Discussion Paper No. 550

JOINT DETERMINATION OF
INTERNAL ORGANIZATIONAL DESIGN:DECISION-MAKING, TASK ALLOCATION,
AND INCENTIVE SCHEME

Son Ku Kim
andKeunkwan Ryu

July 2001

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

Joint Determination of Internal Organizational Design:
Decision-Making, Task Allocation, and Incentive Scheme
Son Ku Kim
Dept. of Economics, Hong Kong University of Science and Technology
andKeunkwan Ryu
Department of Economics, Seoul National University
and ISER, Osaka University

Keywords: agency problem, complementarity, decision-making structure, incentive
contract, task allocation.
Abstract: This paper studies the issue of designing an optimal organizational form:
design for sub-units’ task allocation, decision-making structure, and incentive schemes
for organizational members. Depending on the way tasks are allocated between
the sub-units, and whether decision-making is centralized or not, organizations facea trade-oﬀ between coordination and information. Task allocation by production
processes calls for coordination more strongly than the allocation by ﬁnal products.
Centralized decision-making serves for better coordination, whereas decentralization
serves for better information. The coordinational beneﬁt under centralization getsbigger as the organization’s common uncertainty increases, and this beneﬁt is magniﬁed when the sub-units are functionally divided by production processes. The
informational beneﬁt under decentralization gets bigger as the organization’s local
uncertainty increases, and this beneﬁt is magniﬁed when the sub-units are designed
autonomous. Thus, complementarily designed organizations tend to have centralized
decision-making structures and ﬁxed salary scheme, whereas less complementarily
designed organizations tend to have decentralized decision-making and ‘pay for performance’ incentive contract.

1

Introduction

In designing an organization, a designer has to consider several basic internal structures of the organization, including what kind of and how much interaction be implemented among its sub-units, how much of decision-making power be delegated tothem, and what kind of incentive schemes be provided for its members. These organizational design variables, say task allocation among sub-units, decision-making
structure, and incentive scheme, usually diﬀer across organizations, and often appear
in speciﬁc combinations. For example, armies and government bureaucracies rely
more on centralized control, and they design their subdivisions more or less complementary (that is, mutually supportive). Consider the relationship between theinfantry unit and the artillery unit in an army and the relationship between the state
department and the justice department in a government. The members in thoseorganizations usually receive a ﬁxed salary. On the other hand, investment banks
and general hospitals rely more on decentralized delegation, and they design theirsubdivisions rather self-contained. In investment banks, the relationship is rather
autonomous between foreign currency dealers and bond traders. Also autonomousis the relationship between the ENT department and the psychiatric department ina general hospital. In those organizations, several incentive schemes are often usedother than a ﬁxed salary. In most investment banks, for example, fund managers areusually rewarded according to the ’pay for performance’ scheme.
Dependence of an organization’s internal structures on its external environmenthas been widely reported by contingency theorists in management. The contingency
theory postulates that an organization’s internal structures and its members’ behavioral patterns are to a great extent aﬀected by its external conditions. Woodward(1958) reports that successful organizations in diﬀerent industries are characterized by
diﬀerent internal structures. After analyzing the history of several pioneering ﬁrms,
Chandler (1962) also concludes that organizational structures follow, and are guided
by strategic decisions, which, in turn, must respond to environmental changes.
1According to classical economic theories, economic agents’ activities are mosteﬃciently coordinated through the market mechanism. However, various market imperfections give rise to organizational coordination as an alternative. Among thoseimperfections, we especially emphasize on the fact that organizations are operating in uncertain environments and organizational members have bounded rationality.
The organizational members are hierarchically arranged, diﬀering in their decisionmaking authority and accessibility to various sources of information. Thus, two basic
elements must be considered for better organizational performance. One is ‘eﬃcient
information transmission’, referring to how to convey each member’s information toothers, and the other is ‘eﬀective incentive provision’, referring to how to align members’ diverse interests with the organization’s objectives. The internal structures ofan organization ought to be chosen to maximize information ﬂow and to minimize
incentive distortion.
In this paper, we are interested in studying how an organization’s external environments shape its internal structures. Thus, we ask why some organizations havemore centralized decision-making structures than others, why some organizations ask
their subordinates to specialize in a certain function (process), whereas others ask
them to produce a certain ﬁnal product, and why some organizational members arepaid for their performance while others are paid a ﬁxed salary. Especially, we areinterested in seeing relationships among these organizational design variables.
We consider an organization which produces two ﬁnal goods. Each good, to be
produced, needs to go through two production lines. The organization is composedof a single top manager and two functionally interrelated subordinates. The top
manager designs the organizational internal rules and structures, and monitors thesubordinates’ eﬀort levels if necessary. He does not participate in production itself,
though. The subordinates actively participate in production by providing eﬀorts,
guided by the organizational rules and incentives.
It is natural to assume that the top manager can determine the degree of inter-2

action between the sub-units by choosing the way to allocate the subordinates. The
top manager, by allocating the sub-units along the production lines (U-form organization), magniﬁes the degree of interaction. By allocating the sub-units along theﬁnal products (M-form organization), he reduces the degree of mutual dependence.
In our model, the degree of interaction between the subordinates is captured throughthe extent that one subordinate’s eﬀort level helps the other’s performance.
From a diﬀerent perspective, the organization, by allocating its sub-units along
the processes, makes each sub-unit specialize in a certain function and can exploit
returns to scale, presumably arising from division of labor. But, by allocating its
sub-units along the ﬁnal products, it makes each sub-unit’s task overlap with others
and incurs waste of resources at the beneﬁt of increased autonomy and the resulting
ﬂexibility.
There are various kinds of uncertainties the organization faces, common uncertainty, two line-speciﬁc uncertainties, and two good-speciﬁc uncertainties. The common uncertainty inﬂuences the entire organization, whereas each line-speciﬁc uncertainty only aﬀects that particular production line and each good-speciﬁc uncertainty
only aﬀects that particular good. Due to the hierarchical arrangement, the top manager has privileged access to the common uncertainty, and the subordinates haveprivileged access to their own line-speciﬁc uncertainty when they are allocated along
the production lines and to their own good-speciﬁc uncertainty when they are allocated along the goods.
To reduce the uncertainty the organization faces, information needs to be shared
among the organizational members. In general, there are two kinds of information
ﬂows within the organization. One is top-down information ﬂow and the other isbottom-up ﬂow. In this paper, we only consider the ﬁrst one. Due to the pyramid
shape of the organization, the top-down information ﬂow does not face traﬃc jamming, whereas the opposite ﬂows face capacity constraints. To simplify, we assume
that there is no jamming at all in the top-down information ﬂow while there is extreme

3jamming in the opposite information ﬂow.
After receiving a signal about the common uncertainty, the top manager conveys
his information to the local subordinates (top-down information ﬂow). The top manager can use either instruction or suggestion for communication, depending on the
degree of hierarchical control he would like to impose. Under the instruction mode,the subordinates must fulﬁll the instruction without having ﬂexibility to revise it.
We call this mode centralization. Under the suggestion mode, the subordinates canrevise the suggestion by incorporating their own local information which is either linespeciﬁc or good-speciﬁc depending on the organizational form . We call this mode
decentralization.
There are trade-oﬀs between centralized control and decentralized delegation.
Centralization has coordinational advantage, blocking the subordinates’ incentive distortion, whereas decentralization has informational advantage, utilizing the local information. From a diﬀerent perspective, centralization incurs an information cost,
while decentralization incurs an agency cost. The agency cost of decentralization
depends on the incentive contracts for the local managers.
The coordinational advantage of centralization is large when the common turbulence is big and when the sub-units are designed along the production processes.
To ensure that the sub-units follow the top manager’s instruction, the top manager
must monitor each unit’s activity level. Thus, input monitoring and a ﬁxed salaryscheme are usually observed under centralization. As the size of common uncertainty increases, the organization tends to rely more on centralized control, design
its sub-units along the production processes, and provide a ﬁxed salary for its local
managers.
The informational advantage of decentralization, is large when the local turbulence is big, whether line-speciﬁc or good-speciﬁc. Under delegation, observing eachunit’s activity level directly is meaningless, and incentive for each local manager mustbe given by an incentive contract contingent on his performance. Thus, output mon-4

itoring and incentive payment scheme are often observed under decentralization. In
this paper, we only consider two kinds of incentive contracts which are two dominant
contractual features in the real world: individual incentive contracts and group incentive contracts. Under the individual incentive contract, each subordinate’s payoﬀ
depends only on his performance, whereas it depends on the team performance under
the group incentive contract.
Decentralization with group incentive scheme hits a balance between the combination (centralization, ﬁxed salary) and the combination (decentralization, individual
incentive). In terms of agency cost, by making each sub-unit’s salary contingent on
their combined performance, it reduces the agency cost of the (decentralization, individual incentive) combination at the cost of creating a new, free-rider problem. In
terms of information, by delegating the authority to ﬁnalize decisions, it utilizes the
local information which is not available under the former combination.
We expect to derive that the organization tends to use centralized control if thecommon uncertainty is big and the local uncertainty is small, if the degree of interaction among the subordinates is high, and if the input monitoring cost is low. Moreover,the centralized organization provides ﬁxed salary schemes for the subordinates andalways organizes them according to the production line (i.e., U-form centralization).
On the other hand, the organization tends to decentralize and use individual incentive
contracts if the market uncertainty is small and the local uncertainty is big, and if
the degree of interaction is low, whereas it tends to decentralize and use group incentives if both the market and local uncertainties are big. Decentralized delegation may
come along with an M-form organizational mode (i.e., organizing the subordinatesaccording to the good) if the good-speciﬁc uncertainty is suﬃciently big comparedwith the line-speciﬁc uncertainty. These expected results look quite consistent withmany empirical ﬁndings in the organizational literature.
There are several papers that study the organization’s internal design issues. However, most of them address only one issue out of these inter-related design issues. For

5

decision-making structure, Bolton and Farrel (1990) ﬁnd, in the context of an entry game into a natural monopoly, that centralization is preferred to speed up theentrance decision, whereas decentralization is preferred to make use of potential entrants’ private information. In comparing the relative eﬃciencies of centralized control
and decentralization, Aoki (1986) argues that decentralized ﬁrms have an advantage
in identifying and quickly responding to emergent events, while centralized ﬁrms haveadvantage in coordinating the operating units through the use of common technology.
More recently, Aghion and Tirole (1997) show that delegating (formal) authority to
the agent can facilitate the agent’s participation in the organization and enhance theagent’s incentive to acquire information about the project alternatives. At the sametime, it can involve a costly loss of control since the agent may choose the projectthat is not best for the principal.
Regarding task allocation for organizational sub-units, Maskin, Qian, and Xu(1997) show that if the regional shocks are more closely correlated than the industrial
shocks, an M-form organization is better than a U-form organization, and vice versa.
It is because, when the regional shocks are more closely correlated than the industrial shocks, designing relative incentive contracts for regional operating managers iseasier than designing relative contracts for industry-wise operating managers. Thus,an M-form organization enables the top management to design relative incentive contracts for the local managers that are less costly in the sense of Blackwell’s eﬃciency.
Aghion and Tirole (1995) show that a growing ﬁrm eventually switches from a Uform organizational mode to an M-form. As a ﬁrm grows, the headquarter’s overloadincreases. To reduce the headquarter’s overload, it is a good idea to create several
proﬁt centers.
However, none of the above papers study the interrelationship between the organization’s decision-making structure and other internal design issues. One exception
is Holmstrom and Milgrom (1994). Using a multi-task principal-agent model, they
study the complementarities of various incentive instruments such as asset ownership,6

decision-making structure, and incentive contract. They show that, as the diﬃcultyof evaluating performance and the importance of non-selling activities increase, ﬁrms
tend to choose direct selling rather than using independent sales representatives. And
that the in-house sales agents tend to face more restrictions for outside activities andto receive a ﬁxed salary. However, they do not analyze the organizational design for
sub-units’ task allocation.
The rest of the paper is organized as follows. In section 2, we present a simple organizational model. In section 3, we investigate a hypothetical case in which
the top manager commands perfect information on both the common shock and the
local shocks. In sections 4 and 5, we derive the organization’s expected proﬁts under centralization and decentralization, respectively, assuming that the top manager
has information only on the common shock. In section 6, by comparing the organization’s expected proﬁts under centralization and decentralization, we identify the main
factors that determine the organization’s optimal decision-making structure and its
design for sub-units’ task allocation. In section 7, we apply our results to explaining
several stylized phenomena in organizations. Concluding remarks follow in section 8.
All the proofs of the Lemmas and Propositions are deferred to the Appendix.

2

The Model

We view an organization as a collection of decision-makers with bounded rationality.
Iin order for an organization to function eﬀectively, information that each organizational member has must be fully utilized, and each organizational member’s interest
must be aligned to the organization’s objectives. Accordingly, the organization’s internal structures must be designed to minimize both information loss and incentive
distortion.
For analytical simplicity, we consider an organization which produces two diﬀerent
goods, good A and good B. Each good, to be produced, needs to go through two

7

production lines, line 1 and line 2. One may think of line 1 as a production process
which translates natural resources into intermediate goods, whereas line 2 as anotherproduction process which transforms those intermediate goods into ﬁnal ones. Thus,
there are four tasks that the organization must accomplish to produce both goods.
They are denoted as A1, A2, B1, and B2, where A1 represents the task associatedwith the ﬁrst production line for good A, and so on.
In performing those tasks, the organization faces with several kinds of uncertainties. We denote θm as a market shock which commonly aﬀects the performances of
all the tasks such as the government’s economic policies. We denote θA (or θB ) as agood A (or good B) speciﬁc shock which only aﬀects the performances of the tasks
associated with producing good A (or good B), i.e., A1 and A2 (or B1 and B2). An
example of this shock is change in consumers’ taste for a good. Denote θ1 (or θ2 )as a line 1 (or line 2) speciﬁc shock which only aﬀects the performances of the tasks
associated with line 1 (or line 2), i.e., A1 and B1 (or A2 and B2). An example ofthis shock is change in technology in a production line. All shocks are assumed to2, σA2 , σB2 , σ12 , σ22 ,be mutually independent with zero means and variances equal to σmrespectively.
Organizations diﬀer in assigning various tasks to their members. Some organizations emphasize more on each member’s expertise in a certain function. The ﬁnal
products are produced by combining those specialized functions. An extreme organizational form toward this direction is a U-form organization according to Chandler’s(1962) deﬁnition. Other organizations instead emphasize more on each member’s
general knowledge that helps him perform various functions and produce a certain
product. An extreme organizational form toward this direction is an M-form organization according to Chandler’s deﬁnition.
To model these features, we assume that the organization comprises of a top
manager and two sub-units. The top manager is assumed risk-neutral. The two subunits are run by two local managers who are also risk-neutral and have a reservation

8

utility level of U. Each local manager is supposed to perform two tasks. Thus, there
are two reasonable ways the top manager assigns the above four tasks to two local
managers. First, the sub-units are organized according to the production line, which
resembles a U-form organization. In this case, the local manager 1 performs A1 andB1, while local manager 2 performs A2 and B2. Second, the sub-units are organizedaccording to the good, which resembles an M-form organization. In this case, local
manager A performs A1 and A2, while local manager B performs B1 and B2.1 (Notethat, when the sub-units are organized according to the production line, we denotethe local managers as manager 1 and manager 2, whereas we denote them as manager
A and manager B when they are organized according to the ﬁnal product.)
To accomplish the assigned tasks, each manager i, i = 1, 2, or A, B, provides an
eﬀort, ai , which costs him c(ai ) = c0 ai . Given manager j’s eﬀort level, aj , j = i,manager i’s eﬀort ai contributes to the organization a unit value (average value perunit eﬀort) vi which is denoted as
1
vi = µ − ai + δaj + ui , i = j i, j = 1, 2 or A, B,
2(1)

where δ denotes the degree of interaction between the two sub-units and ui denotes
the uncertain factors involved.
The above equation indicates that the unit value of a local manager’s eﬀort decreases as his own eﬀort level increases, reﬂecting diminishing marginal productivityof eﬀort. In the above equation δ takes two values, δl and δg , depending on the organizational form, where δl denotes the external eﬀect between the two sub-units when
they are organized according to the production line, and δg denotes the external eﬀect
when they are organized according to the good. We assume that δg ≤ δl , implying theexternal eﬀect is greater when they are organized according to production lines. For
instance, in a university, the economics department and the physics department are1

One more possible task assignment is that one local manager performs A1 and B2, whereas theother local manager performs A2 and B1. However, since it is unreasonable in terms of specialization,
we do not consider this case.

9rather independent, whereas, in an army, the infantry unit and the artillery unit are
mutually supportive in the sense that a good eﬀort from the artillery unit improves
the infantry unit’s performance. Also, it is reasonable to assume that the maximum
cross eﬀect is smaller than the own eﬀect, i.e., 0 < δg ≤ δl < 12 .
When the organization designs the sub-units according to the production line, thetotal amount of uncertainty involved with manager i’s eﬀort becomesui = θm + θi + θA + θB , i = 1, 2.

(2)

It is because manager i in charge of production line i faces the market uncertainty
and its own production line uncertainty, and because the manager performs two tasks
Ai and Bi .
On the other hand, when the organization designs its sub-units according to thegood, the total amount of uncertainty involved with manager i’s eﬀort becomesui = θm + θi + θ1 + θ2 , i = A, B,(3)

We assume that neither manager’s unit value vi nor his eﬀort level ai is directly
observable to the top manager. However, the top manager can observe (ai , aj ), i, j =1, 2 or A, B, by investing M into monitoring both managers’ eﬀort levels directly. On
the other hand, there is a performance measure for unit i such as unit i’s accounting
sales value which is observable to the top manager without cost. We assume that
unit i’s accounting sales value xi comprises of its true contribution, vi ai and a white
noise ηi ,xi = vi ai + ηi , E(ηi ) = 0, i = 1, 2 or A, B.

(4)

The organization members have diﬀerent access to diﬀerent information sources.
Due to hierarchical structure, it is quite natural to assume that the top manager
has privileged access to the information about the market turbulence, while the local
managers have privileged access to the information on their own local turbulence.
Furthermore, since the area in which each local manager specializes varies with the10organizational form, the local managers have access to diﬀerent local information
depending on how they are organized. For instance, if a local manager is designed
to specialize in a certain production line, he has more information about the shockthat is speciﬁc to that line, and if he is designed to specialize in a certain good, he
has more information about the shock that is speciﬁc to that good. For simplicity,
we assume that the top manager only observes the market shock, θm , whereas local
manager i only observes his own speciﬁc local shock, θi .2 In other words, managers
1 and 2 observe θ1 and θ2 , respectively, when the sub-units are organized according
to the production line, whereas managers A and B observe θA and θB , respectively,
when the sub-units are organized according to the good.
After observing the true value of the market shock θm , the top manager chooses
each unit’s eﬀort level to maximize the whole organization’s proﬁt based on θm . It
is because the top manager’s maximizing the organization’s joint proﬁt is equivalent
to maximizing his own proﬁt after giving each local manager the reservation level ofutility. Let ai be the optimal eﬀort level for unit i as determined by the top manager,i = 1, 2 or A, B. Then, the top manager has to decide how to convey ai to sub-unit
i. There are two ways for the top manager to communicate his decision ai with the
sub-units. One is ‘instruction’ and the other is ‘suggestion’, diﬀering in the degreeof delegation. If ai is given as instruction, the sub-units have no other option but tocarry out ai as instructed. We call this a centralized decision-making structure since
the decision-making power lies with the top management. In this case, in order toensure each unit to make the instructed level of eﬀort, the top manager must invest
M to observe ai , and design a forcing contract for each local manager i.
On the other hand, if ai is given as suggestion, manager i can revise his eﬀort
level based on his own local information θi . We call this a decentralized decision2

So far as the top manager has more precise information on the market shock and less precise

information on the local shocks than the local managers, the main implications in this paper still
hold qualitatively.

11

making structure since the ultimate decision right is delegated to each local manager.
Since the ﬁnal eﬀort level is determined by each local unit under decentralization,
the top manager will have to design an incentive contract based on (xi , xj ) for each
local manager rather than a forcing contract. Whether the sub-units will maximize
the organization’s proﬁt or not in this case depends on how the local managers’
compensation contracts are designed.
In sum, the top manager jointly determines the decision-making structure, theorganizational form, and incentive contract for each local manager. When the organization is centralized, it cannot use the local managers’ useful local information,
incurring information loss. On the other hand, when the organization is decentralized, it cannot coordinate the local managers eﬃciently, incurring an agency cost.
The amount of the agency cost depends on the organizational form as well as the
local managers’ incentive contracts. Thus, information and coordination are two basic elements to be considered in designing an optimal organization. To analyze thisdesign problem, we adopt a backward induction. Given the organization’s internal
design (decision-making structure, organizational form, and incentive contracts for local managers), the top manager computes the organization’s expected proﬁt. Then,choose an optimal internal design to maximize the proﬁt among all possible combinations of the decision-making structure, the organizational form, and the incentive
contracts for local managers.

3

Full Information and Full Coordination

To mainly focus on the relative eﬃciencies of the two decision-making structures
mentioned above, we start with a counterfactual benchmark case in which the top
manager commands perfect information on all shocks and he fully coordinates thetwo sub-units (i.e., the top manager observes ai without cost). In this hypotheticalcase, the optimal decision-making structure must be a centralized one since the top

12manager knows everything.
First, suppose that the sub-units are organized according to the production line.
As mentioned earlier, since the top manager’s maximizing his own proﬁt with guaranteeing the local managers the reservation level of utility, U , is technically equivalent
to his maximizing the organization’s joint proﬁt, the top manager’s decision for bothunits’ eﬀort levels (ah1 , ah2 ) satisﬁes(ah1 , ah2 ) = argmaxa1 ,a2 (v1 a1 + v2 a2 ) − c0 (a1 + a2 ).

(5)

From the ﬁrst-order conditions, we haveah1 = (R1 + 2δl R2 )/(1 − 4δl2 ),ah2 = (R2 + 2δl R1 )/(1 − 4δl2 ),(6)where Ri = (µ−c0 )+θm +θi +θA +θB , i = 1, 2. We need δ < 1/2 to satisfy the secondorder condition. This condition states that, in determining unit i’s contribution tothe organization, its own eﬀort plays a bigger role than the other unit’s eﬀort.
This hypothetical situation will yield the maximum expected proﬁt for the wholeorganization. Let v1h and v2h be the unit values corresponding to ah1 and ah2 , that is,vih = µ − ahi /2 + δl ahj + θm + θi + θA + θB , i = j, i, j = 1, 2. Thus, when the sub-units
are organized according to the production line, the optimized expected proﬁt under
the hypothetical situation is
πlh = ER [(v1h − c0 )ah1 + (v2h − c0 )ah2 ]= ER [R1 (R1 + 2δl R2 ) + R2 (R2 + 2δl R1 )]/2(1 − 4δl2 ),(7)

where ER denotes that the expectation is taken with respect to R ≡ (θm , θ1 , θ2 , θA , θB ).
Using (1) and (2), we derive
πlh =

1
1
2
(σ 2 + σ22 ).
[(µ − c0 )2 + σm
+ σA2 + σB2 ] +1 − 2δl2(1 − 4δl2 ) 1(8)Equation (8) shows that the organization’s proﬁt under the hypothetical situation
increases with the size of any uncertainty. This is because, when the organization
13

obtains full information about all kinds of uncertainties, the organization’s expected
proﬁt increases with the amount of information on all kinds of uncertainties, and theamount of information on any uncertainty is measured by the corresponding variancebecause the unit value function is linear.
Likewise, one can easily derive that the optimized expected proﬁt under the hypothetical situation when the sub-units are organized according to the good is
πgh =

4

1
1
2
(σ 2 + σB2 ).
[(µ − c0 )2 + σm
+ σ12 + σ22 ] +1 − 2δg2(1 − 4δg2 ) A(9)Centralization

We now turn to a realistic case in which the top manager has information only
on the market shock. Suppose that the organization chooses centralization as its
decision-making structure and the sub-units are organized according to the production
line. Then, since the top manager’s maximizing his own proﬁt with guaranteeing the
local managers the reservation level of utility, U , is equivalent to his maximizing theorganization’s joint proﬁt, the top manager chooses the optimal eﬀort levels (ac1 , ac2 )for both local units to maximize the expected joint proﬁt based on his information
θm . That is,(ac1 , ac2 ) = argmaxa1 ,a2 ER [(v1 − c0 )a1 + (v2 − c0 )a2 |θm ],(10)

where ER[·|θm ] denotes that the expectation is taken with respect to R given θm(similarly deﬁned, hereafter). By solving the ﬁrst-order conditions, we haveac1 = (γ1 + 2δl γ2 )/(1 − 4δl2 )
ac2= (γ2 + 2δl γ1 )/(1 − 4δl2 ),

(11)

where
γi = ER (Ri |θm ) = µ − c0 + θm , i = 1, 2.

14

(12)

Under centralization, the top manager must invest M to ensure that both subunits carry out aci as instructed by the top manager, and design forcing contracts forboth local managers. Thus, by plugging (11) into (10) and taking expectation withrespect to θm , we obtain the optimized expected proﬁt under centralization when the
sub-units are organized according to the production line as12[(µ − c0 )2 + σm
] − M.
(13)
1 − 2δl
By subtracting (13) from (8), we have the cost of centralization compared withπlc =the hypothetical case when the sub-units are organized according to the production
line as1
1(σ 2 + σ22 ) + M.
(σA2 + σB2 ) +(14)
1 − 2δl2(1 − 4δl2 ) 1
The ﬁrst two terms on the right-hand side of the above equation represent the eﬃπlh − πlc =ciency loss of the centralized decision-making structure compared with the hypothetical case arising from the organization’s inability to utilize information on the local
shocks. Under the hypothetical case, every piece of information on (θ1 , θ2 , θA , θB ) isused cooperatively. Especially, when the sub-units are organized according to the
production line, the good-speciﬁc information, (θA , θB ), is used commonly by bothline managers, whereas the line-speciﬁc information, (θ1 , θ2 ), is used independently.
However, under centralization, no local information is used at all. We term these as
an information cost of U-form centralization. Obviously, the third term represents
the monitoring cost that is necessary for implementing the forcing contracts for both
local managers under centralization.
Likewise, one can easily derive the optimized expected proﬁt under centralization
when the sub-units are organized according to the good as
πgc =

1
2
[(µ − c0 )2 + σm
] − M,
1 − 2δg(15)

and the cost of centralization compared with the hypothetical case in this case as
πgh − πgc =1
1(σ 2 + σB2 ) + M.
(σ12 + σ22 ) +1 − 2δg2(1 − 4δg2 ) A
15

(16)

Since δg ≤ δl , by comparing (13) and (15), we have
πgc ≤ πlc ,(17)

implying that the sub-units must always be organized according to the production
line under centralization. This is because only the market information is used undercentralization regardless of the organizational form, and the organization will enjoy
the maximum interaction eﬀect when the sub-units are organized according to the
production line because δg ≤ δl .
This result under centralization is summarized in the following proposition.
Proposition 1: Under centralization, to ensure that both sub-units choose ac1 and ac2
as instructed, the top manager designs forcing contracts for both local managers, andthe sub-units are always organized according to the production line (U-form centralization).

5

Decentralization

Suppose that the organization chooses a decentralized decision-making structure. Under decentralization, the top manager’s decision on the optimal eﬀort levels of both
local managers based on his information, θm , is the same as (ac1 , ac2 ) determined inequation (11) if the sub-units are organized according to the production line, and(acA , acB ) which is similar to (ac1 , ac2 ) if the sub-units are organized according to thegood. However, he conveys (aci , acj ), i = j, i, j = 1, 2 or A, B, to the sub-units assuggestion. Thus, after receiving aci , each manager i revises it based on his local
information θi , i = 1, 2 or A, B.
Since, given the top manager’s decision rule, manager i can always recover the
top manager’s information θm from his suggestion aci , the information available tomanager i ultimately expands to (θm , θi ). However, this augmented information may
not be used in an optimal way from the whole organization’s perspective. In fact,
16

local manager i determines his ﬁnal eﬀort level, say adi , by maximizing his own proﬁt
which is determined by his incentive contract.
Generally, the top manager has a limited ability in processing all the bottom-up
information ﬂows mainly due to his limited time and/or the headquarter’s overload.
Thus, to make our analysis simple, we assume that, although the local managers
obtain private information on their own local shocks before choosing their eﬀort levels,
they cannot report their own information to the top manager. As a result, the top
manager cannot design truth-telling contracts for both local managers.3
In this paper, we only consider two kinds of incentive contracts: an individual
incentive contract, i.e., si = si (xi ), and a group incentive contract, i.e., si = si (xi +xj ), i = j, i, j = 1, 2, or A, B. These incentive contracts well cover the typical work
practices in most organizations.4 Although the organization’s use of incentive schemesthat are sensitive to individual performance measures has been considered as one of
traditional work practices, the team-based group incentives recently receive growing
attention in the literature as an alternative.5
Since the top manager and the local managers are assumed to be risk-neitral,
without loss of any generality, one can only consider linear contracts. Thus, wedenote the individual incentive contract for local manager i as
si (xi ) = ki xi , 6 , ki ≤ 1, i = 1, 2, or A, B,
3(18)

Even if the top manager can design truth-telling contracts for local managers, our main re-sults will not change qualitatively as long as the full information outcome is not obtainable. For
some practical reasons why the top manager cannot design truth-telling contracts, see Laﬀont andMartimort (1997).
4
For empirical evidence for the use of team-based group incentives, see Boning, Ichniowski, andShaw (1997), and Ichniowski, Shaw, and Prennushi (1998).
5
See Kandel and Lazear (1992), Baker, Gibbons, and Murphy (1994), Holmstrom and Milgrom(1994), and Milgrom and Roberts (1995).
6
We do not need to consider a lump-sum transfer between the top manager and each local
manager because the top manager’s maximizing the joint proﬁt is equivalent to maximizing his own
proﬁt with guaranteeing the local managers the reservation level of utility.

17and the group incentive contract as
si (xi + xj ) = hi (xi + xj ), 0 ≤ hi ≤ 1, 0 ≤ hi + hj ≤ 1, i = j, i, j = 1, 2, or A, B, (19)where ki and hi in the above two equations denote manager i’s incentive powers thatare attached to his individual performance and the group performance, respectively.
The reason we specify in the above equation that ki ≤ 1 and hi +hj ≤ 1 is because,
if ki > 1 or hi + hj > 1, then the top manager will actually try to minimize each
sub-unit’s accounting sales value (top manager’s sabotaging activity). For example, if
ki > 1 in the individual incentive contract, the top manager’s payoﬀ will be negatively
tied to the manager i’s accounting sales value. Thus, the top manager will face an
incentive to exercise his sabotaging activity to reduce local manager i’s performancexi . Likewise, if hi + hj > 1 in the group incentive contract, the top manager will
have an incentive to exercise his sabotaging activity to reduce the joint performancexi + xj .

5.1

Decentralization with Individual Incentives

Suppose that the top manager designs individual incentive contracts, si (xi ) = ki xi
for both managers. We also start with the case in which the sub-units are organizedaccording to the production line.
Since unit j’s local information is not revealed to unit i, unit i has to form an
expectation on unit j’s eﬀort level based on its information Ii ≡ {θm , θi }, i = 1, 2.
Here, unit j’s optimal eﬀort level should be consistent with unit i’s expectation, andvice versa. To satisfy this requirement, we adopt a Bayesian Nash solution concept.
Thus, the top manager’s optimization program in this case is:MaxEθm {ER [(v1 − c0 )a1 + (v2 − c0 )a2 |θm ]}k1 , k2 s.t.
(i) a1 ∈ argmax EY [k1 x1 − c0 a1 |I1 ](ii) a2 ∈ argmax EY [k2 x2 − c0 a2 |I2 ],18

where Y ≡ {θm , θ1 , θ2 , θA , θB , η1 , η2 , ηA , ηB , } denotes a set of all uncertainties in themodel, and Ii ≡ {θm , θi } is an information set available to manager i. The constraints
in the above program denote local managers’ incentive constraints.
Thus, given (k1 , k2 ), each unit’s decision problem under decentralization is characterized byad1 (k1 , k2 ) = argmaxa1 EY [k1 (v1 a1 + η1 ) − c0 a1 |I1 ],ad2 (k1 , k2 ) = argmaxa2 EY [k2 (v2 a2 + η2 ) − c0 a2 |I2 ].

(20)

By solving (20) as detailed in the appendix, we derive
1
1
c0
c0
(µ + θm ) + θ1 − 1−δ
ad1 (k1 , k2) = 1−δ
2 ( k + δl k )
1
2
l
l

1
1
c0
c0
ad2 (k1 , k2) = 1−δ
(µ + θm ) + θ2 − 1−δ
2 ( k + δl k ).
2
1
l

(21)

l

By plugging (21) into (1), we obtain the unit values for both local managers given(k1 , k2 ) as
v1d (k1 , k2 ) =1(µ + θm ) + θ21 + δl θ2 + θA + θB
2(1−δl )(1−2δ2 )cδl c0+[ 2(1−δ2l )k01 − 2(1−δ2 )k ],2llv2d (k2 , k1 ) =1(µ + θm ) + θ22 + δl θ1 + θA + θB
2(1−δl )(1−2δ2 )cδl c0+[ 2(1−δ2l )k02 − 2(1−δ2 )k ].
1
l
l

(22)

Thus, as shown in the Appendix, given (k1 , k2 ), the expected proﬁt in this case is

πlId (k1 , k2 ) =10 )c0 1−k1
22[(µ − c0 )2 + σm
] + 12 (σ12 + σ22 ) − (µ−c( k1 + 1−k)(1−δl )2
(1−δl )2k2
3 c2
(1−3δl2 )c20 1−k1 2
2δ
2 2
1
2
) ] + (1−δl 20)2 ( 1−k)( 1−k).
− 2(1−δ2 )2 [( k1 ) + ( 1−k
k2
k1
k2
l
l

(23)

From (23), we directly obtain the following lemma:
Lemma 1: Let kid be the optimal incentive power of the individual incentive contract for local manager i, i = 1, 2, under decentralization. Then, k1d = k2d = 1, i.e.,the organization must provide high-powered incentives for the local managers when it
implements individual incentive contracts.

19

From (21), we have∂adi (ki , kj )
c0
=
> 0,
∂ki
(1 − δl2 )ki2

implying that as the local managers are provided with higher incentive, they increase
their eﬀort levels. If the incentive power is set equal to one, the local managers
are induced to maximize their own proﬁt which is diﬀerent from maximizing theorganization’s joint proﬁt due to the existence of the external eﬀect. In fact, since
δl > 0, the eﬀort level chosen by the self-interested local manager will be lower thanthe eﬀort level that would be chosen by the joint proﬁt maximizing manager withthe same information (θm , θi ). Thus, the top manager would like to provide higher
incentive to increase each sub-unit’s eﬀort level, if possible. However, it is not possible
because, as discussed earlier, kid cannot exceed one. Therefore, the optimal incentive
power given to each local manager, kid , must be one, and there arises an eﬃciency
loss due to lack of coordination under decentralization with individual incentives.
By plugging k1d = k2d = 1 into (23), we eventually derive that the optimized
expected proﬁt under decentralization with individual incentives when the sub-units
are organized according to the production line is
πlId =

1
12[(µ − c0 )2 + σm
] + (σ12 + σ22 ).
2(1 − δl )2(24)

By subtracting (24) from (8), we have
δ2

1
2
2
2
2
l
πlh − πlId = (1−2δl )(1−δ
2 [(µ − c0 ) + σm ] + 1−2δ (σA + σB )
l)
l
4δ2

2
2
l
+ 2(1−4δ
2 (σ1 + σ2 ).
l)

(25)

As shown in (25), the cost of U-form decentralization with individual incentives compared with the hypothetical case is composed of three parts. Note that each local
manager is maximizing his own proﬁt rather than the organization’s joint proﬁt under
decentralization with individual incentives. Thus, the ﬁrst term on the right-hand sideof (25) represents the cost that arises from that information on the market shock, θm ,is used non-cooperatively under decentralization with individual incentives. We term
this as a cost of less coordination under decentralization with individual incentives,20which increases with the size of the common shock. The second term represents thecost arising from that information on the good-speciﬁc shocks, (θA , θB ), is not used
under decentralization when the sub-units are organized according to the production
line, whereas the third term is the cost arising from that manager 1 only uses his own
production line information, θ1 , by taking expectation on θ2 and vice versa.
Likewise, one can easily derive the optimized expected proﬁt under decentralization with individual incentives when the sub-units are organized according to thegood as
d
=
πgI

1
1
2
[(µ − c0 )2 + σm
] + (σA2 + σB2 ).
2(1 − δg )2(26)

The cost of M-form decentralization with individual incentives compared with the
hypothetical case as
δ2

1
g
d
2
2
2
2
= (1−2δg )(1−δ
πgh − πgI
2 [(µ − c0 ) + σm ] + 1−2δ (σ1 + σ2 )
g)
g
4δ2

+ 2(1−4δg g )2 (σA2 + σB2 ).

5.2

(27)

Decentralization with Group Incentives

Now, suppose that the top manager designs group incentive contracts, si (xi + xj ) =hi (xi + xj ), for both managers. Again, we start with the case in which the sub-units
are organized according to the production line. Thus, the top manager’s optimization
program in this case is:MaxEθm {ER [(v1 − c0 )a1 + (v2 − c0 )a2 |θm ]}h1 , h2 s.t.
(i) a1 ∈ argmax EY [h1 (x1 + x2 ) − c0 a1 |I1 ](ii) a2 ∈ argmax EY [h2 (x1 + x2 ) − c0 a2 |I2 ].
Given (h1 , h2 ), each unit’s decision problem under decentralization in this case is21

characterized byad1 (h1 , h2 ) = argmaxa1 EY [h1 (v1 a1 + v2 a2 + η1 + η2 ) − c0 a1 |I1 ],ad2 (h2 , h1 ) = argmaxa2 EY [h2 (v1 a1 + v2 a2 + η1 + η2 ) − c0 a2 |I2 ].

(28)

Thus, we similarly derive
1
1
c0
c0
(µ + θm ) + θ1 − 1−4δ
ad1 (h1 , h2 ) = 1−2δ
2 ( h + 2δl h )12llad2 (h2 , h1 )

1
1
c0
c0
= 1−2δ
(µ + θm ) + θ2 − 1−4δ
2 ( h + 2δl h ).
2
1
l
l

(29)

The expected proﬁt given (h1 , h2 ) in this case isdπlG(h1 , h2 ) =12
2(µ2 + σm
) + 12 (σ12 + σ22 ) − 1−2δ
µc0
1−2δl
l
2
c0
2(1+2δl )l)l+ 2(1−4δ
− h12 + 2(1+2δ− h12 − h4δ
]
2) [
h1
h2
1 h2
1
2
l

(30)

From (30), we obtain the following lemma:
Lemma 2: When the organization implements group incentive contracts for the local
managers under decentralization, the optimal incentive power on the joint sales value
must be hd1 = hd2 = 12 .
We now make the following assumption.
Assumption 1: µ > 2c0 .
This assumption is needed to make hd1 = hd2 = 12 a meaningful solution. Otherwise,
ER (ad1 (h1 , h2 )) < 0 and ER (ad2 (h2 , h1 )) < 0, which implies that designing a group
incentive contracts will never be optimal.
By substituting hd1 = hd2 = 12 , into (30), we derive that the optimized expected
proﬁt under decentralization with group incentives when the sub-units are organizedaccording to the production line is
d
=
πlG

1
1
1
2
[(µ − c0 )2 + σm]−
c20 + (σ12 + σ22 ),1 − 2δl1 − 2δl2(31)

and by subtracting (31) from (8), we haved=πlh − πlG

1
1
4δl2
c20 +
(σA2 + σB2 ) +(σ 2 + σ22 ).
1 − 2δl1 − 2δl2(1 − 4δl )2 1
22

(32)

The cost of U-form decentralization with group incentives compared with the hypothetical case is also composed of three parts. Note that each local manager with agroup incentive contract maximizes his proﬁt that is positively tied to the organization’s joint proﬁt. Thus, unlike the case in which individual incentive contracts aredesigned, there is no coordination problem. However, there arises a new free-rider
problem on each manager’s side because hd1 = hd2 = 12 < 1. The ﬁrst term in theright-hand side of (31) represents the cost arising from the free-rider problem. The
second and third terms are the same as previously explained. Note that the cost of afree-rider problem is independent of the size of any uncertainty.
Likewise, one can easily derive the optimized expected proﬁt under decentralization with group incentives when the sub-units are organized according to the good
as
d
=
πgG

1
1
1
2
[(µ − c0 )2 + σm]−
c20 + (σA2 + σB2 ).
1 − 2δg1 − 2δg
2(33)

The cost of M-form decentralization with group incentives compared with the hypothetical case isd=πgh − πgG

4δg2
1
1
c20 +
(σ12 + σ22 ) +(σ 2 + σB2 ).
1 − 2δg1 − 2δg2(1 − 4δg )2 A

(34)

By comparing (24) with (26) and (31) with (33), we directly obtain the following
proposition:
Proposition 2: Under decentralization (using either individual incentives or group
incentives), even if δg ≤ δl , the sub-units may be organized according to the good (i.e.,
M-form decentralization) if δl − δg is small and the size of good-speciﬁc uncertainties,
σA2 +σB2 , is suﬃciently big compared with the size of line-speciﬁc uncertainties, σ12 +σ22 .
Otherwise, the sub-units will be organized according to the production line (i.e., Uform decentralization).
As shown in Proposition 1, the sub-units will always be organized accoding to23

the production line under centralization (U-form centralization). However, under
decentralization, diﬀerent kinds of local information will be used depending on theorganizational form. For example, line-speciﬁc information (θ1 , θ2 ) will be used regardless of incentive contracts when the sub-units are organized according to the
production line, whereas the good-speciﬁc information, (θA , θB ), will be used when
they are organized according to the good. Thus, if the value of information associatedwith the good-speciﬁc shocks, i.e., σA2 + σB2 , is suﬃciently bigger than that associatedwith the line-speciﬁc shocks, i.e., σ12 + σ22 , then designing M-form decentralization (either with individual incentives or group incentives) will improve on the organizationaleﬃciency compared with U-form decentralization.
Also, by comparing (24) with (31) and (26) with (33), we derived=πlId − πlG

1
δl2
2
c20 −
[(µ − c0 )2 + σm],
1 − 2δl(1 − 2δl )(1 − δl )2

(35)

d
d
πgI
− πgG
=

δg2
1
2
c20 −
[(µ − c0 )2 + σm].
1 − 2δg(1 − 2δg )(1 − δg )2

(36)

and

The ﬁrst terms in the above two equations represent the cost of free-riding under decentralization using group incentives. The second terms represent the cost ofless coordination under decentralization using individual incentives. From the above
equations, we obtain the following lemma:
Lemma 3: There always exists a unique δ̂ ∈ (0, 12 ) such that the group incentive
contract is preferred to the individual incentive contract under U-form (or M-form)
decentralization if and only if δl (or δg ) ≥ δ̂.
Therefore, since δg ≤ δl , we can directly obtain the following proposition from
Lemma 3:
Proposition 3: The group incentive contract is more likely to be designed under
U-form decentralization than under M-form decentralization.
24

Proposition 3 shows that group incentive contracts for local managers will be more
likely when the sub-units are organized according to the production line than when
they are organized according to the good. It is because if the group incentive contract
is more eﬃcient than the individual incentive contract under M-form decentralization,then it is always more eﬃcient than the individual incentive contract under U-form
decentralization. On the other hand, individual incentive contracts for local managers
will be more likely when the sub-units are organized according to the good than when
they are organized according to the production line.

6

Centralization vs. Decentralization

There is a trade-oﬀ between the centralized and decentralized decision-making structures. The decentralized decision-making structure is subject to incentive distortion
either from less coordination when the individual incentive contracts are designed orfrom free-riding when the group incentive contracts are designed. On the other hand,the centralized decision-making structure is subject to information loss by not utilizing the local information. Thus, the answer to the question of which decision-making
structure must be adopted and which incentive contract must be designed for each
local manager, depends on the relative magnitude of the above three costs.
To simplify, let us assume that δg = δl = δ. (Toward the end of this section, we
will relax this assumption). Deﬁne2σlocal= max{σ12 + σ22 , σA2 + σB2 }.

Then, the optimized expected proﬁts under centralization, decentralization with individual incentives, and decentralization with group incentives reduce to, respectively:
πc =

1
2
[(µ − c0 )2 + σm
] − M,
1 − 2δ

d}=πId ≡ max{πlId , πgI1
1 2
2[(µ − c0 )2 + σm
] + σlocal,
2(1 − δ)
2
25

(37)
(38)

and
d
d
d
πG
≡ max{πlG
, πgG
}=

1
1
1 2
2
[(µ − c0 )2 + σm
c20 + σlocal]−.
1 − 2δ
1 − 2δ
2(39)

By subtracting (38) from (37), we obtain the beneﬁt from centralization overdecentralization using individual incentives as
22, σm) ≡ π c − πId =P (σlocal

δ2
1 2
2[(µ − c0 )2 + σm
] − σlocal− M.
2(1 − 2δ)(1 − δ)2(40)

As shown earlier, the ﬁrst term in the right-hand side of the above equation represents the cost of less coordination under decentralization with individual incentives
arising from the fact that the sub-units are looking for a Nash solution rather thana team-eﬃcient solution under decentralization with individual incentives. The second term represents the information cost of centralization arising from the fact thatno local information is used under centralization. Obviously, the third term is themonitoring cost of centralization.
By subtracting (39) from (37), we obtain the beneﬁt from centralization overdecentralization using group incentives as
2
2
d
, σm
) ≡ π c − πG=Q(σlocal1
1 2
c20 − σlocal− M.
1 − 2δ
2(41)

The ﬁrst term represents the cost of free-riding under decentralization with group
incentives, whereas the second and third terms are the same as above.
Also, by subtracting (39) from (38), we obtain the beneﬁt from decentralization
using individual incentives over that using group incentives as

2
2
d
, σm
) ≡ πId − πG=
T (σlocal

1
δ2
2
c20 −
[(µ − c0 )2 + σm].
2
1 − 2δ
(1 − 2δ)(1 − δ)

(42)

2
2
2
2
2
2
Finally, by drawing P (σlocal, σm) = 0, Q(σlocal, σm) = 0, and T (σlocal, σm) = 0 in2
2
, σm)-space, we obtain Figure 1.
(σlocal26

[Insert Figure 1 here]

From Figure 1, we obtain the following proposition:
Proposition 4:(1) If the local uncertainty is big and the market uncertainty is small, then the organization will be decentralized, and the local managers will be provided with high-poweredindividual incentive contracts.
(2) If both the local uncertainty and the market uncertainty are big, then the organization will be decentralized, and the local managers will be provided with group incentive
contracts.
(3) If the local uncertainty is small and the market uncertainty is big, and/or if
the monitoring cost is low, then the organization will be centralized, and the local
managers will be provided with forcing contracts.
Note that the information cost of centralization increases as the local uncertainty
increases, that the cost of less coordination under decentralization using individual incentives increases as the market uncertainty increases, and that the cost of free-riding
under decentralization using group incentives is independent of both uncertainties.
Therefore, if the organization faces with a big market uncertainty along with a small
local uncertainty, designing a centralized decision-making structure is optimal. However, if the organization faces with a small market uncertainty along with a big local
uncertainty, then designing a decentralized decision-making structure with providing
individual incentives is optimal. On the other hand, if both the market and local
uncertainties are big, then designing a decentralized decision-making structure with
providing group incentives is optimal.
Brickley and Dark (1987) found that most franchising companies, when deciding whether to franchise or not their units, are more likely to choose to franchise27

a unit as it is harder to monitor that unit (i.e., input monitoring). Also, Krueger(1991) reported that franchisees typically receive very high-powered incentives, while
employed managers receive little or no explicit incentive pay. If we understand acompany’s choice between company ownership and franchising as a choice between
centralized control and decentralized delegation, these empirical ﬁndings are quiteconsistent with the result reported in (3) of Proposition 4.
Regarding decentralization using group incentives, we would like to mention arecent paper by Ichniowski, Shaw, and Prennushi (1997). Ichniowski et. al., byinvestigating steel ﬁnishing processes in the U.S., concluded that the use of problemsolving team is more eﬀective in improving worker productivity when it is adopted
together with other work practices such as group incentives and ﬂexible assignmentof workers. In problem-solving teams, the members are usually empowered to makeday-to-day decisions on project assignment and problem-solving (decentralization).
Also, from Figure 1, we can have the following proposition:
Proposition 5: As the external eﬀect among local managers gets bigger (i.e., δ getscloser to 1/2), the organization will be more likely to adopt centralization, while it
will be more likely to adopt decentralization and to use individual incentives as theexternal eﬀect gets smaller (i.e., δ gets closer to 0).
From (40), (41), and (42), note that the cost of decentralization gets bigger asδ gets bigger, whether it is the cost of less coordination using individual incentives
or the cost of free-riding using group incentives, and that the information cost ofcentralization remains constant regardless of the value of δ. Also note that the costof less coordination under decentralization with individual incentives approaches zeroas δ goes close to zero, and that both the free-riding cost of decentralization usinggroup incentives and the information cost of centralization remain substantial.
Anderson and Schmittlein (1984) and Anderson (1985) reported that the ﬁrms selling electronic components are more likely to choose to use independent sales agents as28

their true performances get more diﬃcult to evaluate (i.e., output monitoring) and as
their non-selling activities get more important, whereas they are more likely to choose
to use in-house sales agents (i.e., employees) otherwise. Moreover, independent sales
agents typically receive commission and work under little or no regulation, whereas
the employed sales agents receive salary and work under the ﬁrms’ strict regulations(such as work time, freedom of selling other companies’ products, and buyers they
can sell to). Note that δ in our model can be interpreted as the diﬃculty of evaluatingeach worker’s true performance or the importance of non-selling activities. Therefore,
our result in the above proposition is consistent with the empirical ﬁndings in Anderson and Schmittlein (1984) and Anderson (1985). It is also consistent with Aghion
and Tirole’s (1997) argument that decision rights tend to be delegated as the interestsof subordinates and bosses get suﬃciently correlated since δ can be explained as thedegree of interest conﬂict between the top manager and the local managers.7
Up to now, we have assumed that δg = δl = δ. Now, we return to our originalassumption that δg ≤ δl . Then, whether the organization adopts a U-form organizational mode or an M-form organizational mode depends on δl − δg and the relative
sizes of σ12 + σ22 and σA2 + σB2 . Thus, as shown in Proposition 1, the organization always adopts a U-form organizational mode under centralization. However, as shownin Proposition 3, under decentralization, the organization will adopt an M-form organizational mode if σA2 + σB2 is suﬃciently big compared with σ12 + σ22 and if δl − δgis small, and vice versa.
7

In a repeated setting in which delegation cannot be committed by a contract and only informaldelegation is feasible through the top manager’s reputation concern, Baker, Gibbons, and Murphy(1999) showed that informal delegation is infeasible when the subordinate’s interests are too highly
correlated with the boss’s because the fallback is too attractive to the boss in this case. However,in this paper, we assume that formal delegation can be committed by a contract.

29

7Applications

Here, we will consider two simple applications. These applications are not new. Neither, are they developed in full. Rather, they are taken to illustrate the implicationsof the model we have developed in this paper.

7.1

Environments and Organizations

As we already mentioned in the introduction, many contingency theorists observe several patterns regarding the relationship between organization’s external environments
and its internal structures.
One of the most common ﬁndings is that organizations in stable environments,
compared with organizations under unstable environments, have more formalized
structures (i.e., their decision-making practices are more centralized). For example,
Lawrence and Lorsch (1968) reported that, in major plastic manufacturing ﬁrms
in the U.S., the production department faced the least amount of uncertainty andwas the most formally organized, the research department faced the largest amountof uncertainty and was least formally organized, and the sales department was inbetween in terms of both external uncertainty and internal structures. The workers
in the production department were usually organized as mutually supportive, whereas
the sales agents were usually organized as rather autonomous.
The sales department’s less predictable environments compared with that of the
production department are mainly due to its large randomness at the local levels.
We would like to quote from Lawrence and Lorsch’s (1968) survey to emphasize thediﬀerence in the amount of uncertainty across sales and production departments.
On sales department: “The market we sell to is broad and diverse. For example,
in the toy business if the product (plastic materials) comes out in the right color
at the right price, anybody will buy it, and anybody can make it. In contrast, forwire and cable customers, the right technology, service, and delivery are critical, and30

price is at the end of the line.” On production department: “In production, life isreally plain, as it is geared to running the kind of plant and equipment which they
currently have and where most of the decisions are built in.” Thus, as predictedfrom Proposition 4, the sales department relies more on decentralized delegation (lessformality) and designs the workers rather autonomous, because its local uncertainty
is big and typically speciﬁc to the business area in which each sales worker specializes,
while the production department relies more on centralized control (more formality)and designs the workers complementary because its local uncertainty is small.
Another stylized phenomenon is that organizations, faced with emergency, tend
to centralize their decisions. For example, centralized rationing is favored in warfare
rather than the market system.8 Also, Stiglitz (1989) said that the political decisionmaking process had to be centralized during war time. In warfare, what drasticallyincreases is generally the randomness of the common shock for the whole economy.
Thus, as predicted from Proposition 4, the economy as an organization must have amore centralized structure in the war time.
As stated in Proposition 4, the relative sizes of external uncertainties are importantin determining the organization’s internal structures.

7.2

The Dynamics of Organization

Blau and Meyer (1987), like many other sociologists, observe that as a bureaucracy
grows, (i) the proportionate size of its administrative component gets smaller (ﬂattening of bureaucracy), and (ii) authority over decisions is more likely delegated fromthe top management to lower levels (decentralization of bureaucracy). Although theseﬁndings seem to contradict the stereotypical view that a large bureaucracy is highly
centralized and inﬂexible, they are well documented in the literature.9 As proposedby Blau and Meyer, economies of scale in administration may explain the ﬂattening
8

See Milward (1977).

9

See, for example, Williamson (1986).

31trend in a bureaucracy. However, the decentralization trend is hard to explain by thesame argument.
Similarly, Chandler (1962) found that a growing ﬁrm eventually switched from a
U-form organizational mode to an M-form organizational mode.
When an organization is newly established, it generally faces a great deal of uncertainty mainly because it is newly introduced to the environment. As the organization
develops over time, it accommodates itself to the environment, by internalizing theuncertainty into its structure, by making operation rules more routine and formal, andby deﬁning duties and powers more precisely. Since common features of an organization are easier to internalize than idiosyncratic features and since the uncertainties
associated with the production processes are easier to internalize than those associated with the products themselves, mature organizations seem to reduce more ofcommon uncertainties than local uncertainties and more of line-speciﬁc uncertainties
than good-speciﬁc uncertainties. As the relative magnitude of common uncertainty
gets smaller, the organization will adopt a decentralized decision-making structure,
and as the relative magnitude of line-speciﬁc uncertainty gets smaller, the organization will more likely take an M-form. Considering that less need for coordination
under decentralization would demand a smaller size of the administrative component,
our model also explains why bureaucracy shows the ﬂattening trend as well as thedecentralization trend. Along this line of argument, Williamson (1986, p.118) writes:“To the extent that uncertainty decreases as an industry matures (which is the usualcase) the beneﬁts that accrue to integration presumably decline. Accordingly, greater
reliance on obligational market contracting is commonly feasible for transactions ofrecurrent trading in mature industries.”
Such organizational dynamics may explain, to some extent, the changing patternof Korea’s development strategy as well.10 The Korean government, at an early stageof economic development in the 1960s, used so-called ‘mandatory planning’, relying
10

For details of Korea’s development strategy, see Amsden (1989).

32

heavily on the government’s coercive instructions rather than the market mechanism.
However, around the 1980s, it began to switch to ‘indicative planning’, introducing
rough guidelines with less coercion and delegating more economic decisions to theprivate sectors. Such a decentralization trend still continues even nowadays.
In the 1960s, Korea’s economic infrastructure was poorly developed. The accounting, banking, and legal systems were yet to be developed. The capital market was not
functioning eﬀectively. Such lack of sound economic infrastructures contributed tomagnifying common turbulence for the economy as a whole. Furthermore, the shortage of employment opportunities in the private sector made government jobs most
attractive. Thus, the government was able to absorb the elite into its bureaucracy,
resulting in the government’s dominance over the private sectors in terms of information processing capacity. Consequently, at an early stage of development, a big
macro uncertainty together with the government’s dominance in informational ability
made direct government interventions through mandatory planning more attractive
than laissez-faire.
However, as the economy successfully grew, the lack of infrastructures was substantially ameliorated. In the meantime, the Korean society became more diﬀerentiated and sophisticated. This evolution has reduced the common uncertainty, while
it has increased the local uncertainty. Also, rapid accumulation of know-how (including network) in the private sectors considerably undermined, and even reversed
the government’s dominance in information processing. These, in all, made economic
decentralization and indicative planning more attractive at a later development stagein Korea around the 1980s, as predicted from Proposition 4.
The Korean economy should have moved further toward an autonomous structurefrom an initial central control mode. As the private sector becomes more diversiﬁed,
the Korean government lacks in adequate knowledge needed to coordinate such asophisticated economy well. This explains why, at a later stage of development,
the Korean economy should have moved further toward the market system with less33

governmental interventions and less bureaucracy. However, the Korean economy has
not been successful in restructuring its economy more toward the market system
mainly due to strong resistance from various interest parties who were against sucha move. This began to create ineﬃciency for the Korean economy as early as mid
1980s and resulted in serious economic crisis in the late 1990s.
The organizational theory developed in this paper also has useful implications
for explaining Chinese ‘success’ vs. Soviet ‘failure’ in their transition from planned
economies to market economies. When the transformation is under process at a
massive level, it is mainly the randomness of common uncertainty which drasticallyincreases. According to Proposition 4, the increase in common uncertainty calls forcentralization, which is exactly opposite to the liberalization trend and leads to adilemma.
Between the two countries, the shock arising from transition was much bigger for
the former Soviet Union than for China. The former Soviet Union had a functionallydivided economy. Each local republic was able to manage its economy only under
the former Soviet block’s coordination, whereas the Chinese provinces were rather
autonomous even before the transition.11 In the case of the former Soviet block, theadditional common uncertainty results from unstable political situations, lack of conﬁdence in money, high and uncertain inﬂation rates, and lack of central coordination.
Accordingly, the dilemma was much larger for the former Soviet Union.
It is frequently argued that the establishment of well-functioning legal, banking,and accounting systems is a prerequisite for a successful, full-scale transformation.12
This argument is consistent with our organizational theory since such establishment
will reduce the common uncertainty, nullifying the demand for more centralization,and thus removing major obstacles to the liberalization movement. However, full11

See Qian and Xu (1993) for diﬀerences in initial conditions and reform policies between China

and Eastern European countries.
12

See, among others, Litwack (1991), McKinnon (1991, 1994), and Calvo and Frenkel (1991).

34

establishment of such systems will not be realized in a short period of time. In
the meantime, these economies will be better operated by a centralized authority(decentralization through centralization) as is the case in China or in the earlier
stage of the Korean development process. However, as Korea has already experienced,
China’s smooth and government driven transition will inevitably create many interest
groups who will be against the move toward decentralization and competition in laterstages. Thus, China’s ‘success’ today can potentially cause a big problem in the
future.

8Concluding Remarks

This paper examines the issue of designing an optimal organizational form in terms oftask allocation among sub-units, decision-making structure, and incentive schemes fororganizational members. We view an organization as a collection of decision-makers
at various hierarchical levels. Being bounded rational, the decision-makers have limited capacity to identify unstable environments that an organization faces. Eﬃcient
information ﬂows and incentive alignments among the organizational members must
be taken into account in designing an optimal organizational form.
By distinguishing the uncertainty an organization faces into two types, common
uncertainty and local uncertainty, we clarify the relationship between the organization’s internal structures and its external environments. Depending on the organization’s design for task allocation, the internal impacts of the common and local
uncertainties are diﬀerentially realized. The common uncertainty has a bigger internal impact on complementarily designed organizations, while the local uncertainty
has a magniﬁed impact on autonomously designed organizations. Also, the interaction between the sub-units gets stronger when tasks are functionally allocated along
the production processes than when they are allocated along the ﬁnal products.
Centralization serves for better coordination and decentralization serves for bet-

35

ter information. The coordinational beneﬁt under centralization increases as therandomness of the common uncertainty gets bigger, and this beneﬁt is magniﬁed
when the organization designs its sub-units complementary. The informational beneﬁt increases as the randomness of the local uncertainty gets bigger, and this beneﬁt
is magniﬁed when the organization designs its sub-units rather autonomous. Thus,
we derive a relationship between the organization’s designs for task allocation anddecision-making structure. That is, complementary organizations tend to adopt centralized decision-making and autonomous organizations tend to adopt decentralized
decision-making.
The organization in our model is assumed to make only one kind of decision. In
reality, however, most organizations make many diﬀerent kinds of decisions, ranging
from strategic decisions such as long term investments to operating decisions likedaily productions. Diﬀerent decisions involve diﬀerent kinds of uncertainties. For
most strategic decisions, the common uncertainty outweighs the localized uncertainty,
whereas the opposite is the case for most operating decisions. Our model explains
why most strategic decisions are made by the top management with the help ofspecialized staﬀ members and why most operating decisions are made by the operating
units rather autonomously. Our model also explains why, during war time, moststrategic decisions are handled by a commanding center, while most tactic decisions
are delegated to combat units.
Our model set-up is partly motivated by many diﬀerences between U-form organizations and M-form organizations. In a U-form organization, there exists a strong
interrelation among diﬀerent divisions. The nature of this interaction is often complementary. In U-form organizations, the common uncertainty is more important.
On the other hand, in an M-form organization, diﬀerent divisions are operating in geographically separated areas or are targeting diﬀerentiated markets. Each division’s
operation is rather autonomous. The common uncertainty is less important and theinteraction among the divisions is weak.

36

We close this section by pointing out two limitations of this paper. First, thispaper does not address other closely related organizational issues such as why mostorganizations are hierarchically designed, and what determines the span of control.13
Second, in this paper, we only consider top-down information ﬂow among the organizational members. In reality, however, there are bottom-up information ﬂows as well.
We believe that incorporating the bottom-up information ﬂows into the model will
be useful.

APPENDIX

Derivation of Equation (21):
From the ﬁrst-order conditions of the optimization problem (20) in the text, wederivead1 (k1 , k2 ) = µ − kc01 + θm + θ1 + δl EY [ad2 (k2 , k1 )|θm , θ1 ],ad2 (k2 , k1 ) = µ − kc02 + θm + θ2 + δl EY [ad1 (k1 , k2 )|θm , θ2 ].

(43)

From (43), by plugging the second equation into the ﬁrst and by using the fact thata repeated conditional expectation is equivalent to a single expectation conditional
upon the least common information, we obtain
ad1 (k1 , k2 ) = µ −c0c0+ θm + θ1 + δl (µ −+ θm ) + δl2 EY E[ad1 (k1 , k2 )|θm ].
k1
k2

(44)

By taking a conditional expectation given θm on both sides of (44), we obtain
EY [ad1 (k1 , k2 )|θm ] =

c0
1
1
c0
(µ + θm ) −( + δl ).
2
1 − δl1 − δl k1
k2(45)

Thus, by plugging (45) into (44), we derivead1 (k1 , k2 ) =
13

1
1
c0
c0
(µ + θm ) + θ1 −( + δl ).
2
1 − δl1 − δl k1
k2

Williamson (1967), Calvo and Wellisz (1978), and Qian (1994) consider these issues from an

incentive perspective. Marschak and Radner (1972), Radner (1992,1993), and Geanakoplos andMilgrom (1991) consider the same issues from an information perspective.

37

And, likewise, we derivead2 (k2 , k1 ) =

c0
1
1
c0
(µ + θm ) + θ2 −( + δl ).
2
1 − δl1 − δl k2
k1

Derivation of Equation (23): We can rewrite (21) as
1
c0
1−k1
2
ad1 (k1 , k2 ) = 1−δ
(µ − c0 + θm ) + θ1 − 1−δ+ δl 1−k
),
2( k
k2
1
l
l

ad2 (k2 , k1 )

1
c0
1−k2
1
= 1−δ
(µ − c0 + θm ) + θ2 − 1−δ+ δl 1−k
).
2( k
k1
2
l
l

(46)

Also, using (22), we have1c0
2 1−k12(µ − c0 + θm ) + θ21 + δl θ2 + θA + θB + 2(1−δ) − δl ( 1−k)],v1d (k1 , k2 ) = 2(1−δ2 ) [(1 − 2δl )( k
k2
1
l)
l

v2d (k2 , k1 )1
c0
2 1−k21= 2(1−δ(µ − c0 + θm ) + θ22 + δl θ1 + θA + θB + 2(1−δ) − δl ( 1−k)].
2 ) [(1 − 2δl )( k
k1
2
l)
l

(47)
Therefore, by using (46) and (47), we derive
πlId (k1 , k2 ) ==Eθm {ER [(v1d − c0 )ad1 + (v2d − c0 )ad2 |θm ]}10 )c0 1−k1
22[(µ − c0 )2 + σm
] + 12 (σ12 + σ22 ) − (µ−c( k1 + 1−k)(1−δl )2
(1−δl )2k2
2232
(1−3δ )c
2δ c
1 2
2 2
1
2
) + ( 1−k) ] (1−δl 20)2 ( 1−k)( 1−k).
− 2(1−δl2 )20 [( 1−k
k1
k2
k1
k2
l
l

Proof of Lemma 1:
From (23), given k2 , we obtainc02δl3 c0 1 − k2
1 − k1 (1 − 3δl2 )c20
∂πlId (k1 , k2 )
= 2
[µ
−
c
−
]
+
.
0
∂k1
k1 (1 − δl )2(1 + δl )2 k2
k13(1 − δl2 )2Since, from (46), we see that (k1 , k2 ) must satisfy thatµ − c0 ≥1 − k2
c0 1 − k 1
δl c0 1 − k2
(
+ δl
)≥
.
1 + δl k1
k2
1 + δl k2

Otherwise, we have that ER [ad1 (k1 , k2 )] < 0, which is obviously not optimal. Since0 ≤ δl ≤ 12 , we haveµ − c0 ≥δl c0 1 − k22δl3 c0 1 − k2≥,
1 + δl k2(1 + δl )2 k2
38

and

1 − 3δl2> 0.
(1 − δl2 )2Therefore, we ﬁnally derive∂πlId (k1 , k2 )> 0, ∀k1 ∈ [0, 1] for any given k2 ∈ [0, 1].
∂k1
As a result, we have k1d = 1, and by the same method, we have k2d = 1.
d
Proof of Lemma 2: By taking a ﬁrst derivative of πlG(h1 , h2 ) in (30) with respect

to h1 given h2 , we haved(h1 , h2 )1∂πlG
= 3 [2h2 + 4δl h1 − (2 + 4δl )h1 h2 ].
∂h1
h1 h2

Since 0 ≤ h1 , h2 ≤ 1, we obtaind(h1 , h2 )∂πlG
> 0, ∀h1 ∈ [0, 1 − h2 ] for any given h2 ∈ [0, 1].
∂h1Thus, since h1 + h2 ≤ 1, we have h1 + h2 = 1. By plugging h2 = 1 − h1 into (30), we
derived(h1 ) =πlG

112(µ2 + σm
) + 12 (σ12 + σ22 ) − 1−2δ
µc0
1−2δl
l
c20
2
1
1
+ 2(1−4δ2 ) [ h (1−h ) − h2 − (1−h )2 ],
1
1
1
1
l

which will be maximized at h1 = 12 . Thus, we derive that the optimal incentive power
for the group incentive contracts is hd1 = hd2 = 12 .
Proof of Lemma 3:
2

δ
1
Let φ(δ) ≡ (1−δ)
2 . Then, we have φ(δ) is increasing in 0 ≤ δ ≤ 2 with φ(0) = 0

and φ( 12 ) = 1. Since µ > 2c0 , we have
c20
< 1.
2
(µ − c0 )2 + σm
Therefore, there always exists δ̂ ∈ (0, 12 ) satisfying
φ(δ̂l ) =c20.
2(µ − c0 )2 + σmdSince φ(δ) is increasing in δ, from (35) and (36), we can easily prove that πlG≥ (<)πlIdddif δl ≥ (<)δ̂, and πgG≥ (<)πgI
if δg ≥ (<)δ̂.

39

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42