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Organizational Structure and Product-Market Competition Jung Hur y Yohanes E. Riyanto z December 2008 Abstract This paper analyzes an interaction between an entrant rms choice of organizational structure for the decision-making authority and product-market competition. We consider two organizational structures, namely a centralized organization, whereby formal authority is retained by a principal, and a decentralized organization, whereby formal authority is delegated to an agent. The entrants choice of organizational structure hinges on a trade-o/ between operating prot and managerial e/ort. The principal may choose an organizational structure that generates lower operating prot to motivate the agent to work hard. The incentive to delegate formal authority is decreasing with the toughness of product-market competition. The choice of organizational structure may also determine market structure. Keywords: Formal and Real Authority, Delegation Structure, Product Market Competition JEL Classication: D20, L22 We thank conference participants at the Far Eastern and South Asia Meeting of the Econometric Society 2008 held at the Singapore Management University. Research grant support R-122-000-100-112 from FASS-NUS is gratefully acknowledged. y School of Economics, Sogang University, Shinsu-dong, Mapo-gu, Seoul, Korea 121-742; , email: ec- [email protected]. z (Corresponding author) Department of Economics, FASS, National University of Singapore, AS2 1 Arts Link, Singapore 117570; ph: +65-6516-6939, email: [email protected]. 1
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Page 1: Organizational Structure and Product-Market Competitionexpernomics.com/yer/papers/Org Structure and Prod Mkt...3The following two examples are taken from Brickley, Smith, and Zimmerman

Organizational Structure and Product-Market Competition�

Jung Hury Yohanes E. Riyantoz

December 2008

Abstract

This paper analyzes an interaction between an entrant �rm�s choice of organizationalstructure for the decision-making authority and product-market competition. We considertwo organizational structures, namely a centralized organization, whereby formal authorityis retained by a principal, and a decentralized organization, whereby formal authority isdelegated to an agent. The entrant�s choice of organizational structure hinges on a trade-o¤between operating pro�t and managerial e¤ort. The principal may choose an organizationalstructure that generates lower operating pro�t to motivate the agent to work hard. Theincentive to delegate formal authority is decreasing with the toughness of product-marketcompetition. The choice of organizational structure may also determine market structure.

Keywords: Formal and Real Authority, Delegation Structure, Product Market Competition

JEL Classi�cation: D20, L22

�We thank conference participants at the Far Eastern and South Asia Meeting of the Econometric Society2008 held at the Singapore Management University. Research grant support R-122-000-100-112 from FASS-NUS isgratefully acknowledged.

ySchool of Economics, Sogang University, Shinsu-dong, Mapo-gu, Seoul, Korea 121-742; , email: [email protected].

z(Corresponding author) Department of Economics, FASS, National University of Singapore, AS2 1 Arts Link,Singapore 117570; ph: +65-6516-6939, email: [email protected].

1

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1 Introduction

Ronald Coase�s seminal publication (Coase, 1937) provided an impetus to the burgeoning lit-

erature on the theory of the �rm. A �rm was no longer seen as merely a production function

that transforms inputs into outputs, but instead as a complex organization that consists of self-

interested agents coordinating their activities in a hierarchy-of-command with a principal (CEO)

acting as the ultimate decision-maker. However, it is obvious that the principal faces some in-

evitable constraints such as a limited span of control, attention, and ability, and thus may wish

to delegate the decision-making authority to her subordinates to relax these constraints.

Aghion and Tirole (1997) develop a theoretical model that deals with the delegation of au-

thority in a �rm. In their paper, the principal has formal authority to make a decision a¤ecting

the �rm�s payo¤.1 Obviously, she will only be able to make a decision if she is informed about the

available choice of actions and their payo¤ consequences. Having the formal authority also enables

her to overrule any decision proposed by her subordinate that is not in line with her interests.

However, she may decide not to overrule the agent�s proposal and prefer instead to delegate the

decision making authority to the agent when she is uninformed. This implies that although the

principal has the �formal�authority, it is the agent who actually has the �real�authority due to his

superior information. Formal authority itself may also be delegated by the principal to the agent,

thereby empowering the agent to make a decision that cannot be overruled by the principal. In

general, the optimality of the delegation of authority depends on a trade-o¤ between the loss of

control that the principal experiences and managerial initiative. Delegation is thus like a double-

edged sword: it induces the agent to work harder, but it may result in a suboptimal decision by

the agent.

In this paper, we further extend the model of Aghion and Tirole (1997) to explicitly incor-

porate an interplay between the delegation of authority and the product-market competition. In

particular, we have in mind a setting in which a potential entrant is contemplating entering a

market served by an incumbent. The former must take into account its incumbent rival�s optimal

1Throughout the paper we use �her�for the principal and �him�for the agent.

2

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competitive-strategy when choosing its optimal competitive-strategy, and in turn this choice is

in�uenced by the adopted organizational structure upon entry; that is, whether or not the formal

decision-making authority is delegated to the agent. Thus, a �rm�s organizational structure is

developed in response to its competitive strategy.2

The following examples further illustrate the important link between organizational structure

and business strategy.3 Prior to 1980, Eastman Kodak was virtually a monopolist in photographic

�lm production. However, during the early 1980s, Kodak�s market share was diminishing rapidly

due to intense competition from its rival Fuji Corporation which produces a higher quality �lm than

Kodak. As a response to this competitive pressure, Kodak decided to reorganize the structure of its

decision-making authority. It shifted to a more decentralized structure that allowed managers to

make important decisions without approval from its CEO. Another example is the case of Honda

Motor Company in 1991. Prior to 1991, the company adopted a decentralized decision-making

structure, in which important decision-making authority was delegated by the CEO to managers.

However, by the late 1980s, the company�s market share had dropped to fourth position after

Mitsubishi, Nissan and Toyota. In 1991, the new CEO of Honda, Nobuhiro Kawamoto, decided

to centralize decision-making within the company. These two examples clearly demonstrate that

competitive pressure can lead to either a more centralized or a more decentralized decision-making

structure.

In our model, the action chosen by either the principal or the agent when formal authority

is delegated in�uences the �rm�s relative competitive-position vis-à-vis its rival, and hence the

�rm�s operating pro�t. We derive the conditions under which the principal may or may not want

to be the one making the decision. Our approach in modeling the principal�s decision and the

corresponding trade-o¤ follows that of Marin and Verdier (2003). However, their paper aims at

explaining the link between �rm structure, international trade and globalization. For that purpose,

they adopt a general-equilibrium macro framework. In contrast, our model aims at capturing the

2This is an in�uential idea that was put forth decades ago by Alfred Chandler in his seminal book (Chandler,1962) examining the historical evolution of the organizational structure of big US corporations like Du Pont,Standard Oil and General Motors. Chandler (1962) concludes that organizational structure is adapted to suitbusiness strategy.

3The following two examples are taken from Brickley, Smith, and Zimmerman (2006).

3

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details of product-market competition and its role in shaping organizational structure, for which

a partial-equilibrium Industrial Organization (IO) framework is more appropriate.4

The following hypothetical scenario illustrates the essential elements of our model. Consider a

�rm, consisting of a principal and an agent, that is contemplating entering a market served by an

incumbent. Before entering the market, the �rm must choose a production process to employ out

of several possible production processes. A priori, both the principal and the agent are uninformed

about the marginal-cost implications of these production processes. However, they will become

informed with some probability if costly e¤ort is exerted. Assume that there are exactly two

production processes that give non-negative operating pro�ts to both the principal and the agent

when implemented, and one of them is preferred by the principal while the other one is preferred

by the agent. When the former is implemented, the agent gets no private bene�ts. Only when

the latter is implemented does the agent get some positive private bene�ts.

The principal�s most preferred production process entails a lower marginal cost than that of the

agent. When the agent has a delegated authority and is entitled to choose a production process,

he will surely choose the one that generates private bene�ts. Accordingly, from the principal�s

view-point, a delegation of authority entails a trade-o¤ between motivating the agent to exert

e¤ort using private bene�ts and employing an ine¢ cient production process.

The principal�s payo¤ is not only determined by the choice of production process but also by the

extent of product-market competition between the �rm and its competitor. Thus, in contrast to

the paper of Aghion and Tirole (1997), which considers the principal�s payo¤ as being exogenous,

our paper considers it as being endogenously determined.

Suppose that upon entering the market, the entrant engages in Cournot duopoly competition

with the incumbent �rm, whose marginal cost lies in between the marginal costs resulting from

the preferred production process of the principal and the agent of the entrant �rm. Consequently,

when authority is delegated to the agent, he will choose a less e¢ cient production process than

that of the incumbent, and thereby put the entrant �rm at a disadvantageous position vis-à-vis

4Another paper that uses the Aghion-Tirole framework to analyze international trade and globalization issuesis Puga and Tre­ er (2007).

4

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the incumbent. As a result, the entrant can potentially only carve out a smaller market share than

the incumbent. Nevertheless, the delegation of authority and the presence of private bene�ts may

stimulate the agent to work harder to acquire information about the marginal-cost parameters of

all the available production processes. Thus, the delegation of authority may still be bene�cial to

the principal as it allows her to lower the cost of exerting e¤ort and to induce the agent to exert

greater e¤ort.

We show that the entrant�s optimal choice of organizational structure essentially depends on

a trade-o¤ between inducing the agent to exert greater e¤ort and the reduction in operating

pro�ts. Under some conditions, the principal may prefer to choose an organizational structure

that gives lower operating-pro�ts in order to motivate the agent to work harder. We provide

some comparative statics results of a change in the intensity of product market competition on

the optimal organizational structure.We also show that the choice of organizational structure may

shape the prevailing market structure as it determines whether a rival incumbent remains active

in the market or is forced to exit.

The rest of this paper is organized as follows. Section 2 presents the model, while Section 3

presents the solutions. Section 4 discusses several market structure con�gurations arising from

these solutions. Section 5 summarizes the results and concludes.

2 The Model

There are essentially two building blocks of the model, the �rst one is the choice of organizational

structure and the second one is the product market competition.

2.1 Organizational Structure

The �rst building block is based on Aghion and Tirole (1997). Assume there are two �rms, called

1 and 2. The former is a potential entrant and the latter is an incumbent. Firm 1 consists of a

principal (P ) and an agent (A). The principal must decide which organizational structure of the

decision-making authority to adopt in the �rm. There are two organizational structures available,

namely a centralized decision-making authority (P -organization), in which the principal retains the

5

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formal decision right (formal authority) in the �rm, and a decentralized decision-making authority

(A-organization), in which the principal delegates formal authority to the agent. Throughout

this paper, we focus our analysis on the entrant �rm 1�s choice of organizational structure in

anticipation of the arising product market competition with the incumbent (�rm 2) upon entry.

There are several ways to give justi�cation to this particular setup. First, the incumbent �rm

could be a family �rm which is fully owned and managed by the family (i.e. the principal). Thus,

there is no separation between ownership and control in the �rm. The entrant, on the contrary,

is a public �rm which is owned by a large shareholder (i.e. the principal) and several minority

shareholders and managed by a professional manager (i.e. the agent). The principal must decide

how much discretionary power should be delegated to the agent.5 Second, the incumbent �rm may

have already been active in the market for sometime and have chosen a particular organizational

structure. It is well known from some empirical works that �rms exhibit structural inertia, that

is their organizational structure is rarely altered unless they experience a crisis a¤ecting their

survival ability.6 The entrant, in contrast, is still in the process of entering the market served by

the incumbent and choosing an organizational structure to adopt.

The entrant (�rm 1) must choose a production process to employ out of N available options.

The marginal cost implications of all available production processes are initially unknown, but

they can be inferred by exerting e¤ort. The principal�s e¤ort is denoted by E and the agent�s

e¤ort is denoted by e. Exerting e¤ort is costly for both. The costs incurred by the principal and

the agent takes quadratic forms of E2=2 and e2=2 respectively. Upon exerting e¤ort they will be

informed about the marginal cost parameters with probabilities E and e.

The principal�s most preferred production process gives marginal cost cp when implemented,

but provides no private bene�ts to the agent.7 Likewise, the agent�s most preferred production

process gives marginal cost ca = cp with � 1 when implemented as well as private bene�ts b to5Burkart, Gromb, and Panunzi (1998) shows that one way for the principal to credibly commit to giving greater

discretionary power to the manager is by holding a smaller fraction of ownership in the �rm. The smaller theownership fraction, the lesser is the large shareholder�s incentive to �monitor�the manager.

6See for instance Schaefer (1998), Colombo and Delmastro (1999), Colombo and Delmastro (2002).7We can also easily consider a less extreme case in which the agent receives some positive private bene�ts instead

of no private bene�ts when the principal�s most preferred production process is implemented. Such a considerationwill not qualitatively a¤ect our results.

6

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the agent. The incumbent employs a production process that gives marginal cost c. Essentially,

the principal of the entrant �rm faces a managerial moral hazard problem. When the agent has

some discretion in choosing the production process, he may not always select the most e¢ cient

production process if doing so forces him to forego substantial private bene�ts. We rule out

random picking of the production process by assuming that at least one of the available production

processes is extremely ine¤cient and will result in a very large marginal cost. This also implies that

when neither is informed, she (he) will prefer to maintain the status quo; that is, not implementing

any project.

The party with formal authority, who could either be the agent or the principal, has the

ultimate right to choose which production process to employ. Obviously, she (he) will choose her

(his) most preferred production process when informed.8 The formal authority may be retained

by the principal or delegated to the agent. When it is delegated, the agent has the power to

choose a production process to employ without being overruled by the principal. When the

formal authority holder is uninformed, she (he) will be willing to implement the other party�s

most preferred production process. Thus, in such a case, the other party e¤ectively has the

real-authority in the �rm. Throughout the paper, we thus follow Aghion and Tirole (1997) in

distinguishing between formal authority and real authority.

Upon entering the market and competing with the incumbent, the principal receives the �rm�s

pro�t �1i , where i 2 fp; ag denotes the chosen production process, which could either be the one

that is most preferred by the principal (p) or the one that is most preferred by the agent (a). The

magnitude of �1i depends on the relative marginal cost of the �rm vis-à-vis that of the incumbent,

and also on the nature of the product-market competition. Thus, in our framework the payo¤

of the principal is going to be endogenously determined. When the principal�s most preferred

production process is implemented, she obtains �1p ; however, when the agent�s most preferred

production process is implemented instead, she obtains only �1a . Given that cp � ca = cp, we

have �1p � �1a , and we can express the relationship between the two pro�ts as, �1a = ��1p where8Similar to Aghion and Tirole (1997), we essentially assume here that the agent is solely motivated by private

bene�ts. Examples of private bene�ts are perks, prestige, and other non pecuniary bene�ts.

7

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� 2 [0; 1]. We interpret � as the degree of interest-congruence between the principal and the

agent. When � = 1; their interests are perfectly aligned, and accordingly, the principal receives

the same amount of pro�t no matter which production process is implemented. For the purpose

of our analysis, we thus de�ne the degree of interest congruence as

� =�1a�1p

: (1)

This endogenous determination of the interest-congruence parameter represents a departure from

the Aghion-Tirole framework.

2.2 Product Market Competition

Firms 1 and 2 produce di¤erentiated goods. The demand side is characterized by the following

quadratic representative consumer�s utility function:

U = q1i + q2i �1

2

�q21i + q

22i + 2�q1iq2i

�+ z;

where i 2 fp; ag denotes the chosen production process, � 2 [0; 1] is a parameter measuring the

degree (strength) of product di¤erentiation, q1i and q2i are the goods produced respectively by

�rms 1 and 2, and z is a numeraire good. The two products are independent, that is, completely

di¤erentiated, when the degree of product substitution equals zero (� = 0), and they are homoge-

nous when � equals one. This utility function is a variant of the one used in Singh and Vives

(1984) and Zanchettin (2006).

From the utility maximization problem, we obtain the following linear demand functions:

q1i = �0 � �1p1i � �2p2i (2)

q2i = �0 � �1p2i � �2p1i ; (3)

where �0 = 11+� , �1 =

11��2 , and �2 =

��1��2 . Assuming that � < 1, these linear demand functions

can be inverted to yield

8

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p1i = 1� q1i � �q2i (4)

p2i = 1� q2i � �q1i : (5)

Firms 1 and 2 engage in Cournot duopoly competition.

2.3 The Timeline

The timeline of the model is summarized in Figure 1. At t = 0, prior to entering the market, the en-

trant �rm�s principal chooses either a centralized decision-making structure, called P -organization,

or a decentralized decision-making structure, called A-organization. In the former organizational

structure, the principal has the formal authority over the choice of production process, while in

the latter, the principal delegates the formal authority to choose the production process to the

agent. At t = 1, upon entering the market, both the principal and the agent of the entrant

�rm simultaneously exert costly e¤ort to acquire information on the marginal-cost parameters

of the production processes. When informed, the holder of formal authority chooses which pro-

duction process to implement; otherwise, when she (he) is uninformed, the other informed party

will choose which production process to implement. When both are uninformed, no production

process is chosen and the �rm is inactive. At t = 2, the entrant �rm begins its production using

the chosen production process and competes with the incumbent in a Cournot fashion. Finally,

at t = 3, all payo¤s are realized. We solve the model using backward induction.

9

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0 1 2 3

•organizational structure

is chosen, i.e. eithercentralized (P­Authority)or decentralized(A­Authority) decision­making authority.

•principal (P) and

agent (A) exerteffort E and e,with costs E2/2 ande2/2, and obtaininfo with prob. E and e.

•The holder of decisionright chooses aproduction processwhen informed, otherwisethe other party canchoose when informed.

•production begins

using the chosenproduction process.

•Firms 1 and 2 engagein product­marketcompetition.

•payoffs are

realized.

Figure 1: The Timeline of the Model

3 Solution of the Model

We begin with the product-market competition. At this stage, we take the optimal organizational-

structure chosen in an earlier stage as given.

3.1 Product-Market Competition

The �rms�pro�t functions can be expressed as

�1i = (1� q1i � �q2i)q1i � ciq1i (6)

�2i = (1� q2i � �q1i)q2i � cq2i ; (7)

with i 2 fp; ag. Recall that ca = cp with � 1. Both �rms will be active in the market when

their optimal quantities are positive. Whether or not a �rm�s optimal quantity is positive depends

on the magnitude of the degree of product substitution (�) and the marginal cost of the two

competing �rms (c and ci).

Under duopoly, given that the production process i is chosen by the entrant �rm, the optimal

10

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quantities can be derived as follows:

q1i;d =2� �� 2ci + �c

(4� �2) (8)

q2i;d =2� �� 2c+ �ci

(4� �2) : (9)

Subscript d denotes the duopoly case. Firms 1 and 2 will be active and produce positive quantities

if and only if

1

�[2c� (2� �)] < ci <

1

2[�c+ (2� �)] : (10)

When ci > 12 [�c+ (2� �)] prevails, it implies that the marginal cost of the entrant �rm 1 resulting

from the production process i is excessively high so that it is not possible for the �rm to be

active in the market. Consequently, the incumbent �rm will be a monopolist. On the other

hand, when ci < 1� [2c� (2� �)] prevails, it implies that the marginal cost of �rm 1 resulting

from the production process i is su¢ ciently lower than that of the incumbent �rm. As a result,

the incumbent �rm cannot pro�tably compete with the entrant, and thus the latter will be a

monopolist. Since the focus of our analysis is on entrant �rm 1�s choice of organizational structure,

we only consider cases in which entrant �rm 1 is active in the market irrespective of the production

process i 2 fp; ag chosen. We therefore impose the following assumptions.

Assumption 1 For all i 2 fp; ag, ci < 12 [�c+ (2� �)] :

This assumption essentially implies that �rm 1�s marginal cost ci should not be too high relative

to the incumbent�s marginal cost c. Otherwise, �rm 1 can never be active in the market. For

notational simplicity, we de�ne

� =1

�[2c� (2� �)]

� =1

2[�c+ (2� �)] :

If the entry by �rm 1 forces the incumbent to exit the market, the optimal monopoly-quantity

can be straightforwardly derived as9

9Thus, when the rival�s marginal cost is too high relative to �rm 1�s marginal cost, we have (2� �� 2c+ �ci) < 0.Firm 2 will produce nothing (q2i;d = 0).

11

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q1i;m =1� ci2

: (11)

Subscript m denotes the monopoly case. Next, we assume

Assumption 2 (2��)2 < c < 1 and for all i 2 fp; ag, 0 � ci < 1.

The �rst part of the assumption ensures that 1� [2c� (2� �)] and

12 [�c+ (2� �)] in (10) are,

respectively, the lower and upper bounds of ci that give us the duopoly case given that � � 0.

The second part of the assumption implies that the case in which entrant �rm 1 is a monopolist

is potentially viable.

The prevailing market structure depends on the relative magnitude of ci; i 2 fp; ag; vis-à-vis

c. The following lemma describes the prevailing market-structure con�gurations.

Lemma 1 Given the entrant�s choice of production process i 2 fp; ag, the resulting marginal cost

ci, the incumbent �rm�s marginal cost c, and also Assumptions 1 and 2, we have the following

market-structure con�gurations upon entry by �rm 1:

(i) For � < cp < cp < �, both �rms are duopolists no matter which production process is

chosen by the entrant.

(ii) For cp < � < cp < �, the entrant will become a monopolist when the production process p

is chosen by the entrant; otherwise, when the production process a is chosen by the entrant,

both �rms are duopolists .

(iii) For cp < cp < � < c < �, the entrant is a monopolist no matter which production process

is chosen by the entrant.

Essentially, case (i) prevails when both �rms�marginal costs are not so di¤erent from each

other, irrespective of which production process is chosen by entrant �rm 1. Thus, �rms are

relatively more homogenous in terms of their production technology. Case (ii) prevails when

�rm 1�s marginal costis signi�cantly lower than �rm 2�s marginal cost when the most preferred

12

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production process of the principal is implemented. Finally, case (iii) prevails when �rm 1 is vastly

more e¢ cient than �rm 2 , irrespective of which production process is chosen by �rm 1. Thus,

both �rms are very heterogenous in terms of their production technology. It is interesting to note

that as the degree of product substitution � approaches one (zero), the range of cp that allows

for duopoly competition becomes smaller (larger). A higher � (i.e. closer to 1) implies tougher

competition since both products become less di¤erentiated. Consequently, a �rm that has a lower

marginal cost will likely be a monopolist. The opposite prevails for a lower �.

The resulting duopoly pro�ts are

�1i;d =(2� �� 2ci + �c)2

(4� �2)2 (12)

�2i;d =(2� �� 2c+ �ci)2

(4� �2)2 ; (13)

while the resulting monopoly pro�t is

�1i;m =(1� ci)2

4: (14)

Using the above expressions for equilibrium pro�ts, we can derive the congruence parameters

�j 2 [0; 1]; where j 2 f1; 2; 3g denotes various market-structure con�gurations stated in Points

(i), (ii), and (iii) of Lemma 1.

Lemma 2 The degree of interest-congruence between the principal and the agent of the entrant

�rm under all market-structure con�gurations, �j ; j 2 f1; 2; 3g, can be derived as follows: �1 =�1a;d�1p;d

=(2���2 cp+�c)2(2���2cp+�c)2

; �2 =�1a;d�1p;m

=4(2���2 cp+�c)2(4��2)2(1�cp)2

; and �3 =�1a;m�1p;m

=(1� cp)2(1�cp)2

:

The congruence parameter �, to some extent, also captures the cost of delegation for the

principal. Delegation of formal or real authority reduces a �rm�s pro�t as it leads to the agent

choosing an ine¢ cient production process. Nevertheless, despite the pro�t reduction, the principal

may still be willing to delegate authority in order to motivate the agent to work hard. To have

�j 2 [0; 1], we require that �1a;d � �1p;d in market-structure con�guration 1 and �1a;d � �1p;m in

market-structure con�guration 2. Since the agent�s most preferred production process is clearly

13

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less e¢ cient than the principal�s most preferred production process it is obvious that we have

�1a;d � �1p;d . It is also straightforward to verify that �1a;d � �1p;m .10 The interests of the

principal and the agent are diametrically opposed (perfectly aligned) when � = 0 (� = 1).

Note that when approaches one, that is, when the marginal cost resulting from the principal�s

most preferred project is the same as that resulting from the agent�s most preferred project, �1

and �3 in Lemma 2 should also approach one, implying that the interests of the principal and the

agent become almost perfectly aligned. It is also obvious that �3 does not depend on the degree

of product di¤erentiation � because no matter which production process is chosen, the entrant

will always be a monopolist under this market-structure.

Subsequently, we evaluate the impact of an increase in: 1) the degree of product-substitution

�, 2) the incumbent�s marginal cost c, 3) the entrant�s marginal cost when the principal�s most

preferred production process is implemented cp, and 4) the cost-ine¢ ciency of the agent�s most

preferred production process , on the congruence parameters �1 and �2.11 We have the following

result.

Proposition 1 The degree of interest congruence between the principal and the agent of the en-

trant �rm under all market-structure con�gurations, �j, j 2 f1; 2; 3g, is a¤ected by the rival�s

marginal cost (c), �rm 1�s marginal cost when the principal�s most preferred production process

(cp) is implemented, the cost-ine¢ ciency of the agent�s most preferred production process ( ), and

the degree of product substitution (�) in the following ways

(i) @�1@c > 0;

@�1@cp

< 0; @�1@ < 0; and @�1@� < 0.

10The proof of �1a;d � �1p;m can be outlined as follows. The f.o.c.s of (12), (13), and (14) with re-

spect to their own quantity variables are respectively @�1i;d=@q1i;d =�1� q1i;d � �q2i;d � q1i;d � ci

�= 0;

@�2i;d=@q2i;d =�1� q2i;d � �q1i;d � q2i;d � ci

�= 0; and @�1i;m=@q1i;m =

�1� q1i;m � q1i;m � ci

�= 0: Next,

we can express the monopoly and duopoly pro�ts as �1i;m =�q1i;m

�2and �1i;d =

�q1i;d

�2. We know that if

q1i;m � q1i;d then �1i;m � �1i;d . Using f.o.c. @�1i;m=@q1i;m = 0, we can simplify @�1i;d=@q1i;d

���q1i;d=q1i;m

=�1� q1i;m � �q2i;d � q1i;m � ci

�into @�1i;d=@q1i;d

���qC1i;d

=q1i;m

= ��q2i;d , which is clearly non-positive given that

0 � � � 1. Hence, we can establish that q1i;m � q1i;d , which implies that �1i;m � �1i;d .11Only the congruence parameters under market-structure con�gurations 1 and 2, that is, �1 and �2, are going

to be a¤ected by the degree of product substitution �. This is because duopoly competition can potentially existonly in these two con�gurations.

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(ii) @�2@c > 0;

@�2@cp

< 0; @�2@ < 0; and @�2@�

�<0 if 14� [(4+�

2)c�(2��)2]< cp<�>0 if �< cp< 1

4� [(4+�2)c�(2��)2].

(iii) @�3@cp

< 0; @�3@ < 0.

Proof. See Appendix.

The non-negative signs of @�1@c and@�2@c can be explained as follows. An increase in the incum-

bent�s marginal cost c, ceteris paribus, softens the product-market competition for the entrant

and boosts its pro�t. We also know that �1a;d � �1p;d � �1p;m , and thus the positive impact of

an increase in c will be larger when the pro�t is smaller. This implies that �1a;d will increase the

most, followed by �1p;d and �1p;m , when c increases. Since �1 = �1a;d=�1p;d and �2 = �1a;d=�1p;m ,

both �1 and �2 will increase when c increases. All in all, the higher the cost advantage of the

entrant vis-à-vis the incumbent is, the higher will be the interest alignment between the principal

and the agent of the entrant.

The explanation behind the non-positive signs of @�1@cp

and @�2@cp

is analogous to explanation

given above. An increase in the entrant�s marginal cost cp, ceteris paribus, toughens the product-

market competition for the entrant, and reduces its pro�t from entering the market regardless of

whether the �rm is a monopolist or a duopolist. Given that we have �1a;d � �1p;d � �1p;m , the

reduction in �1a;d will be the largest, followed by the reduction in �1p;d and �1p;m . Consequently,

the higher is the cost disadvantage of the entrant vis-à-vis the incumbent, the lower will be the

interest alignment between the principal and the agent.

The degree of product substitution � only in�uences �1 and �2 but not �3. In market-structure

con�guration 1, an increase in � toughens the product-market competition for both �rms and

squeezes their pro�ts. The reduction in �1a;d dominates the reduction in �1p;d and consequently

�1 falls. In market-structure con�guration 2, an increase in � will only a¤ect the numerator of �2.

However, the e¤ect is ambiguous depending on the magnitude of entrant �rm 1�s marginal cost

under the agent�s most preferred production process ( cp) relative to incumbent �rm 2�s marginal

cost (c).

The ambiguous impact of a change in � on �2 can be intuitively explained as follows. Recall

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that � only in�uences �2 =�2a;d�2p;m

through the numerator of �2 (�2a;d). Thus, when evaluating

the impact of a change in � on �2, we can con�ne our attention on the impact of a change in

� on �2a;d . Essentially, market structure con�guration 2 exists when c is relatiely bigger than

cp. Now suppose that c is only slightly larger than cp. This implies that the entrant�s optimal

quantity (q�1a;d) is only slightly larger than the incumbent�s optimal quantity (q�2d). An increase in

� increases the slope of both �rms�s reaction functions by an almost equal amount. Consequently,

both �rms�new optimal quantities (q��1a;d and q��2d) will be lower than previous optimal quantities

(q�1a;d and q�2d). The fall in q1a;d leads to a reduction in �1a;d , which results in a lower �2. Figure

3(a) illustrates the case.

Now, suppose that c is much larger than cp. This implies that the entrant�s optimal quantity

(q�1a;d) is going to be much larger than the incumbent�s optimal quantity (q�2d). If � increases, the

entrant�s reaction curve will rotate a bit to the left, but the incumbent�s reaction curve will rotate

a lot to the left. Thus, the slope of both �rms�s reaction functions become steeper, however the

slope of the entrant�s reaction function is going to be much steeper than that of the incumbent.

As a result, optimal q�1a;d increases to q��1a;d

and optimal q�2d decreases to q��2 d. The rise in q1a;d

leads to an increase in �2a;d , which results in a higher �2. Thus, when there is a relatively large

marginal cost asymmetry between the two �rms (with the entrant being much more e¢ cient), an

increase in � will increase the congruence of interests between the agent and the principal. Figure

3(b) illustrates the case.

Finally, an increase in implies that the duopoly pro�t �ia;d and the monopoly pro�t �ia;m

decrease, while the duopoly pro�t �ip;d and the monopoly pro�t �ip;m remain unchanged. Accord-

ingly, it is straightforward to see that �1, �2, and �3 will fall when increases.

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a,d

*1R

a,d

**1R

d

*2R

d

**2R,1a d

q

2 dq

d

*2q

d

**2q

ρ ↑

ρ ↑

a,d

**1q

a,d

*1q

,1a dq

2dq

d

*2R

d

**2R

a,d

*1R

a,d

**1R

ρ ↑

ρ ↑

( )a)   is smallpc cγ− ( )b)   is largepc cγ−

a,d

*1q

a,d

**1q

d

**2q

d

*2q

Figure 2: Reaction Curves in Market Structure Con�guration 2

3.2 The Optimal Choice of Production Process and E¤ort Levels

Next, we move to the earlier stage. In a P -organization, the principal retains formal authority

and chooses the production process whenever she is informed. If she is uninformed, she is willing

to delegate the choice to an informed agent. The principal�s and the agent�s expected payo¤s can

be expressed as

UP = E�1p + (1� E) e��1p �E2

2(15)

UA = (1� E)eb� e2

2: (16)

The above expected payo¤s are constructed in the following way. With probability Ee, the

principal and the agent are both informed, and the principal overrules the agent�s choice of pro-

duction process and asks the agent to implement the principal�s most preferred production process

instead. The principal obtains �1p and the agent obtains no private bene�ts. The magnitude of

pro�ts �1p depends on the market-structure con�gurations derived previously. Recall that the

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entrant may become either a monopolist and obtain �1p = �1p;m , or a duopolist and obtain

�1p = �1p;d .

With probability E (1� e), only the principal is informed, and thus she would prefer to im-

plement her most preferred production process, which yields pro�ts �1p for the principal and no

private bene�ts for the agent.

With probability (1� E) e, only the agent is informed, and thus it is optimal for the principal

to let the agent implement his most preferred production process. Thus, here, the agent has the

real authority. The principal obtains ��1p , � 2 [0; 1], while the agent obtains b. Recall that � is

endogenously determined and its value depends on the prevailing market-structure con�guration

j 2 f1; 2; 3g that was derived in the previous section.

Finally, with probability (1� E) (1� e), both the principal and the agent are uninformed,

status quo prevails and payo¤s are normalized to 0.

Exerting e¤ort is costly for both the principal and the agent, and the costs are assumed to be

increasing at an increasing rate in the amount of e¤ort exerted, that is, E2=2 and e2=2.

The principal and the agent choose E and e respectively to maximize their expected payo¤s.

The best-response e¤ort functions can be derived as E� = (1� e�)�1p and e� = (1� E�) b.12 We

can also observe that e¤ort levels are strategic substitutes: E is decreasing in e and vice-versa.

Solving the best-response functions simultaneously yields the following optimal e¤ort levels:

E� =(1� �b)�1p1� �b�1p

(17)

e� =

�1� �1p

�b

1� �b�1p: (18)

It can be straightforwardly veri�ed that @E�

@�1p> 0, @E

@b < 0, and @E�

@� < 0 for the principal; and

@e�

@�1p< 0, @e

@b > 0,and@e�

@� > 0 for the agent. These are essentially the results obtained by Aghion

and Tirole (1997). Higher pro�ts induce higher monitoring e¤ort by the principal, and less e¤ort

by the agent. Higher private bene�ts motivate the agent to work harder and lower the monitoring-

12We require 0 � �1p � 1 and 0 � �b � 1 for stability and to ensure that the equilibrium e¤ort levels arenon-negative.

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e¤ort by the principal. Finally, when the interests of the principal and the agent become more

aligned, the principal lowers her monitoring e¤ort and the agent exerts more e¤ort.

In an A-organization, the principal delegates the formal decision right to the agent. The agent

will then choose which production process to implement whenever he is informed and the principal

cannot overrule the agent�s decision. However, when the agent is uninformed while the principal is

informed, the principal will instead choose the production process. Thus, in this case the principal

has the real decision-right. The principal�s and the agent�s expected payo¤s (denoted by VA and

VP ) can be written as

VP = e��1p + E(1� e)�1p �E2

2(19)

VA = eb� e2

2: (20)

The above expected payo¤s are constructed in a similar fashion as the expected payo¤s under P -

organization. The best-response e¤ort functions can be derived respectively as E�� = (1� e��)�1p

and e�� = b.13 The optimal e¤ort levels under A-organization can be derived as

E�� = (1� b)�1p (21)

e�� = b: (22)

It can be easily veri�ed that under A-organization, we have @E��

@�1p> 0, @E

��

@b < 0,and @E��

@� = 0 for

the principal; and @e��

@�1p= 0, @e

��

@b > 0,and @e��

@� = 0 for the agent.

3.3 The Choice of Organizational Structure: P -organization versus A-organization

We now evaluate the principal�s choice of organizational structure, beginning with the principal�s

expected payo¤s under P -organization. By putting the solutions for the optimal e¤ort levels (17)

and (18) back into (15), we can express the principal�s expected payo¤s as UP��; b; �1p

�, in which

�1p is the optimal pro�t derived from the product-market competition stage. We can then show:

13We require the same condition as stated in footnote 11 for stability and to ensure that the equilibrium e¤ortlevels are non-negative.

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Lemma 3 The principal�s expected payo¤s under P -organization UP��; b; �1p

�have the following

characteristics:

(i) UP��; b; �1p

����1p=0

= 0 and UP��; b; �1p

����1p=1

= 1=2.

(ii)@UP (�;b;�1p)

@�1p� 0, @UP (�;b;�1p)

@�1p

�����1p=0

= �b, and@UP (�;b;�1p)

@�1i

�����1p=1

= 1.

(iii) For 0 � �b � 1=3 we have @2UP (�;b;�1p)@�21p

� 0.

(iv) For 1=3 < �b � 1 we have;@2UP (�;b;�1p)

@�21p< 0 if �1p <

3�b�12�b ,

@2UP (�;b;�1p)@�21p

> 0 if �1p >

3�b�12�b , and

@2UP (�;b;�1p)@�21p

= 0 if �1p =3�b�12�b .

Proof. See Appendix.

Thus, UP is increasing in �1p , and given that �1p 2 [0; 1], the lower and upper bounds of UP

are equal to those stated in Point (i). Also, UP is concave in �1p for �1p <3�b�12�b and convex

in �1p for �1p >3�b�12�b , and �1p =

3�b�12�b is the in�ection point of UP . It can be easily veri�ed

that there exists a non-negative in�ection point if and only if 1=3 < �b � 1. Consequently, when

0 � �b � 1=3 prevails, UP is convex in �1p .

Next, we evaluate the principal�s expected payo¤s under A-organization. By putting (21) and

(22) into (19), we can express the principal�s expected payo¤s as VP��; b; �1p

�, where �1p is the

optimal pro�t derived from the product-market competition stage. We can then show:

Lemma 4 The principal�s expected payo¤s under A-organization VP��; b; �1p

�have the following

characteristics:

(i) VP��; b; �1p

����1p=0

= 0 and VP��; b; �1p

����1p=1

= �b+ (1�b)22 .

(ii)@VP (�;b;�1p)

@�1p� 0; @VP (�;b;�1p)

@�1p

�����1p=0

= �b;@VP (�;b;�1p)

@�1p

�����1p=1

= �b+ (1� b)2

(iii)@2VP (�;b;�1p)

@�21p� 0.

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Proof. See Appendix.

Thus, VP is increasing and convex in �1p , and given that �1p 2 [0; 1], the lower and upper

bounds of VP are equal to those stated in Point 1.

Lemmas 3 and 4 can be used to compare the magnitude of UP��; b; �1p

�and VP

��; b; �1p

�for the admissible range of �, b, and �1p to determine under what conditions P -organization is

superior to A-organization, and vice versa. The result is stated in the following proposition.

Proposition 2 The principal prefers P -organization to A-organization, that is, UP��; b; �1p

�>

VP��; b; �1p

�, when 0 � �b � 1

3 and b < 2(1� �). She prefers A-organization to P -organization,

that is, UP��; b; �1p

�< VP

��; b; �1p

�, when 1

3 < �b � 1 and b > 2(1� �).

Proof. See Appendix.

Figure 3 depicts the above proposition graphically. On the x-axis, we have the interest

congruence-parameter � and on the y-axis we have private bene�ts b. When the degree of in-

terest congruence � is su¢ ciently small, it is always better for the principal to retain formal

authority by adopting P -organization. However, when the congruence parameter � is su¢ ciently

high, the attractiveness of A-organization increases because of the private bene�ts b. This is be-

cause, when the principal and the agent have su¢ ciently aligned interests and private bene�ts b

are su¢ ciently high, delegation of formal authority to the agent will motivate the agent to exert

greater e¤ort. This will increase the probability of the agent�s being informed. Accordingly, there

is a higher chance that the agent�s most preferred production process is implemented. Since the

congruence parameter � is su¢ ciently high, the principal will not su¤er much from being forced

to choose the agent�s most preferred production process.

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0

1

10.79

0.33

0.33

0.42

0.5b

a

UP

(P­Organization)

b=2­2αb=1/(3α)

VP

(A­Organization)

Figure 3: The Optimal Choice of Organizational Structure

Proposition 3 Under A-organization, the agent�s most preferred production process (a) is more

likely to be chosen than the principal�s most preferred production process (p). The latter is more

likely to be chosen under P -organization.

Proof. See Appendix.

In the next section, we will evaluate what happens to the optimal choice of organizational

structure when the intensity of product-market competition changes.

4 Discussion

Lemma 1 gives the conditions for all three market-structure con�gurations that we consider in this

paper. These conditions depend on the exogenous variables (c; cp, , �). Notice that we may shift

from one con�guration to another when exogenous variables change. This would make it di¢ cult

to get a clear cut analysis. To simplify our analysis, we therefore con�ne our attention on small

changes in exogenous variables that take place within each market structure con�guration. We

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will also use the case in which the principal is indi¤erent between the two organizational structures

as our benchmark point.

4.1 Market-Structure Con�guration 1: The Duopoly Case

Under this con�guration, which prevails when both �rms�marginal costs are not so di¤erent from

each other, irrespective of which production process is chosen by entrant �rm 1, the assignment

of real authority does not really matter for the market structure. The selected production process

will always result in a duopoly competition. However, the principal�s and the agent�s expected

payo¤s will depend on who has the formal authority in the �rm. The principal will therefore

choose an organizational structure that gives her the highest expected payo¤s.

Figure 4 depicts the principal�s choice of organizational structure. A-organization dominates

P -organization for all pairs of (�; b) located in the VP area, while P -organization dominates

A-organization for all pairs of (�; b) located in the UP area. Note that private bene�ts b are

exogenously determined, while the degree of interest-congruence �1 depends on, among other

factors, the incumbent�s marginal cost c, the entrant �rm�s marginal cost under the principal�s most

preferred production process cp, the ine¢ ciency parameter of the agent�s most preferred production

process , and the degree of product substitution �. The following proposition summarizes the

impacts of a change in the exogenous variables (c; cp, , �) a¤ecting �1 =(2���2 cp+�c)2(2���2cp+�c)2

; and a

change in the level of private bene�ts b; on the optimal choice of organizational-structure.

Proposition 4 Suppose that initially the principal of the entrant �rm is indi¤erent between re-

taining formal authority, that is, choosing P -organization, and delegating formal authority, that

is, choosing A-organization, and the relative marginal-costs con�guration is given by � < cp <

cp < �.

(i) Holding b constant, the principal delegates (retains) formal authority if any of these changes

prevails; c increases (decreases), cp decreases (increases), decreases (increases), or � de-

creases (increases).

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(ii) Holding � constant, the principal delegates (retains) formal authority if the agent�s private

bene�ts (b) increase (decrease).

Points (i) and (ii) above are derived using the results stated in Propositions 1 and 2. Choosing

A-organization implies that the principal is willing to give up formal authority. This also implies

that, when the agent is informed, the principal will never be able to force the agent to implement

her most preferred production process, which is more e¢ cient. Nonetheless, the principal�s ex-

pected payo¤ under A-organization may still be higher than that under P -organization. Under

A-organization, the agent will be more motivated to exert e¤ort. Since e¤ort levels are strategic

substitutes, an increase in the agent�s e¤ort levels should lead to a decrease in the principal�s e¤ort

levels, thereby allowing the principal to gain from a reduction in the cost of e¤ort and from an

increase in the probability of implementing a production process other than the status quo. As

long as the gains outweigh the reduction in the �rm�s operating pro�t (�1a;d � �1p;d) due to the

adoption of a less e¢ cient production process, choosing A-organization is indeed optimal for the

principal. All in all, we have shown that the optimal choice of organizational structure crucially

depends on a trade-o¤ between operating pro�t and managerial e¤ort.

It is also worth noting that our results point to a negative relationship between the toughness

of product-market competition and the incentive of the principal to delegate formal authority.

Competition becomes tougher for the entrant when its marginal cost increases, or the incumbent�s

marginal cost decreases, or the ine¢ ciency parameter of the agent�s most preferred production

process increases. In such cases, the incumbent is relatively more e¢ cient than the entrant. Its

pro�t will increase at the expense of the entrant. Competition also becomes tougher when products

are more substitutable. However, it negatively a¤ects both �rms in a similar fashion. We show

in this paper that a tougher competition makes the principal less inclined to delegate formal-

authority to the agent when both �rms are not so di¤erent in terms of their production e¢ ciency.

The case of delegation of formal authority (or A-organization) can also be loosely interpreted as

outsourcing or divestiture, while the case of no-delegation of formal authority (or P -organization)

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can be loosely interpreted as a merger or integration. On the basis of this loose interpretation, our

results suggests that more intense competition should result in a higher prevalence of integrated

�rms when �rms are relatively more homogenous in terms of their production e¢ ciency.

4.2 Market-Structure Con�guration 2: The Mixed Case

Recall that under this con�guration, which prevails when cp < � < cp < �, the entrant will be

a duopolist when the agent selects his most preferred production process. However, the entrant

will be a monopolist when the principal selects her most preferred production process. In other

words, when the most preferred production process of the principal is implemented, entrant �rm

1 is going to be much more e¢ cient than incumbent �rm 2. However, they will be relatively

equally e¢ cient when the agent�s most preferred production process is implemented. Similar to

the previous market-structure con�guration, the assignment of formal authority determines the

magnitude of the agent�s and the principal�s expected payo¤s.

The following proposition summarizes the impacts of a change in the exogenous variables

(c; cp, , �) a¤ecting �2 and the level of private bene�ts b on the optimal choice of organizational-

structure.

Proposition 5 Suppose that initially the principal of the entrant �rm is indi¤erent between re-

taining formal authority, i.e. choosing P -organization, and delegating formal authority, i.e. choos-

ing A-organization, and the relative marginal-costs con�guration is given by cp < � < cp < �.

(i) Holding b constant, the principal delegates (retains) formal authority if any of these changes

prevails; c increases (decreases), cp decreases (increases), or decreases (increases).

(ii) Holding b constant, the principal delegates (retains) formal authority if � increases (de-

creases) provided that � < cp < 14�

h�4 + �2

�c� (2� �)2

i, however when 1

4�

h�4 + �2

�c� (2� �)2

i<

cp < � prevails, she retains (delegates) formal authority if � increases (decreases).

(iii) Holding � constant, the principal delegates (retains) formal authority if the agent�s private

bene�ts (b) increase (decrease).

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The above results are derived using Propositions 1 and 2. Thus, when the entrant �rm faces

less intense product-market competition because of an increase in the rival�s marginal cost (c),

or a decrease in its own marginal cost (either cp), it is more likely that its principal will choose

A-organization than P -organization.

However, it is interesting to see that the impact of a change in � on the choice of organizational

structure is ambiguous. Essentially, the direction of impact depends on the magnitude of cp, that

is, whether it is only marginally lower than c or it is much lower than c. When the marginal cost

di¤erence is relatively small, an increase in �will give an incentive to the entrant �rm�s principal to

retain formal authority. However, when the marginal cost di¤erence is relatively large, an increase

in � will instead give an incentive for the entrant �rm�s principal to delegate formal authority to

the agent.

From Proposition 3, we know that in an A-organization, production process a has a higher prob-

ability of being chosen than production process p. We also know that under this market-structure

con�guration, duopoly competition prevails when a is being implemented, while monopoly prevails

when p is being implemented. Therefore, we can establish the following proposition.

Proposition 6 In market-structure con�guration 2, duopoly competition is more likely to occur

when A-organization is chosen by the entrant �rm, while monopoly is more likely to occur when

P -organization is chosen by the entrant �rm.

All in all, the results presented in this sub-section have an interesting implication. We show

that when the product-market competition becomes softer for the entrant due to an increase in c, or

a decrease in cp, or a decrease in , then A-organization is more likely to be chosen by the entrant,

and this implies that duopoly competition is more likely to happen. We know that a duopoly

pro�t is less than a monopoly pro�t, and yet the entrant would rather choose A-organization than

P -organization and obtain the duopoly pro�t. Thus, the entrant �rm would prefer to compete

with the incumbent rather than drive the incumbent out of the market. By sacri�cing some

operating pro�t, the principal can motivate the agent to exert higher e¤ort, and this allows the

26

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principal to economize on her e¤ort cost. Since the product-market competition is softening, the

degree of interest congruence between the principal and the agent increases, and therefore the

reduction in operating pro�t does not dominate the bene�t of the e¤ort-cost reduction. Obviously

the reduction in operating pro�t should not be too large. This requires that the entrant should

have a su¢ ciently lower marginal cost than the incumbent. All in all, we show that the choice of

organizational structure for the decision making authority may have an important implication for

the prevailing market structure.

Finally, when we interpret � as a measure of competitive pressure, we obtain a result that

supports the real life examples of Eastman Kodak and Honda Motor Company presented earlier

in the introduction. That is, an increase in the competitive pressure may have an ambiguous

impact on the incentive of the principal to delegate the decision making authority. It crucially

depends on the magnitude of the marginal cost di¤erence between competing �rms.

4.3 Market-Structure Con�guration 3: The Monopoly Case

Under this con�guration, which prevails when cp < cp < � < �, the assignment of real authority

does not really matter for the market structure. Here, the entrant �rm is so much more e¢ cient

than the incumbent, such that it will always be able to drive out the incumbent when it enters

the market. However, the assignment of formal authority determines the magnitude of the agent�s

and the principal�s expected payo¤s.

Again we have similar impacts of a change in the exogenous variables (cp and ) a¤ecting

�3 =(1� cp)2(1�cp)2

and in the level of private bene�ts b on the optimal choice of organizational-

structure for the decision making authority as those presented in Proposition 4. Notice that c

and � do not in�uence �3. It is interesting to note that we have a contrasting results to those of

Marin and Verdier (2003). In their paper, an increase in the degree of product market competition

induces the principal to move from P -organization to A-organization. We show here that even in

the absence of product-market competition, the principal may choose A-organization instead of

P -organization.

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5 Conclusion

This paper explores the link between a �rm�s choice of organizational structure of the decision-

making process and product market competition. We consider a �rm, consisting of a principal

and an agent, that is contemplating to enter a market served by an incumbent. The incumbent

is a family owned �rm with no separation between ownership and control. Thus, the principal is

the one who manages the �rm. Upon entry, both �rms engange in Cournot duopoly competition.

Two types of organizational structure of the entrant �rm are considered, namely P -organization, in

which formal authority is retained by the principal, and A-organization, in which formal authority

is delegated to the agent. The holder of formal authority is entitled to decide which production

process to implement. If the principal is the holder, she prefers to choose the most e¢ cient one;

that is, the one that gives the lowest marginal cost. If instead the agent is the holder, he prefers

to choose the one that gives him private bene�ts even though it may not necessarily be the most

e¢ cient one.

A priori, the marginal-cost implications of all the available production processes are unknown

to both the principal and the agent. However, they can be learned by exerting costly information-

acquisition e¤ort. The cost of exerting e¤ort is increasing with the amount of e¤ort exerted.

Greater e¤ort is also associated with a higher probability of becoming informed. The presence

of private bene�ts motivates the agent to exert greater e¤ort. Delegation of formal authority to

the agent can thus be bene�cial for the principal as it motivates the agent to acquire information,

although it may lead to a lower operating pro�t for the principal.

We show that there is a negative relationship between the incentive of the principal to delegate

formal authority to the agent and the intensity of the product-market competition. The more

intense the product-market competition is, the less likely it is that the principal delegates formal

authority to the agent.

We also show that under some conditions, the entrant �rm would prefer to choose an organiza-

tional structure that leads to a duopoly competition between the entrant and the incumbent and

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a lower operating pro�t for the entrant. Had the entrant �rm chosen an alternative organizational

structure, the incumbent would have been driven out of the market. Essentially, by sacri�cing

its operating pro�t, the principal can motivate the agent to exert greater e¤ort and this allows

the principal to economize on her e¤ort cost. The reduction in the operating pro�t is o¤set by

the reduction in the principal�s total e¤ort cost. However, under some other conditions, we may

also have the opposite case. That is, the entrant �rm would prefer to choose an organizational

structure that will drive the incumbent out of the market. This only happens when the reduction

in the operating pro�t dominates the reduction in the principal�s total cost of e¤ort.

Our results could also be given another interpretation in the following way. Consider �rm

1 as the incumbent and �rm 2 as the entrant, rather than �rm 1 as the entrant and �rm 2 as

the incumbent as we have done throughout the paper. Assume also that the entrant is a family

controlled �rm with no professional manager. Upon entering the market, the entrant employs a

speci�c production process leading to a given level of marginal cost. The incumbent must choose

the organizational structure of the decision-making process in anticipation of an entry by the en-

trant. Our results show that, under some conditions, the incumbent may choose an organizational

structure of their decision-making process that could either deter entry or accommodate entry. It

is interesting to see that in the latter, the incumbent would prefer to face a competition from the

entrant and obtain lower operating pro�t. Essentially, the incumbent, that is, the principal, faces

a trade-o¤ between lower operating pro�t and higher incentive for the agent to exert e¤ort.

Appendix

Proof of Proposition 1

Market-Structure Con�guration 1

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Taking the derivatives of �1 with respect to c, cp, , and �;

@�1@c

= 4� ( � 1) cp (2� �� 2cp + �c)(2� �� 2cp + �c)3

@�1@cp

= �4 ( � 1) (2� �+ �c) (2� �� 2cp + �c)(2� �� 2cp + �c)3

@�1@

= �4cp (2� �� 2cp + �c)(2� 2cp � �+ �c)2

@�1@�

=4 (2� �� 2 cp + c�)(2� �� 2cp + c�)3

cp (1� ) (1� c)

Using � 1, c < 1, and Assumptions (1) and (2) to evaluate the signs of the above derivatives

gives us the followings: @�1@c > 0,@�1@cp

< 0, @�1@ < 0, and @�1@� < 0.

Market-Structure Con�guration 2

Next, evaluating the derivatives of �2 with respect to c, cp, , and � yields

@�2@c

=8� (2� �� 2cp + �c)(�2 � 4)2 (cp � 1)2

@�2@cp

= �8 (2� �� 2cp + �c)(�2 � 4)2 (cp � 1)3

[2� 2 � �+ �c]

@�2@

= �16cp (�c� �� 2cp + 2)(�2 � 4)2 (cp � 1)2

@�2@�

=

"8 (2� �� 2 cp + c�)(1� cp)2 (4� �2)3

# �4� (1� cp)� (1� c)

�4 + �2

��:

We can easily verify that @�2@c > 0 and@�2@ < 0.

It can also be shown that @�2@cp

> 0. The proof can be outlined as follows. We know that

�2 =�C1a;d�1p;m

, and

@�2@cp

=

@�C1a;d@cp

�1p;m �@�1p;m@cp

�C1a;d��1p;m

�2@�2@cp

=@

@cp

4 (2� �� 2 cp + �c)2

(4� �2)2 (1� cp)2

!

= �

8 (2� �� 2 cp + c�)| {z }>0

(cp � 1)3��2 � 4

�2| {z }<0| {z }>0

(2� �+ c�� 2 ) .

Thus, sign�@�2@cp

�= sign (c� 2 � �+ 2). We have,

@�2@cp

8<: > 0 if < 12 (c+ 2� �)

= 0 if = 12 (c+ 2� �)

< 0 if > 12 (c+ 2� �)

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Let us de�ne b = 12 (c+ 2� �), and suppose that

= b � " = 1

2(c+ 2� �)� ";

with either " < 0 or " � 0. We know that the monopoly pro�t is larger than the duopoly pro�t,

�1p;m > �C1a;d

or,

(1� cp)2

4>(2� �� 2 cp + c)2

(4� �2)2 :

Substituting into the above expression and simplifying the resulting expression we obtain,

0 > 2c� � (2� �) + 4"cp(1� cp)

:

We know that in order to have market-structure con�guration 2, we require cp < [2c� (2� �)] <

cp <12 [c+ (2� �)]. We also know that 0 � cp < 1. Consequently, we should have, 2c�(2� �) >

0. Next, since 0 � � � 1, we have � (2� �) � (2� �), which implies that

2c� � (2� �) > 0:

Suppose that we have " � 0, then

0 > 2c� � (2� �)| {z }>0

+4"cp

(1� cp)| {z }�0

;

which is a contradiction. Thus, in order to satisfy Assumption 2, we should have " < 0 where " is

su¢ ciently high, and hence

= b � "|{z}<0

and > b .Accordingly, since > b we thus have @�2

@cp< 0. This completes the proof.

Next, we prove that, indeed, sign�@�2@�

�< 0. Denote i 2 fa; pg as the production process

implemented. First, we derive the following f.o.c.s for the maximization of (6) and (7):

@�1i;d@q1i;d

=�1� 2q1i;d � �q2i;d � ci

�= 0

@�2i;d@q2i;d

=�1� 2q2i;d � �q1i;d � c

�= 0:

Totally di¤erentiating the above f.o.c.s, while holding ci constant, yields

@2�1i;d

@�q1i;d

�2 dq1i;d + @2�1i;d@q1i;d@q2i;d

dq2i;d +@2�1i;d@q1i;d@�

d� = 0

@2�2i;d

@�q2i;d

�2 dq2i;d + @2�2i;d@q2i;d@q1i;d

dq1i;d +@2�2i;d@q2i;d@�

d� = 0:

We know that@2�1i;d

@(q1i;d)2 =

@2�2i;d

@(q2i;d)2 = �2; @2�1i;d

@q1i;d@q2i;d=

@2�2i;d@q2i;d@q1i;d

= ��; @2�1i;d@q1i;d@�

= �q2i;d ; and@2�2i;d@q2i;d@�

= �q1i;d . Hence,

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��2 ���� �2

� �dq1i;ddq2i;d

�=

�q2i;dq1i;d

�d�:

Thus,

dq1i;dd�

=1

4� �2��2q2i;d + �q1i;d

�dq2i;dd�

=1

4� �2��q2i;d � 2q1i;d

�;

which, using (8) and (9) we can re-write��2q2i;d + �q1i;d

�as

�2q2i;d + �q1i;d =1

4� �2| {z }>0

h� (2� �)2 � 4�ci +

�4 + �2

�ci

sign��2q2i;d + �q1i;d

�= sign

h� (2� �)2 � 4�ci +

�4 + �2

�ci:

We will have sign��2q2i;d + �q1i;d

�< 0 if

ci >1

4�

h�4 + �2

�c� (2� �)2

i:

Recall that market-structure con�guration 2 prevails when cp < � = 12 [2c� (2� �)] < cp < � =

12 [�c+ (2� �)]. It can be veri�ed, using 0 � � � 1, that

� =1

2[2c� (2� �)] � 1

4�

h�4 + �2

�c� (2� �)2

i� � = 1

2[�c+ (2� �)] :

however cp may or may not be bigger than 14�

h�4 + �2

�c� (2� �)2

i. Consequently, we have,

sign��2q2i;d + �q1i;d

��< 0 if 14�

h�4 + �2

�c� (2� �)2

i< cp < �

> 0 if � < cp < 14�

h(4 + �2) c� (2� �)2

iHence, sign

�dq1i;dd�

�is ambiguous. Consequently

@�2@�

=@

@�

��1a;d�1p;m

�=

1

�1p;m

@�q1a;d

�2@�

@�2@�

=1

�1p;m2q1a;d| {z }

>0

@q1a;d@�| {z }?

;

which implies that sign�@�2@�

�is also ambiguous. All in all, we have,

@�2@�

�< 0 if 14�

h�4 + �2

�c� (2� �)2

i< cp < �

> 0 if � < cp < 14�

h(4 + �2) c� (2� �)2

i

Market-Structure Con�guration 3

32

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Finally, evaluating the derivatives �3 with respect to cp and yields,

@�3@cp

= �2 ( � 1) (cp � 1)(cp � 1)3

@�3@

= 2cp(cp � 1)(cp � 1)2

:

It can be straightforwardly veri�ed that we have @�3@cp

� 0 and @�3@ < 0. Thus, we complete our

proof of Proposition 1.�

Proof of Lemma 3 Point 1 can be veri�ed easily by substituting �1p = 0 and �1p = 1 into

UP��; b; �1p

�. Next, taking the �rst derivative of UP

��; b; �1p

�with respect to �1i yields

@UP��; b; �1p

�@�1p

= 1� (1� �b)�1� �1p

�(1� �b�1p)3

> 0:

Recall that we impose 0 � �1p � 1, 0 � �b � 1, and 0 � b � 1, hence it can be veri�ed that the

above derivative has a positive sign as stated in Point 2. It is also straightforward to show that@UP (�;b;�1p)

@�1p

�����1p=0

= �b and@UP (�;b;�1p)

@�1p

�����1p=1

= 1.

Next, taking the second derivative of UP��; b; �1p

�with respect to �1i and simplifying the

resulting expression, we obtain

@2UP��; b; �1p

�@�21p

=1� �b

(1� �b�p)4| {z }>0

(1� 3�b+ 2�b�p) :

Notice that sign@2UP (�;b;�1p)

@�21p= sign (1� 3�b+ 2�b�p), implying that

@2UP (�;b;�1p)@�21p

< 0 if �1p <

3�b�12�b ,

@2UP (�;b;�1p)@�21p

> 0 if �1p >3�b�12�b , and

@2UP (�;b;�1p)@�21p

= 0 if �1p = �1p =3�b�12�b . However,

since 0 � �1p � 1; we know that, when 1=3 � �b � 1, then �1p � 0, and thus we can have@2UP (�;b;�1p)

@�21p< 0 and

@2UP (�;b;�1p)@�21p

> 0 depending on whether we have �1p < �1p or �1p > �1p .

Otherwise, when 0 � �b < 1=3, we only have @2UP (�;b;�1p)@�21p

> 0.�

Proof of Lemma 4 Point 1 can be veri�ed easily by substituting �1p = 0 and �1p = 1 into

VP��; b; �1p

�. Taking the �rst derivative of VP

��; b; �1p

�with respect to �1i yields,

@VP��; b; �1p

�@�1p

= �b+ (1� b)2 �1p > 0

Since we have 0 � �1p � 1, 0 � �b � 1, and 0 � b � 1; the above derivative has indeed a positive

sign, as stated in Point 2. It is also straightforward to show that@VP (�;b;�1p)

@�1p

�����1p=0

= �b and

@VP (�;b;�1p)@�1p

�����1p=1

= �b+ (1� b)2.

33

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Finally, taking the second derivative of VP��; b; �1p

�yields

@2VP��; b; �1p

�@�21p

= (1� b)2 � 0:

Given that 0 � b � 1, the sign of the above derivative is positive.�

Proof of Proposition 2 The proof consists of three parts.

First, we begin with the case of 0 � �b � 1=3. We know from Lemma 5 (Points 2 and

3) that UP��; b; �1p

�is increasing at an increasing rate in �1p . We also know from Lemma

6 (Points 2 and 3) that VP��; b; �1p

�is also increasing at an increasing rate in �1p . Further,

from Lemma 5 (Point 1) and Lemma 6 (Point 1) we know that UP��; b; �1p

����1p=0

= 0 and

VP��; b; �1p

����1p=0

= 0:Thus, both functions start at the same origin. Both functions will have

another intersection, other than �1p = 0, at b�1p = 1�b

�1 +

(1��b)��b+p�2b2+(1�b)2

�(1�b)2

�, and given

that the permissible value of �b is [0; 1] we can establish that b�1p > 1. Accordingly, for the

admissible value of �1p 2 [0; 1], we know that UP��; b; �1p

�and VP

��; b; �1p

�only intersect at

�1p = 0.

Second, we now evaluate the relative magnitude of UP��; b; �1p

�vis-à-vis VP

��; b; �1p

�. From

Lemma 5 (Point 1) and Lemma 6 (Point 1) we know that UP��; b; �1p

����1p=1

= 1=2 and VP��; b; �1p

����1p=1

=

�b+ (1� b)2 =2. Thus, we have �b+ (1� b)2 =2 > 1=2 if b > 2� 2�, and �b+ (1� b)2 =2 > 1=2 if

b < 2�2�. Thus, we can conclude that when b > 2�2� prevails, then A-organization dominates P -

organization, i.e. UP��; b; �1p

�< VP

��; b; �1p

�. A-organization is dominated by P -organization,

i.e. UP��; b; �1p

�> VP

��; b; �1p

�if b < 2� 2�. Thus, we partly con�rm Proposition 3.

Third, we now evaluate the case of 1=3 < �b � 1. From the �rst part of the proof, we know

that for the admissible value of �1p 2 [0; 1], UP��; b; �1p

�and VP

��; b; �1p

�will only have one

intersection at �1p = 0. Also we know that �1p =3�b�12�b is the in�ection point of UP

��; b; �1p

�.

Let us denote this in�ection point by e�1p . For �1p 2 [0; e�1p ], since UP ��; b; �1p� is increasing at adecreasing rate in �1p and VP

��; b; �1p

�is increasing at an increasing rate in �1p and there is no

other intersection point between UP��; b; �1p

�and VP

��; b; �1p

�except �1p = 0, then we know

that UP��; b; �1p

�< VP

��; b; �1p

�. Similarly, it is straightforward to see that for �1p 2 [e�1p ; 1]

we also have UP��; b; �1p

�< VP

��; b; �1p

�. To conclude, whenever 1=3 < �b � 1, then A-

organization dominates P -organization, i.e. UP��; b; �1p

�< VP

��; b; �1p

�. Thus, we complete

the proof.�

Proof of Proposition 3 Let us denote the probability that production process a is chosen in

an A-organization by Pr (a jA-org ) and the probability that production process a is chosen in a

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P -organization by Pr (a jP -org ). Using (17), (21), (18), and (22), we can express

Pr (a jA-org ) = e� (1� E�)

=

�1� �1p1� �b�1p

�2b

Pr (a jP -org ) = e��E�� + e�� (1� E��) = e��

= b

Since 0 � �1p � 1, 0 � � � 1 and 0 � b � 1, we have Pr (a jA-org ) � Pr (a jP -org ).

Next, we denote the probability that production process p is chosen in an A-organization

by Pr (p jA-org ) and the probability that production process p is chosen in P -organization by

Pr (p jP -org ). We can then write

Pr (p jA-org ) = (1� e��)E��

= (1� b)2 �1p

Pr (p jP -org ) = e�E� + (1� e�)E� = E�

=(1� �b)�1� �b�1p

��1pWe will show that Pr (p jA-org ) � Pr (p jP -org ). Suppose, in contrast, we have Pr (p jA-org ) <

Pr (p jP -org ). This implies that (1��b)(1��b�1p)

< (1� b)2 or (1��b)(1�b) < (1� b)

�1� �b�1p

�. We have

(1��b)(1�b) � 1 because �b � b. We also know that (1� b)

�1� �b�1p

�� 1. Hence, we have a

contradiction. Consequently, we indeed have Pr (p jA-org ) > Pr (p jP -org ).�

References

[1] Aghion, P. and J. Tirole (1997), "Formal and Real Authority in Organizations," Journal of

Political Economy, 105, pp.1-29.

[2] Brickley, J., C. Smith, and J. Zimmerman (2006), Managerial Economics and Organizational

Architecture, 4th Ed., Mc-Graw Hill, New York, 730p.

[3] Burkart, M., D. Gromb, and F. Panunzi (1998), "Large Shareholders, Monitoring, and the

Value of the Firm," Quarterly Journal of Economics, 112, pp. 693-729.

[4] Coase, R. (1937), "The Nature of the Firm," Economica, 4, pp. 386-405.

35

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36


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