Resource Allocation and Organizational Form

Abstract

We develop a theory of firm scope and structure in which merging two firms allows the integrated firm's top management to allocate resources that are costly to trade. However, information about their use resides with division managers. We show that establishing truthful upward communication raises the cost of inducing managerial effort compared with stand-alone firms; this effect dominates a positive effect on effort driven by competition for the firm's resources. We derive predictions about optimal firm scope and structure. In particular, we show why it is optimal to separate the tasks of allocating resources and running a division.

Full text

Resource Allocation and Organizational Form∗
Guido Friebel1and Michael Raith2
January 2009
Abstract: We develop a theory of firm scope and structure in which merging two firms
allows the integrated firm’s top management to allocate resources that are costly to trade.
However, information about their use resides with division managers. We show that
establishing truthful upward communication raises the cost of inducing managerial effort
compared with stand-alone firms; this effect dominates a positive effect on effort driven
by competition for the firm’s resources. We derive predictions about optimal firm scope
and structure. In particular, we show why it is optimal to separate the tasks of allocating
resources and running a division.
JEL codes: D23, D82, L22, M52
Keywords: theory of the firm, coordination, authority, incentives, strategic information
transmission, hierarchy
∗We would like to thank Ricardo Alonso, Heski Bar-Isaac, Patrick Bolton, Bruno Cassiman, Mathias
Dewatripont, Florian Englmaier, Bengt Holmstr¨om, Mikko Lepp¨am¨aki, Maike Lentner, Tony Marino,
Niko Matouschek, John Matsusaka, Fausto Panunzi, Paul Povel, Heikki Rantakari, Patrick Rey, Jean
Tirole, Birger Wernerfelt, Jan Zabojnik, and seminar audiences at Albany, Cologne, Columbia, Frankfurt,
Harvard-MIT, Helsinki, Kellogg, LSE, Taiwan National University, USC (Economics Department and
Marshall School), the IIOC and NAES meetings and the Christmas Meeting of German Expatriate
Economists in 2006, the Research Workshop on Industrial Organization and Finance in Barcelona, ESSET
in Gerzensee, Stanford-SITE and the Harvard Strategy Research Conference in 2007 for very helpful
comments and suggestions. The first draft was written while Raith was visiting the Marshall School of
Business at USC, and we would like to thank the school for its hospitality.
1University of Frankfurt and CEPR. Email: friebel@cict.fr
2Simon School of Business, University of Rochester. Email: raith@simon.rochester.edu

1 Introduction
Production in most firms involves scarce firm-specific resources, and allocating them to
different uses is one of the most important responsibilities of managers. Managerial au-
thority replaces the price mechanism when contracting over resources is too costly. This
simple argument, first expressed by Coase (1937), helps us understand why firms exist,
and what motivates some firms to merge: it is often easier to assign decision rights over
resources in an integrated firm than to negotiate the use of resources across firm bound-
aries. Indeed, we often hear that two firms merge in order to pool capabilities and share
resources.1
The benefits of integration follow naturally from limitations in contracting. The costs
of integration, however, are harder to identify. It is widely believed that integration
creates new agency costs, but pinning down their precise nature and origin has proven to
be difficult.
We develop a theory of organizational form that directly relates the costs and benefits
of integration. In an integrated firm, top management can allocate pooled resources
across different units, but to do so efficiently, it requires information about opportunities
to invest resources. This information resides with division managers who may have an
incentive to misrepresent it strategically.2We investigate the tradeoff between eliciting
managerial effort and establishing truthful communication from the divisions to the top,
and derive implications for firm scope, structure, and incentive contracts.
Resources in our theory have two key characteristics: First, they are firm-specific and
1Procter and Gamble’s acquisition of Gillette in 2005 was aimed at sharing complementary capabili-
ties: “P&G is big in female grooming; Gillette excels in male grooming. Gillette is big in India and Brazil;
P&G’s strengths lie in China, Japan and places such as Turkey. P&G knows all about molecules; Gillette
is a dab hand at gadgets. And P&G’s expertise in retail customer development goes hand-in-hand with
Gillette’s mastery of point of purchase” (Marketing Week 2005).
2As Crozier (1965) observed in his field study: “[In making many decisions, higher-level managers]
must rely heavily on the information they receive from the section chiefs... The section chiefs, however,
. . . are running parallel identical units that have to compete for scarce resources. ... Thus they are likely
.... to bias the information they give in order to get the maximum of material resources and personal
factors with which to run their sections smoothly” (p.45).
1

not available in an external market, or only available as inferior substitutes. Second, they
can be allocated to different uses, but doing so by contract is difficult. Resources with
these characteristics fall in between the extremes of easily tradeable commodities on one
hand, and unique capabilities or other custom-made inputs on the other.3
Specialized human resources are the best examples. Many firms’ capabilities consist
of the “know-how” held collectively by individuals in the firm (see Sutton, 2005). We are
interested in resources and capabilities that can be allocated to different possible uses,
which means that the resources themselves must be sufficiently well-defined. On the other
hand, how resources are to be used is often too costly to specify in a contract, for instance,
because the duration of demand for them is uncertain, or because information may leak
to competitors in the case of trade across firm boundaries. The best option then may be
to allocate resources by managerial authority.4
In our model there are two production units that can be run either as stand-alone firms
or as divisions of an integrated firm. Each unit has a fixed endowment of resources. The
use of resources is not contractible, while authority over resources is. This assumption is
a special case of the distinction between actions and authority over actions made in the
recent literature on authority in organizations, see Hart and Holmstr¨om, 2002, Aghion et
al., 2004, and the survey by Dewatripont (2001).5
As an independent firm, each unit uses its endowment of resources, and cannot obtain
more resources elsewhere. When the firms merge, they become divisions of one firm; their
3Our notion of resources is similar to both Chandler’s (1990) notion of “organizational capabilities”
and to the concept of “unique resources and capabilities” in the strategic management literature, see e.g.
Penrose (1959), Wernerfelt (1984) and Barney (1991). The latter literature, in particular, emphasizes the
ability to use unique resources and capabilities in different businesses as the main justification for firms’
expansion of scope (see Teece, 1982). For work in economics that builds on the notion of organizational
capabilities, see Matsusaka (2001) and Sutton (2005).
4In the aviation industry, there is a chronic shortage of engineers who have expertise with composite
materials. In response, the headquarters of Airbus Industries, for instance, deploys teams of specialized
aviation engineers to different units within the firm, based on an audit process designed to ascertain
where the engineers are needed most.
5A resource for which this assumption typically does not hold is capital (money). Our theory is
therefore strictly speaking not one about internal capital markets; see our discussion in Section 2.
2

resources are pooled and placed under the authority of a CEO who can shift the firm’s
resources to the division with the better project.
Each unit is run by a manager whose job is to create profitable projects. A project’s
payoff depends on its quality and the resources invested in it. Project quality, in turn,
depends on the manager’s effort; to induce effort, firms can offer wage contracts based on
the projects’ payoffs. Managers are risk-neutral but protected by limited liability.
In an integrated firm, each division manager has private information about his project.
Realizing the benefit of integration requires that managers communicate their information
truthfully to the CEO. But when a manager’s wage depends on his performance, he may
want to overstate his project’s quality, because the more resources are invested in the
project, the higher his payoff. Individual incentives thus create an endogenous “empire-
building” motive, even though managers have no intrinsic preferences for resources.
The firm can induce truthful communication by paying the managers not only for
their own division’s performance, but for the other division’s as well, or equivalently, for
firm performance. Doing so ensures that a manager with a bad project will not claim
to have a good one, since he can gain from the allocation of the firm’s resources to a
better project. However, providing “team-based” incentives of this sort makes it more
costly to induce managerial effort than under non-integration, an effect we refer to as the
information-rent effect of integration. There is also a second, positive, competition effect
of integration on effort incentives, because shifting resources from bad to good projects
raises each manager’s marginal benefit of having a good project.
We show that under very general contracting assumptions, the information-rent effect
dominates the competition effect. When communication is cheap talk and the managers’
wages can depend only on the divisions’ performance (as we assumed in our discussion
above), the information-rent effect strictly dominates. There is then a tradeoff between
allocating resources optimally and providing effort incentives, and whether integration or
non-integration is optimal depends on the relative importance of these objectives.
We show that the CEO structure considered so far in fact minimizes agency costs
compared with alternative organizational structures. One alternative is a skewed struc-
ture, in which one of the division managers has authority over all resources; another is
3

decentralized horizontal exchange, where each manager can voluntarily lend resources to
the other division. Both alternative structures involve additional incentive constraints
and are dominated by the CEO structure, except for the case of highly complementary
resources for which horizontal exchange works equally well.
Our paper makes three contributions. First, we provide a simple theory of the ben-
efit and cost of integration, and provide an answer to Williamson’s (1985) “selective-
intervention puzzle:”6realizing the benefit of allocating resources by managerial author-
ity requires aggregating dispersed information, but establishing truthful communication
weakens incentives for effort. We take limitations of the market as given, but explain how
integration creates new costs that are directly related to the benefit of integration.
Our results rely on minimal assumptions about the underlying agency problem — the
managers are not empire builders and the CEO always makes value-maximizing decisions
— but hinge on constraints on feasible contracts. Integration strictly raises agency costs
if wages cannot be based on managers’ communication or the allocation of resources.
If either of these restrictions does not hold, integration is either strictly optimal, or the
difference between integration and nonintegration disappears. It also matters that a firm’s
organizational architecture is a long-term choice. If incentive contracts or the allocation
of decision rights could be changed on the fly, integration would be strictly optimal. It
is selective intervention under a given organizational architecture that creates agency
problems further below in the firm.
Second, we provide an agency-based rationale for the organization of firms as hier-
archies in which top management’s main role is to coordinate lower-level units and to
allocate resources, as described by Chandler (1977). Other agency-based theories of hi-
erarchies link the existence of a principal as residual claimant to her role as monitor
of workers (Alchian and Demsetz, 1972, Rayo, 2007) or as budget breaker (Holmstr¨om,
1982). In our theory, a hierarchy with a top manager as coordinator avoids the conflict
of interest that one or both division managers would have if they were given the double
6Williamson (1985, p.131) phrased the puzzle as follows: “Why can’t a large firm do everything that
a collection of small firms can do and more?” The last two words are critical: in our model there is no
cost of integrating two firms and have top management never intervene.
4

task of running a division and allocating resources. A hierarchy emerges endogenously as
the optimal structure even though information is initially dispersed.
Third, our model generates several testable predictions, including the following: (i)
Integration is more likely the more closely related (i.e., the more complementary) the two
units are, consistent with intuition and evidence. (ii) Integration is more likely the more
variable the production units’ profits are. Its purpose here is not to reduce risk, but to
benefit from allocating more resources to the most profitable projects. (iii) Integration is
more likely the better firms can hold division managers accountable for their claims about
investment opportunities (in our model, through the use of message-contingent contracts).
(iv) Horizontal exchange of resources between divisions is more likely to occur the more
related the divisions are, and the more variable their profits are.
The next section relates our paper to the literature. Section 3 sets up the model. The
analysis of the benefits and costs of integration then proceeds in several steps in Section 4.
In Section 5 we study how the optimal firm scope depends on our model’s parameters, and
derive several predictions. In Section 6, we compare different structures of an integrated
firm, and show in what way a CEO structure is optimal. Section 7 concludes.
2 Related Literature
Our paper is related to several strands of the literature. Many elements and effects at
work in our model have been studied individually in other papers. New in our paper is
how these elements are combined.
Theories of the firm: Our paper differs from theories of firm boundaries mainly in
its focus on the communication of dispersed information. One such theory emphasizes
the adverse effects of influence activities; see Milgrom and Roberts, 1988, 1990; Meyer,
Milgrom and Roberts, 1992; and Scharfstein and Stein, 2000. In our model, communi-
cation is not only an influence activity but also a necessary input into efficient resource
allocation. We spell out the channel through which influence activities affect an unbiased
CEO’s decisions, which allows us to link the costs of integration directly to its benefits.
The incentive-system theory of the firm argues that firms can solve multitask problems
5

with systems of organizational rules, asset ownership and incentive schemes; see Holm-
str¨om and Milgrom (1991, 1994), Holmstr¨om and Tirole (1991), Holmstr¨om (1999) and
Gibbons (2005). The managers’ communication in our model can be seen as a second
task, but the nature of the firm’s problem is different: discrepancies between output and
measured performance, which the incentive-system approach takes as given, are absent
in our model; realized output is perfectly measurable. Rather, the organization must
solve a team production problem in which managers strategically communicate private
information.
Our contracting assumptions are borrowed from property-rights theory (Grossman
and Hart, 1986) and the more recent literature on authority in organizations. Like Hart
and Holmstr¨om (2002) and Hart and Moore (2005), we assume that coordination (here, of
the use of resources) requires integration under a central authority because decisions are
non-contractible. But in our theory, authority and incentives interact quite differently. In
Aghion and Tirole, (1997), Mailath et al. (2005), and Dessein et al. (2008), for instance,
top management’s (or the principal’s) decisions have a direct negative effect on other
agent’s utility and incentives. In our model, in contrast, the CEO always makes value-
maximizing decisions based on the available information; if he had perfect information, his
decisions would improve the managers’ incentives. Only when the managers have private
information does a new agency problem emerge, which leads to the tradeoff between
information aggregation and incentives for effort.
Organizational economics: Several papers investigate the interactions between co-
ordination, incentives and communication, taking the boundaries of the firm as given.
Here, we argue that these interactions and tradeoffs are determinants of firm boundaries.
Athey and Roberts (2001) show that individual performance contracts can lead to
distortions in decision-making, which can be alleviated by introducing a top manager as
a pure coordinator. In their model the top manager can obtain all relevant information
at an exogenous cost. In ours, the CEO must obtain information from strategically
communicating managers. As a result, the costs of integration are endogenous, allowing
us to make predictions about integration decisions.
Levitt and Snyder (1997) show that getting an agent to communicate bad news un-
6

dermines ex-ante effort incentives.7In contrast to theirs, in our model contracts cannot
be based on the principal’s decisions (resource allocations) or on messages, leaving team-
based incentives as the only way to establish truthful communication. The multi-agent
structure of our integrated firm thus plays an important role for our result.
Dessein, Garicano and Gertner (2008), Alonso, Dessein and Matouschek (2008) and
Rantakari (2008) all investigate the tension between adaptation of two divisions’ actions to
their environment and coordination between the divisions, and ask when decisions should
be centralized or decentralized. In Dessein et al. there is a conflict between communication
and effort provision like in ours. Alonso et al. and Rantakari have a richer communication
structure but no managerial effort; in their models the managers bias towards their own
division is exogenous. In all three papers, the firm’s three-agent structure (one upstream
and two downstream units) is fixed. Our theory endogenizes both firm scope and struc-
ture: integration of the two production units may or may not be optimal, and it may or
may not be optimal to bring in a third player as coordinator.
Internal capital markets: Our theory of resource allocation in firms naturally over-
laps with the finance literature on internal capital markets. A fundamental difference,
however, is that financial capital is typically contractible. If resources in our model were
contractible, integration would be either unnecessary or always optimal, leaving little
room for a theory of firm scope. Indeed, most work on internal capital markets takes
multidivisional firms as given and hence does not run into this problem. We also do not
assume that managers are “empire builders” as most of the literature does (an exception is
Inderst and Klein, 2007). In our model, an empire-building motive emerges endogenously;
it is caused by incentive contracts that place a large weight on individual performance.
We build on Stein (1997) in modeling our production technology, but otherwise our
assumptions are quite different. Stein does not consider effort provision or incentive con-
tracts, and he assumes that headquarters obtains its information through monitoring
(see Gertner, Scharfstein and Stein, 1994). In our model information is communicated
strategically by division managers; strategic communication is the source of the costs
7The same tradeoff was also identified by Povel (1999) and Aghion, Bolton and Fries (1999).
7

of integration. More recent work focuses on agency problems at the division level. In
Scharfstein and Stein (2000), inefficiencies in an internal capital market result from divi-
sion managers’ influence activities. Brusco and Panunzi (2005), Stein (2002), and Inderst
and Laux (2005) extend Stein (1997) by introducing managerial effort.
This literature is inconclusive about the effect of centralized allocation on managerial
incentives. In Brusco and Panunzi (2005), managers are empire-builders, and reallocation
of resources diminishes effort incentives, while in Stein (2002) and Inderst and Laux
(2005), headquarters creates competition through winner-picking, which increases effort
incentives. In our theory, both effects are present, but we can show that if managers can
lie about projects, the information rent effect always cancels, and often dominates, the
competition effect, even when managers are not empire-builders.
Papers that explicitly model division managers’ private information include Ozbas
(2004), Wulf (2005), and Inderst and Klein (2007). In the capital-budgeting literature,
Harris and Raviv (1996, 1998) and Bernardo, Cai and Luo (2001, 2004) are related,
but they are not concerned with divisional competition, and focus on the efficiency of
investment decisions rather than on firm scope.
3 Model
3.1 Setting
Production units and resources: There are two ex ante identical production units, 1
and 2, each with one unit of resources K= 1. The resources are specific and cannot be
obtained in an external market, but each unit’s resource can be usefully employed in the
other unit.8
We assume that the use of resources is not contractible, whereas authority over the
allocation of resources is contractible. This assumption rules out bilateral spot trade
8The logic of our theory does not depend on the initial distribution of resources. We would expect to
obtain very similar results if, say, unit 1 had two units of resources and unit 2 none. This variation would
correspond to the case of an expansion of one firm into a new line of business based on excess supply of
a unique resource, as envisioned by Teece (1982).
8

between the units. Independent firms, therefore, can only use their own resources. In
an integrated firm, resources still cannot be traded, but a single agent can be given the
authority to reallocate them.
Managerial effort, projects, payoffs: Each production unit is run by a manager,
whose job is to create profitable investment opportunities, or projects. Unit i’s manager
chooses between high (ei= 1) or low effort (ei= 0); his choice is unobservable. The
manager’s cost of low effort is zero; the cost of high effort is c > 0. High (low) effort
generates a good project (type θi=G) with probability p(q) and a bad one (type
θi=B) with probability 1 −p(1 −q). Let θ= (θ1, θ2).
Once a project has been created, it requires resources to be carried out. Resources and
project types translate into expected payoffs as in Stein (1997). The resource investment
in any project can be either 1 or 2; a zero investment has a zero return. If ki∈ {1,2}
is invested in a bad project, unit i’s expected payoff ziis ykiwith y2> y1>0. A good
project has an expected payoff of ϕykifor ϕ > 1:
zi(ki, θi) = 




ϕykiif θi= “G”
ykiif θi= “B”
for ki= 1,2.(1)
Departing from Stein, we assume that the production process is noisy. The actual
payoff for each unit, denoted ˜zi, is either µor 0; let ˜z = ( ˜z1,˜z2). The probability of the
event ˜zi=µis given by zi(ki, θi)/µ, where µis assumed to be large enough so that all
zi/µ are less than 1. It follows that zi(ki, θi) is indeed the expected payoff. Introducing
noise with a “full support” property ensures that kior θicannot be inferred from the
observed ˜zi.
We make two assumptions:
Assumption 1 y2> y1> y2/2>0.
Assumption 2 ϕy2>(1 + ϕ)y1.
Assumption 1 states that a project’s payoff is increasing in the resources invested but
with decreasing returns. Hence, given two equally good or bad projects, it is better to
invest 1 in each project than 2 in one of them, and if the projects are unknown but have
9

the same expected quality, it is best to invest the resources equally. Assumption 2 states
that if there is a good and a bad project, it is optimal to invest 2 units in the good project
rather than 1 in each. Hence, project payoffs are supermodular in project quality and
resources, which is the source of the potential benefit from integration. The efficient way
to allocate two units of resources is given by
k∗(θ) = 












k1=k2= 1 if θ1=θ2= “G” or if θ1=θ2= “B”
k1= 2, k2= 0 if θ1=“G” and θ2= “B”
k1= 0, k2= 2 if θ1=“B” and θ2= “G”
(2)
Firm scope and integration: We assume that both with and without integration,
ownership and control are separated: the units’ managers have no wealth of their own to
finance the necessary assets, and investors lack managerial skills (cf. Stein 1997). This
assumption facilitates comparison of the two cases but is not essential.
Our analysis of integration focuses on a CEO structure, in which the two units are
divisions headed by a CEO, who has authority over the units’ pooled resources. We
abstract from any costs, including agency costs, at the CEO level, and therefore assume
that employing the CEO is costless.9This simplification will highlight that there are
limits to integration even if top management pursues value-maximizing actions.
We are interested in integration that is meaningfully different from nonintegration.
Common ownership of the units, as in property-rights theory, is not enough: where own-
ers remain in the background, a change in ownership alone is immaterial to how the
production units are run. Another uninteresting form of integration is one in which the
CEO never intervenes in resource allocation. Integration then does not entail any costs,
but does not produce any benefits either. For these reasons, we focus on a structure in
which the CEO “selectively intervenes” by reallocating resources with positive probability.
We assume that the choice of firm scope and organizational architecture (allocation
of decision rights and incentive contracts) is a long-term choice. This means that firm
scope cannot be changed or decision rights over resources traded after project types are
9If the CEO of an integrated firm were also its owner, nothing would change in our model. If
independent firms were run by owner-managers, the analysis would be slightly different but the results
still largely the same; see Footnote 15 below.
10

realized. Otherwise, resources could always be allocated optimally without sacrifice in
incentives. The reason for why firms’ scope decisions typically involve tradeoffs is that
they are irreversible in the short run.
Managers’ preferences: Managers are risk-neutral but protected by limited liability.
Without loss of generality, we assume they have zero wealth; wages must therefore be
non-negative. The utility of a manager is given by Ui(wi, ei) = wi−cei, where wiis the
monetary wage and cei∈ {0, c}the disutility of effort. No direct utility is derived from
the allocation of resources or payoffs. We assume that reservation wages are low enough
such that in equilibrium, participation constraints are not binding.
Incentive Contracts: For simplicity, we restrict the analysis to contracts that are
symmetric for both managers. Managers’ wages can depend on both production units’
realized payoffs ˜z1and ˜z2. However, they cannot depend on the use of resources because
the use of resources is not contractible in general. Moreover, following Crawford and Sobel
(1982) and Dessein (2002), we assume that the managers’ communication is cheap talk,
which rules out message-contingent contracts. To understand the role of this assumption,
we examine message-contingent contracts as a benchmark case in Section 4.3.
With two possible payoffs for each unit, there are four possible outcomes. General
performance-based contracts can therefore be described by a quadruple of wages. We
derive results for this general case in a Web-Appendix and summarize them below. The
main results are the same and the exposition much simpler if we restrict attention to
contracts that are separable in the divisions’ payoffs, i.e.:
˜wi( ˜z1,˜z2) = α+β˜zi+γ˜zjfor i= 1,2 and j6=i.
Expected wages are then given by wi(z1, z2) = α+βzi+γzj.10 With a non-binding
participation constraint, the limited-liability constraint must be binding when contracts
are optimal. Since the ˜ziare either zero or positive, αshould be set to zero, which implies
that βand γmust be nonnegative. Optimal contracts are then completely characterized
by the parameters βand γ.
10We refer to βand γas “bonuses” since the ˜ziare binary, but technically βand γare shares of the
units’ payoffs, akin to piece rates.
11

3.2 Independent Firms
When the two units are independent firms, each firm’s resource investment kiis con-
strained by ki≤1. The timing of events is as follows:
1. The owner of firm ioffers her manager a wage contract, which he accepts or rejects.
2. Manager iexerts effort ei∈ {0,1}, and then learns the profitability of his project
θi∈ {G, B}, which is his private information.
3. Manager iinvests ki= 1 in his project.
4. The payoff ˜ziis realized, and the manager is paid according to the contract.
It is optimal for firm i’s owner to give the manager authority over resources, since
it is optimal to invest at least one unit of resources, which the manager will do if given
nonnegative incentives based on ˜zi. To induce low effort, the owner pays the manager
his reservation wage. To induce high effort, firm ican pay the manager a bonus β≥0
(expressed as a share of the payoff) if ˜zi=µ. Firm icould pay for firm j’s output ˜zjas
well, but has no reason to do so as ˜zjcontains no information about manager i’s effort.11
The optimal contract that induces firm i’s manager to exert high effort solves the problem
max
β(1 −β)Eθi[zi(1, θi)|ei= 1] s.t.
(IC-ei)βEθi[zi(1, θi)|ei= 1] −c≥βEθi[zi(1, θi)|ei= 0],
(LL) β≥0.(3)
3.3 Integrated Firm
In the integrated firm, there is only a joint resource constraint k1+k2≤2, ki∈ {0,1,2}.
The CEO allocates the resources to maximize the firm’s profit net of wages, but is initially
uninformed about the division’s projects. Stage 3 of the timing is as follows:
3a. The division managers simultaneously send costless and unverifiable messages b
θi
about their projects to the CEO. Let b
θ= (b
θ1,b
θ2).
11 Once again, the manager’s actual wage is β˜zi∈ {0, β µ}; the expected wage then is βzi.
12

3b. The CEO allocates resources to the two divisions, subject to the constraint k1+k2≤2
and ki∈ {0,1,2}.
Since resources are not contractible, the CEO cannot commit himself to any allocation
rule ex ante, and instead allocates resources ex post. The CEO’s response to the managers’
messages thus becomes part of the contracting problem.
Inducing low effort only requires paying the managers their reservation wage. As
a byproduct, managers communicate truthfully because with a flat wage, they have no
reason to misrepresent their projects. Inducing high effort and truthtelling, however,
requires several incentive constraints to be satisfied. Below, we state the owner’s opti-
mization problem for an unspecified set of feasible contracts C. In subsequent sections, we
solve this problem for different assumptions about C. For any contract ζ∈C, denote by
¯wi(θ, b
θ, ζ ) manager i’s expected wage at stage 3a of the game if his project is of type θand
he reports type b
θ, under the assumptions that manager jexerts high effort and reports
his type truthfully, and that the CEO allocates resources optimally given his information.
Wherever no confusion can arise, we will suppress the argument ζ. The firm’s optimal
contract inducing high effort, truthtelling, and an ex-post optimal allocation of resources
by the CEO, then solves the following problem:
max
ζ,e1,e2,b
θ1,b
θ2,k1,k2
Eθ{[z1(k1, θ1)+z2(k2, θ2)]−¯w1(θ1, θ1, ζ)−¯w2(θ2, θ2, ζ)|e1=e2= 1}s.t.
(IC-e) p¯wi(G, G, ζ ) + (1 −p) ¯wi(B, B, ζ )−c
≥q¯wi(G, G, ζ ) + (1 −q) ¯wi(B, B, ζ ) for i= 1,2
(IC-G) ¯wi(G, G, ζ )≥¯wi(G, B, ζ) for i= 1,2
(IC-B) ¯wi(B , B, ζ)≥¯wi(B , G, ζ) for i= 1,2
(RA) k= arg max
k0
1,k0
2
[z1(k0
1, θ1) + z2(k0
2, θ2)−E[ ˜w1(˜z|k0
1, θ1), ζ]−E[ ˜w2(˜z|k0
2, θ2), ζ]
s.t. k1+k2≤2, ki∈ {0,1,2}
(LL) ˜wi(˜z|ki, θi, ζ )≥0 for i= 1,2.(4)
Condition (IC-e) is the effort incentive constraint of manager i, (IC-G) and (IC-B) ensure
that manager ireports his project type truthfully, and (RA) states that the CEO allocates
13

resources to maximize the firm’s net profit. As we will see, with separable incentive
contracts the constraint (RA) automatically leads to the implementation of the efficient
allocation rule k∗.
Asymmetric contracts can come in two forms, contracts that induce both managers to
exert high effort but only induce one of them to communicate truthfully, and contracts
that induce only one manager to exert high effort. For both kinds of contracts, there are
several cases to distinguish because the CEO’s optimal resource allocation now depends
on the values of pand ϕ. For some parameters, asymmetric contracts may dominate
symmetric contracts, but this possibility is most likely an artifact of the binary structure
of the model and might well vanish in a model with continuous types and effort levels.
At any rate, a formal analysis of asymmetric contracts is unlikely to add much economic
insight, and is hence omitted.
4 Benefits and Costs of Integration
We solve the model stepwise. In Section 4.1, we determine the optimal bonus for an
independent firm; in 4.2 we identify the competition effect in an integrated firm with
symmetric information about the quality of projects. Section 4.3 studies the general case
of private information about projects, and 4.4 the main model with cheap talk.
4.1 Independent Firms
Determining each firm’s optimal incentive contract for its manager is straightforward:
Lemma 1 With independent firms, the optimal contract for each division manager that
leads to high effort is given by
βni =c
(p−q)(ϕ−1)y1
and γni = 0.(5)
For all proofs, see the Appendix.
The optimal bonus for own output, βni, is increasing in the cost of effort c, and
decreasing in the marginal effectiveness of effort in generating a good project (p−q)
14

and in the difference in the marginal profitabilities between a good and a bad project
((ϕ−1)y1). The optimal contract is the same in the general case where non-separable
contracts are feasible.
For the agency problem to be relevant, high effort must be optimal under first-best
conditions. The comparison between integration and non-integration is most interesting
if in addition high effort is optimal under second-best conditions in independent firms.
Otherwise, an integrated firm could induce low effort and truthtelling for the same flat
wage as an independent firm, in which case integration would be strictly optimal because
of its better use of resources. If the reservation wage of the division managers is zero, the
relevant condition is the following:
Lemma 2 With a zero reservation wage, the contract of Lemma 1 is optimal if
(p−q)2(ϕ−1)2y1
p(ϕ−1) + 1 > c. (6)
4.2 The Competition Effect of Integration on Incentives
Suppose that the CEO can perfectly observe the project types θi, while effort remains
unobservable.
Proposition 1 In an integrated firm in which the CEO has perfect information about θ,
the optimal separable contract for each division manager is given by
βpi =c
(p−q)[(1 −p)(ϕy2−y1) + pϕy1]and γpi = 0,
where βpi < βni.
For similar results, see Stein (2002), Inderst and Laux (2005) and Marino and Zabojnik
(2004). The last term in the denominator of βpi is the expected incremental value (say,
from manager 1’s perspective) of having a good project: with probability 1 −p, division
2 has a bad project, in which case division 1’s output is ϕy2if the project is good and y1
if it is bad. With probability p, division 2 has a good project and gets all resources, in
which case division 1’s output is ϕy1if its project is good but 0 if it is bad.
15

Most importantly, βpi < βni, which means that with perfect information, the managers
have better incentives than in independent firms because effort is less costly to induce.
This competition effect of centralized resource allocation is driven by the supermodularity
of resources and project quality: under integration, the expected amount of resources
is larger than 1 for a good project and less than 1 for a bad project, whereas in an
independent firm the resource investment always equals 1. Since managers are rewarded
for division performance, which depends on the resources invested, creating a good project
becomes more valuable to managers in an integrated firm.
4.3 Competition vs. Information Rents: a General Result
When the division managers have private information, the competition effect is coun-
terbalanced by an information-rent effect: getting a manager to reveal that his project
is bad requires rewarding him in some way, which reduces the spread in the manager’s
payoff between a good and a bad project, and thus undermines the incentives for effort
(see Levitt and Snyder, 1997).
Because of the countervailing effects, it is a priori unclear whether centralized re-
source allocation with privately informed division managers leads to higher or lower wage
costs. Our first main result shows that under very general contracting assumptions, the
information-rent dominates at least weakly:
Proposition 2 Any contract that induces truthtelling must lead to a wage bill at least
as high as that under non-integration. The wage bill is strictly higher than under non-
integration whenever ϕ¯w1(B, G)>¯w1(G, G).
What drives this result is that the expected wage ¯w1(B, G) of a manager with a bad
project who claims his project is good is at least 1/ϕ times the expected wage ¯w1(G, G) of
a manager whose project is good. This relation holds because the managers have different
project qualities but receive the same amount of resources. It follows that their expected
division payoffs and hence their variable wages differ by the factor ϕexactly. Any other
portions of their wages, for instance based on the other division’s payoff, must be the
same. Overall, therefore, the relation between their total wages is a weak inequality. This
16

relation, combined with the incentive constraints for truthtelling and effort provision, then
implies that the firm pays the managers at least as much under integration with truthful
upward communication as they receive in non-integrated firms.
Proposition 2 thus sheds light on the interaction of two opposite effects identified in
the literature: we know from Stein (2002) and others that competition for resources can
have a positive effect on incentives, and we know from Levitt and Snyder (1997) and
Dessein et al. (2008) that inducing truthful communication can have a negative effect on
incentives. In our framework, in which both effects are present, the latter always weakly
dominates the former.
The next result shows that if either messages or the use of resources are contractible,
the benefits of integration can be attained without any additional cost. These are cases
in which the condition ¯w1(B, G)≥1
ϕ¯w1(G, G) identified above can hold with equality.
Proposition 3 Let
w0=c[y2−y1+p(2y1−y2)]
p(p−q)(ϕ−1)[py1+ (1 −p)y2]and βcm =c
(p−q)(ϕ−1)[py1+ (1 −p)y2].
(a) If the managers’ messages are contractible and cis not too large, a contract that pays
w0to a manager who reports B while the other reports G, and pays a share βcm of realized
division payoff otherwise, is optimal.
(b) If resources are contractible and cis not too large, a contract that pays w0to a
manager who does not receive any resources, and pays a share βcm of realized division
payoff otherwise, is optimal.
In both cases, the resulting expected total wages are the same as under non-integration.
Like in Proposition 1, the bonus βcm (for “contractible message”) is smaller than that
required under non-integration, which reflects the more efficient use of resources: instead
of y1as in (5), βcm contains the term py1+ (1 −p)y2> y1in the denominator, which is
the expected amount of resources for a division with a good project.
Part (a) implies that when messages are contractible, integration is always optimal
since the benefits of integration can be realized without any increase in wage costs. In
this case, the agency costs of aggregating dispersed information are fully canceled by the
agency benefit of creating competition for resources.
17

Part (b) implies that when the use of resources is contractible, integration is un-
necessary because the contract of Proposition 3 can be implemented even under non-
integration. Specifically, the owners can first have their managers report project qualities,
then trade resources if doing so is efficient, and then pay the managers according to the
final resource allocation and realized outcomes. It is because of this result that capital
is not the kind of resource that motivates integration decisions under our informational
assumptions, as we claimed in Section 2.
The constraint on cin the proposition is necessary for high effort, truthtelling and an
efficient resource allocation to be feasible at all. For if cis “too large”, βas stated is so
high that the CEO, concerned with maximizing profit net of wages, would deliberately
misallocate resources to save on wages. Integration with efficient resource allocation would
then be feasible only with low managerial effort.
4.4 Integration with Strategic Information Transmission
When the managers’ communication is cheap talk, only performance-based contracts are
feasible. Inducing truthful communication then requires a form of team incentives:
Lemma 3 For any contract (β, γ ), and assuming the CEO believes that the division man-
agers’ reports are truthful and allocates the firm’s resources according to k∗, a manager
with a bad project has an incentive to report his type truthfully if and only if
γ
β≥(1 −p)(y2−y1) + py1
(1 −p)y1+pϕ(y2−y1)∈(0,1).(7)
The numerator on the right-hand side of (7) reflects a manager’s (say, 1’s) gain from
lying, assuming that manager 2 communicates truthfully: with probability 1−p, manager
1 gets two instead of one unit of resources, and with probability phe gets one unit instead
of no resources. The denominator reflects division 2’s expected benefit from manager 1’s
telling the truth if his project is bad, which in turn benefits manager 1 through the bonus
γ: with probability (1 −p), division 2 has a bad project and gets one unit instead of one,
and with probability p, it has a good project and gets two units instead of one.
Condition (7) implies that individual incentives alone (i.e. β > 0 and γ= 0) can never
elicit truthful reports; a manager with a bad project always has an incentive to claim
18

that his project is good. Pay for performance endogenously generates “empire-building”
behavior, even though the managers do not derive any intrinsic utility from the resources
they receive. Combining the truthtelling constraint of Lemma 3 with each manager’s
effort incentive constraint leads to the second main result of this section:
Proposition 4 In an integrated firm, the optimal contract that leads to high effort, truth-
ful reports about projects, and an efficient resource allocation, is given by
βint =c
(p−q)(ϕ−1)[(1 −p)y2+py1]and (8)
γint =c[p(2y1−y2) + y2−y1]
(p−q)(ϕ−1)[(1 −p)y2+py1][pϕ(y2−y1) + (1 −p)y1],(9)
where βint ∈(βpi, βni )and γint >0. The expected wage per agent is strictly higher than
under non-integration.
Note that βint =βcm, whereas γint /βint is simply the ratio given in (7). Even when
neither messages nor resources are contractible, the firm can get a manager with a bad
project to communicate truthfully by rewarding him for the other division’s output (or
equivalently, the firm’s profit). That way, the manager participates in the potential gain
from shifting resources to the other division.
Propositions 1 and 4 and Lemma 3 are illustrated in Figure 1. Lemma 3 characterizes a
cone (shaded in light gray) in which γ/β must lie to induce truthful reports about project
types. The lower border of the cone is the lower bound stated in Lemma 3; the upper
border is given by a corresponding condition for a manager with a good project to tell the
truth, which in equilibrium is not binding. Under non-integration, the optimal contract
is given by (βni, γni ); the incentive constraint for effort (not depicted) is a vertical line
through that point. Under integration, the effort incentive constraint changes to the line
IC-e which represents (4). Combinations of βand γthat induce high effort (conditional
on truthtelling) are shown as the medium-gray shaded area to the right of IC-e.
The line IC-e lies to the left of the effort constraint under non-integration because of
the competition effect. With perfect information, the profit-maximizing contract is then
(βpi, γpi). With strategic communication, the contract must lie in the dark-shaded area
in order to satisfy both effort and truthtelling constraints. The profit-maximizing point
19

Figure 1: Truthtelling constraints (IC-B) and (IC-G) and effort incentive constraints
(IC-e) as functions of βand γ.
is (βint, γint) and lies on the IC-e curve to the northeast of (βpi, γpi). The bonus βint
exceeds βpi because manager i’s effort has a negative effect on zj. Rewarding manager
ifor division j’s performance therefore reduces his incentives to exert effort. Thus, if
γ > 0 is required to induce truthtelling, βmust also be raised above βpi to maintain effort
incentives.
The dashed line represents an isoprofit curve with a slope of −1 (assuming high effort
and truthtelling at each point); the lower the curve, the higher the profit. The isocurves
for expected wages look the same but are ordered in the opposite direction. As depicted,
βint is lower than the bonus βni under non-integration, but having to pay γint >0 to
induce truthtelling leads to an expected wage bill for the firm that is strictly higher than
under non-integration. In other words, the competition effect of centralized coordination
on the managers’ incentives is outweighed by the information-rent effect.
20

In this discussion we implicitly assumed that the CEO’s resource allocation decision
(RA) in (4) leads to the efficient allocation k∗. With separable contracts, that is indeed
the case because the firm’s net profit is 1 −β−γtimes expected total payoff, which means
that maximizing net profit and expected output are equivalent (in equilibrium, β+γ < 1).
To conclude, inducing high effort and truthtelling in general requires higher wages
than are needed in independent firms. Alternatively, the integrated firm could pay a
constant wage that induces low effort, which may be optimal even if high effort is optimal
in independent firms. In a model with continuous instead of binary effort, a higher cost
of inducing effort would result in weaker incentives, i.e. a lower reward for a high payoff.12
Results with general contracts. General, non-separable contracts can be charac-
terized by (β, γ, δ), where manager igets paid β(as before, as a share of µ) if only ˜zi=µ,
γif only ˜zj=µ, and δif both units have a high payoff (it is still optimal to pay zero if
neither does). In the general case the CEO’s resource allocation does not automatically
lead to an efficient allocation. If δis too large, the CEO would want to allocate the
resources to one division to prevent an outcome in which both units have high payoff. If
βis large but δsmall, the CEO would want to allocate the resources equally to maximize
the probability that both divisions have a high payoff rather than only one.
There are two main cases to distinguish; see the Web-Appendix for details. If p <
1/(1 + ϕ), then δhas a positive effect on the truthtelling constraint of a manager with a
bad project. It is then possible to induce high effort and truthtelling by setting βand δ
large enough while setting γ= 0. This solution is optimal as long as the CEO does not
misallocate resources, which means that cmust be sufficiently small. With γ= 0, it is not
necessary to pay a manager whose unit does not produce. Consequently, the managers’
information can be elicited without additional cost, implying that integration is always
12 We have studied a variant of our model in which effort is continuous. For the model to be tractable,
we then need to assume that the project qualities are exogenous rather than determined by effort, and
that payoffs depend additively on project quality and effort. In that modified model, our conjecture above
indeed holds; the reward for a high payoff is always lower under integration than under non-integration.
Although this result is appealing, the modified model leads to less rich implications than our main model
because with exogenous project qualities there is no competition effect.
21

optimal, cf. the discussion in Section 4.3.
If p > 1/(1+ϕ), then δhas a negative effect on the truthtelling constraint of a manager
with a bad project. Inducing truthtelling then requires setting γ > 0, and the resulting
wage bill is strictly higher than under non-integration, like in Proposition 4. The wage
bill is also strictly higher than under non-integration if pis small but cis too large.
5 Optimal Firm Scope
In a market for ownership of the production units, the organizational form that emerges
in equilibrium is the one that maximizes total firm value. The value of an independent
firm is its expected payoff minus the manager’s wage. The value of the integrated firm
equals the expected total payoff minus the division managers’ wages.13
Recall from Section 4.1 that non-integration with low effort is strictly dominated by
integration with low effort. This leaves three solutions that can be optimal:
1. Integration with high effort and truthtelling according to Proposition 4,
2. Integration with low effort (β=γ= 0) and truthtelling,
3. Non-integration with high effort according to Lemma 1.
Proposition 5 (a) For any given y1,y2,ϕ,q, and µ, there exists p0<1such that
non-integration with high effort dominates integration with high effort for all p>p0.
Moreover, for any given y1,y2,ϕ,q,µ, and large enough ϕ, non-integration with high
effort dominates integration with low effort.
(b) For any given y1,y2,p,q, and µ, there exists ϕ0>1such that integration with
high effort is optimal for all ϕ > ϕ0.
13 The rents that the managers receive are not to be included in the firm value. If they were (amounting
to calculating a stakeholder value), integration would always be strictly optimal since total surplus can
only increase when resource allocation is improved while effort is held at a high level. But that would
also amount to assuming away agency problems, since the tradeoff between efficiency and rent extraction
is the essence of any agency problem when agents have limited liability.
22

(c) For any given y1,ϕ,p,q, and µ, if integration with high or low effort dominates
non-integration for some y2∈(y1,2), then the same is true for all y0
2> y2.
Proposition 5 is illustrated in Figure 2.14 15 The dashed line is the set of (p, ϕ) pairs
for which condition (6) holds with equality, that is, where high and low effort lead to
equal profits under non-integration. It is downward-sloping because high effort is better
the larger the resulting probability of having a good project (p), or its value (ϕ).
Below the dashed line, low effort is optimal under non-integration; it follows that
integration with low effort strictly dominates. By continuity, the same holds over some
range of pand ϕabove the dashed line, where high effort is optimal under non-integration.
As pincreases, eventually non-integration with high effort becomes optimal, see part
(a) of Proposition 5 and the light-gray area in Figure 2. This is obvious in comparison
with integration with low effort, because the value of providing incentives for high ef-
fort increases with p. Compared with integration and high effort, too, non-integration
eventually dominates: as papproaches 1, both managers likely have a good project, and
the benefit from redistributing resources under integration shrinks to zero. The costs of
integration, however, remain because γ/β must be strictly positive to induce truthtelling,
and γmust be paid whenever the “other” division has a high payoff.16
14 The figure is based on plot obtained by fixing q= 0.2, y1= 1.01, y2= 1.9, and c= 0.2, and letting
pvary between .5 and 1, and ϕbetween 1.5 and 3.
15 The separation of ownership and control is not essential for our story. Suppose that under non-
integration both units are run by owner-managers. Then integration is optimal if the resulting profit
exceeds the owner-managers’ total profits, which equals expected output minus the cost of effort. If
upon integration, the owner-managers are employed as division managers, then, somewhat paradoxically,
integration is always optimal. This is because the owner-managers can be paid off with the rents they
receive as agents of the integrated firm (if necessary, by adding a salary to the total wage). The owner
then has no agency costs of integration to bear, and can pocket the full difference in total surplus
between integration and non-integration as profit. If in contrast the owner of the integrated firm hires
new managers, she must pay for their wages on top of paying off the previous owners. Integration can
still be optimal as long as the benefit from centralized resource allocation is large enough. Replicating
the analysis above for this case leads to qualitatively the same results as are depicted in Figure 2.
16 Figure 2 suggests that whether non-integration or integration is optimal depends monotonically on
pand ϕ, whereas parts (a) and (b) of Proposition 5 only express limit results. All of our numerical
23

Figure 2: Optimal organizational form as function of pand ϕ. Light gray: non-integration;
medium gray: integration with low effort; dark gray: integration with high effort
As ϕincreases, integration with high effort becomes optimal, as depicted by the dark-
gray area in Figure 2. Intuitively, it eventually dominates integration with low effort
because the more valuable good projects are, the important are incentives to create them.
Integration with high effort also eventually dominates non-integration: the integrated
firm benefits from moving all resources to one division only when the divisions’ projects
are of different quality. The benefit is proportional to ϕy2−(1 + ϕ)y1, which is positive
according to Assumption 2, and increasing in ϕ.17
Not depicted in Figure 2 is part (c) of Proposition 5: integration is more likely the
larger y2. This is intuitive since y2is the expected payoff of investing all resources in one
simulations point to monotonic relations, but we have been unable to prove them generally.
17 With continuous effort, the high- and low-effort regions for integration would merge into one region.
Incentives would be weaker than under non-integration but would still vary with pand ϕfor the reasons
described above.
24

project, which is possible only under integration.
Predictions: Our results lead to several testable predictions: First, y2is a measure
of “relatedness” of the two divisions, since it measures the value of using one division’s
resources in the other division. Proposition 5 part (c) then implies that integration is
more likely the more related the two production units are. This is consistent with a large
literature, beginning with Montgomery and Wernerfelt (1988), that documents that more
widely diversified firms tend to be less highly valued.18
Second, ϕmeasures the profitability difference between good and bad projects and
therefore measures the variability of the divisions’ payoffs. Proposition 5 then implies
that the more variable profits in the production units are, the more likely they are to
be integrated, because a greater variability raises the benefit of shifting resources to the
most profitable projects. Moreover, it is straightforward to establish, using (8), that βint,
γint and γint/βint are all decreasing in ϕ. Conditional on integration, both total wages
and the relative weight on firm-based incentives are thus decreasing in the variability of
division profits.19
Third, recall from Propositions 2 and 4 that integration with high effort entails addi-
tional agency costs if communication is cheap talk but not if message-contingent contracts
are feasible. Integration is hence more likely the easier it is to hold managers accountable
for their claims about their investment opportunities. While explicit message-contingent
contracts are rare, reputational concerns ensure that talk is not always cheap.
18 As Stein (1997) observes, focusing on the correlation of project qualities instead of the comple-
mentarity of resources leads to the opposite prediction: the higher the correlation, the more likely the
divisions have the same quality of project, and hence the lower the benefit from being able to reallocate
resources between the divisions. While this is in principle an interesting prediction, it is doubtful on a
priori grounds that the correlation of project qualities is a useful measure of relatedness of two businesses.
It would require that whether people in different divisions have a good idea at the same time depends
largely on the nature of the business, which is a difficult case to make.
19 More precisely, if manager iis paid based on individual and total firm profit according to w=
β0˜zi+γ0( ˜zi+ ˜zj), then according to (8) it is optimal to set γ0=γand β0=β−γ, and the relative weight
on firm-based incentives is γ0/β0= 1/(β/γ −1), which is decreasing in ϕwhenever γ/β is.
25

6 Optimal Structure of the Integrated Firm
We have assumed that the integrated firm is a pyramidal hierarchy with a CEO. Here,
we compare the CEO hierarchy with two structures that do not require a CEO: a skewed
hierarchy in which one of manager allocates the firm’s resources in addition to running a
division, and horizontal exchange where each manager retains authority over his resources
but can lend them to the other division.20
We continue to focus on the managers’ incentive constraints because the role of their
participation constraints seems straightforward: switching from a CEO hierarchy to one
of the structures studied below might lead to tighter incentive constraints and to higher
wage costs for the firm. If the managers earn rents as a result, the firm can offset the wage
increase by reducing their salaries, unless salaries are already at zero and constrained by
limited liability.
Skewed hierarchy: We allow for the managers’ contracts to be different since their
jobs are now different. The modified timing of events is as follows:
1. The firm’s owner offers each manager ia contract (βi, γi), which he accepts or rejects.
2. The managers simultaneously exert effort ei∈ {0,1}. Each manager then learns the
profitability of his project θi∈ {G, B}, which is his private information.
3. Manager 2 sends a costless and unverifiable message b
θ2about θ2to manager 1.
4. Manager 1 allocates resources subject to the constraint k1+k2≤2 and ki∈ {0,1,2}.
5. The payoffs ˜z1and ˜z2are realized, and the managers are compensated.
As before, we look at contracts that lead to high effort and an efficient resource
allocation. For manager 2, nothing changes: if manager 1 exerts high effort and allocates
resources efficiently, manager 2’s effort and truthtelling constraints are the same as before;
hence his optimal wage contract is given by Proposition 4. Manager 1’s effort incentive
constraint remains unchanged, too, provided that manager 2 exerts high effort and reports
truthfully, and that manager 1 himself allocates resources efficiently at stage 4 of the game.
20 We would like to thank Niko Matouschek for suggesting this second solution.
26

The only difference is that instead of a truthtelling constraint, manager 1 must now be
given incentives to allocate resources efficiently. There are two constraints: one ensures
that manager 1 distributes the resources equally if both divisions’ projects are equally
good or bad, instead of allocating all to his own division. The other condition ensures
that he allocates all resources to division 2 if it has a good project and division 1 a bad
one. Both conditions lead to lower bounds on γ/β. We can then show the following.
Proposition 6 Assume that the owner of an integrated firm wants to induce high effort
and an efficient resource allocation. Then the incentive constraints in the skewed hierarchy
are unambiguously more restrictive than those in the CEO hierarchy.
With general contracts the result is the same; see the Web-Appendix. The intuition
rests on an equivalence between lying to the CEO in one structure and misallocating
resources in the other. Suppose that in the skewed hierarchy, manager 1 has a bad
project and learns that manager 2 has a good project. Manager 1 then allocates resources
efficiently if he is better off giving all resources to division 2 rather than dividing the
resources equally. The equivalent situation in the CEO hierarchy is a manager 1 with a
bad project who — contrary to our assumptions — happens to know that manager 2 has
a good project.
Since the outcomes in each structure are the same, the relevant constraints for manager
1 are the same too; this also holds when manager 2 has a bad project. The difference
is that in the CEO hierarchy, manager 1 reports his type without knowing manager 2’s,
while in the skewed hierarchy, manager 1 allocates resources after learning 2’s project type.
The truthtelling constraint in the CEO hierarchy is strictly less restrictive because it is a
weighted average of the two resource-allocation constraints in the skewed hierarchy.21
21 We believe that Proposition 6 is not specific to our binary model setup but quite general. First, the
arguments above should apply to more general type spaces, since what drives the result is the difference
in the timing between the two organizational structures rather than the binary project types. Second,
in a model with continuous effort, we would expect the owner to offer weaker incentives to manager
1 than to manager 2 because his resource allocation incentive constraints are more difficult to satisfy
than the corresponding truthtelling constraint in the firm with CEO. But these more restrictive incentive
constraints are what drives Proposition 6; the precise characteristics of the resulting optimal contracts
27

The logic of Proposition 6 is reminiscent of Dewatripont and Tirole (1999). In our
model the tasks of running a division and of allocating the firm’s resources are not directly
opposed (unlike, for instance, prosecution and defense), but are sufficiently misaligned to
warrant separation into two jobs. This result is driven by the interaction with a third
agent (manager 2), an effect that is absent in Dewatripont and Tirole.
Horizontal exchange: Here, each manager retains authority of his division’s re-
sources. The timing in this case differs from the previous one only in stages 3 and 4:
3. Each manager isends a costless, unverifiable message b
θito manager j6=i.
4. Each manager ican either use division i’s resources in his own division, or lend
them to division j6=i.
Recall that the use of resources is not contractible, which rules out bilateral trade in-
volving direct transfer payments. It does not, however, prevent a manager from providing
resources under his authority to the other division voluntarily.
Horizontal exchange may or may not constitute a case of integration. It is efficient
for (say) manager 1 to lend his resources to division 2 if and only if division 1 has a bad
project and division 2 a good one. For him to do so voluntarily, however, requires a wage
contract that allows him to participate in division 2’s performance, and thus requires some
form of profit sharing between the two production units. Some firms may be able to share
revenues and use team-based incentives while remaining independent, akin to forming a
joint venture. In other cases, formal integration may be necessary.
The conditions for inducing high effort and an efficient resource allocation are very
similar to those of the CEO hierarchy; the next result states when they differ:
Proposition 7 Assume the integrated firm’s owner wants to induce high effort and an
efficient allocation of resources under horizontal exchange. If ϕ≥y2
1/(y2−y1)2, then
the optimal contract for each manager is given by Proposition 4. If ϕ<y2
1/(y2−y1)2,
are secondary.
28

then the incentive constraints are unambiguously more restrictive than those in the CEO
hierarchy.22 23
Proposition 7 states that for large enough ϕ, the incentive-related costs at the division
level are the same as in the CEO hierarchy.
If hiring a CEO is costless, the CEO structure and horizontal exchange are both
optimal (with positive costs, horizontal exchange would dominate). For smaller ϕ, the
CEO hierarchy is strictly optimal.
With zero costs of hiring a CEO, the CEO structure and horizontal exchange are both
optimal (horizontal exchange would dominate if there were costs associated with a CEO).
For smaller ϕ, the CEO hierarchy is strictly optimal in terms of the incentive constraints
involved.
The intuition for Proposition 7 is very simple, since horizontal exchange differs from
the CEO hierarchy only in the constraints that lead to an efficient resource allocation.
That is, assuming that the managers exchange resources efficiently according to k∗, both
managers’ effort and truthtelling incentive constraints are the same as before. Since with
separable contracts the resource allocation constraint (RA) always leads to k∗in the CEO
hierarchy, it follows that the wage contract of Proposition 4 is also the optimal contract
to induce high effort and truthtelling under horizontal exchange.
Under horizontal exchange, however, achieving an efficient resource allocation also
requires that a manager with a bad project is willing to lend his resources to the other
division if it has a good project. The relevant constraint may be more or less restrictive
than (IC-B) depending on the magnitude of ϕ. This leads to the case distinction stated in
the proposition. The larger ϕ, the easier it is to get a manager to lend his resources to the
other division since the manager stands to gain from a larger ϕ, and for ϕ≥y2
1/(y2−y1)2
the corresponding incentive constraint no longer binds if (IC-B) must already hold.
Propositions 6 and 7 shed light on why — as emphasized by Chandler — firms are
22Note that Assumption 2 implies a lower bound of y1/(y2−y1) on ϕ, which given Assumption 1 is
less than y2
1/(y2−y1)2.
23As far as we can tell, Proposition 7 extends to the more general non-separable contracts, but we have
not been able to prove this for all possible cases.
29

often structured as pyramidal hierarchies, with a top management that is in charge of
coordinating a firm’s activities but is not directly involved in production. We already
know from Athey and Roberts (2001) that incentive contracts that provide good incentives
for effort can lead to bad incentives for decision-making. A potential solution is to bring in
an unbiased decision maker, but how can he obtain the information needed to make good
decisions? Athey and Roberts assume the decision maker can gather all information at a
fixed cost. In our model, the information must be communicated by division managers,
which introduces a new agency problem. Nevertheless, as Propositions 6 and 7 show, this
solution is (weakly) more efficient than any other arrangement.
Prediction: Proposition 7 implies that decentralized horizontal exchange of resources
is more likely the more closely related the divisions are (larger y2), and the more variable
the division payoffs are (larger ϕ). This prediction is consistent with broad changes in
the way modern firms organize themselves, as described by Roberts (2003, p.2). One
is a trend towards less diversification and an increased focus on a firm’s core strengths;
another is a trend among firms to facilitate horizontal communication and coordination.
An example is the case of BP, which in the course of extensive restructuring efforts in the
1990s introduced “ ‘peer groups’ that linked assets [e.g. oil fields] facing similar technical
and commercial challenges to provide mutual support” (Roberts 2004, p.26 and p.187).
7 Concluding Remarks
We investigated the benefits and costs of integration by focusing on one of the key tasks
of managers, the allocation of resources. We showed that this task is associated with
incentive conflicts that do not exist in non-integrated firms. Our focus has its origins in
the work of Coase, Barnard, Simon, Williamson and others. These authors’ work suggests
that understanding hierarchies, and the role of managers in coordinating others’ actions
or resolving conflicts, is key to understanding firms’ boundaries.
Methodologically, we borrow from both the incentive-system and the property-rights
theories of the firm. But while each theory emphasizes either incentive contracts or control
rights, in ours the two are inseparable, and are part of the same organizational design
30

problem. We add elements that are prominent in much of recent organizational economics
but have been missing in the theory of the firm: the dispersion of information in a firm, the
need to communicate critical information to decision makers, and the resulting incentive
problems involving the agents who possess information.
It may be considered a limitation of our analysis that we do not consider agency
problems between shareholders and top management. Bolton and Scharfstein (1998)
discuss how to integrate these problems into the theory of the firm. It seems intuitive,
however, that there are limits to organization even in the absence of shareholder-manager
conflicts. While the separation of ownership and control creates its own agency problems,
“managerial diseconomies of scale” — a subject of much discussion in economics since at
least the 1930s — most likely also exist in firms that are run by their owners. As we have
seen, focusing the spotlight on agency problems at lower levels in a firm, while assuming
that top management is benevolent, leads to many new insights into this old problem.
Appendix: Proofs
Proof of Lemma 1: Eθi[zi(1, θi)|ei= 1] in (3) is given by pϕy1+ (1 −p)y1, while
Eθi[zi(1, θi)|ei= 0] equals qϕy1+ (1 −q)y1. The manager’s incentive constraint can thus
be rephrased as β(p−q)(ϕ−1)y1≥c. Under an optimal contract, this condition must
be binding, which leads to the bonus βstated in the Lemma.
Proof of Lemma 2: With high effort, firm i’s profit is (1 −βni )[pϕ + 1 −p]y1, with βni
as given by Lemma 1. Low effort only requires paying the reservation wage, if if that is
zero, the resulting profit is [qϕ + 1 −q]y1. It is straightforward to show that the difference
between these two expressions is positive if and only if (6) holds.
Proof of Proposition 1: Under perfect information, if manager 1 has a good project,
then with probability pmanager 2 has a good project as well, and they receive one unit of
resources each. Manager 1 then earns βµ if division 1 has a high payoff and γµ if division
2 does; the probability of each event is ϕy1/µ. With probability 1 −p, manager 2 has a
bad project. All resources are then allocated to division 1, and manager 1 earns βµ with
31

probability ϕy2/µ. Manager 1’s expected wage from having a good project is thus
W(G) = ϕ[p(β+γ)y1+ (1 −p)βy2].(10)
Similarly, if manager 1 has a bad project, then with probability p, manager 2 has a good
one, and all resources go to division 2; whereas with probability 1 −p, manager 2 has a
bad project as well. Manager 1’s expected wage from having a bad project then is
W(B) = pγϕy2+ (1 −p)(β+γ)y1.(11)
These expressions are the same for manager 2, and so each manager exerts high effort if
pW (G) + (1 −p)W(B)−c≥qW (G) + (1 −q)W(B), or equivalently
(p−q){[(1 −p)(ϕy2−y1) + pϕy1]β−[pϕ(y2−y1) + (1 −p)y1]γ} ≥ c. (12)
The coefficient of γin (12) is negative; hence, γhas a negative effect on effort incentives.
Moreover, γclearly enters negatively in the firm’s net profit function. It is therefore
optimal to set γ= 0. The optimal βis then obtained by solving (12) as equality for β,
setting γ= 0. The result is βpi as stated in the Proposition. To show that βpi < βni, we
need to compare (1 −p)[ϕ(y2−y1)−y1] + ϕy1in the denominator of βpi with (ϕ−1)y1
in the denominator of βni in (5). The difference between these two expressions equals
py1+ (1 −p)ϕ(y2−y1), which is positive, proving our claim.
Proof of Proposition 2: The result is derived from three conditions. First, the effort
incentive constraint of (say) manager 1 can be written as
¯w1(G, G)−¯w1(B, B)≥c
p−q.(13)
Second, the truthtelling constraint for a manager 1 with a bad project is given by
¯w1(B, B)≥¯w1(B, G).(14)
The third condition is
ϕ¯
w1(B, G)≥¯
w1(G, G) or ¯w1(B, G)
¯w1(G, G)≥1
ϕ,(15)
32

which is explained in the text. If manager 1 exerts high effort and communicates truthfully,
his expected wage is
p¯w1(G, G) + (1 −p) ¯w1(B, B) = p[ ¯w1(G, G)−¯w1(B, B)] + ¯w1(B, B),(16)
Both (16) and (13) apply in the same way to a non-integrated firm for a manager with a
good and a bad project, respectively. We know that (13) is binding under non-integration
and may or may not be binding under integration. The difference ¯w1(G, G)−¯w1(B, B)
in (16) must therefore be at least as large under integration as under non-integration.
It follows from (16) that whenever ¯w1(B, B) is higher than a bad manager’s expected
wage under non-integration, then the total expected wage payment to manager 1 must
be higher in the integrated firm. That is indeed the case: (15), (14) and (13), applied in
that order, imply that
(ϕ−1) ¯w1(B, B)≥(ϕ−1) ¯w1(B, G)≥ϕ¯w1(B, G)−¯w1(B , B)≥¯w1(G, G)−¯w1(B, B)≥c
p−q,
(17)
and hence ¯w1(B, B )≥c/[(p−q)(ϕ−1)] = βniy1(cf. (5)), which is the expected wage in a
non-integrated firm. It is also clear from (17) that whenever ϕ¯w1(B, G)>¯w1(G, G), then
wage bill under integration must strictly exceed the wage bill under non-integration.
Proof of Proposition 3: Our proof covers both cases (a) and (b). Consider first manager
1’s incentive to choose high effort, assuming that manager 2 does too. Manager 1 gets at
least one unit of resources if his project is good or if both managers have a bad project.
In each case, he receives a share βof his division payoff. If manager 1 has a bad project
and manager 2 a good one, he receives w0. Manager 1 then chooses high effort if (cf. 12)
(p−q) [pϕy1β+ (1 −p)ϕy2β−pw0−(1 −p)y1β]≥c. (18)
Next, consider manager 1’s truthtelling incentives. If his project is bad and he tells the
truth and manager 2’s project is good, he is paid w0. Otherwise, he receives a share βof
his allocated resources. Manager 1 then reports truthfully if
pw0+ (1 −p)y1β≥py1β+ (1 −p)y2β. (19)
The expressions for w0and βstated in the proposition are the unique solution of (18)
and (19) as equalities. It is easy to verify that this contract also satisfies the truthtelling
33

constraint for a manager with a good project, which is omitted here. The upper bound
on cis required because for large c,βas stated becomes so large that the CEO would
prefer to misallocate resources in order to save on wage costs.
Under non-integration, the expected wage bill per firm is βni times the expected payoff
[pϕ + (1 −p)]y1, which simplifies to
c[pϕ + (1 −p)]
(p−q)(ϕ−1) .(20)
The expected wage bill per manager in the integrated firm is given by
1
2hp22ϕy1β+ (1 −p)22y1β+ 2p(1 −p) (ϕy2β+w0)i
which after substituting the expressions in the proposition simplifies to (20), i.e. the same
as under non-integration. It follows from Proposition 2 that the contract (w0, β) must be
optimal.
Proof of Lemma 3: For a manager 1 with a bad project, the expected payoff from re-
porting truthfully (assuming that manager 2 does, and that the CEO assumes truthtelling
on part of both managers), is ¯w1(B, B) = W(B) as given by (11). If he reports “G” in-
stead, then with probability p, manager 2 has a good project too, in which case each
division gets one unit of resources. With probability 1 −p, manager 2 has a bad project,
and all resources go to division 1. The resulting expected wage for manager 1 is
¯w1(B, G) = p(β+ϕγ)y1+ (1 −p)βy2.(21)
The truthtelling constraint (IC-B) given by ¯w1(B, B)≥¯w1(B, G) therefore is
{p[ϕ(y2−y1)−y1] + y1}γ≥[p(2y1−y2) + y2−y1]β, (22)
which is equivalent to (7). The difference between the numerator and denominator on
the right-hand side of (7) simplifies to −(1 −p)(2y1−y2)−p[ϕ(y2−y1)−y1]<0, which
means the fraction is smaller than 1 (but positive).
Proof of Proposition 4: The integrated firm’s expected total output is
Zint = 2p2ϕy1+ 2p(1 −p)ϕy2+ 2(1 −p)2y1.(23)
34

The first (last) term in (23) represents the case where both divisions have a good (bad)
project and receive one unit of resources each. The middle term represents the case where
only one division has a good project. The firm’s expected net profit therefore is
2(1 −β−γ)[p2ϕy1+p(1 −p)ϕy2+ (1 −p)2y1].(24)
The optimal separable contract maximizes (24) with respect to βand γ, subject to (i) the
effort incentive constraint (12), (ii) the truthtelling constraints (IC-G) and (IC-B), where
the latter is given by (7), (iii) the constraint (RA) that the CEO allocates resources in an
ex-post optimal way, assuming high effort and truthtelling on part of both managers, and
(iv) nonnegativity constraints β, γ ≥0. This optimization problem is a linear program,
and therefore the optimal solution must be a corner solution.
First of all, assuming the other constraints are satisfied, the constraint (RA) leads to
the implementation of the efficient resource allocation k∗. This follows immediately from
the fact that the firm’s profit is 1 −β−γtimes expected total payoff, which by definition
is maximized if resources are allocated efficiently, cf. the discussion in Section 3.1 on the
role of our parameter constraints. Thus, for β+γ < 1, ex-post profit maximization on
part of the CEO leads to an efficient resource allocation, whereas β+γ > 1 would never
be chosen since the resulting profit would be negative.
The relevant constraints are (IC-e) and (IC-B), whereas (IC-G) is redundant. To see
why, observe first that the effort constraint (12) must be binding, for otherwise truthtelling
would be optimally achieved by setting β=γ= 0, when (12) is clearly violated. Second,
we know from Proposition 1 the solution to the relaxed problem in which (IC-G) and
(IC-B) are not imposed, and from Lemma 3 we know that it does not satisfy (IC-B).
Hence (IC-B) must be binding. Finally, it is intuitive and easy to show that any (β, γ)
satisfying (IC-B) also satisfies (IC-G). The optimal contract is therefore given by solving
(7) and (12) as equalities for βand γ; the solution is stated in the Proposition.
Since both (βpi,0) and (βint, γint) solve (12) with equality and since (12) is increasing
in βand decreasing in γ, it follows that βint > βpi , see Figure 2. That βint < βni follows
because py1+ (1 −p)y2in the denominator of βint is greater than y1in the denominator
of βni, and the expressions are otherwise the same.
35

The firm’s total wage bill is given by β+γtimes Zint according to (23), while the
total wage bill for two independent firms is given by βtimes 2[pϕ + (1 −p)]y1. Upon
substituting (βint, γint) into the wage bill of the integrated firm and βni into that of the
non-integrated firms, the difference between the two simplifies to
2cpϕy1
(p−q)(ϕ−1)
y2−y1+p(2y1−y2)
[py1+ (1 −p)y2][p(ϕ(y2−y1)−y1) + y1],
which under Assumptions 1 and 2 is strictly positive.
Proof of Proposition 5: (a) For p= 1, the expected total payoff of both the noninte-
grated firms (given by 2(pϕ + 1 −p)y1) and the integrated firm with high effort (given by
Zint in (23)) equal 2ϕy1. Moreover, both βni and βint equal c/[(1 −q)(ϕ−1)y1], whereas
γint (and the probability that this bonus is paid) is strictly positive. Thus, for p= 1 the
total profit of the non-integrated firms strictly exceeds the integrated firm’s profit. By
continuity, the same holds for some interval of pclose enough to 1.
Comparing non-integration with integration with low effort, observe that the non-
integration profit is increasing in pwhile the integration profit does not depend on p.
Moreover, for p= 1 the difference between these profits is given by
2ϕÃ1−c
(1 −q)(ϕ−1)y1!−2[(1 −q)2y1+q2ϕy1+q(1 −q)ϕy2].
By Assumption 1, this difference is increasing in ϕand grows without bound with ϕ,
which means it is positive for large enough ϕ. A lower bound to ϕis necessary because
for ϕ→1, Condition (6) is violated, in which case we know integration with low effort
dominates non-integration.
(b) First, compare integration with high vs. low effort. The difference between the
expected payoff Zint minus the analogous expression in (23) (with qinstead of p) is
positive and increases without bound with ϕ. This can be seen from the derivative
2(p−q)[y2−(p+q)(y2−y1)], which because of Assumption 1 and p+q < 2 is positive.
Moreover, the managers’ total wages, 2(βint +γint ) times Zint, converge to 4cp/(p−q)
as ϕapproaches infinity. It follows that the net profits under integration with high effort
must be larger than with low effort for ϕsufficiently large.
Comparing integration with non-integration, observe that βni,βint and γint converge
to zero as ϕapproaches infinity; the owners’ share of the payoff thus converges to 1 in
36

both cases. The integration payoff eventually exceeds the total non-integration payoff,
which can be seen by comparing limϕ→∞
1
ϕZint = 2p[py1+ (1 −p)y2] and limϕ→∞
1
ϕ2[pϕ +
(1−p)]y1=py1. Since integration with high effort dominates non-integration for ϕ→ ∞,
the same holds by continuity for an interval of ϕabove some threshold value.
(c) The non-integration profits do not depend on y2. All that remains to show is
that an integrated firm’s profit is increasing in y2. Under integration with low effort, the
firm pays the managers a constant and keeps the rest of the expected payoff 2q2ϕy1+
2q(1 −q)ϕy2+ 2(1 −q)2y1, which is increasing in y2. The same is true for Zint under high
effort. Here, the firm keeps only the share (1 −βint −γint) of the payoff, but this share is
increasing in y2too. To see this, consider the sum βint +γint, which can be expressed as
c[y2+p(ϕ−1)(y2−y2)]
(p−q)(ϕ−1)[py1+ (1 −p)y2][y1+p(ϕ(y2−y1)−y1)].
Its derivative with respect to y2has the same sign as
−hp(1 −p)(ϕ−1)(y2−y1)2−(1 −p)(y2
2−y2
1)−py2
1i,
which is negative, implying that the owner’s payoff share 1 −β−γis increasing in y2.
Proof of Proposition 6: As explained in the text, manager 2’s effort and truthtelling
constraints and manager 1’s effort constraint are the same as for the CEO hierarchy. In
place of manager 1’s truthtelling constraint, there are now two constraints to ensure that
manager 1 allocates resources efficiently.
Suppose that manager 1 has a bad project. Then, if manager 2’s project is bad as
well, allocating the resources equally (the efficient choice) leads to an expected wage of
(β1+γ1)y1for manager 1, while allocating all resources to division 1 leads to an expected
wage of β1y2. Manager 1 therefore allocates resources efficiently if
(β1+γ1)y1−β1y2≥0 (25)
or equivalently γ1/β1≥(y2−y1)/y1. If manager 2’s project is good, then allocating
all resources to division 2 (the efficient choice) leads to a payoff of γϕy2for manager 1,
whereas allocating the resources equally instead leads to a wage of (β+ϕγ)y1. Manager
1 therefore allocates resources efficiently if
γ1ϕy2−(β1+γ1)y1≥0 (26)
37

or equivalently γ1/β1≥y1/[ϕ(y2−y1)]. There are more constraints, but all of them are
equivalent to or less restrictive than (25) or (26), and therefore need not be considered.
To prove the proposition, we show that (25) and (26) are jointly more restrictive than
the truthtelling constraint (22) in the CEO structure. This follows simply from the fact
that if we write (22) as follows,
{p[ϕ(y2−y1)−y1] + y1}γ−[p(2y1−y2) + y2−y1]β≥0,
the left-hand side is equal to 1 −ptimes the left-hand side of (25) plus ptimes the left-
hand side of (26), as is easy to verify. Thus, in the skewed hierarchy, the more restrictive
condition of (25) and (26) must hold, whereas in the CEO structure only a weighted
average of the two constraints must hold, which is a strictly weaker constraint.
Proof of Proposition 7: As explained in the text, the effort and truthtelling incentive
constraints (IC-e), (IC-B) and (IC-G) are the same under horizontal exchange as in the
CEO structure. In addition, an efficient allocation of resource requires that a manager
with a bad project lend his resources to the other division if the latter has a good project.
If he does, his payoff is γϕy2, whereas if he keeps his resource his payoff is (β+γϕ)y1. It
follows that he will lend his resources if γ/β ≥y1/[ϕ(y2−y1)]. It is straightforward to
show that this lower bound on γ/β is lower than the lower bound stated in Lemma 3 if
and only if ϕ < y2
1/(y2−y1)2. In this case, the new constraint γ/β ≥y1/[ϕ(y2−y1)] is not
binding given that (IC-B) must hold; and the contract of Proposition 4 remains optimal.
Otherwise, the new constraint is more restrictive than (IC-B), leading to an optimal wage
contract that implies a higher wage bill for the firm than under the CEO structure.
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43

Web-Appendix: General, Non-separable Contracts
General non-separable contracts specify a wage for each realization of (˜z1,˜z2). For a non-
integrated firm, the contract given by Lemma 1 remains optimal, since there is no reason
to condition wage payments on the other firm’s payoff, and since in each firm realized
payoff is only µor zero, requiring only one non-zero wage variable.
In the integrated firm, limited liability and a non-binding participation constraint
implies that it is optimal to pay each manager zero if both divisions have a zero payoff.
The managers’ (symmetric) contracts can then be characterized by the triple (β, γ, δ),
where manager iis paid β(as a share of µ) if only ˜zi=µ,γif only ˜zj=µ, and δ
if both units have a high payoff. Separable incentive contracts are then a special case
corresponding to the restriction δ=β+γ.
As explained in the text, with general contracts it is no longer the case that the
CEO’s ex-post optimal resource allocation automatically leads to the efficient allocation
k∗. Consequently, in the latter case, solving the firm’s program (4) assuming (but not
imposing as constraint) that the CEO implements k∗may lead to wages for which the
CEO would rather misallocate resources in order to save on wage costs. However, the
only way in which integration can possibly improve over nonintegration is through the
ability to shift all resources to one division if its project is good and the other’s bad, while
any other deviation from k1=k2= 1 cannot create any benefit. Our conjecture hence is
that any optimal solution to (4) is also a solution to the same program with the added
constraint that the CEO implements k∗in allocating resources. Propositions 8-10 below
are therefore stated with this additional constraint imposed.
The firm’s expected net profit is µtimes
hp2ϕ2+ (1 −p)2iy2
1
µ2(2 −2δ)+2(1−β−γ)"p2ϕy1
µÃ1−ϕy1
µ!+ (1 −p)2y1
µÃ1−y1
µ!+p(1 −p)ϕy2
µ#.
(27)
This expression is obtained as follows. If both divisions have a high payoff, the firm’s
profit is (2 −2δ)µ. This can occur only if both projects are good or both bad, which leads
to the first term in (27). Otherwise, if only one division has high payoff, the firm’s profit
is (1 −β−γ)µ; cf. the coefficient of the second term in (27). This occurs if each division
1

gets one unit of resources but only one has a high payoff (the first two terms in []-brackets
in (27)), or if only one division has a good project and gets all resources (the last term in
[]-brackets in (27)).
Our first result generalizes Proposition 1:
Proposition 8 In an integrated firm in which the CEO has perfect information about θ
and allocates resources efficiently, the optimal contract for each division manager entails
γ= 0, and the expected total wage bill is lower than under non-integration.
Proof: Under perfect information, if manager 1 has a good project, then with proba-
bility pmanager 2 has a good project as well and each is allocated one unit of resources.
Manager 1 can then earn either δµ,βµ or γµ (with appropriate probabilities), depending
on which of the two divisions has a high payoff. With probability 1 −p, manager 2 has
a bad project, all resources are allocated to division 1, and manager 1 earns βµ with
probability ϕy2/µ. Overall, manager 1’s expected wage from having a good project is
W(G) = (p"ϕ2y2
1
µ2δ+ϕy1
µÃ1−ϕy1
µ!(β+γ)#+ (1 −p)ϕy2
µβ)µ. (28)
If manager 1 has a bad project, then with probability p, manager 2 has a good one, and
all resources go to division 2; whereas with probability 1−p, manager 2 has a bad project
as well. Manager 1’s expected wage from having a bad project then is
(pϕy2
µγ+ (1 −p)"y2
1
µ2δ+y1
µÃ1−y1
µ!(β+γ)#)µ. (29)
By symmetry, these expressions are the same for manager 2, and so each manager will
exert high effort if pW (G) + (1 −p)W(B)−c≥qW (G) + (1 −q)W(B), or equivalently,
(p−q)(³pϕ2−1 + p´y2
1
µδ+"(1 −p)Ãϕy2−y1Ã1−y1
µ!!+pϕy1Ã1−ϕy1
µ!#β
−"pϕ Ãy2−y1Ã1−ϕy1
µ!!+ (1 −p)y1Ã1−y1
µ!#γ)≥c. (30)
As in the separable case, the left-hand side of (30) is decreasing in γ, meaning that γhas
a negative effect on effort incentives. It is also clear that the firm’s profit is decreasing
in γ. It is therefore optimal to set γ= 0. Moreover, since the owner cannot do worse
2

with general than with separable contracts, it follows from Proposition 1 that the wage
bill must lower than under non-integration.
It is possible but not helpful to derive the precise expressions for βand δfor the optimal
contract. Note that given γ= 0, separability of the contract imposes the restriction δ=β,
whereas in the general case there is no such restriction. With two variables to choose, only
one relevant constraint (IC-e), and a linear program, the optimum is typically a corner
solution with one of βor δset to zero and the other positive. The main conclusion from
Proposition 1, however, remains intact in the more general case: with perfect information,
the competition effect of centralized resource allocation improves effort incentives relative
to non-integration, as reflected in a lower wage bill.
Next, Proposition 2 already covers the general case; there is nothing further to show:
the information-rent always dominates the competition effect in the sense that integration
with high effort always leads to a wage bill at least as high as under non-integration.
Let us now turn to the case where project types are communicated strategically by
the managers. As in Section 4.4, additional constraints come into play. In the following,
we first derive these constraints formally, and then generalize Proposition 4.
First, it must be optimal for each manager to report his type truthfully. For a man-
ager 1 with a good project, the expected payoff from reporting truthfully, and under the
assumption that manager 2 reports truthfully too, is given by ¯w1(G, G) = W(G) as given
by (28). Suppose manager 1 reports “B” instead. Then with probability p, manager 2
has a good project, in which case all resources go to division 2 and manager 1 earns γ
if division 2 has high payoff. With probability 1 −p, manager 2 has a bad project, each
division is allocated one unit of resources, and the manager can earn δ,βor γtimes µ,
depending on both divisions’ payoffs. The resulting expected wage for manager 1 is
¯w1(G, B) = (pϕy2
µγ+ (1 −p)"ϕy2
1
µ2δ+ϕy1
µÃ1−y1
µ!β+Ã1−ϕy1
µ!y1
µγ#)µ. (31)
The truthtelling constraint (IC-G) given by ¯w1(G, G)≥¯w1(G, B) therefore is
ϕy2
1
µ(pϕ −1 + p)δ+ϕ"(1 −p)y2−(1 −p)y1Ã1−y1
µ!+py1Ã1−ϕy1
µ!#β
+"(pϕ −1 + p)y1Ã1−ϕy1
µ!−pϕy2#γ≥0.(32)
3

For a manager 1 with a bad project, the expected payoff from reporting truthfully is
¯w1(B, B) = W(B) as given by (29). Suppose manager 1 reports “G” instead. Then with
probability p, manager 2 has a good project too, in which case each division gets one unit
of resources. With probability 1 −p, manager 2 has a bad project, and all resources go
to division 1. The resulting expected wage for manager 1 is
¯w1(B, G) = (p"ϕy2
1
µ2δ+Ã1−y1
µ!ϕy1
µγ+y1
µÃ1−ϕy1
µ!β#+ (1 −p)y2
µβ)µ. (33)
The truthtelling constraint (IC-B) given by ¯w1(B, B)≥¯w1(B, G) then is
−(pϕ −1 + p)y2
1
µδ−"(1 −p)Ãy2−y1Ã1−y1
µ!!+py1Ã1−ϕy1
µ!#β
+"pϕ Ãy2−y1Ã1−y1
µ!!+ (1 −p)y1Ã1−y1
µ!#γ≥0.(34)
Second, based on our arguments at the beginning of this Appendix, we will look at
contracts that induce the CEO to allocate resources efficiently if he assumes that project
types are reported truthfully. Suppose first that both projects are good. If the CEO
allocates the resources equally (the efficient allocation), the expected profit for the firm is
2(1 −δ)ϕ2y2
1
µ2+ 2(1 −β−γ)ϕy1
µÃ1−ϕy1
µ!(35)
times µ(in the following equations, all profit expressions are stated as shares of µ). If
instead the CEO allocates all resources to one division, then the expected profit would be
(1 −β−γ)ϕy2
µ.(36)
For the CEO to make the efficient choice requires that (35) be at least as large as (36), or
2(β+γ−δ)ϕy2
1
µ+ (1 −β−γ)(2y1−y2)≥0.(37)
By similar reasoning, it can be shown that the condition for the CEO to allocate resources
efficiently if both projects are bad is given by
2(β+γ−δ)y2
1
µ+ (1 −β−γ)(2y1−y2)≥0.(38)
Finally, suppose that division 1’s project is good and division 2’s bad. If the CEO allocates
all resources division to 1 (the efficient allocation), the firm’s expected profit is
(1 −β−γ)ϕy2
µ(39)
4

If instead the CEO allocates the resources equally, then the expected profit would be
2(1 −δ)ϕy2
1
µ2+ (1 −β−γ)"ϕy1
µÃ1−y1
µ!+Ã1−ϕy1
µ!y1
µ#.(40)
For the CEO to choose efficiently requires that (39) be at least as large as (40), or
equivalently
(1 −β−γ)[ϕ(y2−y1)−y1]−2(β+γ−δ)ϕy2
1
µ≥0.(41)
Of these three constraints, (38) is redundant. To see why, notice that since both (37) and
(41) must hold, the sum of their left-hand sides, which yields µ(ϕ−1)(y2−y1)(1 −β−γ),
must be positive. This in turn requires that β+γ < 1. Next, given the last result, both
(37) and (38) can be binding only if δ > β +γ; but in that case (36) is the more restrictive
condition. We can therefore ignore (38).
The problem we are concerned with, therefore, is that of maximizing (27) with respect
to β,γand δ, subject to the effort incentive constraint (30), the truthtelling constraints
(32) and (34), the resource allocation constraints (37) and (41), and the nonnegativity
constraints β, γ, δ ≥0.
Proposition 9 In an integrated firm with cheap-talk communication, the optimal non-
separable contract for each division manager that leads to high effort, truthful reports about
investment projects, and an efficient resource allocation, is given by
β=c1−p(1 + ϕ)
(1 −p)(p−q)(ϕ−1)[(1 −p)y2−p(ϕ−1)y1]
γ= 0,
δ=c(µ−ϕy1)[p(2y1−y2) + y2−y1] + (1 −p)y1[ϕ(y2−y1) + y1]
(1 −p)(p−q)(ϕ−1)y2
1[(1 −p)y2−p(ϕ−1)y1].(42)
if p≤1/(1 + ϕ)and csufficiently small. In this case, the resulting expected wage per
agent is the same as under non-integration. Otherwise, the resulting expected wage per
agent is strictly higher than under non-integration. In particular, if p > 1/(1 + ϕ), the
optimal contract entails γ > 0.24
24 With three variables to specify and eight linear constraints, there are as many as 8!/(3! 5!) = 56
different corner points as possible candidates for an optimal solution in the case p > 1/(1 + ϕ). It is
possible to narrow the set of possible solutions down to only six; however, there is little to gain from a
more complete characterization of the solution.
5

Proof: The contract (42) is the unique solution for which γ= 0 and both (30) and
(34) are binding. Feasibility of this solution requires β, δ ≥0. Since the numerator of δ
in (42) is positive, we need (1 −p)y2> p(ϕ−1)y1for the denominator of δto be positive.
Since the same term appears in the denominator of β, we need p < 1/(1 + ϕ) for βto
be positive as well. Conversely, if p < 1/(1 + ϕ) or 1 −p > pϕ, then it follows that
(1 −p)y2> pϕy1> p(ϕ−1)y1, i.e. the same condition we started with. We can conclude
that p < 1/(1 + ϕ) is necessary for the stated solution to be feasible.
However, the resource allocation constraints (37) and (41) need to be satisfied too. It
can be shown that δ > β for the contract (42). It follows that (41) is always satisfied,
but (37) may not be. As cdecreases to zero, so do βand δin (42), in which case (37)
reduces to 2y1−y2≥0, which means that (42) is overall feasible. However, for larger c,
condition (37) is easily violated.
The total expected wage bill for the integrated firm is µtimes
2δhp2ϕ2+ (1 −p)2iy2
1
µ2+2(β+γ)"p2ϕy1
µÃ1−ϕy1
µ!+p(1 −p)ϕy2
µ+ (1 −p)2y1
µÃ1−y1
µ!#,
(43)
cf. the firm’s net profit in (27). Substituting the contract (42) into (43) and simplifying
leads to 2c(pϕ −1 + p)/[(p−q)(ϕ−1)], which is the same as the total wage bill for both
firms under non-integration, cf. (20). Optimality of the solution (42) then follows from
Proposition 2(a).
The contract (42) is not feasible if either p > 1/(1 + ϕ), or if p≤1/(1 + ϕ) but cis
too large. In the latter case, we just saw that a contract that satisfies (30) and (34) with
equality leads to the lowest possible wage cost. If cis too large, then (37) is violated, and
the optimal contract that satisfies (37) while still satisfying (30) and (34) must lead to a
higher wage bill.
If p > 1/(1 + ϕ), the truthtelling constraint (34) is decreasing in δ. Since it is also
decreasing in β, the only way to satisfy (34) is to set γ > 0. Evaluating the difference
ϕ¯w(B, G)−¯w(G, G), using the expressions in (28) and (33), simplifies to pϕ(ϕ−1)y1γ.
This means that if γ > 0, then ϕ¯w(B, G) strictly exceeds ¯w(G, G). In this case, it follows
from Proposition 2 that the wage bill is strictly higher than under non-integration.
Proposition 9 states that unless both pand care small, the conclusions of Proposition
6

4 carry over to the non-separable case: any feasible solution leads to a wage bill higher
than under non-integration, typically involving a contract with γ > 0.
Only if p≤1/(1+ ϕ) and cis small, the managers’ information can be elicited without
additional cost relative to the case of non-integration, similar to the message-contingent
contract of Proposition 2. What makes this possible is that if p≤1/(1 + ϕ) , the
truthtelling constraint (34) is increasing in δ.25 It is thus in principle possible to establish
truthtelling without requiring γ > 0, by setting δhigh enough. The problem is that the
required δmay be too high to satisfy (37).
Our last result generalizes Proposition 6. Like in Section 6, we allow for asymmet-
ric contracts for the managers. The managers’ wages for the different possible payoff
outcomes can therefore be described by δ1, β1, γ1and δ2, γ2, β2, respectively.
Proposition 10 Assume that the owner of an integrated firm wants to induce high effort
and an efficient resource allocation. Then the incentive constraints in the CEO hierarchy
are unambiguously less restrictive than those in the skewed hierarchy.
Proof: As in the separable case, in the skewed hierarchy all incentive constraints for
manager 2, as well as the effort incentive constraint for manager 1, are the same as in
the CEO hierarchy, cf. the proof of Proposition 6. It remains to show how the resource
allocation constraints for a manager 1 with a bad project compare to his truthtelling
constraint in the hierarchy with CEO. Suppose manager 1 has a bad project. If manager
2’s project is bad too, and manager 1 allocates the resources equally as would be efficient,
his expected wage is "y2
1
µ2δ1+y1
µÃ1−y1
µ!(β1+γ1)#µ.
25 To understand the sign of this derivative, observe first that a manager can earn δonly if both
divisions have high payoffs, which requires that the CEO allocates the resources equally between the
divisions (if one division has no resources, it cannot attain a high payoff). If manager 1 has a bad project
and reports truthfully, he earns δif manager 2 also has a bad project (the probability of which is 1 −p),
and both have high payoff, which occurs with probability y2
1/µ2. In contrast, if manager 1 claims to have
a good project, he earns δif manager 2 has a good project (the probability of which is p), and both have
high payoff, which occurs with probability ϕy2
1/µ2. Thus, the effect of δto report truthfully is given by
(1 −p−pϕ)y2
1/µ, which is positive if and only if p≤1/(1 + ϕ).
7

If instead he allocates all resources to himself, his expected wage is β1y2. Manager 1
therefore allocates resources efficiently if
"y2
1
µ2δ1+y1
µÃ1−y1
µ!(β1+γ1)#µ−β1y2≥0.(44)
If manager 2’s project is good and manager 1 allocates all resources to division 2 as is
efficient, his expected wage is γ1ϕy2. If instead he allocates the resources equally, his
expected wage is
"ϕy2
1
µ2δ1+y1
µÃ1−ϕy1
µ!β1+Ã1−y1
µ!ϕy1
µγ1#µ.
Manager 1 therefore allocates resources efficiently if
γ1ϕy2−"ϕy2
1
µ2δ1+y1
µÃ1−ϕy1
µ!β1+Ã1−y1
µ!ϕy1
µγ1#µ≥0.(45)
It can then be shown that left-hand side of (34) is equal to (1 −p) times the left-hand side
of (44) plus ptimes the left-hand side of (45), which completes the proof (see the proof
of Proposition 6 for further details).
As mentioned in the main text, an attempt to generalize Proposition 7 on horizontal
exchange to non-separable contracts leads to several cases that need to be considered.
Numerical simulations suggest that 7 continues to hold for all cases, but we have been
able to prove this formally only for some of the cases. Thus, we do not have a counterpart
of Proposition 10 for horizontal exchange.
8