 2002,

Rey and Vergé, 2004, Milliou and Petrakis, 2007). Two-part tari¤s, as this literature ex-

tensively demonstrates, outperform wholesale price contracts by, among other things, not

giving rise to the �double marginalization�externality. Still, as many papers in this literature

acknowledge, two-part tari¤s, due to the monopolist�s inability to commit that it will not

behave opportunistically, do not always su¢ ce for the maximization of industry pro�ts. The

timing of contracting has received limited attention in this literature, with most papers as-

suming simultaneous trading. Exceptions include McAfee and Schwartz (1994), Möller (2007)

and Bedre-Defolie (2012) which allow for sequential trading, but assume that the competing

�rms do not have in-house input production capability, and thus, outsourcing is their only

option.11 We contribute to this literature by demonstrating that both the timing of con-

tracting and the contract type can be crucial for the choice of input production pattern, and

thereby, for the vertical structure of the market. In this sense, we provide a justi�cation for

their exogenously assumed vertical market structure.

11Aghion and Bolton (1987) and Marx and Sha¤er (2007) also study a three-players environment withsequential trade. However, in their environment, the common player is the buyer which trades with twocompeting suppliers.

5

3 The model

There are two �rms in the market, �rm 1 and �rm 2, that produce a homogeneous good.

Market demand is given by the standard linear demand function: p(q1; q2) = a � q1 � q2;where p is the price of the good and qi is the quantity supplied by �rm i, with i = 1; 2.

To produce the good, each �rm i uses an input in a one-to-one proportion. Both �rms

produce the input in-house at marginal cost s or outsource it to an external �rm, �rm S,

which also faces marginal cost s, with 5s > a > s > 0.12 When �rm i outsources, it trades

with �rm S via a two-part tari¤ contract, consisting of a wholesale price per unit of input,

wi, and a �xed fee, fi. In section 5, we will indicate how results change when trade is via

wholesale price contracts.

Firms play a three-stage game with observable actions. In stage one, S makes a take-

it-or-leave-it o¤er to �rm 1 over (w1; f1). Firm 1 decides whether to accept or reject it. In

case of rejection, it produces the input in-house. In stage two, S makes a take-it-or-leave-it

o¤er to �rm 2 over (w2; f2) and, in turn, �rm 2 accepts or rejects the o¤er. In the last

stage, �rm 1 and �rm 2 choose their quantities simultaneously and separately. A justi�cation

for this timing is that, as Arya et al. (2008) argue, �rm 1 is an incumbent while �rm 2 is

an entrant in the market. Importantly, as we demonstrate in section 6, this timing arises

endogenously: the supplier prefers to trade sequentially rather than simultaneously with its

potential customers.

In the last stage, each �rm i, with i = 1; 2, chooses qi to maximize its (gross from fi)

pro�ts: �i(qi; qj) = p(qi; qi)qi�kiqi, where ki is �rm i�s per unit cost, with ki = s and ki = wiwhen �rm i opts for insourcing and outsourcing respectively. The �rst order conditions give

rise to: Ri(qj) = (a� ki � qj)=2, with j = 1; 2 and i 6= j. The resulting quantities are:

qi(ki; kj) =a� 2ki + kj

3: (1)

In the benchmark case, there is no outsourcing; �rms produce the input in-house � II

case. Without vertical trading, �rms play the standard Cournot game with marginal costs

kII1 = kII2 = s. The equilibrium net pro�ts, �II1 and �II2 , are included in Table 1 of the

Appendix. Clearly, the external supplier makes no pro�ts, �IIS = 0.

4 Outsourcing

Three cases can arise in the presence of outsourcing: (i) IO, where only �rm 2 outsources

(kIO1 = s and kIO2 = w2), (ii) OI, where only �rm 1 outsources (kOI1 = w1 and kOI2 = s), and

12The upper limit on a ensures that the equilibrium wholesale prices are positive in all cases underconsideration.

6

(iii) OO, where both �rm 1 and �rm 2 outsource (kII1 = w1 and kII2 = w2). In what follows,

we examine what happens in each case before endogenizing �rms�input sourcing modes.

Outsourcing only by �rm 2

When �rm 1 has opted for insourcing, in stage two, �rm S o¤ers (w2; f2) to �rm 2 to maximize

its own pro�ts subject to the constraint that �rm 2 accepts its o¤er; it solves the following:

maxw2;f2

�S(w2; f2) = (w2 � s)q2(w2; s) + f2, (2)

s.t. �2(q2(w2; s); q1(s; w2))� f2 � �dIO2 ;

where �dIO2 is �rm 2�s disagreement payo¤ �outside option: �dIO2 = �II2 . The constraint is

binding. Thus, we rewrite (2) as:

maxw2

�S(w2) = (w2 � s)q2(w2; s) + �2(q2(w2; s); q1(s; w2))� �II2

= [p2(q2(w2; s); q1(s; w2))� s]q2(w2;s)� �II2

This yields �rm 2�s equilibrium wholesale price: wIO2 = 5s�a4 . Note that �rm S sells the input

below its production cost, wIO2 < s �it subsidizes the production of its only customer. As the

literature on strategic delegation (e.g., Fershtman and Judd, 1987, Sklivas, 1987 ) and on ver-

tical separation (e.g., Bonanno and Vickers, 1988, Jansen, 2003 ) has explained, the upstream

�rm has incentives to enhance the output of its customer in order to increase its pro�ts that

it partially extracts them through f2. A straightforward implication is that �rm 1 has a cost

disadvantage in the �nal market. An additional implication is that through contracting, �rm

S manages to transform �rm 2 to a Stackelberg leader that produces the monopoly quan-

tity, qIO2 = a�s2 , and �rm 1 to a Stackelberg follower that produces the respective quantity,

qIO1 = a�s4 .

From the appropriate substitutions, we obtain �rms�net equilibrium pro�ts and include

them in Table 1 of the Appendix. We observe that �IOS > �IIS . Thus, II never arises in

equilibrium; when the �rst �rm opts for insourcing, �rm S pro�tably induces outsourcing by

the rival �rm by o¤ering wIO2 and f IO2 = �2(wIO2 ; s)� �II2 � ", with " > 0 and "! 0.

Outsourcing only by �rm 1

When �rm 2 rejects �rm S�s o¤er in stage two, �rm S solves the following problem in stage

one:

maxw1;f1

�S(w1; f1) = (w1 � s)q1(w1; s) + f1; (3)

s.t. �1(q1(w1; s); q2(s; w1))� f1 � �II1

The equilibrium wholesale price is given again by: wOI1 = wIO2 . Therefore, outcomes are the

same as in the IO case, with the roles of �rm 1 and �rm 2 reversed.

7

Outsourcing by both �rms

Once �rm 1 has agreed to source the input from �rm S, in stage two, �rm S o¤ers (w2; f2)

to �rm 2 given (w1; f1) from the previous stage. That is, �rm S solves:

maxw2;f2

�S(w1; w2; f1; f2) = (w1 � s)q1(w1; w2) + (w2 � s)q2(w2; w1) + f1 + f2, (4)

s.t. �2(q2(w2; w1); q1(w1; w2))� f2 � �dOO2 ;

where the outside option of �rm 2 now is the pro�ts that it makes when it produces the input

in-house whereas its rival outsources: �dOO2 = �2(s; w1). Since �dOO2 does not depend on w2,

it does not a¤ect the choice of w2. The constraint is binding and (4) results in:

w2(w1) =3s+ 2w1 � a

4: (5)

Note that @w2=@w1 > 0. This is because when w1 increases, �rm 2 enjoys a larger competitive

advantage that allows �rm S to increase w2 without restricting too severely its input purchases

(Arya et al., 2008). The opposite holds for f2(w1) = �2(w2(w1); w1) � �2(s; w1), for which,we have @f2=@w1 < 0. That is, the higher is w1, the higher is the advantage that �rm 2

enjoys relative to its competitor when it rejects �rm S�s o¤er, and thus, the lower is the share

of the pro�ts �the piece of the pie �that �rm S extracts from �rm 2 under outsourcing.

In the previous stage, if �rm 1 rejects the �rm S�s o¤er, (w1; f1), the pro�ts of �rm 1 are

given by �IO1 from above. Thus, �rm 1 accepts the o¤er if and only if its pro�ts are higher

with outsourcing than with in-house production. In light of this, �rm S solves the following:

maxw1;f1

�S(w1; f1) = (w1 � s)q1(w1; w2(w1)) + [w2(w1)� s]q2(w2(w1); w1) + f2(w1) + f1; (6)

s.t. �1(q1(w1; w2(w1)); q2(w2(w1); w1))� f1 � �IO1

The constraint is binding and we rewrite (6) as:

maxw1

�S(w1; f1) = (w1 � s)q1(w1; w2(w1)) + [w2(w1)� s]q2(w2(w1); w1) + f2(w1)

+�1(q1(w1; w2(w1)); q2(w2(w1); w1))� �IO1 :

The resulting equilibrium contract terms o¤ered to �rm 1 are: wOO1 = a+25s26 > s and fOO1 =

�25(a�s)226 < 0. Firm 2�s equilibrium wholesale price follows after the substitution of wOO1 into

(5): wOO2 = 16s�3a13 < s. Note that wOO1 > wOO2 . That is, �rm S favors �rm 2; hence, �rm 1

faces a cost disadvantage relative to its rival even when it opts for outsourcing.

Choice of sourcing mode

Next, we examine �rm 1�s choice of input sourcing mode in stage one. Before doing so, we

evaluate the implications of its choice on the input sourcing terms.

8

Proposition 1 When �rm 1 opts for outsourcing, it raises both its own and its rival�s per

unit cost, kOO1 > kIO1 and kOO2 > kIO2 .

Proof: Recall from above that when �rm 1 opts for insourcing, in the following stage, �rm

S optimally induces outsourcing by �rm 2, i.e., we have IO. Thus, when �rm 1 opts for

insourcing, its per unit cost is kIO1 = s. When, instead, �rm 1 opts for outsourcing, its per

unit cost is kOO1 = wOO1 . Since wOO1 > s, it follows immediately that kOO1 > kIO1 :

When �rm 1 opts for insourcing, the per unit cost of �rm 2 is kIO2 = wIO2 , while it

is kOO2 = wOO2 , when �rm 1 opts for outsourcing. We �nd that wIO2 � wOO2 < 0. Thus,

kOO2 > kIO2 . �

Proposition 1 informs us that when �rm 1 outsources, it raises its rival�s cost at the expense of

increasing its own cost. In fact, its own cost increases more than its rival�s cost: kOO1 �kOO2 >

kIO1 � kIO2 . This means that opting for outsourcing, �rm 1 in�icts itself a higher damage, in

terms of per unit cost, than the damage it in�icts to its rival. An implication of this is that

outsourcing decreases �rm 1�s output, qOO1 = 3(a�s)13 < qIO1 , while it leaves �rm 2�s output

intact, qOO2 = qIO2 .13 A further implication is that �rm S compensates �rm 1 for the damage

via the �xed fee, fOO1 < 0, while it uses the �xed fee to extract part of �rm 2�s pro�ts,

fOO2 > 0.

The two-part tari¤s that �rm S o¤ers, (wOO1 ; fOO1 ) and (wOO2 ; fOO2 ), guarantee higher

joint pro�ts for �rm S and �rm 1 when they trade than when they do not trade; hence,

o¤ering such contracts, �rm S induces outsourcing by both �rms in equilibrium.

Proposition 2 Outsourcing by both �rms always arises in equilibrium.

Proof: We �nd �rms�net equilibrium pro�ts in the OO case from the appropriate substitu-

tions and include them in Table 1 of the Appendix. We already know that �rm S prefers to

serve �rm 2 when �rm 1 opts for insourcing; it prefers IO to II. Does it also prefer to serve

�rm 2 when �rm 1 opts for outsourcing? We know that �OIS = �IOS > �II > 0; hence, the

answer to this question is positive. It follows that the only thing we need to check is whether

�rm S prefers IO=OI or OO.

Comparing �rm S�s pro�ts in the two regimes, we �nd: �OOS ��IOS = (a�s)2=1872 > 0. Itfollows that �rm S wants to induce outsourcing by both �rms. Firm S can do so by o¤ering

(wOO1 ; fOO1 � ") and (wOO2 ; fOO2 � ") to �rm 1 and �rm 2 respectively, with " > 0 and "! 0.

Its o¤ers will be accepted since then �OO1 > �IO1 and �OO2 > �OI2 . �

When �rm 1 produces the input in-house, �rm S�s revenues come exclusively from �rm 2,

thereby, �rm S has vested interests only in �rm 2. When, instead, �rm 1 opts for outsourcing,

�rm S can also have revenues from �rm 1. However, it continues to have higher vested

13This is because from (1), we have: dq1=dwO1 =@q1@wO2

@wO2@wO1

+ @q1@wO1

< 0 and dq2=dwO1 =@q2@wO2

@wO2@wO1

+ @q2@wO1

= 0.

9

interests in �rm 2. This is because sequential trading allows �rm S to extract more pro�ts

from the �rm with which it trades second by transforming it into a more aggressive competitor

(see e.g., McAfee and Schwartz, 1994, Bedre-Defolie, 2012). When �rm S serves �rm 1, it

improves the position of the �rm in which it has higher vested interests; it increases the

downstream cost asymmetry in favor of �rm 2. This leads, as mentioned above, to a lower

output for �rm 1 and to the same monopoly output for �rm 2. Firm S manages to do this

and at the same time decrease the subsidy it o¤ers to �rm 2: wOO2 > wIO2 and fOO2 = f IO2 .

Stated di¤erently, outsourcing allows �rm S "to kill two birds with one stone": it improves

the competitive position (and market share) of its preferred customer and increases its own

revenues.

Interestingly, under outsourcing, �rm S purposely makes a net loss from its transactions

with �rm 1. Firm S serves �rm 1 not in order to enjoy higher input demand. It serves �rm 1

to increase the pro�ts that it makes from its sales to �rm 2. In fact, industry pro�ts would be

maximized, i.e., monopoly pro�ts would be achieved, if �rm S fully foreclosed �rm 1 from the

market. To do so, it would have to charge a wholesale price to �rm 1 that exceeds wOO1 . This,

though, would reinforce the competitive position of �rm 2 when it produces in-house, and

thus, enlarge its outside option; recall that f2 increases with w1. In other words, �rm S would

not be able to extract a large share of the monopoly pro�ts. For this reason, it prefers to not

maximize industry pro�ts �to generate a smaller pie, by keeping �rm 1 in the market, and

extract a larger share of the smaller pie. Therefore, the upstream monopolist (�rm S) does

not maximize industry pro�ts, not because of fear that it will behave opportunistically, but

because, here, in contrast to the vertical contracting literature, its customer has an outside

option � it has in-house production capability.14 Stated di¤erently, the external supplier

takes into account not only the rent generation e¤ects of vertical contracting by also its

distributional e¤ects.

It is important to stress that although the supplier does not have a cost-advantage, it

manages to induce outsourcing. The reverse � the existence of a cost advantage � is a

necessary condition for the emergence of outsourcing in the literature (e.g., Arya et al., 2008,

Buehler and Haucap, 2008, Feng and Lu, 2013). As we explain in detail in the next section,

this di¤erence hinges on the contract type.

Outsourcing in our setting is motivated neither by cost reduction nor by collusion (e.g.,

Buehler and Haucap, 2006, Gilbert et al., 2006). In fact, in our setting the price of the

14When products are homogeneous and �rm S can fully extract �rm 2�s pro�ts, as is the case, for instance,when �rm 2 does not have input production capability, �rm S fully forecloses �rm 1 from the market (seee.g., McAfee and Schwartz, 1994, Milliou and Pechlivanos, 2019). When products are di¤rentiated, and thus,industry pro�ts are not maximized with foreclosure, as the vertical contracting literature (see e.g., McAfee andSchwartz, 1994, Rey and Vergé, 2002, Milliou and Petrakis, 2007). has shown, an upstream monopolist dealingwith competing downstream �rms via nonlinear contracts is unable to maximize industry pro�ts because itsu¤ers from the "opportunism problem". That is, when it makes an o¤er to one �rm, it cannot commit thatit will not make a better o¤er to the rival �rm.

10

�nal good is lower when both �rms opt for outsourcing than when neither �rm does: kOO2 =

wOO2 < kII2 = s. This is because of the lower input sourcing cost that �rm 2 faces in the OO

case. Moreover, in our setting, �rm 1 deteriorates its competitive position when it opts for

outsourcing. More speci�cally, the price increase in the OO case relative to the IO case, due

to the higher input sourcing costs (Proposition 1), is not mutually pro�table for all �rms since

it is accompanied by increased cost asymmetry against �rm 1.15 Therefore, our explanation,

in contrast to Arya et al. (2008), is not motivated by the raise in rival�s cost either. In fact,

�rm 1 is also worse o¤, in contrast to its rival, when both �rms outsource than when neither

outsources: �OO1 < �II1 and �OO2 > �II2 ; hence, �rm 1 is trapped into a prisoners�dilemma

situation in equilibrium. Firm 1 would not opt for outsourcing if it was not compensated for

its loss. Thus, f1 serves as a bribe: �rm S pays �rm 1 to abstain from producing the input

itself. The weaker competition faced by �rm 2 in the OO case works not only in favor of �rm

2, but also in favor of the external supplier �it allows �rm S to enlarge its own pro�ts.

We have established that an external supplier, without any cost advantage, can alert a

duopoly market equilibrium non-trivially: it can generate positive pro�ts by harming one

duopolist, while bene�ting the other. Thus, the use of two part tari¤s can facilitate the entry

of a technologically redundant input supplier into the market. It remains to check to which

direction consumers and the economy will be a¤ected.

Proposition 3 When both �rms outsource:

(i) consumer surplus is higher than when neither �rm outsources and lower than when

only one �rm outsources, CSIO > CSOO > CSII ,

(ii) producer surplus is lower than when neither �rms outsources and higher than when

only one �rm outsources, PSII > PSOO > PSIO, and

(iii) welfare is higher than when only one �rm outsources, while it is higher in the latter

case than when neither �rm outsources, WOO > W IO > W II .

Proof: (i) Consumer surplus is given by CS = aqv1 + aqv2 � (1=2)(qv12 + qv22 + qv1q

v2) � (a �

qv1 � qv2)q1 � (a� qv2 � qv1)qv2 , with v = OO; IO;OO. We �nd: CSOO � CSII =545(a�s)212168 > 0

and CSOO � CSIO = �77(a�s)25408 < 0.

(ii) Producer surplus is given by PSv = �v1+�v2+�

vS . We �nd: PS

OO�PSII = �150(a�s)26084 < 0

and PSOO � PSIO = 25(a�s)22704 > 0.

(iii) Welfare is given by W v = PSv + CSv. We �nd: WOO � W IO = 109(a�s)2416 > 0 and

W IO �W II = 7(a�s)2288 > 0. �

Interestingly, outsourcing enhances consumer and total welfare. In disparity with cost-

reduction explanations and Arya et al.�s (2008) explanation of outsourcing, this result is not

15This �nding is consistent with the empirical �ndings of Görzig and Stephen (2002) and Marjit and Mukher-jee (2008), according to which outsourcing can reduce �rm�s pro�tability.

11

driven by the fact that a more e¢ cient supplier produces the input. The welfare-increasing

impact of outsourcing is exclusively induced by vertical contracting, which when it is con-

ducted via two-part tari¤s results in better input sourcing terms for one of the �rms.

On the basis of the above, we can conclude that the use of two-part tari¤s in trading

between a contract manufacturer and its customers can result in the presence of an otherwise

redundant �rm in the market �the external supplier �a presence which is socially desirable.

This conclusion can be relevant for antitrust policy and, in particular, for the ongoing discus-

sion regarding the Robinson-Patman Act and the use of non-discrimination or most-favored

customer clauses.16 It is claimed that such clauses, by preventing selective price cuts, can

restrict a supplier�s urge to o¤er better terms to some of it customers. In our setting, in

principle, �rm 1 should be in favor of such clauses since in equilibrium it is in a less favorable

position relative to its rival, �OO1 < �IIi < �OO2 . Firm S should welcome such clauses only

as long as they allow it to generate higher industry pro�ts �bring it closer to the industry

pro�ts maximization outcome �and at the same time do not impede its rent extraction abil-

ity. McAfee and Schwartz (1994), considering a setting in which the monopolist supplier�s

customers do not have outside options and industry pro�t maximization precludes foreclo-

sure (e.g., there is product di¤erentiation), demonstrate that non-discrimination clauses do

not "have a bite". More speci�cally, they show that the �rst �rm, which accepts a higher

wholesale price and a lower �xed fee, may prefer to stay with its contract rather than ex-

change it with the contract o¤ered to its rival contract that includes a lower wholesale price

and a higher �xed fee. Clearly, if such clauses do not have a bite, the discussion over their

use is meaningless unless their form is altered.17 If, on the other hand, such clauses have a

bite even in their current form, the policy question that needs to be addressed is whether

they are desirable from the viewpoint of consumers and the economy as a whole. That is,

whether their enforcement would lead to a more competitive market outcome. On the basis

of our analysis, we know that if non-discrimination clauses do not induce outsourcing, they

will harm consumer and total welfare.

5 Wholesale price contracts

We now examine what happens when �rms trade through wholesale price contracts. In the

last stage, the equilibrium quantities are given by (1). In stage two, when �rm 1 has opted for

insourcing, �rm S solves: maxw2 �S(w2) = (w2 � s)q2(w2; s). This yields: bwIO2 = (a+ 3s)=4.

As expected, in the absence of a �xed fee, �rm S sets a positive mark-up on the wholesale

16These clauses entitle �rms to replace their contracts with any other contract accepted by its rivals. Theymake past customers eligible for future discounts.17For instance, if, alternatively, they are designed in a way that they force the supplier to o¤er the same

terms to all of its customers; hence, it is not in the potency of �rms to choose between the di¤erent contractsthat they are o¤ered.

12

price, bwIO2 > s, generating a cost disadvantage for �rm 2. In turn, �rm 2 will be better o¤ if

it rejects the o¤er, �II2 > �2( bwIO2 ; s). In fact, �rm 2 will outsource only if w2 < s, and thus,

if �rm S makes a loss; hence, IO again never arises in equilibrium.

When �rm 1 has opted for outsourcing, in stage two, �rm S solves:

maxw2

�S(w1; w2) = (w1 � s)q1(w1; w2) + (w2 � s)q2(w2; w1) (7)

This leads to: w2(w1) = (a + s + 2w1)=4. In the previous stage, �rm 1 will accept �rm S�s

o¤er if and only if:

�1(w1; w2(w1))� �II1 =(a+ 5s� 6w1)(3a� s� 2w1)

12> 0: (8)

Condition (8) is not satis�ed when w1 > s. Consequently, bwOO1 = bwOO2 = s. A lower w1,

i.e., w1 < s, would trigger a lower w2 in the next stage, since dw2=dw1 > 0, and result in

a higher quantity for �rm 1, since dq1=dw1 < 0, and no change in the quantity of �rm 2,

since dq2=dw1 = 0: Hence, �rm S would end up selling more units to �rm 1 at a loss and the

same amount of units to �rm 2 at a lower wholesale price than before. In other words, the

supplier would experience a loss from one customer and a decrease in its revenues from the

other. Clearly, this would not be pro�table.

Proposition 4 When wholesale price contracts are used, outsourcing does not arise in equi-

librium.

An external supplier without a cost advantage is not in the position to pro�tably induce

outsourcing with wholesale price contracts. A similar result can be found in Arya et al.

(2008). As we know from Proposition 2, the opposite holds with two-part tari¤s. Therefore,

the contract form is not innocuous: it can have signi�cant implications for the production

pattern that emerges in equilibrium. Intuitively, with two-part tari¤s �rm S can generate

cost asymmetry so as to increase the size of the pie and in turn use the fees to compensate

and extract.

On the basis of the above and Proposition 3, we can conclude that, as standard in the

vertical contracting literature, two-part tari¤s generate a more e¢ cient outcome � higher

consumer and total welfare �than wholesale price contracts. Given the contract type�s crucial

role for market outcomes, a question that arises is which type will be used in equilibrium.

We �nd that the supplier will always opt for two-part tari¤s. This is so because only with

two-part tari¤s the supplier induces outsourcing by both �rms and makes positive pro�ts

(Proposition 2).

Corollary 1 The external supplier strictly prefers trading through two part tari¤ contracts

than through wholesale price contracts.

13

In other words, when, an otherwise redundant, supplier enters into the upstream market and

approaches its potential customers incumbents, it will optimally o¤er them two-part tari¤s

and not wholesale price contracts.18 Clearly, Corollary 1 provides a justi�cation for the use

of two-part tari¤s in our main model.

6 Simultaneous trading

Next, we modify our model and assume that in stage one, �rm S makes simultaneous and

secret o¤ers to �rm 1 and �rm 2 over (w1; f1) and (w2; f2) respectively and, in turn, each

�rm decides whether it accepts or rejects its o¤er without knowing the o¤er made to its rival.

In the next stage, each �rm chooses its quantity after learning all the contract terms. 19 As

noted in the literature, multiple equilibria can arise in such a setting, due to the multiplicity of

the beliefs that �rms can form when they receive out-of-equilibrium o¤ers. Following Cremer

and Riordan (1987) and O�Brien and Sha¤er (1992), and Milliou and Petrakis (2007), we

obtain a unique equilibrium by imposing pairwise proofness on the equilibrium contracts: we

require that a contract between �rm S and �rm i is immune to a bilateral deviation of �rm

S with �rm j, holding the contract with �rm i constant.

The solution of the last stage is given again by (1).20 Moreover, the solution to stage two

when �rm S outsources to only one �rm coincides with the respective one in our main model;

hence, we have wIO2 , �IOS ; �IO1 and �IO2 from before. When, instead, �rm S outsources to both

�rms, it o¤ers (wi; Fi) to �rm i, taking as given its equilibrium o¤er to �rm j, ( ewOOj ; efOOj ).

In particular, it solves the following:

maxwi;fi

�S(wi; fi) = (wi � s)qi(wi; ewOOj ) + ( ewOOj � s)qj( ewOOj ; wi) + fi + efOOj ; (9)

s.t. �i(qi(wi; ewOOj ); qj( ewOOj ; wi))� fi � �IOi

The constraint is binding. Rewriting (9) and solving for wi, we �nd: ewOOi = 3s�a+s2 . Note

that, ewOOi < s. This is due to the opportunism problem �the �commitment problem��that

an upstream monopolist faces when it trades with two competing �rms and cannot publicly

commit to the contract terms that it will o¤er; it cannot commit to �rm i that it will not

behave opportunistically and o¤er better terms to �rm j (e.g., McAfee and Schwartz, 1994,

18Firm 2 is also better o¤ with two-part tari¤s, �OO2 > �IIi . Even though �rm 1 makes higher pro�ts withwholesale price contracts, �OO1 > �II1 , if its rival trades with a two-part tari¤, it can be convinced by �rm S,through an appropriate transfer, to also trade with a two-part tari¤.19Note that in this setting, as in many papers in the vertical contracting literature (e.g., McAfee and

Schwartz, 1994, Rey and Vergé, 2004, Milliou and Petrakis, 2007), the contracts terms are not observablein the contracting stage, while they are observable in the quantity competition stage. They are ex-postobservable or interim observable. We will discuss shortly the case in which they are ex-post unobservable orinterim unobservable.20A similar analysis can be found in Feng and Lu (2013) under the assumption that the supplier has a cost

advantage.

14

Rey and Vergé, 2004, Milliou and Petrakis, 2007). Note also that, ewOOi < wIO2 ; hence, in

contrast to our main model, outsourcing now decreases both �rms�cost. A straightforward

implication of these observations is that outsourcing leads to the disappearance of the cost

asymmetry between �rm 1 and �rm 2.

Making the appropriate substitutions, we obtain the equilibrium pro�ts of �rm S under

outsourcing by both �rms and note that they are negative, e�OOS < 0. Thus, �rm S will

not induce outsourcing by both �rms in equilibrium. This is so because of the opportunism

problem. Nevertheless, it will induce IO. Since under sequential trading �rm S makes higher

pro�ts with outsourcing by both �rms than with outsourcing by one �rm, we reach the

following conclusion.

Proposition 5 The external supplier strictly prefers trading with �rm 1 and �rm 2 sequen-

tially rather that simultaneously.

The supplier�s preference of sequential trading is due to the presence of the opportunism

problem when trading is simultaneous. Clearly, this conclusion points out that in three-party

trading, the order in which trading occurs may a¤ect the size of the generated pie and its

division. Importantly, it reveals that the order of moves that we adopt in our main model

can arise endogenously. That is, if we include a stage in the beginning of our game in which

�rm S decides the order in which it will approach its potential customers and make its o¤ers,

�rm S would decide to approach �rms sequentially.

The supplier�s preference of sequential over simultaneous trading also holds when contracts

are never observed �secret contracts. The equilibrium outcome is then for the supplier to

always set the wholesale prices equal to marginal cost, wOO1 = wOO2 = wOI1 = wIO2 = s, and

thereby, to always makes zero pro�ts (e.g., Bakaouka and Milliou, 2018, Katz, 1991, Pagnozzi

and Picolo, 2012). Under sequential trading, instead, �rm S makes positive pro�ts; it creates

a market for itself.

7 Further extensions

7.1 Price competition

Here, we brie�y discuss what happens when �rms compete in prices.21 We assume that �rm

1 and �rm 2 produce imperfect substitutes, and in particular, that the demand for �rm i�s

product, with i; j = 1; 2 and i 6= j, is given by: qi = (a�pi)� (a�pj)1� 2 . The parameter , with

2 (0; 1), denotes the degree of product substitutability.With the prices being strategic complements, �rm S does not longer want its customer(s)

to behave aggressively (e.g., Bonanno and Vickers, 1988); hence, it does not subsidize them.

21The detailed analysis is available from the author upon request.

15

More speci�cally, in the IO case, �rm S sets a positive mark-up to its unique customer,

�rm 2, wBIO2 > s. Doing so, it manages to relax downstream competition and, in turn,

increase �nal prices and industry pro�ts relative to the benchmark II case, pBIOi > pBIIi and

PSBIO > PSBII . Firm S manages to further increase industry pro�ts in the OO case, by

setting a positive mark-up on both �rms, wBOOi > s, as well as by raising its mark-up on �rm

2, wBOO2 > wBIO2 . Since �rm S manages to extract, via the wholesale prices now, a piece of

the larger pie, just like in our main model, it pro�tably induces outsourcing by both �rms in

equilibrium.

It follows from the above that, independently of the mode of competition, two-part tari¤s

allow the external supplier to induce outsourcing by both �rms. Moreover, in line with our

main analysis, when �rm 1 opts for outsourcing, it raises both its own cost and the cost

of its rival � Proposition 1 continues to hold � and the raise in its own cost exceeds the

respective raise in its rival�s cost. Thus, outsourcing is again not driven by the raise in rivals�

cost. Since though subsidization is now absent, outsourcing results in higher �nal prices.

In other words, here, in contrast to our main analysis, there are collusion motives behind

outsourcing. A straightforward implication is that the welfare implications of outsourcing

di¤er signi�cantly under price and quantity competition. When �rms compete in prices, the

entry of an upstream monopolist in the market �a dominant contract manufacturer �can

facilitate downstream collusion, harm consumers, and decrease welfare.

7.2 Bargaining

Our results extend to situations where bargaining power is more evenly distributed and the

external supplier does not make take-it-or-leave-it contract o¤ers. To show this, we modify

our model and assume that �rm S engages in sequential negotiations with �rm 1 and �rm 2,

in which the bargaining power of �rm S and �rm i is given by � and 1� � respectively, with� 2 [0; 1).

In the last stage, �rms produce their quantities according to (1). In the previous stage,

if �rm 1 has not reached an agreement with �rm S, �rm S and �rm 2 solve the following

problem:

maxw2;f2

[�S(w2) + f2]� + [�2(w2; s)� �dIO2 � f2]1�� ; (10)

where �S(w2) are �rm S�s pro�ts gross from f2 and, as in our main analysis, the disagreement

payo¤ of �rm 2 is �dIO2 = �II2 . Maximizing with respect to f2, we �nd: f2 = �[�2(w2; s) ��II2 ] � (1 � �)�S(w2). From this it follows that (10) corresponds to an expression which

is proportional to the joint pro�ts of �rm 2 and �rm S minus the former�s disagreement

payo¤. This expression is maximized again by wIO2 . The �xed fee though now depends on

the distribution of �, and in particular: f IO2 = (9+�)(a�s)272 . The pro�ts of �rm 1 remain the

same as in our main analysis, �IO1 :

16

When �rm 1 agrees to outsource, (10) becomes as follows:

maxw2;f2

[�S(w1; w2) + f1 + f2 � �dOOS ]� + [�2(w2; w1)� �dOO2 � f2]1��; (11)

where �S(w1, w2) are �rm S�s gross pro�ts from sales to �rm 1 and �rm 2 and the disagree-

ment payo¤ of �rm 2 is �dOO2 = �OI2 . Note that �rm S also has a disagreement payo¤ now;

its pro�ts in the OI case, �dOOS = �OIS . This results in (5). Taking this into account, we

move to the �rst stage of the game, in which �rm S bargains with �rm 1 over (w1,f1): In

particular, they solve the following:

maxw1;f1

[�S(w1; w2(w1)) + f1 + f2(w1)� �dOOS ]� + [�1(w1; w2)� �dOO1 � f1]1��:

The above results in: wOO1 = a(3�2�)+s(27�2�)30�4� > s. This, in turn, leads to wOO2 = �3a+2s(9��)

15�2� <

s. So, in line with our main analysis, �rm S continues to favor �rm 2. The pro�ts of �rm S

are now lower than in our main analysis, since its customers, due to the fact that they have

positive bargaining power, manage to extract a bigger piece of the joint pro�ts that they

generate than in our main analysis. Still, �rm S continues to make higher pro�ts in the OO

case than in the IO case. Therefore, just like in our main analysis, via the use of two-part

tari¤s, it pro�tably induces outsourcing by both �rms.

8 Conclusion

We have shown that outsourcing to a common external input supplier without a cost ad-

vantage can emerge in equilibrium when vertical contracting is through two-part tari¤s and

occurs sequentially. Two-part tari¤s allow the supplier to alter the cost of its customers and

arti�cially create cost asymmetries that work in its favor.

We have also shown that outsourcing increases consumer surplus and welfare. The in-

creased e¢ ciency does not arise from the higher e¢ ciency of the input producer. It is induced

exclusively by vertical contracting.

When wholesale price contracts are used or when the external supplier trades simultane-

ously with its potential customers, it is not in the position, unless it has a cost advantage,

to induce outsourcing. Therefore, we point out that both the contract type and the order of

trading can be signi�cant for the emergence of outsourcing. In fact, the supplier will not enter

into the market unless it can trade with two-part tari¤s. Since, as we have demonstrated, it

is in its best interest to approach its potential customers sequentially, there is no reason to

assume that it will do otherwise.

Our analysis suggests that the emergence of large input suppliers �contract manufacturers

�is not necessarily due to their cost advantages. It can also be due to the contract type and

17

terms that they can o¤er to original brand manufacturers. Furthermore, it suggests that the

presence of otherwise redundant input producers in the market can be socially desirable.

Our conclusions persist qualitatively when products are di¤erentiated, when �rms nego-

tiate over the contract terms, and/or when one of the �rms does not have in-house input

production capability.22 In all cases, the supplier generates cost asymmetry and transforms

the �rm with which it trades second to a Stackelberg leader. However, the supplier abstracts

from maximizing industry pro�ts, not because it su¤ers from opportunism, but in order to

secure a larger share of the generated pie.

In future work, we plan to explore the incentives for outsourcing when the supplier is

vertically integrated or outsourcing causes its entry both in the upstream and downstream

segments of the market �a practice which is commonly referred to as supplier �encroachment�.

9 Appendix

Table 1: Pro�ts with Symmetric Input Sourcing Options

�OOS = 3(a�s)2208 �OO1 = (a�s)2

16 �OO2 = 81(a�s)2676

�IIS = 0 �II1 = (a�s)29 �II2 = (a�s)2

9

�OIS =(a�s)272 �OI1 =

(a�s)29 �OI2 =

(a�s)216

�IOS = (a�s)272 �IO1 = (a�s)2

16 �IO2 = (a�s)29

References

[1] Aghion, P. and P. Bolton (1987), �Contracts as a Barrier to Entry�, American Economic

Review, 77, 388-401.

[2] Arya, A., B. Mittendorf, and D. Sappington (2008), �The Make-or-Buy Decision in

the Presence of a Rival: Strategic Outsourcing to a Common Supplier�, Management

Science, 54, 1747-1758.

[3] Bakaouka, E. and C. Milliou (2018), �Vertical Licensing, Input Pricing, and Entry�,

International Journal of Industrial Organization, 59, 66-96.

[4] Bedre-Defolie, O. (2012), �Vertical Coordination through Renegotiation�, International

Journal of Industrial Organization, 30, 553-563.

[5] Bonnet, C. and P. Dubois (2010), �Inference on Vertical Contracts between Manufac-

turers and Retailers Allowing for Non-Linear Pricing and Resale Price Maintenance�,

Rand Journal of Economics, 41, 139-164.

22The analysis is available from the author upon request.

18

[6] Bonanno, G. and J. Vickers (1988), �Vertical Separation�, Journal of Industrial Eco-

nomics, 36, 257-265.

[7] Bonnet, C. and P. Dubois (2015), �Identifying Two Part Tari¤ Contracts with Buyer

Power: Empirical Estimation on Food Retailing�, TSE Working Paper N. 15-575.

[8] Buehler, S. and J. Haucap (2006), �Strategic Outsourcing Revisited�, Journal of Eco-

nomic Behavior and Organization, 61, 325-338.

[9] Cachon, G. P. and P. T. Harker (2002), �Competition and Outsourcing with Scale

Economies�, Management Science, 48, 1314-1333.

[10] Cachon, G. P. and M. A. Lariviere (2005), �Supply Chain Coordination with Revenue-

Sharing Contracts: Strengths and Limitations�, Management Science, 51, 30-44.

[11] Chen Y., J. Ishikawa and Z, Yu (2004), �Trade Liberalization and Strategic Outsourc-

ing�, Journal of International Economics, 63, 419-436.

[12] Chen, Y., P. Dubey, and D. Sen (2011), �Outsourcing Induced by Strategic Competi-

tion�, International Journal of Industrial Organization, 29, 484-92.

[13] Coase R. H. (1937), �The Nature of the Firm�, Economica, 4, 386-405.

[14] Colombo, S. and M. Scrimitore (2018), �Managerial Delegation Under Capacity Com-

mitment: A Tale of Two Sources�, Journal of Economic Behavior and Organization, 150,

149-161.

[15] Cremer, J. and M. H. Riordan (1987), �On Governing Multilateral Transactions with

Bilateral Contracts�, Rand Journal of Economics, 18, 436-451.

[16] Deloitte (2016), Deloitte�s 2016 Global Outsourcing Survey, Deloitte Development LLC.

[17] Feng, Q. and L. X. Lu (2012), �The Strategic Perils of Low Cost Outsourcing�, Man-

agement Science, 58, 1196-1120.

[18] Feng, Q. and L. X. Lu (2013), �The Role of Contract Negotiation and Industry Structure

in Production Outsourcing�, Production and Operations Management, 22, 1299-1319.

[19] Fershtman, C. and K. Judd (1987), �Equilibrium Incentives in Oligopoly�, American

Economic Review, 77, 927-940.

[20] Gilbert, S. M., Y. Xia, G. Yu. (2006), �Strategic Outsourcing for Competing OEMs that

Face Cost Reduction Opportunities�, IIE Transactions, 38, 903-915.

[21] Görzig B. and A. Stephen (2002), �Outsourcing and Firm-level Performance�, Discussion

Paper, 309, DIW Berlin.

19

[22] Grossman, S. and O. Hart, O. (1986), �The Costs and Bene�ts of Ownership: A Theory

of Vertical and Lateral Integration�, Journal of Political Economy, 94, 691-719.

[23] Grossman, S. and E. Helpman (2002), �Integration Versus Outsourcing in Industry Equi-

librium�, Quarterly Journal of Economics, 117, 58-119.

[24] Jansen, J. (2003), �Coexistence of Strategic Vertical Separation and Integration�, Inter-

national Journal Industrial Organization, 21, 699-716 .

[25] Katz, M. (1991), �Game-Playing Agents: Unobservable Contracts as Precommitments�,

Rand Journal of Economics, 22, 307-322.

[26] Lewis, T. R. and D. Sappington (1989), �Technological Change and the Boundaries of

the Firm�, American Economic Review, 81, 887-900.

[27] Liu, Y. and R. Tyagi (2011), �The Bene�ts of Competitive Upward Channel Decentral-

ization�, Management Science, 57, 741-751.

[28] Marjit, S. and A. Mukherjee (2008), �Pro�t Reducing International Outsourcing�, Jour-

nal of International Trade & Economic Development, 17, 21-35.

[29] Marx, L. and G. Sha¤er (2007), �Rent Shifting and the Order of Negotiations�, Inter-

national Journal of Industrial Organization, 25, 1109-1125.

[30] McAfee, P. and M. Schwartz (1994), �Opportunism in Multilateral Vertical Contracting:

Non-discrimination, Exclusivity, and Uniformity�, American Economic Review, 84, 210-

230.

[31] Milliou, C. and L. Pechlivanos (2019), �Upstream Entry and Foreclosure�, unpublished

manuscript, Athens University of Economics and Business.

[32] Milliou, C. and E. Petrakis (2007), �Upstream Horizontal Mergers, Vertical Contracts,

and Bargaining�, International Journal of Industrial Organization, 25, 963-987.

[33] Möller, M. (2007), �The Timing of Contracting with Externalities�, Journal of Economic

Theory, 133, 484-503.

[34] O�Brien, D. and G. Sha¤eer (1992), �Vertical Control with Bilateral Contracts�, Rand

Journal of Economics, 23, 299-308.

[35] Pagnozzi and Picolo (2012), �Vertical Separation with Private Contracts�, Economic

Journal, 122, 173-207.

[36] National Academy on Engineering (2008), The O¤shoring of Engineering : Facts, Un-

knowns and Potential Implications, The National Academies Press, Washington D.C.

20

[37] Pearce, J. (2014), �Why Domestic Outsourcing is Leading America�s Reemergence in

Global Manufacturing?�Business Horizons, 57, 24-36.

[38] Rey, P. and T. Vergé (2004), �Bilateral Control with Vertical Contracts�, Rand Journal

of Economics, 35, 728-746.

[39] Singh, N. and X. Vives (1984), �Price and Quantity Competition in a Di¤erentiated

Duopoly�, Rand Journal of Economics, 15, 546-554.

[40] Shy, O. and R. Stenbacka (2003), �Strategic Outsourcing�, Journal of Economic Behav-

ior and Organization, 50, 203-224.

[41] Sklivas, S. D. (1987), �The Strategic Choice of Managerial Incentives�, Rand Journal

Economics, 18, 452-458.

[42] Taylor, T. A. (2002), �Supply Chain Coordination under Channel Rebates with Sales

E¤ort E¤ects�, Management Science, 48, 992-1007.

[43] van Mieghem, J. (1999), �Coordinating Investment, Production and Subcontracting�,

Management Science, 45, 954-971.

[44] Villas-Boas, S. (2007) �Vertical Relationships between Manufacturers and Retailers: In-

ference with Limited Data�, Review of Economic Studies, 74, 625-652.

21