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Institute of
A THEORY OF
FIRM SCOPE
Oliver Hart
Bengt Holmstrom
Working Paper 02-42
November 2002
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Firm Scope v 32.wpd
"A Theory
of Firm Scope"
by
Oliver Hart (Harvard University and
NBER)
and
Bengt Holmstrom (MIT and
November
*An
earlier version
4,
NBER)
2002*
of this paper circulated as "Vision and Firm Scope." The material presented
here formed part of the
first
author's
Munich Lectures
(University of Munich,
November 2001)
and Arrow Lectures (Stanford University, May 2002). We are especially grateful to Andrei
Shleifer for insightful comments. We would also like to thank Philippe Aghion, George Baker,
Lucian Bebchuk, Pablo Casas-Arce, Mathias Dewatripont, Robert Gibbons, Meg Meyer, Chris
Snyder, Jeremy Stein, Lars Stole, Eric van den Steen and seminar audiences at CESifo,
University of Munich, Harvard University,
University, Stanford University, the
London School of Economics, George Washington
Summer 2002 Economic Theory Workshop
at
Gerzensee,
Switzerland and the University of Zurich for helpful discussions. Research support from the
National Science Foundation
is
gratefully acknowledged.
Abstract
The
existing literature
on
firms, based
on incomplete contracts and property
rights,
emphasizes that the ownership of assets— and thereby firm boundaries— is determined in such a
way as to encourage relationship-specific investments by the appropriate parties. It is generally
accepted that
paper
we
this
approach applies to owner-managed firms better than large companies. In
this
attempt to broaden the scope of the properly rights approach by developing a simpler
key ingredients: (a) decisions are non-contractible, but transferable through
ownership, (b) managers (and possibly workers) enjoy private benefits that are non-transferable,
and (c) owners can divert a firm's profit. With these assumptions firm boundaries matter.
Nonintegrated firms fail to account for the external effects that their decisions have on other
firms. An integrated firm can internalize such externalities, but it does not put enough weight on
the private benefits of managers and workers. We explore this trade-off first in a basic model
that focuses on the difficulties companies face in cooperating through the market if benefits are
unevenly distributed; therefore they may sometimes end up merging. We then extend the
analysis to study industrial structure in a model with intermediate production. This analysis
sheds light on industry consolidation in times of excess capacity.
model with
three
1.
Introduction
In the last fifteen years or so, a theoretical literature has developed that argues that the
boundaries of firms— and allocation of asset ownership— can be understood
incomplete contracts and property rights.
1
The basic idea behind
in
terms of
the literature
is
that firm
boundaries define the allocation of residual control rights and, in a world of incomplete
contracts, these matter. In the standard property rights model, parties write contracts that are
ex
ante incomplete, but that can be completed ex post; the ability to exercise residual control rights
improves the ex post bargaining position of an asset owner and thereby increases her incentive,
and the incentive of those
specific investments;
who
enjoy significant gains from trade with her, to
and as a consequence
it is
make
relationship-
optimal to assign asset ownership to those
who
have the most important relationship-specific investments, or who have indispensable human
capital.
2
Although the property
benefits of integration, as a
managed
approach provides a clear explanation of the costs and
number of people have argued,
firms better than large companies.
to the theory, the
rights;
rights
major impact of a change
3
the theory seems to describe owner-
There are several ways to see
in
ownership
is
however, in a merger between two large companies
this.
First,
according
on those who gain or lose ownership
it
is
often the case that the key
decision-makers (the CEOs, for example) do not have substantial ownership rights before or
after the merger.
rather than
Second, the relationship-specific investments analyzed are made by individuals
by firms;
'See
this
again resonates more with the case of small firms than large companies.
Grossman and Hart (1986), Hart and Moore (1990), and Hart
(1995). This literature
builds on the earlier transaction cost literature of Williamson (1975, 1985) and Klein, Crawford
and Alchian (1978).
Extensions of the model show that it is sometimes optimal to take assets away from
someone to improve their incentives to make relationship-specific investments (e.g., to
discourage rent-seeking behavior).
(1998), de
empirical
Meza and Lockwood
work supporting
Elfenbein and
3
On this,
see Baker, Gibbons and
Murphy
(1998), and Rajan and Zingales (1998). For
the property rights approach, see Baker and
(2002a), Chiu
some
recent
Hubbard (2002),
Lemer (2002) and Woodruff (2002).
For a discussion of this and related points, see Holmstrom and Roberts (1998) and
Holmstrom(1999).
Third, and perhaps
most important, the approach envisions a
the relevant parties
meet and bargain ex post over the gains from
has the right to walk
away with which
room
stands the model has no
assets; there are
situation
of "autarchy,"
trade,
in
which
and the only issue
no other decisions
in the
is
model. As
all
who
it
for "organizational structure," "hierarchy" or "delegation"; in an
important sense, the model continues to describe a pure market economy, although one enriched
by the idea
The purpose of the
be applied
can be empowered through the ownership of key nonhuman
that individuals
to a
broader
set
current paper
is
to
modify
we will
we
and
ask
how
activities.
We suppose that the
irreducible set of activities that
also
can
it
economy has
these activities should be grouped to form firms.
associate each activity with a production unit.
manager and possibly
it
We begin by describing the key ingredients of our general approach.
Firms are characterized by the scope of their
concrete,
the property rights approach so that
of organizational issues, including industrial organization and the
organization of large firms.
a given set of activities
assets.
would be meaningless
to
We may think of a unit as
break up
some workers. The owner of the
unit
To be
is
further.
the boss.
Each
The
an
unit has a
unit
manager
could be the boss or the unit could be owned by an outside boss (sometimes referred to as a
professional manager).
The decisions
The
in
identity
of the boss will be important.
each unit are noncontractible (ex ante and ex post). Units can be bought
and sold. Ownership of a unit confers the
right to
make
the decisions in that unit.
The
fact that
decisions can be transferred only through ownership, and are not even ex post contractible,
central feature of our
model and distinguishes
it
from
the standard property rights
which decisions are ex ante noncontractible but ex post
contractible.
Many
model
is
a
in
decisions are of
course contractible; for instance those involving trade between two firms. But there are probably
many more
decisions that firms
make
unilaterally,
such as setting prices, choosing production
techniques, deciding on marketing campaigns, assigning workers, determining incentive
schemes, and so on.
Some of these
decisions); others are
on decisions
that
made
decisions have to be
unilaterally,
have potential external
made
unilaterally (e.g. pricing
because no one else has an interest
made and how
Full integration
them. Our focus
is
effects (positive or negative), yet are impossible to
agree upon contractually. In these cases, changes in ownership are the only
decisions are
in
way
to affect
how
well they take into account external effects.
would always be optimal
if all the benefits
and costs from decisions were
transferrable through ownership.
unit generates
To avoid
two kinds of benefit: monetary
form of job satisfaction for those working
manager
the only
is
this uninteresting conclusion,
profit
For the most part
worker and hence private benefits
we
will
assume
To
way
illustrate
with two units
manager
each
more
detail later.)
in the
that the
will
We assume that the boss of a
by ruling out
to influence incentives.
how
A and B.
accruing to each by (v A
(We
refer to her job satisfaction.
unit can divert all the profit from that unit to herself. This simplifies the analysis
profit sharing as a
that
and private (nontransferable) benefits
in the unit.
return to discuss the source of private benefits in
we assume
,
firm boundaries affect decision making, consider the simplest setting
Denote the pair of profits and private benefits (measured
wA
)
and (v B
A is the boss of unit A,
,
wB
),
Then
respectively.
and manager
B
if the units are
the boss of unit B,
manager
in
money)
nonintegrated, and
A will maximize vA
w A since she diverts the profit from unit A and cares about her own private benefits; and
manager B will maximize v B + w B for similar reasons. In contrast, if units A and B are
integrated, then what happens depends on who is the overall boss. If manager A is the overall
boss, manager A will maximize v A + v B + w A since she diverts the profit from both units, and
+
,
cares about her
own
private benefit but not
wB
boss, she will
maximize v A + v B +
boss, she will
maximize v A + v B since she
.
,
manager
B's. Similarly, if manager
Finally, if a (professional) outsider
diverts
all
is
B
is
brought
the overall
in to
be the
the profit and does not care about private
benefits.
As
vA + v B +
a reference point, note that social optimality
wA + w B
benefits than nonintegration.
is that
total surplus:
integration results in less weight being placed on private
Under nonintegration
function. In contrast, under integration, at least
objective function.
However,
under integration
In
achieved by maximizing
.
The important point here
that
is
this
w A w B each appear in one boss's objective
,
one of the w's
fails to
appear in the overall
diminished influence of private benefits
total profits rather than individual unit profits are
summary, under nonintegration, bosses maximize the
benefits) but are parochial (they
do not take
is
offset
by the
fact
maximized.
right thing (profits plus private
into account their effect
on the other
unit),
while
under integration they maximize the wrong thing but are broad.
We
analyze two models of firm boundaries based on the general trade-off described
above. The
first,
simplify matters,
discussed in Section 2,
we suppose that
accommodating way
is
concerned with interactions between two
each unit has a binary decision to make:
it
can either act in an
accommodate by
vis-a-vis the other unit or not. For example, the unit could
deciding not to poach on the other unit's territory or by being less aggressive in
or the unit could choose a technology or a standard that
is
To
units.
its
advertising;
beneficial to the 'other unit; or
it
could
provide the other unit with some key piece of knowledge. Each of these examples has the
characteristic that
by owning the
We
it
may be
unit can
too costly or impossible to agree on a decision contractually.
one control the decision.
ask whether units
if they integrate.
A and B will be regulated better if the units remain independent or
Call the case
where both
parties
accommodate coordination
under reasonable assumptions, nonintegration leads to too
values for which coordination
is
two reasons why
dilemma problem: both
units
The other reason
is
may be
that
little
may happen. The
this
.
We show that,
coordination; for
optimal, coordination will not be a
stay separate. There are
deviate.
Only
some parameter
Nash Equilibrium
first is
the well
known
if units
prisoner's
better off with coordination, but unilaterally each prefers to
while coordination
maximizing), the distribution of gains
may be
may be
socially optimal (total surplus
so uneven that one of the parties will not want to
go along (accommodate).
In contrast, under a
weak assumption— specifically,
reduction in "independence" and therefore causes a
too
much
though
it
coordination.
The reason
is
that
fall in
model described above there
is
no
it is
is
may choose to
more
coordinate even
profitable.
role for outsourcing: decisions are always
inside the units and the only question is whether they are
outsourcing of a decision or activity
private benefits— integration leads to
an outsider boss
destroys significant private benefits, because
In the
that coordination represents a
made by one boss
made
or two. In reality,
often a viable alternative for an organization. For
example, consider two units in the output market that need a specialized input. Then each unit
can remain separate and provide the input in-house; or the units can merge horizontally and
collectively provide the input in-house; or the units can remain separate and procure the input
from an independent
In Section 3
ground
to
supplier.
we
present a
model
that analyzes these choices (the
Bolton and Whinston (1993), but the approach
is
different).
model covers similar
We assume that the two
units, or buyers,
have stochastic input demands or valuations. The buyers can collectively choose
whether to have one or two units of capacity in the upstream market. With two units of capacity,
both buyers will be supplied, while with one unit only one buyer will be supplied. Given that
valuations are stochastic,
it
may be
on capacity and have only one
efficient to save
However, saving on capacity typically requires coordination and
unit.
specialization: the limited
capacity must be dedicated or directed to the buyer with the greater needs. There are two leading
organizational forms with one unit of capacity. In one the supplier
two buyers and a
("outsourcing"); in the other the
integration").
(We
also
single seller
is
merge
an independent firm
into
one firm ("complete
compare these with an organizational form with two
units
of capacity.)
We show that in some cases potential savings in capacity can be exploited only under complete
integration.
The reason
that
is
specialize to any one buyer.
under other organizational forms the supplier may be unwilling to
We argue that this model captures the idea of "integrating for
we have
synergy." Note that in order to allow for outsourcing
trade
is
noncontractible; instead
we suppose
to drop the
assumption that ex post
that the decision to specialize to a
buyer
is
noncontractible.
The
that
it
interpretation that private benefits are enjoyed
by a single manager
companies.
One can
interpret the private benefit
satisfaction of all the unit
that there is a population
i
w
(i
;
to the case
= A,B)
its
profits,
,
B
;
A
boss
large
and others of whom care only about money. Call the
is
while a unit
B
an enthusiast corresponding to each
unit: a unit
A
A workers, and hence puts
enthusiast has goals that are (partially) congruent with those of
workers, and hence puts some weight on
4
where the units are
as representing the aggregate job
enthusiast has goals that are (partially) congruent with those of unit
wA
worth
of bosses with different preferences, some of whom care about the
group enthusiasts and suppose that there
some weight on
It is
workers rather than the private benefits of a single manager. Suppose
firm's activities in addition to
unit
restrictive in
implies that the units are in effect sole proprietorships under nonintegration.
mentioning a second interpretation of the model that applies
first
is
may be biased toward
its
wB
4
.
Assume
as before that a boss can divert
workforce because sustained contact with workers
and empathy. Wrestling with the same problems, sharing the same
all conducive to a common vision
that aligns interests, particularly on issues such as the strategic direction of the firm. Shleifer and
fosters friendship
information, and having a similar professional background are
some
fraction of the profit of any unit
less than
1
.
under her control
to herself— but that this fraction is
Then, under an appropriate assumption about the degree of congruence between
bosses and workers and about the fraction, of profit diverted, a unit
+
i
enthusiast will
maximize
Wj under nonintegration. In contrast, under integration, a professional will maximize v A
We will
now
show
that this version
of the model
is
analytically identical to the first one.
A and B is that,
owners of units
benefit of nonintegration for the
are respected by an enthusiastic boss, workers will
Our paper
First, there is
is
related to a
number of ideas
work
that
for
Vj
+ vB
.
Now the
since workers' private benefits
lower wages. 5
have appeared elsewhere
in the literature.
an overlap with the recent literature on internal capital markets; see particularly
Stein (1997, 2002), Scharfstein and Stein (2000), Rajan, Servaes and Zingales (2000), Brusco
Panunzi (2000), and Inderst and Laux (2000). This
a conglomerate firm, even if she
is
literature
an empire builder,
is
and
emphasizes the idea that the boss of
interested in the overall profit of the
conglomerate, rather than the profits of any particular division.
As
a result, the conglomerate
boss will do a good job of allocating capital to the most profitable project ("winner-picking").
Our idea
the
that the professional boss
main differences
integration as
total profit is similar to this;
are that the internal capital markets literature does not stress the
we do— the
that the allocation
of an integrated firm maximizes
insufficient
emphasis on private benefits— or allow for the possibility
of capital can be done through the market
Summers (1988) argue
that
may be an
it
(in
our models, the market
efficient long-run strategy for a firm to bring
prospective bosses to be committed to workers and other stakeholders (on
Stout (1999)).
same cost of
Milgrom and Roberts (1988) argue
this,
is
always
up or
train
see also Blair and
that frequent interaction gives
workers the
opportunity to articulate their views and influence the minds of their bosses, sometimes to the
detriment of the firm. All these explanations are consistent with our assumption that the boss of
a firm with broad scope will put less weight on private benefits than a boss of a firm with a
narrow scope. The reason
is that,
more heterogeneous, making
intensity
workers
5
with a broader range of activities, the firm's workforce will be
empathy for any given group. Also the
of contact with any particular group will go down, reducing the ability of that group's
the boss experience less
to influence the boss.
There
is
some evidence
consistent with
this.
Schoar (2001),
in a
study of the effects of
corporate diversification on plant level productivity, finds that diversified firms have on average
7% more productive plants but pay their workers on average 8% more than comparable
alone firms.
stand
an alternative to centralized decision-making), or consider general coordination (or
accommodation) decisions. Second, the idea
scope and/or choose a boss that
Summers
Shleifer and
it
may be
efficient for the firm to
biased toward particular workers
is
familiar
is
have narrow
from the work of
Rotemberg and Saloner (1994, 2000), and Van den Steen (2001).
(1988),
These papers emphasize the
that
effect of
narrow scope and bias on worker incentives rather than on
private benefits or wages, but the underlying premise, that workers care about the boss's
preferences,
is
However, none of these papers analyzes firm boundaries. Third,
the same.
are several recent papers that like this one use the idea that
ante and ex post but
Rey
may be
(2002), Baker et
al.
They analyze
a
actions are noncontractible ex
transferable through owership; see, e.g., Aghion, Dewatripont and
model
et al. (2002).
in
Mailath
et al.
(2002)
is
which the boss of an integrated firm maximizes
2.
from hold-up, rather than an
is
total profit
and
a decline in worker
emphasis on private benefits.
A basic model of coordination
Our
first
model concerns two
interaction
between units
they integrate.
units,
makes decisions
input markets. Each unit
will
that
it
does not.
To have
it
if
same or
similar output or
We will analyze whether the
the units remain independent or if
can choose "Yes" or "No."
the binary case, because
Here efficiency
a concrete
to cater to the
unit corresponds to the case
it
is
where
Of course,
it
example
in
We interpret Yes to mean
vis-a-vis the other unit,
and
No
mind, think of two newspapers. Each
mass of readers or
to specialize.
specializes, for instance,
highlights clearly the two
Accommodation by one
by going up market.
main economic reasons
We focus on
for integrating.
defined with respect to the owners, managers and workers of the units.
We ignore the impact of the units'
competition.
that affect the other unit.
"accommodating" (or compromising) way
one can decide whether
6
in the
6
that the unit acts in an
mean
which might operate
be regulated more efficiently
Each unit has a binary decision:
to
insufficient
(2000),
probably the paper closest
so internalizes externalities. However, the cost of integration in their paper
initiative resulting
Moore
(2002b), Bolton and Dewatripont (2001), Hart and
Holmstrom (1999), and Mailath
to ours.
some
there
decisions on consumers,
in certain contexts,
e.g., in
such "anti-trust" issues
the form of reduced
may be
very important.
8
At
the beginning an organizational form
be separate firms (nonintegration,
(integration,
i.e.,
there
is
selected— specifically, whether the units should
there are two bosses) or should
merge
into
one firm
one boss), and also what kind of boss should be in charge. Next, each
unit decides whether to choose
Figure
i.e.,
is
Yes or No.
Finally, the payoffs are realized.
The time-line
is
as in
1.
Organizational
Decision
Payoffs
form chosen
made
realized
Figure
We
assume
that the decision in
each unit
is
1
made by
the boss of that unit.
We also
suppose that these decisions are noncontractible, both ex ante and ex post. This implies that
contracts in
which one
unit agrees to choose Yes, say, in return for a side-payment
from the other
unit cannot be enforced. In other words, Coasian bargaining will not ensure efficiency of the
accommodation decisions.
We represent the payoffs from different outcomes in the
following matrix.
that these payoffs are nonverifiable and, for simplicity, perfectly certain.
We assume
9
UnitB
N
Y
A: v A (Y,Y),
wA (Y,Y)
A: v A (Y,N),
w A (Y,N)
B: v B (YY),
wB (Y,Y)
B: v B (Y,N),
w B (Y,N)
A: v A (N,Y),
w A (NY)
A: v A (N,N),
w A (N,N)
B: v B (N,Y),
wB(N,Y)
B: v B (N,N),
wB (N,N)
A
Unit
N
Figure 2
A is the row player and unit B is the column player.
Here unit
The
coordinate "v" refers to profit and the second coordinate
first
benefits are
measured
wB
unit B's.
and (v B
,
It
)
will
zA = vA
+
entries are the payoffs.
to private benefits (private
(v A ,
w A ) denotes unit A's payoffs
to total surplus in unit B,
and zA + z B equals aggregate
money). Subscripts refer
be convenient
(2.1)
Here z A
in
"w"
The
to units,
i.e.,
to introduce the notation
w A ,z B
=
vB +
refers to total surplus in unit
wB
.
A, z B
social surplus.
As noted
in the introduction, private benefits refer (broadly) to job satisfaction, or on-the-
job consumption.
It is
reasonable to suppose that part of job satisfaction stems from the ability to
pursue an independent course or agenda. Thus
by both
(2.2)
we
will
assume
that coordination
units) leads to a reduction in total private benefits:
w A (Y,Y) + w B (Y,Y)
<
w A (N,N) + w B (N,N).
(accommodation
10
Note
that
we
allow one side, but not both, to benefit privately from coordination. This
if coordination
be reasonable, for instance,
(see later). Also, note that
profits;
moreover, even
than the
fall in
(z A (Y,Y)
+
if
we
>
coordination increases total profits, profits
(Y,Y) may be more or
i.e.,
+
z A (N,N)
We mentioned in the
common
may
rise
there are
w;
Manager A
:
units are sole proprietorships.
(2) Integration
:
We begin by
boss can divert
the profit
all
who
enjoys the
from the units she operates. Then
is
the boss of unit
Manager
A and manager B is the boss of unit B, i.e., the
A maximizes z A and manager B maximizes z B
.
A professional manager (outsider) is the boss of both units and managers A and
are subordinates.
Note
The professional manager maximizes vA + v B
that, in (1), the
managers play
a noncooperative
.
game, while
elements are involved: the professional manager simply maximizes
Note also the
critical role
accommodation decisions
to
(N,N)
z B (N,N)).
introduction several interpretations of private benefits.
in addition, a
less
two leading organizational forms:
(1) Nonintegration
B
by more or
less (socially) efficient than
focusing on the simplest one: Each unit contains one individual (a manager),
private benefits
standard
put no restrictions on whether coordination increases or decreases
private benefits,
z B (Y,Y)
corresponds to the adoption of a
may
in (2)
no
strategic
total profit.
played by the assumption that the accommodation/non-
are noncontractible. In the absence of this, the parties
an efficient ex post outcome using sidepayments,
i.e.,
zA
+
zB
would negotiate
would be maximized under
all
organizational forms.
(1)
and (2) are not the only possible organizational forms.
ownership, manager
A
(resp.,
manager B),
would then maximize v A + v B +
A could be the boss
of unit
B
always be achieved by (1) or
).
Furthermore, even
by a professional manager
and vice versa). However,
(2).
common
under
rather than a professional, could be the boss; she
w A (resp., v A + v B + w B
separately owned, they could be run
If the units are
Thus we focus on
(it is
in the case
these.
if the units are
even possible
that
of certainty, the
manager
first-best
can
No
Although the decisions Yes or
that organizational
form
manager
efficiently,
lump sum she receives
managers
prices such that
all
i's
A
owned by
and
B
i.e.,
to
symmetric).
integration
is
more
A and B
maximize
To
total surplus (zA
spell this out a little
is at least
+
more:
zB )
if
efficient, then a professional
at prices
such that
private benefit under the professional
for her control rights
if the units are initially
efficient, then
manager
is
from managers
will purchase control rights
In
chosen
manager-owned but
are better off (in particular,
and
is
no wealth constraints and information
the units are initially
we will assume
contractible at the beginning of the period. Coasian bargaining will
is
then ensure that organizational form
(there are
are noncontractible ex ante and ex post,
all
three parties
manager plus the
equal to her payoff under nonintegration);
a professional manager, and nonintegration
will purchase control rights
is
more
from the professional manager
at
three parties are better off.
summary, organizational form
is
chosen
at the
beginning of period
1
to
maximize the
value of zA + z B in the subsequent game.
We will make the following technical
total profit are
(2.3)
(2.4)
Max
Max
maximized
[z A (Y,Y)
[v A (Y,Y)
assumption.
either if both parties
+
z B (Y,Y), z A (N,N)
>
Max
[z A (Y,N)
+
+
We will
accommodate or
suppose that
if neither does.
total surplus
That
is,
z B (N,N)]
z B (Y,N), z A (N,Y)
+
z B (N,Y)],
+ v B (Y,Y), v A (N,N) + v B (N,N)]
>Max
[v A (Y,N)
+ vB (Y,N), v A (N,Y) + vB (N,Y)].
We will see that in this model nonintegration can cause two kinds of inefficiency.
first
occurs
loses out,
when
i.e.,
The second
The
coordination yields greater social surplus than non-coordination, but one party
the distribution of payoffs
inefficiency occurs
not a Nash equilibrium,
dilemma
and
i.e.,
when
at least
or free rider problem).
is
uneven;
this party will
then refuse to accommodate.
both parties benefit from coordination but coordination
one party wants
to deviate (this is the standard prisoner's
is
12
Pure coordination
It
will be useful to separate out these effects
they are combined. Thus
present;
we
in
most
begin by analyzing the case where only the
pure coordination
call this
(2.5)
we
even though
world situations
real
first
inefficiency
is
:
v A (Y,N) = v A (N,Y) = v A (N,N),
v B (Y,N) = v B (N,Y) = v B (N,N),
w A (Y,N) = w A (N,Y) = w A (N,N),
w B (Y,N) = w B (N,Y) = w B (N,N).
Pure coordination refers to a situation where accommodation by one party has no effect
all
on payoffs,
i.e., it
"takes two to accommodate."
An example would be
if
at
each party must
decide whether to adopt a standard, and the standard has no force unless both parties adopt.
Under pure coordination,
accommodation by
Given
(2.5),
the prisoner's
dilemma
either party is equivalent to
it
is
or free rider
problem does not
arise since
non-
non-accommodation by both.
easy to see what the trade-off between nonintegration and integration
Under nonintegration, each boss
in effect has a veto
is.
on coordination, since by choosing non-
accommodation she can achieve the (N,N) outcome. Thus (Y,Y)
will occur if and only if (Y,Y)
Pareto dominates (N,N):
z A (Y,Y) > z A (N,N),
(2.6)
Note
however,
that
we
It is
even
will
holds, (N,N)
is
always a Nash equilibrium along with (Y,Y);
suppose that the parties do not pick a Pareto dominated equilibrium.
of course immediate that (2.6) implies that (Y,Y)
z A (Y,Y)
(2.7)
However, equally
of winners and
distribution
if (2.6)
z B (Y,Y) > z B (N,N).
+
z B (Y,Y) > z A (N,N)
clearly, the
losers,
may be
converse
mentioned
is
earlier.
+
is
socially efficient:
z B (N,N).
not true: (2.7) does not imply (2.6). This
Even though aggregate
surplus
may
is
the problem
rise, the
such that one party loses out, and this party will then veto coordination,
leading to the outcome (N,N).
13
Let us
maximizes
now
It
integration, a single boss chooses the
v A (Y,Y) + v B (Y,Y)
that
v A (N,N) + v B (N,N).
>
follows from (2.2) that, under integration, (Y,Y)
be the outcome even
outcome
This outcome will be (Y,Y) or (N,N) according to whether
total profit.
(2.8)
Under
turn to integration.
if
is
always the outcome
if
it
is efficient,
is inefficient.
it
7
Figure 3 illustrates the outcomes under nonintegration and integration. In the figure,
v,(Y,Y)
-
v,(N,N) and Awj
private benefits that result
figure keeping
to stay within
Aw A Aw B
= Wj(Y,Y)
from
-
w,(N,N),
a decision
fixed and letting
,
i
= A, B;
by both
,
w into the choice of organizational
accommodate.
parties to
Av A Av B be
Av =
;
these are the changes in profits and
We have drawn the
variable, but this of course
two dimensions. In general, we are interested
private benefits
may
but
in the
mapping from
is
done merely
profits
v and
form.
Figure 3 here
The
(Av A Av B )
,
first-best decision rule (2.7) is represented
that fall
above
is
above
The
I-I,
shows
inefficient.
It
NI-NI
may
is
not occur
(Y,Y)
is
too
if
little
it
way,
pairs of profit gains
line I-I represents the
Note
coordination in the sense that (Y,Y) never occurs
always the outcome
Under
if
it
is efficient,
but
achieves the first-best
if
(Y,Y)
We thank George
is
Baker
if
(2.2).
it
is
too
much
may be
the
outcome even
integration, there
follows that nonintegration achieves the first-best if (N,N)
little
FB-
that
and integration make the opposite kind of mistake.
is efficient.
nonintegration errs on the side of too
7
all
the decision rule under non-integration.
that nonintegration
Under nonintegration there
in the sense that
FB-FB;
because the sum of the changes in private benefits are assumed negative by
figure
inefficient, but
line
this line call for coordination. In a similar
decision rule (2.8) and the quadrant
FB
by the
is
is
coordination
if
it is
efficient (since
coordination but never too much), while integration
efficient (since integration errs
for suggesting this picture.
on the side of too much
14
coordination but never too
also clear
It is
both achieve the
when (N,N)
from Figure
first-best.
the
is
little).
This
is
outcome under
3 that for
the case
some parameter
when (Y,Y)
is
the
moving
in parallel
move
the
with
it
will eventually take us outside the
FB-FB/NI-NI
first-best choice.
We
part
essential to
if profit
1
.
gains from coordination are
line
and
to the
North-East and eventually
make (N,N)
the
8
Assume pure
manager
if profit
FB-FB
NI-NI acceptance region. Integration
in
coordination,
(2.5).
i.e.,
Then,
if
(N,N)
(with unit managers as bosses) achieves the first-best. If (Y,Y)
professional
choose the right
from coordination are large enough; raising private costs
of the figure
summarize the discussion
Proposition
optimal
it is
unevenly distributed between the two firms; staying above the
will lead to inefficiency if private costs
will
outcome under nonintegration or
integration. In all other cases
organizational form. Nonintegration will lead to inefficiency
sufficiently
values nonintegration and integration
is
efficient, nonintegration
integration (with a
is efficient,
as boss) achieves the first-best. Furthermore, integration will be uniquely
gains from coordination are sufficiently unevenly divided between units.
Nonintegration will be uniquely optimal
if
from coordination are
private costs
sufficiently high in
aggregate.
General Coordination
The case of pure coordination
party's decision to
accommodate
is,
of course, quite
will affect payoffs,
restrictive.
8
its
output), or not to poach
on the
many
to a decision
unit's territory.
by one unit
manager
way B's
private benefits
by
would be accounted
A would be happy with as long as she also dislikes coordination.
A enjoys private benefits from coordination (say, because
the case where
her firm's technology). In that case, (2.2) implies that manager
relative to first-best
and hence the comparison
We do not explore these
options here, since
to a professional
we
get
one
first
to raise
its
If the other unit produces a
In Figure 3 the region of inefficient integration could be reduced
run the integrated unit. This
situations,
whether or not the other party
accommodates. For example, accommodation could refer
price (or lower
In
B would
letting
for,
manager B
something
However,
it
(2.2) admits
involves the use of
coordinate too
little
manager would be ambiguous.
best either way.
15
substitute good, this will increase the other unit's profit, regardless of whether
it
raises
price,
its
or decides not to poach too.
We
two
An
to
show
Appendix
accomodate," as long as
that our analysis generalizes to cases
we
make some
are prepared to
where
it
does not "take
assumptions.
alternative interpretation ofprivate benefits
So
that is also
i
unit,
who
of interest.
the interpretation
is
where
i.e.,
bosses, unit
the private benefits w, are enjoyed
by
the boss under nonintegration and a subordinate under
second interpretation of the model
in the introduction, there is a
We can imagine that the private benefits refer to the job
workers and that some bosses have goals that are
workers,
;
each
in
However, as noted
integration.
unit
we have emphasized
far
manager
a single
wB
in the
(partially)
satisfaction of
congruent with those of the
they care about the same things. In particular, suppose that there are three types of
A
enthusiasts with preferences
m+
A.
A
wA
m
and professional managers with preferences m. Here
congruence between a boss's goals and those of unit
Suppose now
imagine that she uses
enthusiasts with preferences
money and XA
is
,
m+
B represent
^.
<
1
of total profit toward herself; one can
perks or empire-building activities that benefit her alone-
fancy offices, secretaries, pet projects,
etc.
Denote
profit
by
v.
Then
a unit
i
enthusiast will
maximize
\ w„
9v +
(2.9)
while a professional manager will maximize
If we
make
v.
9
the simplifying assumption that
function for the different kinds of bosses as in the
9
profits
With
partial diversion,
of unit
10
It is
B
it
may be
=
A.
in order to get closer to first-best, but
is
,
this
would
yield the first-best.
=
A.
B , this yields the
same objective
model without workers described above. 10
manager
we will
A
a share of the residual
not pursue this possibility here.
no boss who is an enthusiast for both
+ v B ) + A. A w A + XB w B and,
B. Under integration such a boss would maximize 0(v A
XB
A
desirable to give
obviously important that there
A.
A and B workers.
that a boss can divert a fraction
this profit for
B
unit
;
,
units
if
A and
= XA =
B
16
In this interpretation, the choice of organizational form
units
A and B
at the
(total)
that
wage
owners face
(2.10)
where
©i
U
benefits.
in
for unit
CO;
i
a competitive labor
what kind of boss
to put in charge.
front.
Then
the
workers will satisfy
+ Wi=U,
Suppose
that the initial owner(s)
money. Then, given
maximize the
the initial owner(s) of
market and wages are agreed up
the (total) market clearing reservation
is
made by
beginning of the period. They must decide whether the units should be
separate (nonintegration) or together (integration), and
Assume
is
total
wish
wage and
to sell out
w
;
and
refers to (expected)
retire, i.e.,
that side -payments are possible, organizational
value of the two units net of wages,
i.e.,
worker private
they are interested only
form will be selected
given (2.10), vA
+ vB +
to
wA + w B (we
ignore the private benefits and remuneration of bosses).
We may conclude that the analysis
of this second interpretation of the model
is
identical to
the previous one.
Discussion
We have interpreted the model
suggesting that
it is
needlessly narrow.
unilaterally,
primarily about interactions between firms in the
Our approach has
Knowledge
party.
It is
The
potential relevance
because bargaining over those decisions
briefly the broader relevance of the
codify.
in this section as being about "horizontal interaction",
transfers
.
model using two
Knowledge
is
is
whenever firms have
too costly. Here
notoriously difficult to
from one firm
to
another
to
we want
make
is
decisions
to discuss
examples.
illustrative
also hard to circumscribe the use of knowledge once
transfer of knowledge
same market. This
it
sell. It is
often difficult to
has been transferred to another
may be very valuable,
but
it
may be
very difficult to arrange things so that the benefits of the transfer are appropriately divided
between the firms. For
The 1960s saw
partly
a
this reason,
knowledge
wave of mergers and
transfer can be a
acquisitions,
were guided by new management technology
which
that
major impetus for
partly
was
integration.
were driven by regulation and
best appropriated
by buying up firms
17
and implementing the new management systems
Note
that
running, one
once the knowledge transfer
may
may be
To
misguided.
periods. In the first period the
if
study this sequence of events,
key decision
come
significant private benefits
is
new systems
the initial reason for a merger
is
whether
second period, assuming a merger, divestment
model
complete and the
is
are
up and
well expect divestment of some of the units. Subsequent divestments are often
read as signs of failed mergers, but
verdict
after that."
to
we
transfer, that
could extend our model to two
to transfer
may become
was knowledge
knowledge by merging.
In the
optimal, because decisions with
dominate the payoffs. The analysis of such a two-period
more complicated than piecing together two one-period
from the second stage will determine
how much
analyses, because the payoffs
should be paid in the first-period merger. Also,
the first-period decision will in general influence the second period payoffs and options.
Technology choice Standards are important
.
technology. The social benefits from a
common
in
emerging industries
standard can be huge, because
overall market. Yet, getting parties to agree to a standard
industry agreements have to rely on self-enforcement,
proprietary systems
may become
like information
is
very
difficult.
which tends
to
be
it
increases the
Most of the time
ineffective. Instead,
de facto standards. Cisco's operating system
is
an example of a
dominant standard/platform in the Internet space. Should an entrepreneur with a new idea choose
to
develop
it
for the Cisco standard or should
it
try to
do something more generic? The
entrepreneur needs to be assured that Cisco will not take advantage of his choice later on. If this
difficult contractually, as
it
This situation again
he unilaterally chooses
Then,
if the social
entrepreneur.
The
to
often
fits
is,
the alternative
may be
is
integration.
our model. Suppose the entrepreneur's total payoff goes
down
if
choose Cisco's standard, because contractual guarantees are ineffective.
value of using Cisco's standard
transfer of decision rights
is
sufficiently positive, Cisco could
would justify the
1990s Cisco was very active buying start-ups as a
buy out
transfer of payments. In the late
way of expanding
its
technology base. Cisco's
reputation for preserving the entrepreneur's "private benefits" inside the firm
made
this strategy
work
particularly well (until the
days.
"Much of the knowledge transfer is conducted by management consulting firms these
The outsourcing model in the next section could be used to study that development.
downturn
the
hit).
A richer analysis would
include an innovation stage as well as a buy-out stage.
It
seems
reasonable to assume that the entrepreneur's private benefits are initially high relative to the
benefits of a buy-out.
12
Indeed, one typically does not
successful and if so, whether the innovation will
fit
know whether the
Cisco's technology rather than
company. (An important reason why private benefits are so high
has exaggerated beliefs about the probability of success; see,
is
often best to
stage
e.g.
Van den
other
entrepreneur
Steen, 2001). Thus,
it
clearly in
view a buy-out may be optimal.
worth noting that dynamic extensions of the basic model would often lead to analyses
resemble those encountered
entrepreneur
by
initially is that the
some
innovation take place on a stand-alone basis. Once the project has matured to a
where valuations are more
It is
that
let
entrepreneur will be
may
in traditional
models of hold-up. In the Cisco case the
not want to specialize to Cisco's standard, because he fears that Cisco will then
virtue of controlling the technology
be able
much
to appropriate
of the
later benefits
of
cooperation. There are important differences, however, between our approach and the traditional
way of modeling
noncontractible
hold-ups using incomplete contracts. In the traditional model, individuals
human
investments, but not
typically, but
determines
capital investments; asset
who makes
the investments.
make
ownership influences the payoffs from these
Our focus
is
not on
human
capital investments,
on strategic decisions with opportunity costs for the organization; asset ownership
who makes
these decisions. This structure reflects the reality that firms are
organizational entities rather than
mere entrepreneurs.
It is
also a potentially simpler
way of
studying hold-up problems.
3.
An
extension to outsourcing.
In Section 2
we
analyzed a model in which two units
behavior (achieve accommodation) under
that
model
there
was no
I2
It
work
hard.
common ownership
role for outsourcing: decisions
only question was whether they were
may
made by one boss
may, of course, also be more important
find
it
easier to coordinate
than under separate ownership. In
were always made
inside the units and the
or two.
at this stage to
motivate the entrepreneur to
19
In reality, outsourcing of a decision or activity
organization. For example, consider
often a viable alternative for an
units, operating in the
same or similar output markets,
need a specialized input. The input could be an intermediate good or
that
Each
like advertising or marketing.
the
two
is
two
units can
unit can
merge horizontally and
it
could be a service
remain separate and provide the service in-house; or
collectively provide the service in-house; or the units
can remain separate and procure the service from an independent supplier. In
this section
we will
develop a model that allows us to analyze the trade-off between these choices (and others too).
Among other things the model
will
throw
light
on the often-mentioned idea
that firms
merge
horizontally to exploit "synergies"; here the synergies will stem from the ability to reduce costs
by sharing scarce input capacity.
In order to allow for the possibility of outsourcing,
we have
ie.,
Instead
we
to relax the
will
suppose
assumption of Section 2 that everything
that the parties
time of delivery. However,
how
by
specialized the input
is.
we
will
made
assume
To make
be stochastic ex ante; that
is,
is
to
permit some contractibility;
ex post noncontractible.
can contract on the quantity and quality of input
This decision
the boss of the supplying unit.
profits to
we need
that at
is
an
earlier stage a decision
must be made as
noncontractible (ex ante and ex post) and
the trade-offs interesting,
we will
we
at the
is
to
made
also need the units'
depart from the assumption of perfect certainty
in Section 2.
The economy
lasts for
one period. At the beginning of the period, organizational form
chosen. In the middle of the period any uncertainty
made. Finally,
at the
is
resolved and a specialization decision
end of the period trade occurs and payoffs are realized. The time-line
in Figure 4.
Organizational
form chosen
State learned
and specialization
decision
made
Figure 4
Trade and
payoffs
realized
is
is
is
as
20
One
buyer.
We
start
with the simplest case of one buyer operating
operating in the input market— we refer to them as
B
and
S.
in the output
B
market and one
seller
requires a specialized input, one
widget, say, at the end of the period. S has one unit of capacity, costing k, which can be used to
supply one widget
supplied either to
at the
B
or to the outside market, which
competitive market price
S must
make
must specialize
end of the period. S's variable costs are zero. This widget can be
is
assumed
to
be competitive. The
is r.
a choice in the middle of the period.
To supply B
at the
end of the period, S
to B; but then S can't supply the outside market. Alternatively, S can
choose to
"remain flexible" and supply the outside market; but then S cannot supply B.
The value
benefit
r
B
of a (specialized) widget
w if the widget is supplied.
in the outside
w,
to
market;
we assume
(We
is v.
verifiable).
is
manager receives
a private
ignore any private benefits of S's manager or managers
they are independent of transactions with B.)
However, the uncertainty
are uncertain at the beginning of the period.
specialization decision
In addition B's
made; moreover,
v,
w,
r
are observable to
B and
is
The
variables v,
resolved before the
S (but are not
We assume that no long-term contracts can be written about the end-of-period widget
price (because widget characteristics cannot be specified in advance) although spot contracts at
the end of the period are possible.
As
in Section 2,
we suppose
that the boss
of a unit diverts
all
the profit from that unit.
We
also suppose that all parties are risk neutral.
In this model, the key decision
is
the boss of S.
is
whether
to specialize. This decision is
We focus on two organizational forms:
(1)
B
and S are independent firms and each
(2)
B
and S are a single firm run by B's manager
As
in Section 2, these are not the
separate and
B
made by whoever
is
run by
its
manager (nonintegration).
(vertical integration).
only possibilities. For example,
could be run by a professional manager. Or
B
B
and S could be
and S could be one firm run by S's
manager. But (1) and (2) are leading cases.
Assume
first that
of the period S and
B
B
and S are nonintegrated. Suppose S specializes
will bargain about the price of the input.
Assume
to B.
Then
at the
end
that they divide the gains
,
21
from trade 50
this
means
:
that
Since B's boss values the widget
50.
S will receive
market, S will receive
It
r.
A
l
(v
+
at
v+
w
and S's (variable) cOsts are zero,
w). In contrast, if S does not specialize and sells on the open
follows that S will specialize to
B
if
and only
if
/2 (v + w)>r.
1
(3.1)
(Recall that S
knows
v,
w,
r
when
she decides whether to specialize.)
In other words,
we have
a
classic hold-up problem.
Now suppose B
of B,
1
if
who maximizes
and S are integrated. Then the specialization decision
total profit
plus her private benefits w.
So
is
made by
the boss
specialization will occur at date
and only
v+
(3.2)
Of course,
this is also the first-best rule.
one buyer and one
integration
is
w>r.
We conclude that in the simple case where there is only
seller integration is superior to nonintegration.
The
total net surplus
under
given by
E Max
where the expectation
is
(v
+ w,
r) - k,
taken with respect to the probability distribution of (v, w,
r).
Two buyers
Let us consider next what happens
if
we have two
buyers
in the output
market:
call
them
Bl, B2.
We assume that a second unit of capacity is available in the input market at the same cost
k as the
first unit.
which case supply
conditional on
B2 each
A key question is whether there should be two units of capacity or just one (in
is
two
obviously available ex post to only one buyer).
We
units of capacity being available the first-best can
vertically integrate with a supplier. This
is
already
know
that
be achieved by having Bl
illustrated in Figure 5
(i).
On
the other hand,
22
if there is
only one unit of capacity, then there are two leading organizational forms, also
illustrated in Figure 5. In
(ii),
Bl, B2 and a single S
all
merge. In
(iii),
Bl, B2 and a single S
all
stay separate
Figure 5 here
As
boss.
To
in Section 2, an important aspect
simplify matters
manager, while
in
(iii)
we
of organizational form concerns the identity of the
will suppose that in
each of Bl,
B2 and S
is
two other "non-leading" organizational forms.
staying independent. Second,
We
assumption
is
to
own manager. Note
also that there are
Bl and B2 may merge horizontally with S
vertically,
with
B2
staying independent (or
forms below.
maximize the expected value of total
Bl
or
B2 cannot
form has been determined. And
S.'
S are run by a professional
is
chosen
(separately) sell off
if,
say,
(iii) is
at
the
surplus. Implicit in this
the idea that organizational form, and capacity, are contractible. That
optimal, then
with
First,
its
B2 and
suppose that Coasian bargaining ensures that organizational form
beginning of the period
is
run by
Bl and S may merge
We will return to these two
vice versa).
Bl,
(ii)
some of their capacity
is, if,
say
(i)
after organizational
optimal, one of the buyers cannot merge (secretly)
3
To understand
the trade-offs
between
(i) - (iii), it is
useful to
work with
example. Suppose both buyers have the same private valuations, denoted
the following
w = w, = w
2
.
Assume
w and the outside value r are constants, while v can take on two values: v = v H with probability
and v L with probability
(1 - 7i).
Assume
also that v L
+
w>
r,
so that
it
is
always
Bl and/or B2 rather than the outside market. Then, with two units of capacity,
(expected) gross surplus
B An
supply
first-best
is
alternative assumption is
to this in footnote 14.
efficient to
made
in (part of)
Bolton and Whinston (1993).
n
We return
23
Z** =
(3.3)
+ w) +
2{t:(v h
(1
-tt)(v l
+ w)}
since each buyer will always receive a widget (whose value
may be v L
with one unit of capacity, first-best (expected) gross surplus
is
Z* =
(3.4)
(2tt -
2
7i
)
(v H
+ w) +
(1
nf
-
(v L
+
or v H ).
B
(3.5)
The
first
Z**
-
thing to notice
Z* =
2{ti (v H
<
i.e.,
has v
(2?r -
(v H
is
-
1
(1 - ji) (v L
+ w) +
(1
+ w)}
- ti)
there are diminishing returns to capacity.
from the
first
(1 - n)
2
-
- tt
{(2ti -
it )
.
2
+ w) =
(v L
(v H
+ w) +
is
that with
where
it
is
(v H ) at the
it is
first-best
(v l
+ w)}
side represents the marginal gain
from the second
is
The
unit.
possible
(cf.
most needed; moreover, with positive
same
first-best optimal, while, if Z**
> Z*,
2
one unit of capital, winner-picking
Bl and B2 do not have strong needs
first-best optimal. Finally, if k
(1 - ti)
Z*,
The right-hand
Stein (1997)): the scarce input can be directed to
Z*, two units of capacity are
one, and the
2
= 2n
unit of capital and the left-hand side the marginal gain
reason for the diminishing returns
probability
2
is
that
is
+ w) +
2
7r )
= vH
other hand,
w),
since the single widget will be supplied to the buyer with value v H if there
probability that at least one
On the
-
time.
It
follows that, if k
Z* < k < Z*, one
optimal to close
down
(i.e.,
< Z**
-
unit of capacity is
to
have zero units
of capacity).
Consider
now
the second-best.
We know that,
if two units
of capacity are
first-best
optimal, then since symmetric vertical integration achieves the first-best, two units of capacity are
also second-best optimal. Similarly, if close-down
is first-best
optimal, then close-down
is
second-best optimal.
The
interesting case
unit of capacity.
is
where Z**
Under these conditions
-
Z* < k < Z*,
the first-best
is
i.e., it is
first-best
optimal to have one
no longer generally achievable since
24
forms
(ii)
Form
(ii)
and
Form
may each be
(iii)
(ii)
may be
We
inefficient.
analyze them in turn.
because the single merged firm
inefficient
manager. The manager, since she maximizes
total profit
run by a professional
is
but ignores private benefits, adopts the
following specialization rule:
(3.6)
where v„ v 2
Bl
if v,
Specialize to
B2
if
v2 =
Max
Don't specialize
if
Max
(v„ v 2 ) <
Specialize to
Bl
if v,
Specialize to
B2
if v 2
Don't specialize
see that under
the private benefit w.
B2
right:
Form
(v„ v 2 ) >r,
(v,,
v2 )
>r,
r,
are respectively Bl, B2's valuations. In contrast, the first-best specialization rule
(3.7)
We
= Max
Specialize to
(ii)
if
w = Max (v, + w, v
+ w = Max (v, + w, v
+
Max
(v,
+ w, v 2 + w) <
manager
the professional
However, conditional on
she specializes to
Bl
if
and only
if v,
2
+ w)
>r,
2
+ w)
>
r,
r.
specializes too
little
because she ignores
specializing, she gets the balance
>v 2
,
that
is:
is,
whenever
v,
+
w
between Bl and
>v 2 + w.
(iii)
Form
(iii)
has the advantage over form
private benefits w.
manager recognizes
and will
split
However, form
(iii)
(ii)
that
Bl and B2's managers
has the disadvantage that there
that if she specializes to
Bl or B2 she
is
Bl
if v, >
v2 and
Vi (v,
+ w)
a hold-up problem.
will be locked into this particular
the surplus with them. Hence, S adopts the following rule:
Specialize to
internalize the
>r,
S's
buyer
25
Specialize to
(3.8)
B2
Don't specialize
It
follows that under
this
time because
+ w)
balance between Bl and
is,
whenever
We
+
v,
w
if
and
A Max (v,
X
!/2
is
B2
+ w)
(v 2
>r,
+ w, v 2 + w) <
there will again be too
(iii)
(Vj
if v, > v,
little
r.
specialization relative to the first-best, but
multiplied by the coefficient 'A. Note also that S again gets the
right:
she specializes to
Bl
if
and only
!/2
(v,
+ w)
>!/2 (v 2
+
w), that
v 2 + w.
>
see that forms
and
(ii)
(iii)
may
both be inefficient, but in different ways.
present examples showing that, depending on the circumstances,
vice versa. In fact, in the
(iii)
if
example,
first
(ii)
(ii)
We now
can be better than
(iii)
or
achieves the first-best, while in the second example
show
achieves the first-best. Hence these examples also
that (ii)
and
can both be second-
(iii)
best optimal organizational forms.
Example
1
:
This example
(ii)
that
v H =12, v L =
is
8,
7i
=
'/2
w
,
very simple given that
=0,
r
w = 0.
=
7.
It is
clear
from a comparison of (3.6) and
achieves the first-best conditional on one unit of capacity being optimal. However,
one unit of capital
It
is
indeed first-best optimal
only remains to check that
that fact that, since
'/2
(v H
(iii) is
if
Z**
suboptimal
-
Z* < k < Z*,
when
+ w) < r, S won't be prepared
9
<k<
11.
i.e., if
But
9 <k<
(3.7) that
we know
11.
this follows
to specialize to either
Bl
or
from
B2 when S
is
independent.
Example 2
:
Now,
vH =
9,
vL =
4,
n=
'/2
,
w
=7, r
=
5.
conditional on one unit of capacity being used, outsourcing
complete integration
(ii).
The reason
is
that since
'/2
(v L
+ w) >
r,
(iii) is
superior to
an independent supplier will be
prepared to specialize to either buyer, and will obviously prefer to specialize to the buyer with the
higher
v, i.e., (iii)
achieves the
first-best.
In contrast, complete integration
the boss will direct input to the outside market
when both buyers have low
(ii) is
inefficient since
v's, since
vL <
r.
26
The
final point to note is that
one unit of capacity
is
if Z** -
indeed first-best optimal
Z*
13'/2<k<19 3/4 = Z*.
Examples
this will not
be
1
The general
so.
-
and 2 are special
(ii)
or
->
<-
->
(ii)
or
optimal
Z**-Z*
2 units
->
no capacity
>
optimal
(iii)
|
optimal
!
—
achieves the first-best. Typically,
<
|
|
<
(iii)
situation is illustrated in Figure 6.
—
(i)
in that either
Z*
a
<-
unit
1
units
<-
->
first-best
first-best
first-best
efficient
efficient
efficient
Figure 6
To understand
the figure, note that in the second-best the comparison
depends on the probability distribution of (v, w,
and
(iii)
(iii)
are conditional
on one
unit of capacity being
r),
between forms
but not on k, because both
employed. Let
Z be
(ii)
(ii)
and
the gross surplus
corresponding to the better of these two forms. Then the optimal capacity in the second-best
depends on a comparison between
a = Min {Z**
Then 2
units
-
k,
Z**
Z**/2},
-
p
2k and
0.
= Max
{Z, Z**/2}.
of capacity are second-best optimal
units are optimal if k
less than p.)
- Z,
Z
>
p.
(The role of Z**/2
if k
<
a,
Define
1
unit
in the definitions
is
optimal
of a and p
is
if
a < k < p and
to
make
sure that a
is
27
We know that Z
<
Z*, because
it
is
second-best. Therefore, using (3.5),
P < Z*, implying that the region in which one unit of capacity
is
second-best than in the first-best and strictly smaller whenever
a= P
optimal
Z<
is
a
>
Z**
no larger
Z*, as drawn
in
-
Z* and
in the
Figure
6. (If
the middle region will disappear altogether.)
Other organizational forms
Let us
first,
now
consider the two "non-leading" organizational forms mentioned earlier. In the
Bl and B2 merge
vertically,
horizontally, with S staying independent. In the second
Bl and S merge
with S staying independent (or vice versa).
The
first
of these can easily be ruled out
(at least if the
boss of B1/B2
is
a professional
manager). Under a B1/B2 merger, the specialization rule becomes:
(3.9)
(3.9)
Max
(v,,
v 2) >
r,
Av =
!/2
Max
(v„ v 2 ) >
r,
if Vi v,
Specialize to
B2
if
l
2
if Vi
Max
(v,,
v2 ) <
r.
always better to go the extra step and include S
integration (form
(3.10)
Vi
Bl
Don't specialize
It is
=
Specialize to
(ii))
the specialization rule
(v,,
v 2) >
r,
v2 =
Max
(v,,
v2) >
r,
Max
(v,,
v2 ) <
Bl
if v,
Specialize to
B2
if
Don't specialize
if
and (3.10) both lead
closer to the optimum.
to
Thus
two
a
little
r.
specialization relative to the first-best (3.7), but (3.10) gets
complete B1/B2/S merger dominates a
The second "non-leading" organizational form
B2
merger. Under complete
is:
= Max
Specialize to
in the
is
partial
B1/B2 merger.
where Bl and S merge
vertically,
staying independent ("asymmetric" vertical integration). This leads to the following
specialization rule:
with
28
(3.11)
Specialize to
Bl
if v,
Specialize to
B2
if v,
w>
+w<
+
/4(v 2
+
'/2 (v
2
+ w),
w), v,
+
w
!/2 (v
2
>
r,
+ w)
>
r,
Don't specialize otherwise.
The reason
+ w) on
a
that the boss
is
of Bl/S puts value
we
decision concerning whether to supply
that she will
+
w on a widget sold to Bl, but only value A
+
l
widget sold to B2, given that half the surplus goes
Relative to the first-best (3.7),
!/2 (v
2
v,
be biased
in favor
some
integration
is
see that the boss of Bl/S
Bl
cases, the first effect
may
the socially correct
B2
+
w to r), but
(she compares v,
+
w to
Vi
be important enough that asymmetric vertical
if
+ w) < v L + w,
(v H
B2
then the boss of Bl/S will never specialize the widget to
even when B2's value
is
high and Bl's
is
low.
equivalent to vertical integration between
7i
H (v H
nn ( v h + w) +
(
makes
or the outside market (she compares v,
of specializing to Bl rather than
indeed optimal. However,
(3.12)
%
B2.
w)).
In
surplus
to
(v 2
+ w) +
7iL
(v L
7t
L (v L
+ w))
+ w)
or
-
As
since specialization
unprofitable
a result asymmetric vertical integration
Bl and S with B2 absent (which
k); but this in turn
by symmetric
is
is
yields net social
dominated either by zero capacity
vertical integration,
i.e.,
form
is
(i) (if
k < nH
(v H
(if k
>
+ w) +
v l + w)).
Discussion
We conclude this
section
by mentioning
a piece of empirical evidence that is consistent
with our analysis, and by relating our model to that of Bolton and Whinston
evidence. There are several studies that
units
and these are often sold
Meyer
et al.
(1992)).
model provides an
Meyer
show
that,
to other firms in the
at al.
when
same
(1
a sector is in decline, firms divest
line
A
fall in a
weak
of business (see the references in
offer an influence cost explanation for this
alternative explanation.
993). First the
phenomenon. Our
sector's prospects can be represented
by an
29
increase in the cost of capacity k. Consider Figure
assumption that
(v H
V2
+ w) <
r, i.e.,
the hold-up
never occurs under outsourcing. Then form
the
economy
will
move from
where complete integration
a region in
is
6.
Suppose
problem
(ii) is
optimal. That
is, it
superior to form
It
(iii).
way
follows that as k rises
vertical integration is optimal to
becomes advantageous
save costs by sharing scarce input capacity, and the
the plausible
sufficiently severe that specialization
is
which symmetric
we make
that
for
them
to
do
for the
this is to
one
two buyers
to
merge
horizontally (they are already integrated vertically with their suppliers). In effect, there
is
industry consolidation.
Consider next the comparison with the work of Bolton and Whinston (1993) (henceforth
BW).
BW
is
one of the
first
papers to analyze integration decisions in a situation where several
buyers are supplied input by a seller S that
where there
are
probability (1
two buyers Bl and B2
may have
scarce capacity.
downstream market and
in a
BW
a single seller S that with
has the capacity to supply both, and with probability
- A.)
consider a situation
A.
can supply only one.
BW employ a traditional property rights model in which bargaining leads to ex post efficiency
and the only distortions are
(the
we
manager of S does not
in the (nontransferable) ex ante investments
invest).
With
this setup
BW analyze
do, with the exception of symmetric vertical integration (for
only one
seller).
all
by managers of Bl, B2
the organizational forms that
most of the paper, they consider
14
BW show that nonintegration (form
vertical integration (one
since, given their
(iii)),
complete integration (form
of our "nonleading" forms) can
be optimal. NI
all
(ii)),
and asymmetric
is efficient if A.
=1,
assumption of outside option bargaining, the downstream firm that receives the
scarce input pays a price equal to the value of the input to the other downstream firm;
downstream firms are therefore not held up by S and invest
be
efficient if A.
<
1,
since although one downstream
efficiently.
manager
Complete integration may
will underinvest given that he will
be held up by the owner of the single firm, the other downstream manager,
invest efficiently.
14
is
As we
Asymmetric
vertical integration has the
pointed out in footnote 13,
not contractible.
They show
that,
when
if he is the
owner, will
advantage over complete integration in
BW also consider the case where organizational form
nonintegration
is
the buyers secretly to integrate vertically with S. Although
here, our analysis could be modified to do so.
socially optimal,
we do
it
may pay one of
not consider this possibility
30
that the
manager of the nonintegrated downstream firm
in that the
manager of the integrated downstream firm
will underinvest less; but the disadvantage
will overinvest, given that this increases his
bargaining power with respect to the nonintegrated downstream firm. Finally, a horizontal
merger by Bl and B2
is
not optimal since this allows S to hold up both downstream firms.
While several of our
(iii)
may be
results are similar to those
of
BW (like us they find that forms
optimal, but are able to rule out a horizontal merger
significant differences. First,
and most obviously,
we
focus on
the trade-off between private benefits and profits, rather than
managerial investments. Second,
integration
is
we
how
on
there are also
the trade-off between different
that
symmetric vertical
a possible organizational form. Third, with a not unreasonable assumption,
Perhaps the most important difference
is
horizontally to exploit "synergies."
that
we
we
believe that our analysis
all
is
we
are
simpler.
are able to capture the idea that firms
BW's framework
idea of a synergy since, given their assumption that
or
organizational form affects
endogenize capacity choice, so
able to rule out asymmetric vertical integration. Fourth,
may merge
by B1/B2),
(ii)
is
not able to incorporate the
variables except for nontransferable
investments are ex post contractible, bargaining leads to ex post efficiency under any
organization form,
4.
i.e.,
the only inefficiencies are in ex ante managerial investments.
Conclusion.
In the traditional property rights
individuals; asset transfers
investments. In our
change individual incentives
is
in
many ways
technologically defined entity that
is that
choose a boss
traditional
to invest, but not
who makes
close to the traditional view of the firm as a
makes decisions about
inputs, outputs
our firm does not necessarily maximize profits, because
that
opens the door
barring regulatory constraints,
fact that
approach easier
to
it
to a discussion
would be optimal
our view of the firm
the
are transferable through
and
it
prices.
may be
that cares about nontransferrable private benefits. It is this small
model
The
are inalienably attached to
model decisions, including investment decisions,
ownership. Our structure
difference
model investments
is
The
desirable to
wrinkle in the
of boundaries. In the traditional model,
to organize all activity in a single firm.
so close to the traditional view should
make our
apply to questions of industrial organization. The model in Section 3 on
31
outsourcing
is
indicative of this.
One could pursue
firms to understand industry structure.
entrepreneurial growth followed
Our framework may
in future research.
influences and
is
dynamics - times of
also study industry
by times of industry consolidation,
for instance.
we
looked
at a
simple model of delegation and
we
plan to return to
We are interested in understanding how the internal organization of the firm
influenced by
its
boundaries. Delegation creates new, hybrid opportunities for
matching decision making objectives with decision making authority.
objectives change with delegation and
these are examples of questions
how do
we would
How do the
firm's de facto
-
additional activities influence what gets decided
like to
understand better. Because our approach
emphasizes the role of the firm's objective function
alternative
number of
also be helpful for analyzing the internal structure of the firm. In a
previous version of the paper,
it
One could
a similar analysis with a larger
it
would
also be of interest to analyze
governance structures for decision making, such as cooperatives.
Private benefits play a pivotal role in our analysis.
It
could have been more natural to
incentive effects counter-balance the benefits from integration (as in Mailath, et
al,
2002).
let
We
chose the current path, because the framework seems more flexible and the analysis more
tractable. It
remains to be seen whether private benefits can be defined tightly enough and are
empirically important enough for the approach to be useful.
One of our
objectives in writing this paper has been to
from assets towards
will
activities.
Asset ownership
is at
move
the focus of attention
the core of the property rights theory and
remain important for understanding boundaries. At the same time
practitioners, organizational consultants
disciplines than
economics
(e.g.
capabilities
it
it is
remarkable
it
how few
and researchers studying organizations within other
sociology and organizational behavior) ever talk about firms in
terms of asset ownership. For most of them a firm
knowledge and
away
is
defined by the things
it
does and the
possesses. Coase (1988) in his article "Industrial Organization:
Proposal for Research," makes clear that he too
is
looking for "a theory which concerns
with the optimum distribution of activities, or functions,
among
firms." (p 64).
He
A
itself
further notes
"the costs of organizing an activity within any given firm depend on what other activities the firm
is
engaged
in.
A given
set
of activities will
facilitate the carrying out
the performance of others."
The model we have proposed
is in this spirit.
of some activities but hinder
)
32
APPENDIX: General
coordination.
Here we show
hold more generally.
that the
main conclusions of Proposition
From now on we drop
(2.5),
but replace
(A. 1
zA (N,Y) > z A (N,N), z B (Y,N) > z B (N,N),
(A.2)
zA (N,N) > z A (Y,N), z B (N,N) > z B (N,Y).
Condition (A.l) says
accommodating, given
nonintegration,
Note
it
that,
that she
,
concerning pure coordination,
by:
under nonintegration, each boss
is
better off if the other boss is
does not accommodate. Condition (A.2) says
never pays a boss to be accommodating
that these
it
1
assumptions are implied by (2.5),
if
that,
under
the other boss is not accommodating.
i.e.,
they hold under pure coordination.
Also, they are plausible in the case where the two units produce substitute goods and
accommodation
refers to a decision
by one unit
to raise price or not
poach on the other unit's
territory.
Given (A.l)
-
(A.2),
we can
establish the following proposition.
Assume
(A.l)
(A)
(N,N)
always a Nash equilibrium in the game in Figure
(B)
Suppose (N,N)
Proposition 2
:
is
-
(A.2). Then:
is efficient.
Then
all
Then,
if
Nash
2.
equilibria generate the
same payoff
vector (z A (N,N), z B (N,N)).
Suppose (Y,Y)
(C)
is efficient.
z A (Y,Y) > z A (N,Y) and z B (Y,Y) > z B (Y,N),
(A.3)
(Y,Y)
is
hand,
if
As
a
Nash equilibrium and Pareto dominates
(A.3)
before,
is
violated, all
we will assume
Nash
all
other
Nash
equilibria.
On the other
equilibria are payoff equivalent to (N,N).
that, if there are
multiple equilibria, the parties will never pick
33
a Pareto
dominated equilibrium. Thus
nonintegration, if (N,N)
the
outcome
will
To
z B (Y,Y)
concreteness
- will
(A.l)
-
if
Part (A)
:
is
a
<
is
outcome
obvious; (N,N)
(Y,Y) yields
if
=
(C), the
Milgrom and Roberts,
If (A.3) is violated,
game
is
is efficient,
is
than (N,N), either z A (Y,Y)
A
or boss
Nash
is efficient,
is
a
B - say,
A
boss
for
equilibrium. (The
Nash Equilibrium. Then
=
z A (N,N)
z A (N,Y) by (A.l). So,
A parallel argument establishes that if (Y,N)
is
a
Nash
to (N,N). This proves part (B).
supermodular, and so by standard results for such games (see
1990), (Y,Y), being efficient, Pareto dominates
(Y,Y)
(Y,Y)
always a Nash Equilibrium given (A. 2).
Suppose (N,Y)
z B (N,Y) and, because (N,N)
must be payoff equivalent
Case
if
(Y,Y) yields the same surplus as (N,N).) Furthermore, given
(N,Y) yields the same payoffs as (N,N).
In
is
deviate from (Y,Y) and so (Y,Y) cannot be a
(A.2) implies z B (N,N)
it
be (N,N). In contrast,
strictly less surplus
N is a dominant strategy for boss A.
(A. 2),
Equilibrium
will
z B (N,N). But then, given (A.l), either boss
more complex
little
can rephrase Proposition 2 as follows. Under
(A.3) holds but (N,N) otherwise.
establish (B), note that, if
< zA (N,N) or
argument
efficient, the
is
be (Y,Y)
Proof of Proposition 2
we
not a
Nash Equilibrium and
the
all
other
argument proceeds
Nash
as in
equilibria.
Case B.
Q.E.D.
Like Proposition
efficient,
may not
but
nonintegration
may
1,
Proposition 2 says that nonintegration achieves efficiency if (N,N)
achieve
it
if
(Y,Y)
not achieve (Y,Y)
is efficient.
when
it
is
However, there
efficient (as
are
opposed
is
now two reasons why
to the single reason in the
case of pure coordination). First, as in the case of pure coordination, the benefits from
may be
coordination
we may have
violated.
z A (N,N)
>
Second, even
unilateral deviation
defeating
so unevenly distributed that (Y,Y) does not Pareto dominate (N,N). That
(it
z A (Y,Y) or z B (N,N)
if
this
z B (Y,Y), which, given (A.l), implies that (A.3) is
(Y,Y) Pareto dominates (N,N), (A.3)
from coordination may be
leads to the
Given
>
is,
in the interest of
Nash equilibrium (N,N)
may
not hold anyway,
one party, even though
i.e.,
it
a
is self-
that both parties dislike).
second reason, the characterization of the outcome under nonintegration
is
not
quite as simple as in the case of pure coordination. Specifically, the set of parameter values under
which nonintegration yields (Y,Y)
is
now
a subset of the
NI-NI quadrant
in Figure 3, rather than
34
the
whole quadrant. Note, however,
on the side of too
The
coordination.
little
analysis of integration
coordination (2.5)
that this merely reinforces the result that nonintegration errs
was never used
is
unchanged under (A.l)
-
(A. 2), since the assumption of pure
in this case. Since, as in the case
nonintegration errs on the side of too
little
of pure coordination,
coordination, while integration errs on the side of too
much, we have established
Proposition 3
first-best.
.
Assume
On the
(A.l)
-
(A. 2). Then, if (N,N)
other hand, if (Y,Y)
We may conclude that,
and binary decisions, the main
general kinds of decisions.
is efficient,
is efficient,
nonintegration achieves the
integration achieves the first-best.
given the (admittedly very strong) assumption of perfect certainly
results
of the pure coordination case continue
to
hold for more
35
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Mexican
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