MIT LIBRARIES
3 9080 02238 6053
.;.:.
'•^l'-«7.
(>
.1.
'
•.
DEWEY
HD28
.M414
S9
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
A THEORY OF INEFFICIENT
INTRAFIRM TRANSACTIONS
Julio J. Rotemberg
Working Paper #2084-88
November 1988
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
A THEORY OF INEFFICIENT
INTRAFIRM TRANSACTIONS
Julio J. Rotemberg
Working Paper #2084-88
November 1988
A
Theory of
Inefficient
Intrafirm Transactions
Julio J.
*
Rotemberg
Sloan School of Management,
Massachusetts Institute of Technology
current version:
November
14,
1988
Abstract
This paper presents a model in which goods market distortions lead firms to
socially inefficient
aversion
modes
of internal organization.
The model
seeks to capture the
documented by Eccles and White (1988) of middle management aversion
to inter-profit center transactions.
I
consider situations where reputational forces
are able to support equilibria in which goods are of high quality.
These forces
can break down when the transactions take place within the firm. Integration
may
nonetheless be privately worthwhile
•I wish to thank
if
price exceeds marginal cost.
OhverHart, Jim Poterba, Jean Tirole and Garth Saloner
for research support
for
comments and the NSF and Sloan Foundations
A Theory
of Inefficient
Intrafirm Transactions
Julio J.
Rotemberg
Sloan School of Management,
Massachusetts Institute of Technology
Unrelated individuals work together within firms.
relationships of these individuals.
At
lets outsiders
least since
which make
to
pay them. They also decide what
activities
carry out under contract.
Coase (1937) economists have viewed these arrangements as adaptations
profits higher
profits does not
individuals within the firm have authority, they
how much
decide what others should do and
the firms
Some
Firms have rules governing the
than they would be otherwise. Obviously, this maximization of
imply that the organization of firms maximizes the social good. The usual
product market imperfections can lead firms to make money while providing a socially
inefficient level of
output. Authors concerned with the internal organization of the firm
tend to ignore these imperfections. Perhaps for this reason the analysis of Coase (1937),
Alchian and Demsetz (1972), Williamson (1985) and Grossman and Hart (1986) implies
that the authority relations within firms are optimal from a social perspective.
"This book advances the proposition that the economic
(1985) goes so far as to state:
institutions of capitalism have the
this
paper
I
show that
main purpose
this optimistic appraisal
market imperfections. The
Williamson
of economizing
is
inefficiencies associated
due at
on transactions
costs." In
least in part to the exclusion of
with product market power can distort
not only the level of output but also the transactions which
make
this level of
output
possible.
The
some
basis for this paper
firms earn
monopoly
is
that the existence of goods market distortions implies that
rents.
As a
result, firms
would willingly tolerate organizational
'See the survey by Holmstrom and Tirole (1987) for additional references.
1
inefTiciencies
may
rents
if
such
inefficiencies help
them capture these
Some
rents.
of the economy's
be thus dissipated in the form of inefficient organization of production.
dissipation of this kind
may
help explain
why
Rent
conventional meaisurements of profits do not
uncover a much monopolistic conduct.
The work
which
in
I
focus.
of Eccles
and White (1988) has influenced the particular
They interviewed managers who buy and
The impression
multi-profit center firms.
prefer external to internal transactions.
management.
Frictions are
goods across
by these interviews
left
is
much more common
all
in
on
profit centers
that managers
They would rather buy from and
Internal transactions occur at
outside the firm.
sell
inefficiency
sell
to agents
because they are mandated by top
these
mandated transactions than
in
Eccles and White (1988) justly regard their findings as a
their external counterparts.
challenge to Williamson's (1985) view of firms. Their evidence suggests that transactions
costs actually increase
models
In the
are allowed.
The
I
when
firms engage in internal transactions.
present below, sellers provide high quality
reaison they
do so
is
when only spot markets
that customers change suppliers whenever they have
an unsatisfactory experience. Suppliers remain diligent because they are afraid of losing
customers
in this
way. Customer mobility
is
essential for ensuring high quality.
Long term contracts which penalize the buyer when he changes
mobility. Mobility
is
integrated enterprise
mechanisms
has
little
If
is
also reduced
mandate
if
internal transactions.
If
a supplier cannot lose a particular customer he
him with high
quality goods.
ments are attractive when price exceeds marginal
from reducing mobility. The reduction
only
Whichever of these mobility reducing
long term contracts and integration reduce quality,
the buyer and seller.
when
The
They
reduce this
the buyer and seller integrate and the managers of the
adopted, quality suffers.
incentive to provide
sellers
in
why do
they arise? Such arrange-
cost. In this case, there
is
an advantage
mobility increases the overall rents earned by
get to keep the difference between price
and marginal cost
the buyer remains attached to the seller.
excess of price over marginal cost necessary to induce quality reducing associations
'For other modcli in which locially inefficient contract! ariie bccauie they help capture renta tee Aghion and Bolton (1987),
Dewatripont (1988) and Ordovcr, Saloner and Salop (1988).
between buyer and
it is
can be due to a variety of reasons. In the
seller
the result of implicit collusion
model high
finitely
many
price-setting firms. In
develop this model as well to show that
I
Informational imperfections play a crucial role in
my
results
my
my
second
in
do not hinge on the
models. With perfect informa-
tion about quality, contracts can force sellers to provide high quality.
is
explore
I
supergame models.
multiplicities inherent in
quality
model
due to the presence of quantity setting firms which compete
prices are
Cournot fashion.
among
first
I
assume instead that
observable but not verifiable by outsiders. Examples of quality which have this
feature include the willingness of the supplier to
work hard on the customer's
particular, the supplier can try to change delivery schedules
modate changes
in the
and
behalf. In
specifications to
customer's needs. Alternatively, the supplier can insist on
accom-
fulfilling
only those obligations written into the contract.
The paper proceeds
sellers. In
the
first
as follows. Section
subsection
It differs
mainly
among
in that
good quality because buyers change suppliers
The formal model
quality proves to be low.
(1981).
considers a model of implicit collusion
consider equilibria with spot markets only. These equilibria
Sellers provide
often exhibit high quality.
when
I
1
I
is
very similar to Klein and Leffler
provide reasons for customers to leave after encountering
low quality while they do not.
In the second subsection
ity
I
consider long term contracts. These contracts reduce mobil-
by forcing the buyer to compensate the
seller
when he changes
partners. This reduces
the seller's fear of losing the buyer. This increases the rents of the seller at the cost of re-
ducing quality.
all
I
provide conditions under which the optimal contract of this sort impedes
mobility and provides only bad quality goods.
In the third subsection
I
argue that outright integration can alleviate the low quality
consequences of long term contracts. The idea
both the
his
seller
is
that quality becomes easier to verify
and the buyer come under the authority of a conmion boss. This boss can use
power to gather evidence on the quality of the goods that are provided. The
of this evidence
suppliers can
if
makes
more
it
easily
possible to
make compensation depend on
be induced to furnish high quality goods.
quality.
availability
Therefore,
Top management,
with a role similar to that
in
in
Alchian and Demsetz (1972), thus emerges endogenously
From
a social point of
thus inferior to spot markets.
Therefore, this
the model. Quality verification via integration costs resources.
view this method of improving quality
why
subsection both explains
firms
is
who
transact internally are created and
why
these
intrafirm transactions might be inefficient.
Section 2 then considers a model with Cournot competition
its first
among
Again
sellers.
subsection deals with separate firms, the second with associated firms. Section 3
concludes.
1.
Repeated Oligopoly
The upstream market
intermediate good. They can then
cost of a bad quality version of the
for the effort
is
worth
e
to him, the
good
good
is c.
With probability
(1
-
effort,
o),
it
quality.
They
A
to a variety of customers.
This cost
their
firms can produce a
is
homogeneous
The marginal
the cost of compensating workers
worker spends an additional
I
effort
assume that
which
if
the
the good becomes a high quality good with probability
remains a low quality good.
The downstream customers buy Y
each unit of good quality.
If
good
The
sometimes, of good quality.
at least
is,
firms.
sell this
needed to produce the good.
worker spends the requisite
a.
N
consists of
They
units of the good.
unit of bad quality
is
worth
/i
less to
are risk neutral so that they are willing to pay (r
are willing to pay r for
them than a
—
xfi) for
unit of good
a unit which
is
of low quality with probability i.
Contracts cannot specify the level of quality. This occurs because outsiders cannot
observe quality so they cannot enforce contracts which stipulate payments as a function
of quality.
High quality thus includes the provision of services which, while not easy to
stipulate, are important to the buyer.
prompt handling
of complaints.
meeting changes
in
These services can include courteous service and
High quality also includes the
flexibility of
the seller in
the buyers needs. Suppose the buyer originally wrote a contract for
delivery at the beginning of December.
delivery in the middle of
The buyer then
November. A high quality
of changing the delivery at a low cost.
A
seller of
4
realizes that he
seller
is
bad quality
would much prefer
flexible so that
finds
it
he
is
capable
very costly to change
the delivery date.
effort
made
in
The
being
courts see only the ex post cost of changes in deliver and not the
flexible.
While payments cannot depend on
quality, they
can depend on the number of units
transacted. Spot markets allow only this type of payment.
payments to take place when a buyer changes
supplier.
I
Long term contracts
also allow
consider these two institutional
structures in turn.
1.1.
Spot Markets
In the case of spot markets each purchasing transaction has three stages.
all
upstream suppliers announce
how many
specifying
their prices.
Second, buyers and
sellers sign
units are sold at this price in the current period.
occurs either with low or high quality. Customers
know what
First,
a contract
Finally, delivery
quality they have received.
After receiving a good of either high or low quality the customer has the option of changing
suppliers.'*
Customers constantly update
pliers.
their beliefs
about the quality offered by different sup-
Before knowing current prices, customer j assigns a subjective prior probability z^j
to the event that firm
updates this prior as
Xij that low quality
is
t
is
providing low quality. After observing the price P,, the customer
in Klein
and
Leffier (1981).
being provided.
She calculates a posterior probability
The customer then computes
expected net surplus that she can obtain from supplier
t.
[r
—
{P^
+ x,y^)],
the
She purchases only from those
suppliers with the highest net surplus.
The purchaser drops
the previous period's supplier
if
he
is
not
among
those providing
highest net surplus. In this case, she randomly picks one cheap supplier. Otherwise, she
stays with her previous supplier.
is
that there
supplier.
is
Even
quality, there
is
One
difficulty
with Klein and LefHer's original model
never any equilibriimi reason to either leave or stay with
if
last period's
a particular supplier deviates from the equilibrium by supplying bad
no reason to suppose that he
will
supply bad quality in the future. His
^This example of quality is very reminiscent of Grossman and Hart (1986). As will be clearer below, this moral hazard
problem of the seller is not cis easily solved by integration as those they consider.
*In Klein and Leffler (1981) customers who have received bad quality can also communicate this to other potential buyers.
Including this possibility would not affect the analysis. It is excluded here because I stress below the difficulties in communicating
the level of quality one has received to one's superior.
incentives to provide
is
only
compounded
good quality do not change
if
one recognizes that,
after supplying
particularly
if
in
it
is
less
is
difficulty
costly to the
reason to leave a supplier
the deficiency of quality might be due to bad luck.
To circumvent
that
even
is
This
quality.
changing suppliers
in practice,
customer. In the presence of such mobility costs, there
bad
this difficulty,
I
introduce an equilibrium reason for customers to infer
worthwhile to leave suppliers whose quality
one of two regimes.
In the usual
is
low.
I
assume that firms can be
regime they are well managed. In other words they
take the actions which maiximize profits. Sometimes, however, firms are badly managed.
When
firms are in this bad regime they provide only
managed
I
firms
fail
bad
quality.
In other words, badly
to give their employees the necessary incentives to Jissure
good
quality.
assume that well managed firms randomly become poorly managed. They then tend
to remain poorly
poorly
managed.
In particular, well
managed than poorly managed
firms are in state
managed
in
becomes
well
the next period
managed
is
(1
The
6.
is
—
V')-
(1
I
—
firms are less likely to
firms are to remain so.
ideas by letting firms be in two states.
managed
managed
Well
managed
The
assume that
managed
w
exceeds
4)
while poorly
firm remains well
probability that a poorly
ip
capture these
I
firms are in state
probability that a well
4>).
Formally,
become
so that bad
managed
firm
management has
a tendency to persist.
These transition probabilities imply a steady state probability of being
equal
essentially always well
almost equal to zero. Indeed, the analysis
to zero. For simplicity
same
w
to:
To capture the idea that firms are
is
in state
I
also
is
assume that the
simplest
initial
managed,
when one
I
assume that
takes the limit as
probability of being in state
w
4>
<l>
goes
is
the
as the steady state probability (1).
Supplying firms do not observe each other's quality. They do however observe each
other's prices.
I
assume below that firms can follow pricing strategies which depend on
prices charged earlier.
As
is
typical of supergames, there are
outcome depends on customer's
beliefs
many
possible equilibria.
The
about quality as well as on supplier reactions to
6
other firms' prices.
The worst equilibrium
provided. As long as
charge
c
(r
—
customers believing that bad quality
for suppliers has
/x)
and provide bad
>
there
c,
then an equilibrium where
is
him
suppliers
who
active suppliers
all
him
to deviate by raising
have customers
initially believe that
all sales.
and
Equilibria reminiscent of Klein
all
always
For a producer to deviate by either providing good
quality.
quality or lower prices represents a simple gift to customers. For
his price loses
is
Leffler (1981)
charge relatively high prices try to provide good quality. Because price
is
high, managers then do try to provide high quality. There are generally several equilibria
They
of this kind.
differ in
the price charged by firms.
actually have a bigger incentive to provide high quality.
when customers
leave
At these
unhappy with the quality they have
equilibria with higher prices. Thus,
if
Equilibria with higher prices
equilibria firms lose
more
received. Sellers also prefer the
they can meet ab initio and agree on an equilibrium
me
they would pick the one with the highest price. These considerations lead
on
to focus
this particular equilibrium.
At
this equilibriimi, sellers try to
bility that firms are well
at
managed
random obtains a good
willing to
is
supply good quality. Since the unconditional proba-
^
i_
,
of high quality
pay to a firm chosen
at
random
y
the probability that a buyer choosing a seller
,
is
i
,
,
_^
Therefore, the most a customer
is:
(i-rr^)"It
is
more
profitable than one of providing low quality.
can obtain while offering low quality
to attempt to provide high quality
high quality.
I
show below
average. Since badly
(Tfj,
exceeds
that,
managed
the quality implicit in (2)
long as
(^)
only makes sense for the firms to focus on high quality equilibria with this price
this strategy
is
|
r
is
if
—
/x.
The higher
The
price in (2)
\,J_J^ exceeds the
when
is
if
highest price firms
makes
it
worthwhile
cost of attempting to provide
the firms are well managed, this cost equals
e
on
firms do not incur this cost, the average cost from sustaining
,
,
_'!
.
Thus the attempt to provide quality
e.
7
is
worthwhile as
I
now show
that,
under some additional conditions, there
charge the price given by
and
(2)
is
try to provide high quality.
in
doing their best.
prove that customers come back to sellers
quality while they desert those that haven't. Then,
it is
not
in
To do
when customers
the presence of this price
customer behavior
I
an equilibrium where firms
this,
believe that sellers are
who have
them high
given
consider seller behavior.
I
consider
first
I
show that
I
the interest of sellers to deviate from this price and from the attempt to provide
high quality.
Suppose a customer receives high quality from a
that the seller
is
is
thus
remain with
have cissumed,
—
cr(l
exceeds
By
(f>).
random
high quality from a seller chosen at
I
now
assign to having a badly
above, this prior probability
this particular seller
Let
6(
He thus concludes
is
only ^.T^
j^
He
(f>.
.
This latter term
therefore finds
it
is
smaller
in his best interest to
his old seller.
a.t
is
t
—
highest
1.
managed
managed
prior probability of having a badly
from
t.
contrast, his probability of obtaining
Suppose instead that the customer receives low quality
does he
period
currently well managed. His probability of obtaining high quality next
period from this particular seller
whenever, as
seller in
if
the event that he provides low quality at
What
probability
the argument of the paragraph
is
ceise first.
badly managed at
t
while Lt represents
Then, the probability of event
t.
managed and
P{bt\Lt,Wt_i)
t.
the customer has bought a high quality good
represent the event that the seller
the seller was previously well
By
thus consider this
I
period
This probability depends on his
seller?
seller.
in
that he provides bad quality at
bt
t
given that
is:
P{bt,Lt\wt-i)
=
ryot,i^t\wt-l)
P{bt,Lt\wt-))
+ P{wt,Lt\wt-i)
^{Wt,^t\^t-1)
-t-
A,
<f>
This probability exceeds the probability
^
managed
J_
,
that a firm chosen at
random
is
poorly
as long as:
In other words, as long as well
quality,
(3)
+ {l-a){l-4>)
managed
customers abandon suppliers
firms are sufficiently likely to produce high
who suddenly
8
sell
low quality.
If (4)
is
met buyers
leave even those sellers with which they have been previously successful.
satisfied,
customers
who have
previously received good quality leave
What about customers which have
bad.
when
equation
is
then only
provided bad quality
T^
.
The
,
who have had no
probability that he
experience with this seller
badly managed given that he has
is
P{bt,Lt)+P{wt,Lt)
+
{1
-
who have
poorly managed. The customers
when
In conclusion,
(4)
(5)
-
a){l
This probability always exceeds the probability
quality.
well
is
P{bt,Lt)
=
(f>
them bad
seller
is:
Pibt\Lt)
is
becomes
quality
because they have just changed suppliers. Their prior probability that the
managed
(4) is
not received a good quality unit in the past from
Consider in particular buyers
this seller.
If
^
xi^y
?_
,
,
that a firm chosen at
just arrive always leave a supplier
is
met,
all
buyers leave firms
who
random
who
gives
offer
low
quality.
I
now turn
to seller behavior.
provide bad quality, sellers find
it
I
show
that, given that
in their best interest to
consumers leave those who
supply good quality.
I
later turn
to sellers' incentives to change prices.
To
offer
good
quality, a seller
must provide appropriate incentives
cLssume that the seller does not observe quality directly.
can
offer his
paid
is
if
well
managed
seller,
however,
worker a contract which makes compensation depend on whether a particular
purchaser comes back next period.
sible to
A
to his workers. I
pay them
less
than
c in
the customer does not
I
assume workers are
any time period.^
come back while
7i
is
I let
the
risk neutral
Iq
but that
it is
impos-
be the amount the worker
amount he
gets
when
is
the purchase
repeated. For the worker to try to provide high quality the following conditions must
be met:
Io
+ aIi>c +
a{h -
/o)
it
is
e
(6)
(7)
type have very similar impHcations to risk aversion but are much easier to analyie. The more
only necessary to pay them a nonnegative amount complicates the analysis without affecting the
* Liquidity constraints of this
usual assumption that
>
e
conclusions.
9
Condition
dition (7)
good
necessary for workers to be willing to work hard
is
quality.
conditions
is
If
to
income cannot be
let Iq
equal
now ask whether a
I
that the worker earn on average the value of their effort. Con-
(6) requires
librium where he
c
less
while
/]
than
c,
equals
c
the lowest cost
+
Suppose
In the future he regains
To consider a
current suppliers.
some customers who become
single deviation in isolation
I
he
in particular that
He then
neglects to provide these incentives just in the current period.
customers.
for satisfying these
wants to deviate from an equi-
seller
providing incentives for high quality.
is
method
^.
managed
currently well
the hope of providing
in
loses all his current
dissatisfied
with their
suppose that the supplier
does attempt to give these later customers good quality.
By deviating
in
this
workers for their extra
successful
manner, the supplier avoids the cost ^ of compensating the
Naturally, he only incurs this cost
effort.
and customers return
he also gains 6{P
-
c)
where P
in
is
One
period.
Once again
this
is
offset
the discount factor. Using
long as (8)
is
if
The
(8) is positive.
for the
is
that one can avoid paying
who
customers
return in the next
net gains from the avoidance of effort inducing payments
By
(8).
Given
this proportionality, these deviations
contrast, firms are
happy to
try to provide quality as
negative and:
c
—
"(l-V-)
J
1
All that
(2),
by the fact that such payments only occur when customers
the next period are thus proportional to
are worthwhile
is
is:
needed to produce high quality
arc returning a second time.
in
is
additional gain from deviating and providing low quality
for the effort
the quality effort
the following period. So, whenever he incurs this cost
the price charged and 6
the net gain over the next period
if
is
necessary for
(9) to
hold
Ts
-|-(^-0_
is
S
"•
(""
that the willingness to pay r be sufficiently
large.
I
now consider
change
in price is
seller deviations in the price that
observable by competitors.
It is
10
they charge.
I
assume that any such
viewed by them as well as by customers
Therefore
as a violation of the collusive understanding.
firms expect that, one period after the deviation price will
the customers as well as the
all
to c
fall
and quality
be low.
will
Since this deviation reduces profits to zero from next period on, firms will refrain from such
deviations as long as they do not discount the future too severely. There
reason
why
this deviation
quality for the future,
it
unattractive to sellers.
is
eliminates
all
Because
leads
it
is
all
an additional
to expect
bad
firms' (including the deviator's) incentive to provide
high quality in the current period. Thus the deviator can only
sell
low quality goods at
relatively low prices even in the current period.
This section has demonstrated that, when only spot contracts are possible, equilibria
with high quality often
exist.
These equilibria are
in principle
even possible when a
agent owns the assets used by buyer as well as the assets of a
this
common owner has
When
buyers and
sellers' assets are
these equilibria
do so because
from a
seller
is
They tend
more
to be
goes to zero,
all
is
bad
quality.
profitable to implicitly colluding
seller's
perspective) with
seller.
They
usually
ben unlucky and has been unable to produce good quality
Only very seldom are these separations useful
who
in this case
agents, these high quality
that buyers often sever their relationship with their
their seller has
spite of trying.
1.2.
owned by separate
than equilibria with lower quality. One problem (from the
sellers
However,
to let the buyer change suppliers every time he receives
equilibria are quite plausible.
(f)
seller.
common
in that a
buyer
is
in
separating
not trying to produce high quality goods. Indeed, in the limit where
separations are the result of mistakes.
Long Term Contracts
I
now
consider the possibility of long term contracts. In particular, there
period before any sales take place. In this
seller
initial
period, a particular buyer
can write such a contract. For simplicity
I
assume that
is
an
initial
and a particular
this particular
buyer buys
one unit per period. The long term contract stipulates not only a price paid
for the
but also stipulates payments that must be made
The purpose
to reduce the
number
if
the buyer changes sellers.
good
of accidental separations which are so ubiquitous
of this contract
is
when only spot
contracts are allowed. This
is
advantageous to the
seller
because
*The punishments I consider I obviously extreme. However, the analysis of FViedman (1971) makes
punishments are generally sufficient to deter changes in observable prices.
11
it
it
allows
clear that milder
him
for
to capture
more
The
rents.
sellers
is
thus willing to compensate the buyer in exchange
reducing his mobility.
The
precise
amount by which the
compensates the buyer
seller
in the contract that
is
actually written depends on the relative bargaining power of the two agents in the initial
make a
period. Suppose the seller can
take-it-or- leave-it ofTer which,
rejected, leads to
if
the sequence of spot contracts analyzed in section 1.1 Then, the buyer will give
seller.
The
opposite
true
is
if
the buyer gets to
make a
little
to the
take-it-or-leave-it offer. Naturally,
the alternating offers scheme of Rubinstein (1982) gives an intermediate answer.
Independently of whose bargaining power
efficient
is
if
bargaining
likely to
power
will
From
is
seller profits.
determine the distribution of these
sum
the perspective of the
when he
arrangement
larger, the
done under complete information.
maximize the sum of buyer and
of the buyer
is
In other words, the
in section
1.1
had A equal
term commitment to buy from
In particular,
arrangement
is
the response
A be the probability that
let
I
The spot market
contracts
contrast a completely binding long
would have a A equal
made
intermediate cases, the buyer must be
By
to zero.
this seller
be
profits.
the buyer comes back to the seller after receiving bad quality.
considered
likely to
Then, the degree of bargaining
of both profits, the principal issue
receives low quality.
is
indifferent
to one.
To implement the
between staying and leaving
after
receiving low quality. This indifference can be accomplished by forcing the buyer to pay
damages whenever he abandons the
There are two
I
return shortly.
assume that the
is
effects
relationship.
from increases
The second
is
level of quality
in A.
The
first is
an increase
that high quality becomes
is
not contractible.
the pattern of payments to the seller's worker.
What can
in rents to
which
more expensive. As before
be
To induce him
made
I
part of the contract
to exert effort the contract
must specify that he gets paid more when the buyer returns than when he doesn't. Once
again,
if
let Iq
be the worker's payment
if
this
buyer changes suppliers while
he doesn't. These payments must both exceed
probability A even
when
quality
/o
is
+
c.
Because
low, the analogues to (6)
(a
+ [l-a]A)/i >
12
c
+
£
this
and
/^
is
his
payment
customer returns with
(7)
are now:
(6')
a{l-X){h-Io)>e
Given that
straints
is
to
cannot be lower than
/q
let (7')
when he
ly
To
is
=
+
,
when he does not engage
this requires
fall,
an increase
sometimes paid when the
also
computing these contracts
now
I
the buyer ever leaves the
good that he buys
is
worth
Similarly, the seller receives
[r
—
A essentially raise the probability
This reduces his incentive
in effort.
is
and
particularly expensive
first
the optimal A
and then the optimal A when they
is
(f)
to him.
a)iJ,]
no surplus from
He
[r
—
(1
Assuming an
(12)
-
Of
—
a)n].
The
seller are,
on average:
[cr
+
(11)
(1
—
we can write
o)\],
overall joint
(11) as:
S[a
+
{1
-
is
-
r
-
c
(1
- a)n
a+{l-a)X
TT^—
f-_
a(l-A)
a)X]
(12)
optimal A therefore ensures that the derivative of
interior solution, the
with respect to A
don't.
buyer once he leaves. By contrast, joint
this
Since the buyer remains with probability
1
the two
thus receives no further surplus.
r-{l-a)n-W.
and
if
zero.
he starts buying at a price of
seller,
whenever the buyer actually purchases from the
profits using (10)
increase.
the one with higher joint profits. For simplicity in
is
—
must
not obvious that contracts
it is
thus analyze
I
is
/q
unsuccessful in producing high quality.
consider only the limit where
(1
Therefore,
(10)
This increase
in 7i.
effort
parties attempt to maintain high quality
these two contracts, the optimal one
•
(^_\\
a(l-A)
with high values of A involve high quality.
profits
—
c-\
£+iLz^,.
Because quality becomes more expensive as A increases,
If
for satisfying these con-
reestablish his desire to work, the difference between /i
Since /q cannot
because Ii
method
induced to provide high quality equal:
is
strictly increasing in A. Increases in
that the worker gets /^ even
to work.
the lowest cost
c,
hold with equality. This implies that /j equals
average payments to the worker
These payments are
(7')
zero:
6{l-a)
(l-% + (l-a)A])2
r
-
c
-
[1
-
a
a)fx
+ (l-a)X
A
a(l
[
o
+
-
TT^e
A)
(1-(7)A
^{1-A)2
13
(13)
'
The term on
the
first line
of (13) captures the fact that an increase in A raises the
The one on
revenues of the seller by reducing separations.
the second line captures the
increased costs of quality which result from higher values of A. Note that the
the expression in (13), evaluated at A equal zero,
interior only
if
optimal A
zero and the buyer and seller are no
is
Note also that the optimal A given by
makes the expression
means that reductions
is
that
it
The
makes
A are profitable.
in
alternative solution
two firms equal
is
positive.
more attached than
strictly smaller
is
in (13) infinitely negative.
infinitely costly to
it
(13)
is
in a
optimum
Otherwise the
spot market.
than one.
A
A of one
Given the second order conditions,
The reason
a A equal to one
is
is
this
unprofitable here
provide high quality.
not to provide quality.
This gives overall profits for the
to:
1
1
The expression
(14)
is
-8\a +
{\
-o)\\
strictly increasing in A.
Once
have everything to gain by remaining together.
other
V-c-n].
quality
(14)
is
abandoned the two agents
They thereby avoid giving
rents to the
sellers.
To obtain the optimal contract we must compare the expression
one with the expression (12) with A given by the solution of
the two firms give up quality and never separate.
If
(13).
the latter
is
If
(14) with A equal to
the former
larger, the
is
larger,
two firms do
separate probabilistically.
I
do not have closed form expressions which determine the outcome that
However,
up high
it is
clear
quality.
A
that the firms have
let
from
high
(12), (13)
—
(r
much
c)
and
(14) that,
means that the
to lose
if
(r
rents
—
c) is sufficiently
from any sale are
by separations. They
will prevail.
big the firms give
large.
will therefore very
This means
much
prefer to
separations be extremely rare. However, the rarer are the separations, the higher
and the more expensive
separations, they
Two
is
the provision of quality.
make do with low
is
A
Thus, when firms are very averse to
quality.
numerical examples illustrate these points. Both these examples have n equal to
^I am ufuming that the quality provided to the buyer who ha* a long term contract doei not affect other buyers' beliefs
about the quality they will receive This it consistent with the absence of communication among buyers assumed so far. Even if
I allowed such communication, outsiders would not be surprised to learn that bondeJ customers receive worse treatment. There
would b« no reason to update the likelihood of receiving good quality on the basis of the quaUty provided to those buyers.
14
one, 8 equal to
equals
(r
—
example
t is
relatively small in that
—
provide quality with spot contracts condition
sellers to
must exceed
c)
to .75. In the first
Therefore, the social gain from providing quality [o^l
.3.
For
.45.
and o equal
.9
f)
a relatively large
is
(9)
it
must be met and
Otherwise the surplus they get from future sales does not justify
.4.
the provision of current quality.
Even when long term contracts (which render A
always chosen. Indeed, for
When
rents
(r
—
between
c)
.4
from customer attachment are
and
positive) are available, they are not
1.13 the firms prefer to let A equal zero.
relatively low
not worth either increasing
it is
the cost of quality (by having an interior A) or foregoing quality completely. For
between 1.13 and
1.2 the
buyer and
Quality remains high but
rents
is
.99.
.25.
example
(r
e
choose a strictly positive A which
higher. For (r
is
equals
let
.5
— c)
altogether.
is
seller
between
Not
.99
now
is
requires that (r
smaller and equals
—
c)
— c)
the optimal contract forgoes quality
social benefit of quality
A below one. As
(r
—
equal at least
term contracts choose spot markets
[r
eager to give up quality in exchange for capturing rents.
strictly positive
below one.
is
1.2 the incentive to capture
surprisingly, as the social value of quality falls, the firms
example where the
c)
access to long
For larger
1.11.
above
c)
so the social gain from quality
who have
and
—
—
A equal one and give up on high quality.
Provision of quality with spot contracts
Even a buyer and
when
cost
so large that they choose to
In the second
only
its
seller
(r
c)
is
What
relatively low
it
is
is
interesting
become more
is
that in this
never optimal to have a
increases the optimal contract
jumps from having
A equal zero to having A equal one.
At
this point
it
is
worth digressing on what would happen
subject to moral hazard. Suppose that, unlike the case
always bring forth the
e
to the worker.
Now
effort that brings
I
the seller wants to spend
anyway. So,
in
A the
is
e
less
seller
can
about high quality with probability a by paying
suppose that the contract
Also, the higher
the worker was not
have considered, the
specifies that the
with probability A when he receives low quality. The higher
rents.
if
is
buyer leaves this
A, the higher are the seller's
the seller wants to provide high quality.
to keep his customer but with high A the customer
a sense, the moral hazard of the worker
15
is
seller
inessential.
As soon
With low A
comes back
as the seller
is
assured of the buyer's business, he
On
feels little desire to
provide quality.
the other hand, without worker moral hazard, there exists an empirically unap-
This solution involves
pealing but theoretically viable solution to the quality problem.
The contract
writing contracts with a third party.
some
third party
must
also
that he
sum
make payments
is
indifferent
indifference
party
large
make
the buyer changes supplier.
if
to a third party
if
he moves.
The
must pay the
buyer, on the other hand
The payments by
the buyer ensure
between moving and not moving after receiving low
necessary for A to be positive.
is
specifies that the seller
The payments from
the seller very keen on keeping the customer happy.
quality.
This
the seller to the third
They thus ensure that
improve quality.
seller tries to
In practice,
we do not observe such
third party contracts, probably because they are
subject to a moral hazard of their own. After the contract
is
signed the third party and
the buyer have an incentive to gang up against the seller. Rather than pursuing this line
of
argument
directly.
I
With
have chosen instead to
this
let
the seller's worker be subject to moral hazard
worker moral hazard, third parties cannot help to resolve the quality
problem.
In this section
I
have shown that the buyer and
seller will
sometimes
like to
be joined
by a long term contract which eliminates high quality. Since this contract does not affect
the
number
of units purchtised
has a social cost of [on —
The way
tially
its
only substantive effect
the reduction in quality. This
().
to understand the results of these
repeated spot market purchases
it is
two sections
is
the following.
If
punish each other
for entering
if
such contracts, the provision of high quality
Long term contracts have
With poten-
possible to support socially desirable equilibria
long term contracts are then permitted, in particular
with high quality.
impossible.
is
firms do not
may become
at least the potential for reducing the efficiency of
transactions.
*The
kna)y*>* impliei that any buyer
luch a contract
is
and
leller
who hav«
attractive to one buyer-seller pair
these contracts. In practice, heterogeneity
all
among buyers
access to long term contracts act in the
spot markets di'.appear as soon as
will
we
same way
Thus when
buyers and sellers sign
only make the contracts attractive to some.
16
let all
Outright Integration
1.3.
Section 1.2 has shown the benefits of long term contracts and their potentially adverse
impact on
quality.
However, the motivation
transactions. In this subsection
I
for the
paper
is
the low quality of intrafirm
argue that outright integration
is
probably useful when
the buyer and seller decide to write a contract with A equal to one.
the buyer
it
is
completely bound to the
seller
and quality
is
very low. In such circumstances
becomes worthwhile to attempt to employ other mechanism
One
In such contracts,
for assuring high quality.
natural mechanism of this type requires that both buyer and seller
come under the
authority of a conmion employer.
Before showing that integration can be useful
cannot do.
First, unlike
the seller does not, by
worth stressing some things
is
it
Grossman and Hart (1986)^ giving control
itself,
to either the buyer or
Grossman and Hart
solve the quality problem. In
it
(1986) these
changes of control help because they change the payoffs to both parties from some project
they have in common. Here,
if
seller control
would solve the
the seller could thereby receive the buyer's payoff.
quality
if
he himself gained
(j,
when
where a separate agent who buys
quality
is
has to incur personal costs equal to
is
high.
The
By
seller
contrast,
needed even when the
fi if
quality
is
seller's
moral hazard problem
would try hard to provide
I
seller
have
in
mind a
situation
has control. That buyer
low. Seller control of the joint enterprise
does not change the identity of the person incurring the costs of low quality. Thus, seller
control does not, by
common
reduce the costs of providing quality. For this reason
ownership by a third party rather than on buyer or
Second,
the requisite
common
effort.
compensate buyers
seller
itself,
would
like
itself,
make
Because top management must pay
for receiving
it
The buyer would
undo the consequences
like
of the
is
easier for the seller to provide
sellers
more
for high quality
spending the
effort
lie.
and
The
necessary to
top management to believe that she must
bad quality she
cannot ascertain quality on the basis of their words alone.
'See also the version of their model in Holmstrom and Tirole (1987).
17
focus on
seller control.
bad quality both agents have an incentive to
top management to believe that he
provide good quality.
exert herself to
ownership does not, by
I
is
receiving.
Management
suppose that top management can ascertain quality by the expenditure of
Finally,
some
resources. This
assumption
is
not sufficient to solve the problem.
is still
observed by buyers.
is
management
is
to
know whether
idea
is
quality.
payments
that, for
to verify its presence.
earlier
It is
to
depend on
not enough for
quality has been provided.
nonetheless one mechanism which can help the top
company induce high
management
of a
common
Suppose that by spending V, top management discovers
whether quality has been provided
is
The
must be able
the level of quality, outside courts
There
my
essence of
that contractual payments cannot depend on the level of quality even though
this level of quality
top
The
way which
a
in
is
later verifiable at
no
cost.
After
spent, there exists objective evidence on quality which an outside court can use.
spending
V
every period
is
V
Then
worthwhile after a contract with A equals one has been signed
if:
V<an-e.
After
V
is
spent, quality
the selling worker ^
when he
worthwhile for the worker.
the expenditure of
V
This means that management can offer to pay
contractible.
is
(15)
successful in providing quality.
is
When
(15)
is
payments to the worker
satisfied these
worthwhile to a combination of buyer and
is
This makes the
seller
effort
as well as
which refuses to
separate under any circumstances.
When
(15)
is
satisfied,
it
is
sometimes worthwhile to make A equal to one when,
The reason
in
the absence of this monitoring technology, the optimal A
is
now the buyer and
separations without sacrificing
as
much.
seller
Thus, the presence of
management.
It
integration wastes
Thus,
The
in
my
this technology
also encourages this
buy from the in-house
common.
gain the rents from eliminating
V
seller
encourages integration under
common management
whenever
this
feasible.
is
is
that
common
to order the in-house buyer to
From
a social point of view such
since high quality can be achieved without any monitoring.
favored interpretation of
Society would be better off
role of top
all
smaller.
management
if
my
results intrcifirm transactions are excessively
more transactions took place through the market.
in this
subsection
18
is
to
spend
V
collecting evidence on
quality.
Management
of Eccles
the monitor as in Alchian and Demsetz (1972).
is
and White (1988), management
in transactions
between
As
study
They show
settles disputes over quality. ^^
profit centers, disputes arise
in the
and top management
that,
acts as the
arbiter. I interpret these disputes as disputes over the quality actually provided.
The
resources spent on verifying quality (the role of
many
take
The work
forms.
of Eccles
management
I
stress)
can
and White (1988) suggests that these resources
Managers encourage these
often take the form of conflict between buyers and sellers.
fights
that
because they reveal information. Buyers and
Their wages must compensate them for this
sellers
utility loss.
depending on the actual number and intensity of
presumably
dislike these fights.
It is difficult
fights. It is
more
likely
to imagine wages
that pay depends
only on the average, or expected, level of conflict. Then, both buyers and sellers will be
averse to any increased conflict.
They
both route transactions externally whenever
will
they can. The aversion to internal transactions on the part of both buyers and
amply documented
One
issue
in Eccles
which
sellers
and White (1988).
arises at this point
why
is
the
must be spent by the top management of a common
V
that
firm.
is
spent on verifying quality
Why,
for instance, can't these
resources be spent by outside auditors or even by the courts? There are two reasons.
first,
and
principal, reason
is
that monitoring, policing and verification require power.
monitor must be able to change the conditions of production to find out how the
buyer are actually behaving. This
flexibility is essential precisely
because
how
a legal point of view, such residual control
verification
is
for
must be
and
in a
is
management. Indeed, from
the purview of the owner of the asset.
having top management perform the verification
considerably simplified
if
one
taining this familiarity takes time. There
if
The
the assets with which buyer and seller work are used. Such residual
control over the use of assets virtually defines the role of top
The second reason
seller
The
difficult to
it is
predict in advance the form of high vs. low quality. Therefore the monitor
position to dictate
is
is
is
familiar with both buyer
is
and
that such
seller.
Ob-
thus a benefit to having the monitor remain
'"Their model assumes there is a technological reason for monitors. As a result the monitoring that emerges
not inevitable. By contrast, the monitoring that takes place here could usefully be replaced by a market.
"This arbiter role is also stressed by Williamson (1975).
'^Grossman and Hart (1986) equate residual control over the use of assets with ownership.
19
is
socially good,
in
By nnaking the monitor part
job for a long time.
his
of the firm, one increases his
mobility costs and thereby one ensures that he learns the personal characteristics of buyer
and
seller.
The shortcomings
of long term contracts
and the advantages of mergers that
As
contracts cannot specify
when
that literature,
all
contingencies. These individuals get to decide
the contract does not specify
what
is
model seem quite
human
this.
on contractual incom-
difficult to
it
The owner
human
capital accumulation accrue to others.
gets to decide on
all
human
capital accumulation.
human
capital accumulation of the owner.
owner/manager. Perhaps
In this case
Ownership
and
his underlings
This alleviates the moral hazard problem inherent
They
some
uncontracted transactions ex post.
therefore receives a disproportionate share of the payoff to both his
of an
pay individ-
capital that they get. In the absence of ownership rights,
of the benefits of an individual's
can ameliorate
to proceed
from the one presented
different
They focus on the contractual incompleteness which makes
uals for the specific
how
to follow.
also base their theory of the firms
pleteness. Yet, the implications of their
He
individuals are put in charge because
in
Grossman and Hart (1986)
here.
some
describe
Holmstrom
are similar to those of the "incomplete contracts" theory of the firm surveyed by
and Tirole (1987).
I
are careful to present their
their theory applies also to corporate top
model
in
the
as
one
management.
one would expect top managers compensation to be closely related to firm
performance.
In
my
story,
by contrast, moral hazard may not be an
issue for top
managers. Top
managers are policemen. The competence with which they dispatch these functions may
be easy to determine from their reports. Top managers could
still
earn large sums
if
the
skills
needed to investigate wrongdoing, and apportion blame are
case,
one would expect larger firms, whose policing problems are more complex, to hire
in short supply.
In this
more competent policemen. This suggests that management compensation should increase
with firm
size.
By
contrast their wages need not bear any particular relationship to firm
performance. Jensen and
Murphy
(1988) suggest that compensation depends on firm size
but rises only very slowly with firm performance.
20
One critical
question faced by
and Williamson
(1937)
all
theories of the firm
The question
(1985).
what
is
is
the
conundrum posed by Coase
limits firm size. If top
managers can
intervene selectively and obtain whatever advantages there are to integration a single firm
should control the whole economy obtain. This argument gains additional force
when we
recognize that integration eases collusion in product markets.
Williamson (1985) gives a variety of reasons
selectively.
One
are imperfect
reeison
why managers cannot
which appears particularly germane
and sometimes make mistakes. For managers
must have great authority, so these mistakes can be
larger
is
by many individuals when
is
dangerous.
more
attractive.
The
By
him
basic message of these three subsections
is
that managers
to be effective at policing they
They become more
that firms
is
I
it
may
costly the
is
common
needed often
well disrupt their
many models where
probably true of
their attendant multiplicity of equilibria
firms can earn
does not depend on supergames with
consider next a finite horizon model.
given purcheisers beliefs about quality, the equilibrium
I
is
these rights where intervention
such ex post rents in equilibrium. To show that
A
context
his decisions only rarely contribute to the
contrast, giving
organizations to capture rents. This
2.
my
the manager's span of control. Giving a manager residual decision rights over the
is
assets used
good
costly.
in
actually intervene so
is
There,
unique.
Cournot Model
now
consider a duopoly which
is
active for only two periods.
The use
of a finite
horizon rules out the sort of supergame strategies which were central to the previous
analysis.
I
now
capital gives
assiune that the firms must initially invest simultaneously in capital. This
them the capacity
to this capacity but
it
to produce in
both periods. Production
price, they each sell the
demand
its price.
at
minimum
one firm has a lower
If
curve horizontally.
then costless up
cannot exceed capacity.
In each period, both firms choose price simultaneously.
this price.
is
The other
The extent
of their capacity
price,
firm's
it sells
demand
is
the
both firms choose the same
and half the quantity demanded
minimum
of
its
is
the
amount
at
capacity and total
obtained by shifting the overall
of this horizontal shift
21
If
demand
sold by the firm with
a lower price. Aside from the issue of quality, the structure of duopolistic interaction
in
Kreps and Schcinkman (1983). Therefore,
Cournot
their
as
for a given level of quality, capacities equal
levels.
In a finite horizon
customers
is
will leave
model
when
is
it
offered
unavailable in the last period.
I
more
bad
difficult to
The reason
quality.
therefore
sustain quality with the threat that
assume that quality
capital needed to produce one unit of high quality
good
which produces one unit of low quality good costs only
c.
in
is
is
that this punishment
embodied
The
extra
e
The
in capital.
each period costs
c
+
e.
is
That
again represents the
cost of unobservable managerial effort.
Buyers
differ in their reservation prices.
of low quality
units
Q
quality
for
is
n lower than that
For any buyer, the reservation price for a unit
for a unit of
high quality. In each period, the
which purchasers would be willing to pay
P
if
they believe
them
number
of
to have high
is:
Q = a-bP.
(16)
Contractual payments cannot depend on the quality provided. With spot contracts,
payments can only depend on the units received
in
each period. Payments to workers can
depend on whether customers come back and continue buying at
Long term contracts between buyers and
relatively high prices.
can also specify payments
sellers
if
the pattern
of purchases changes over time.
2.1.
Spot Markets
Firms
1
and
2 install capacity
Ki and K2
respectively.
Under the informational
assumptions discussed below, the cost to a firm of a unit of high quality capacity
and both firms decide to
level
is
install
then equal to the Cournot
only high quality capacity.
level.
This occurs because, as
is (c
+ t)
The equilibrium capacity
in
Kreps and Scheinkman
(1983), firms sell their entire capacity in the subsequent pricing game. In other words, firms
expect to charge prices which clear the market
price equals [a
- K\ - K2)/b
in
when both
sell
their capacity.
both periods. Assuming the cost of capacity
22
Therefore
is
(c
+
e),
firm
i's
present discounted value of profits
l-c-e
{1+6)
where 6
is
then:
is
»/y
1,2,
again the discount factor. In equilibrium each firm maximizes
(17)
its
own
profits
taking the other's capacity as given. This gives:
Ki = K2 ^
a
b{c
—
1
Given these capacities, the market clearing price
Pn
=
a
2(c
b^
1
+ e)
+6
/3.
(18)
is:
+ e)
+6
/3.
(19)
Profits are:
l+l
TT
b{c
a
96
1
+ e)
+6
(20)
For this to be an equilibrium, firms must not wish to deviate when they choose quality,
capacity or price. Given these capacities, cutting prices below (19) just reduces revenues
since sales cannot increase.
The
following argument shows that raising prices
profitable. If the firm could ignore the capacity constraint, its price
revenue to a marginal cost of zero. This price
is
Consider
know
now
would equate marginal
lower than that given by (19) since that
price equates marginal revenue to a positive marginal cost.
the capacity constraint, the firm wishes to lower
also not
is
its
This means that, except for
price below that given in (19).
deviations in the level of capacity, taking quality choice as given.
If
firms
that they will charge the market clearing price, then (18) gives their optimal capacity.
Kreps and Scheinkman (1983) have shown that
capacities even
when
(18)
still
gives the
Nash equilibrium
may
firms properly recognize that other capacities
in
lead to non-market
clearing prices.
Before considering deviations at the quality stage and deriving the equilibrium cost of
high quality capacity,
I
assume that buyers
by
tell
(19).
I
present
initially
my
assumptions regarding consumer learning about quality.
expect high quality from any firm which charges a price given
After purchasing, the buyers informally trade information about quality.
each other the quality of the units produced by each
23
seller.
I
also let
them
tell
They
each
other which units of capital from a particular seller have low quality output. ^^ Buyers are
then willing to pay
less for
Consider a firm which
quality.
these units.
installs a capacity given
The equilibrium then
by (18) where some units are of low
involves second period prices given by (19) for the units of
good quality and prices given by
A
for the units of
a
= - +
2(c
-^
b
1
+
+
f)
/3
(21)
6
low quality. At these price, the market clears in the second period. Cus-
tomers want to buy exactly the units on offer at the posted prices. The firm thus gains no
sales by cutting its price.
It
will also
choose not to raise
its
price as long as the derivative
of profit with respect to price:
K, - bP,
is
nonpositive. Using the expressions in (19) and (20) this requires that:
a
—
b{c
l
+ ey
/3<6
+S
/i<
a
This analysis assumes that the incremental cost of high quality capacity
payments to workers cannot depend on the
suppose the
(19)
pays
seller
worker |
its
and obtains the same
is
By
(21).
between
diff"erence
when Sn >
e
price (19).
They then pay
firms
who
succeed
is
if
if
(19). In particular,
the firm charges the price given by
it
pays |
if it
repeats
its
period
the firm chooses to charge the price given
Then
it
is /x.
Therefore,
in the latter case
if
S^ exceeds
charging (19)
c,
one avoids the payment of
fail
It
Thus
from the necessary
e.
effort
and provides low quality
to sell at the price given by (19).
The
price given
can hope to earn. Moreover, by charging this price,
payment of | to the worker.
|.
providing high quality prefer to charge the high quality
refrains
the firm would
the most that
earns only
in
if
(21)
their workers a present value of
Suppose that the worker
(21)
contrast,
and
(19)
preferable to charging (21) even
capacity.
period two
by
need not pay | to the worker.
it
The
sales at the price given
sales as in period one. Similarly
one sales at any price above
in (21),
in
Yet,
e.
However, they can depend on
level of quality.
whether the firm continues to make the same
is
therefore charges the price given by (21)
it
by
avoids the
and the worker
c.
Confronted with this environment, workers choose to provide quality. Moreover the
cost (in present value terms) of supplying a unit of high quality
of a unit of low quality
It is
is
only
indeed
lost
fj,
and has low quality are those
+
^
—i,P
-\
+
e
while that
second period sales in the event the firm continues
to customers with low reservation prices. In
particular, the lost sales are those to customers with reservation prices
units below
c
c.
important to stress that the
to charge (19)
is
/3.
Sellers are disciplined
R
for
high quality
by buyers with low reservation
prices.
Note that
management
this equilibrium does not really require that quality
at the
buying company. Suppose that
which serves the same
decisions
buy from
from
its
role.
Then top management
R
is
be observable to top
the cost of an alternative input
of the buying
company obtains
efficient
buying personnel by giving them a choice. Management allows them to
either the original or the alternative source as long as they are willing to
25
pay
their
employer the price
2.2.
Two
The
difference.
Period ContractB
role of long
term contracts
is
somewhat
different here
these contracts have the objective of capturing rents.
than
Section
in
Now, however,
rents
As before
1.
do not increase
by reducing customer mobility since customers typically remain with their supplier.
I
thus assume that there
to a specific seller.
As a
is
an
initial
result of this
period where a specific buyer can become attached
attachment the buyer purchases
his
B
units from
the seller in both periods. ^"^ Because the attachment reduces the need for the seller to
this particular buyer,
that,
frees the seller to
the buyer and the seller do
if
demand
equally
seller
spend more time
selling to others.
become attached, the two
when they both charge
random. Thus a
at
it
who manages
the
same
price.
sellers
I
woo
thus assume
share the remaining
Unattached buyers pick
sellers
to attach himself to a buyer in the initial period
has more sales. This assumption embodies the idea that long term contracts with buyers
capture rents by increasing sales.
I
also
assume that the buyer who considers becoming attached
a high reservation price.
for
He
even low quality units.
is
willing to pay
more than the duopoly
This abstracts from one of the
common
integration with imperfect competition. This standard recison
more
to, say, seller
is
one has
price given in (19)
reasons for vertical
that integration leads to
efficient purcheises of inputs.
In the initial period this specific
buyer and
seller
one bargain.
If
they agree to a long
term attachment the benefits are shared according to the bargaining strength of the two.
If
they
fail
When
for
P
both
if
to reach agreement the
game proceeds with
the spot contracts of Section 2.1.
the buyer and seller one agree to a two period contract, the external market
sellers shrinks. In particular, the
number
of units which can be sold at a price of
they are believed to be of high quality becomes:
Q = a- B-bP.
'*I could alto co.iiidcr attachmenta like thoie I considered in Section 1 which the buyer breaka probabiliaticaJly
he receives low quality This would conaiderable complicate the analyais without affecting the main conclusion.
26
(23)
in
the event
Since this outside market behaves like the market considered in Section 2.1 the equi-
librium
analogous.
is
equal their Cournot
Quality
is
high and the capacities for external sales,
b{c
B-
l
Given these capacities, the market clearing price
Pv
B
=
+ €)
+S
who
Moreover, since the buyer
on whether these
The question
is:
a-B
2(c
b
1
+ e)
+6
/3
(25)
seller
is
made
attached, the payment cannot usefully be
sales take place in the
that remains
is
is
whether quality can be improved by
letting these pay-
period
for these unit in
purchased by an outside buyer. However, the outside buyer
is
embodied
contingent
second period.
might try to switch the units sold to the attached buyer
Since quality
The reason
His payment cannot depend on the level of quality.
ments depend on how much outsiders are willing to pay
switch.
(24)
builds the capacity for these units cannot be induced to bring forth
the effort needed for high quality.
words, the
/3.
units sold by seller one to his attached buyer are of low quality.
that the worker
i^^
level:
K{ = Kl =
The
K^ and
in capacity
is
likely to
2.
In other
for those initially
be leary of such a
and the outside buyer already knows that
the units he received in period one were of high quality he will not welcome switches.
In particular, suppose that unattached buyers do not
know the
quality received
by
attached buyers. Then, they would rationally perceive the quality of the units originally
sold to the attached buyer to be low.
The reason
this perception
is
They would pay
rational
is
make
less for
the following.
them than
for other units.
Suppose outside buyers always
Then, the worker who builds the capacity
regard these units as being of good quality.
to
//
these units knows that even outside sales will take place at a high price.
compensation does not usefully depend on whether these
provides low quality.
Knowing
this,
sales take place.
He
His
therefore
the seller would always switch switch these units with
those previously purchased by an outside buyer. Outside buyers would therefore only pay
H
less for
these units. ^^ Since they do so regardless of actual quality, the compensation of
'Of course the outside buyer would then learn their
quality.
This
27
is
of
no help since the game ends
after period two.
made
the worker cannot usefully be
The
for these units.
contingent on the amount outsiders are willing to pay
quality of these units will be low.
B
Given that the
and
units are of low quality, profits for the attached buyer
seller
considered together are are:
+
1
B{l +
where the second term
rely only
market
R-ti
6)
1+S
price.
96
B
is
b{c
B-
a-
1
By
+ e)
+6
contrast,
+
Q
(r
6)
2(c-f
\
e)
1
,
1
+
(26)
the buyer and seller
if
times the difference between
So total benefits of the two firms with spot markets
b
+
6
6
1
= B
+
'a{l
c
6)
Two period
(19) yields the
contracts are
+ 6)Pn and
e
9
c
=^(where use of
+
(1
96
+
+
e)
n2
(27)
6
e
6)n
+
t
+ 6)n-e]\ +
-\{l
+
{1
{l
+
6)B'
96
+ 6]B^
(28)
96
second equality. Equation (28) has the following interpretation.
more
unit costs c
—
+
+
attractive the higher
is
the difference between unit revenues
under spot markets. This
e
is
when
the extra sales brought
about by the contract are valuable. The benefit from capturing these rents
in
part by the quality loss. This has an overall cost of (1
in (28) reflects
less
and the
are:
b{c
a
/3
R
net benefits from the two period contract equal:
<i>
(1
6
also equals the profits of firm 2.
on spot contracts, buyer surplus
B{l
The
+
in the
in
repeated
term equals the
game
context, contracts which bind the buyer
profits of firm 2.
This term
spot markets given by (21). In contrast to
gain from these attachments.
It is
of
per unit.
The
last
term
B.
because they take rents away from one's competitors. This
price.
e
offset at least
that the duopoly's losses from the price reduction caused by integration are
than linear
As
+ 6)n —
is
some
interest to
The two
is
is
may be
clear in (17)
there
is
compare these two period contracts
profits
now
firms, perceiving a smaller external
28
whose second
unambiguously lower than the
my supergame model
to spot
attractive
under
also a social
market lower
markets from
The
a social point of view.
units are sold (this
is
loss
simply that quality
is
gain in consumer plus producer surplus
B
r=-'+*
+
2(c
l
+
So, the net social gains
the difference between
is
gain
+ K2)
[Ki
Pn and
is
5/3 more
leading to a
The
Py).
total
f)
(
The expression
(19).
in (29)
from becoming attached are
Thus equilibrium contracts
private gains.
The
therefore:
is
where the second equality follows from
in (28).
lower.
+ K2 + B) and
the difference between (/TJ
reduction in market price of B/3b (this
is
of the type
I
is
smaller than that
strictly smaller
than the
have considered can be socially
detrimental.
Before closing this section,
example shows that
it is
and
meet
and
for
all
the conditions necessary to sustain high
two period contracts to be attractive from a private
To some extent these requirements
point of view.
if
worthwhile to go through a numerical example. This
possible both to
quality spot market equilibria
quality
it is
6n exceeds the
cost of quality
e.
On
conflict.
Spot markets provide high
the other hand, a large difference between
/i
makes attachments unattractive. Firms may become attached nonetheless because
e
the attractiveness of two period contracts increases as a
rises.
Increases in a lead to higher
prices without affecting the conditions for the existence of high quality equilibria.
I
assume that
condition (13)
e,
b
and
B
satisfied as
is
equal
is
1.0,
ft
equals 1.5, c equals 10, and 6 equals
the condition that requires that
S^i
be larger than
a greater than or equal to 13.5 two period attachments are worthwhile.
socially
As
worthwhile only
assets can
What makes
sets.
I
e.
For
They become
can sometimes improve on exclusive sales con-
have studied. In particular,
make
Then,
a also exceeds 15.
in Section 1.3, outright integration
tracts like those
all
if
1.0.
if
quality verifiable at cost Q,
this agent a top
manager
is
a top manager
it
who
may be worth
precisely that he
is
is
giving control over
hiring such a manager.
given control over
all as-
This manager then ends up using a socially inferior (to spot markets) mechanism for
elliciting
high quality.
29
3.
Conclusion
Ever since the important work of Coase (1937) economists have generally viewed the
internal organizations of capitalistic firms as benign.
Even Williamson (1975, 1985), who
concedes that vertical integration sometimes reduces competition, asserts that the main
purpose of integration
is
to reduce "transactions costs."
This paper suggests a
helpful
less
sanguine view. Whether the organization of firms
an empirical question.
is
It
not a question economists should
is
answering on a priori grounds alone. Since
we should play
of institutions exists,
In this
paper
little
feel
is
socially
capable of
other information on the actual functioning
close attention to the
comments
of managers.
have taken a particular interpretation of the managerial displeasure
I
with internal transactions reported by Eccles and White (1988).
I
have viewed this
dis-
pleasure as arising from the inability of internal transactions to give satisfactory results
when
contracts are incomplete. Alternative readings
dislike intrafirm transactions only
transfer prices are to
some extent
may
because they cloud managerial compensation. Because
arbitrary, the existence of intrafirm transactions
the profits reported by profit centers less meaningful. This
wages to
risk.
managers'
Holmstrom and
dislike of centralized
some reason
for
be possible. Perhaps managers
may
adversely subject
procurement. This story
is
efficiency reasons for
risk.
One
possibility,
GM,
is
very similar to the story pursued here. There
exposing the managers to this
Information gathered from managers
may
risk.
also illuminate
by Williamson (1975, 1985) and Grossman and Hart (1986).
is
inducing specific investments. Similarly,
less
severe
it
that firms wish to
may
be alternative,
when
discovery.
whether organizations are
is
One open
the idea stressed
issue
is
whether
firms are very concerned with
we do not know whether monopolistic conduct
product markets exacerbates this unhappiness.
predicts that
which seems
They await empirical
particularly effective at inducing investments in specific capital. This
manager unhappiness with integration
GM
not complete. Firms must have
particularly plausible in the case of centralized procurement at
is
manager
Tirole (1987) use an analogous argument to explain
exposing their employees to additional
capture rents. This
makes
does.
30
My
in
"rent capture" theory of integration
The theory presented here may
of firms accross nations.
also be able to explain differences in the organization
Japan and Korea both have
than the US. In Korea large conglomerates dominate
carry out
many
transactions with other
and Japanese cultures, which
members
extoll the
team
relatively
all
industries. In
of their
spirit,
more intrafirm transactions
own
make
it
keiretsu.
Japan keiretsu firms
Perhaps the korean
possible to maintain higher
quality in intrafirm transactions. This reduces the organizational cost of rent extraction
through integration.
31
4.
References
Alchian, Armcn and Harold Demsetz: "Production, Information Costs and Economic
Organization", American Economic Review, 62, December 1972, 777-95
Aghion, Philippe and Patrick Bolton:"Contracts as a Barrier to entry", American
Economic Review, 77, June 1987, 388-401.
Coase, Ronald H.:"The Nature of the Firm", Economica, 4, November 1937: 386-405.
Reprinted in G. J. Stigler and K. E. Bouiding: Readings in Price Theory, Irwin,
Homewood, IL, 1952
Dewatripont, Mathias: "Commitment through Renegotiation-Proof Contracts with
Third Parties", Review of Economic Studies, 55, July 1988, 377-91.
and Harrison C. White: "Price and Authority in Inter- Profit Center
Transactions" American Journal of Sociology, 94 (supp.), S17-S51.
Eccles, Robert G.
Friedman, James W.: "A Non-Cooperative Equilibrium
Economic Studies, January 1971, 38, 1-12
for
Supergames", Review of
Grossman, J. Sanford and Oliver D. Hart: "The Costs and Benefits of Ownership: A
Theory of Vertical and Lateral Integration", Journal of Political Economy, 94,
August 1986, 691-719
Holmstrom, Bengt R. and Jean Tirole: "The Theory of the Firm" forthcoming
Schmalensee and R. VVillig: Handbook of Industrial Organization, 1987.
in
R.
Jensen, Michael C. and Kevin J. Murphy: "Are Executive Compensation Contracts
Structured Properly?" Harvard Business School Working Paper, February 1988
Klein, Benjamin and Keith B. Leffler: "The Role of Market Forces in Assuring Contractual Perfomance", Journal of Political Economy, 89, August 1981, 615-41
Kreps, David M. and Jose A. Scheinkman: "Quantity Precommitment and Bertrand
Competition Yield Cournot Outcomes", Bell Journal of Economics, 14, Autumn
1983, 326-37
Ordover, Janusz A., Garth Saloner and Steven C. Salop: "Equilibrium Vertical Foreclosure", Sloan School of Management Working Paper 1978-88, January 1988
Rubinstein, Ariel: "Perfect Equilibrium
1982, 97-109.
William.son, Oliver E. .Markets
in
a Bargaining Model", Econometrica, 50,
and Hierarchies, Macmillan
32
,
NY
1975
The Economic Institutions of Capitalism, Macmillan,
33
NY
1985
Date Due
'"Tf'
MIT LIBRARIES
DUPL
3 9080 02238 6053
.':/./.
.'./u ; ..f''TV
/."