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of economics
H^lB^iB!^
UNVERIFIABLE INFORMATION, INCOMPLETE
CONTRACTS, AND RENEGOTIATION
Georg Noldeke
Klaus M. Schmidt
No.
92-6
Feb. 1992
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
UNVERIFIABLE INTORMATION, INCOMPLETE
CONTRACTS, AND RENEGOTIATION
Georg Noldeke
Klaus M. Schmidt
No.
92-6
Feb. 1992
IMASP. eSF- itUH.
TJTTTiBR»^HS
AUG
4 1992
RfcUcivcU
Unverifiable Information, Incomplete
Contracts, and Renegotiation*
Georg Noldeke
University of
Bonn
Klaus M. Schmidt
Massachusetts Institute of Technology
February 1992
Abstract: Hart and Moore
(1988) argued that non-verifiability
jor cause for contract incompleteness
if
and leads
in general to
the parties can not commit not to renegotiate their
is
a ma-
underinvestment
initial contract.
We
show that this result relies on the assumption that the courts cannot distinguish which party refused to trade. If this assumption is relaxed the first
best can be achieved by giving control to one party which can decide unilaterally
whether or not to enforce trade. Our
specific investments are non-verifiable,
result suggests that
then vertical integration
if
relationship
may perform
better than seperate ownership.
Keywords:
'We would
Incomplete Contracts, Renegotiation,
Verifiability.
thank Dieter Balkenborg, Frank Bickenbach, Oliver Hart, Bengt Holmstrom, Albert
Ma, Benny Moldovanu, John Moore, Michael Riordan, Monika Schnitzer and Urs Schweizer for many
helpful discussions. This research was initiated during the International Summer School of the Center for
the Study of the New Institutional Economics in Wallerfangen, Germany, August 1990. We are grateful
to Professor Rudolf Richter for providing this stimulating atmosphere. Financial support by Deutsche
Forschungsgemeinschaft, SFB 303 at the University of Bonn, is gratefully acknowledged.
like to
Introduction
1
Long-term contracts are necessary
joint project
investments.
is
as a safeguard against opportunistic behaviour
undertaken by several parties who have to make relationship
However, long-term contracts are often incomplete.
if
a
specific
This observation
is
the starting point of a rapidly growing literature which interpretes institutions, such
as ownership or the financial structure of the firm, as incomplete contracts
and
tries to
explain their forms and functionings. This literature faces two ba^ic theoretical questions:
(i)
Why
are contracts incomplete? and
(ii)
When
does contract incompleteness lead to
investments?
inefficient
While the early literature just assumed that contingent contracts are not
before the parties have to
gued that non-verifiability
impossible to achieve
it
It is
ric
well
make
is
first
known from the
their investment decisions^.
Hart and Moore (1988)
a major cause for contract incompleteness and
best investments.
literature
At
first
on implementation
glance this result
in
is
ar-
may make
surprising.
environments with symmet-
information that quite generally the problem of non-verifiability can be overcome by
conditioning the contract on the verifiable outcome of a revelation
However, these mechanisms usually
of a deviation
is
feasible
from the equilibrium
rely
on the threat of
strategies.
game
inefficient
or mechanism.^
punishments
in case
Hart and Moore argue that this threat
not credible in a contracting environment, because the parties can always tear up the
old contract and renegotiate.
framework
in
To analyse
which renegotiation
analysis shows that
if
is
this issue
Hart and Moore provide a formal
taken explicitly into account. Their path-breaking
contracts can be renegotiated then non-verifiability will, in general,
lead to underinvestment.
Given that most of the incomplete contracts literature
result,
we consider
it
important to point out that
it
relies
refers to this
underinvestment
not only on the renegotiation
constraint, but also on one particular modelling assumption. Hart
situation in which the private investments of two parties, a seller
and Moore consider a
and a buyer,
^Grossman and Hart (1986) is the most notable contribution using such an approach.
^See Moore (1990) for a recent survey of this literature.
affect the
that these additional degrees of freedom are not necessary to achieve the
The
model
for
rest of the
is
organized as follows: In Section 2
we
briefly
and Moore and show how the renegotiation outcome
of Hart
summarize the
affected
is
best.^
if
we
allow
an option contract. Furthermore, we outline the intuition for why an option contract
can achieve the
is
paper
first
first
best while a Hart-Moore contract cannot. In Section 3 this argument
developed formally. Section 4 concludes.
The Basic Framework
2
Consider a buyer and a
both of
seller
whom
are risk neutral.
At some
initial
date
they
can write a contract specifying the terms of trade of one unit of an indivisible good which
may want
they
to
exchange
some future date
at
2.
The
buyer's valuation v and the seller's
production costs c are random variables depending on the realization of the state of the
world,
uj,
which
After date
0,
vestments,
/3
measured
in
determined at date
is
but before date
G
[0,
oo)
and a €
1,
1.
Let
u
be uniformly distributed on
the buyer and the seller
[0, cxs)
respectively,
which
make
We
and
c.
assume that
v{u>,/3)
bounded and non-negative;
more
a and
us suppose that c{uj,a)
is
non-increasing in
[0, 1]^.
Investments are
c{uj,a) are continuous in both arguments, uniformly
let
=
relationship specific in-
affect v
terms of their costs, and these costs are sunk.
fi
u(a;,/3) is
and
further-
non-decreasing
in
/9
for all possible states of the world.
Let q E {0, 1} be the level of trade and p the net payment of the buyer to the
^Also related to our work
is
a recent paper by Hermalin and Katz (1991),
who
use a
somewhat
formal framework than Hart and Moore and show that in their model a class of contracts they
seller.
different
call "fiU-
mechanisms" may be used to implement efficient investment decisions. However, to derive
Hermalin and Katz assume that the seller's cost of production and the buyer's benefit from
consumption are independent random variables. The model we consider throughout the paper violates
in-the-price
this result
this requirement.
®If the set of relevant states of the world can be represented by a subset of the real numbers then the
assumption of a uniform distribution on [0, 1] is without loss of generality. Suppose the "true" state of
the world is u' which is drawn by nature out of some closed set f^' C 72 according to the cummulative
distribution function F{u'). Using the probability integral transformation
variable
rescale
w =
all
F(cj')
which clearly
functions of
a;'
uniformly distributed on
such that they are functions of w.
is
[0, 1].
we can
Since F{ui')
define a
is
new random
monotonic we can
Then the
Trade
is
the buyer and the seller after date 2 are given by
utilities of
efficient
iff
—
u(a;,/?)
u^
= q-v{ujj)-p-^,
(1)
u^
= p-
(2)
c{u,(t)
q- c{u!,a)-
> OJ
a
.
At date 2 the buyer and the
decide simultaneously whether they do or do not want to trade. Trade
voluntary in the sense that
The problem
takes place
it
of the parties at date
investment and trade decisions,
=
W{/3,a)
is
if
and only
if
assumed
to
be
both parties are willing to trade.
to design a contract
which implements
which maximizes expected
i.e.
is
have to
seller
efficient
social welfare
f [v{uJ)-c{u:,<T)]^du-/3-a,
(3)
Jo
where [•]"''= max{0,
•}.
Note that, given our continuity assumptions on
well-defined and continuous in
set of
maximizers of W{-, )
levels
which maximizes
The
first
of investment.
is
^ and
a. Furthermore,
v{-,-)
and
c(-,-), VK(/?,cr) is
by the boundedness assumption the
always non-empty. Denote by [j3',a') a pair of investment
(3).
best could easily be achieved
if it
were possible to contract upon the
However, we assume that although investments
state of the world
w
always
(and so v and
cannot be verified to any third party,
outcomes contingent on these
c)
are perfectly observable
e.g.
variables.
and a
as well as the
by both players, they
the courts. Thus the contract cannot enforce
The
courts can only observe
trade decisions of the buyer and the seller at date
different prices, pi, p^, pg,
/3
level
2.
payments and the
Thus the contract can
specify four
and p^^ depending on whether trade took place or whether
the buyer, the seller or both parties refused to trade.
Hart and Moore make the following "simplification": they assume that the courts
can only observe whether g
seller or
=
or
1,
but
if
g
=
0,
they cannot distinguish whether the
the buyer was unwilling to trade. Thus, in their setting only two different prices
'Note that the specification of v{-,P) and c{-,a) assumes that there are no direct externalities of
However, there is of course an indirect externality because the investment affects the
probability of trade. It is this indirect externality which is the focus of Williamson (1985) and Grossman
the investments.
and Hart (1986).
are feasible,
namely
=
pi
pi
the main point of this paper
the underinvestment result.
and po
is
If
to
=
=
p^
=
p^
show that
it
p^^.
As noted
in the Introduction,
this simplification
is
which
is
crucial to
the courts can verify whether the seller failed to supply
or the buyer failed to take delivery, then the
first
best can be achieved via a contract of
the following form: Independent of whether or not the buyer wishes to trade, he has to
pay pi
the seller supplies the good, and po
if
if
the seller does not supply.
are again only two different prices, but this time po
=
pp
=
p^^ and
pi
=
Thus, there
pi
=
p^. This
contract does not condition on q but on whether or not the seller supplied the good. Note,
>
that given (po,Pi) and u(-)
trade at date
it is
a weakly dominant strategy for the buyer always to
it is
since the price to be paid
2,
effectively the seller
who
is
independent of the buyer's decision. Thus,
decides whether trade takes place. Such a contract can be
interpreted as an "option contract", saying that the seller has the option to supply at
price pi, but
it is still left
to the buyer to decide
whether he wants to accept delivery of
the good.
Given the
assumed
seller.
as in
right
With
fact that the
from the
buyer
will never refuse to accept the
start that the
may be viewed
separate ownership in which trade only takes place
The
as
an "ownership contract"
(1986), giving the seller the "residual right to control" whether
trade should take place, whereas the model of Hart and
come back
we could have
buyer has no choice but to accept the decision of the
this interpretation our contract
Grossman and Hart
good,
if
Moore corresponds
to the case of
both parties agree to
it*.
We
will
to this interpretation in Section 4.
initial
contract could also condition on messages exchanged between the parties
or any other kind of revelation mechanism.
Hart and Moore show that
if
the contract
can be renegotiated, then (given the above assumption that only q can be verified)
impossible to achieve the
first
best no matter
how
sophisticated the initial contract
Since we want to show that a simple option contract does implement the
®This analogy
is
it
first best,
is
is.
we do
no explicit mentioning of assets that might be owned
The existence of such assets however is the basis
Grossman and Hart (1986). To justify our use of the
not quite precise, since there
is
either by the seller or by the buyer in our story.
of the definition of ownership rights given in
term "ownership contract",
it is necessary to re-interprete our model as one in which the trade decision
corresponds to the decision of whether or not assets that are specific to the buyer, resp. the seller, should
be used in some production process.
not consider these revelation games here.
However, renegotiation
ing that after date
new
contract
old one.
is
the parties are free to send
1
new
Hart and Moore in assum-
contract offers to each other.
signed by both parties and produced to the courts, then
new
there are conflicting
If
We follow
be very important.
will
contracts, all signed
by both
it
If
a
replaces the
parties, then the old
contract remains valid. These offers are transmitted by a completely reliable mail service
which takes one night to transmit the mail and delivers
number
of days between date
The
game
and
following Proposition
to Proposition
1
Then
1
'
which summarizes the outcome of the renegotiation
1',
and
— po <
(ii)
if
V
<
pi
(iii)
if
V
<
c
(iv)
if
V
>
pi
(v)
if
V
>
c
(vi)
if Pi
—
<
result here.
1
in
then q
=
and p
=
po,
Po
<
c,
then q
=
and p
=
po,
— Po,
then q
=
and p
=
pi
then q
=
I
and p
=
p\,
Po, then q
=
I
and p
=
po
=
I
and p
= p\
—
pi
>
V
c,
because
is
1' is
c.
(i)
and
(ii)
In cases (iv)
also efficient.
In
trade
and
all
is
(vi)
0.
—
c,
+
c,
and given
by:
.
easily constructed along the lines of the proof
let
Under an option contract the
p\—po <
and trade
then q
c,
Hart and Moore. So,
takes place: In cases
perfect equilibria
c,
formal proof of Proposition
of Proposition
the counterpart
the buyer to the seller (p)
<
pi
— Po >
payment of
V
— Po >
>
the
subgame
are uniquely determined in all
if pi
is
Let {po,pi) be the initial option contract signed at date
the traded quantity (q)
(i)
a finite
and Moore.
of Hart
Proposition
is
1.^
an option contract (po,Pi) as defined above has been signed,
after
A
once a day. There
it
us just outline the basic intuition for this
seller effectively decides
inefficient
and the
seller
whether or not trade
does not want to trade
the seller wants to supply (because
these cases there
is
no scope
See Hart and Moore (1988) for a discussion of this specification.
p\—po>
c)
for renegotiation, since
an
already result from the initial contract and each player
efficient trade decision will
can guarantee himself at least his share of the total surplus specified through the
initial
contract, by simply refusing to sign any other agreement.
Now
seller
consider case
Trade would be
(iii).
inefficient,
but given the
wants to trade. He can also enforce trade which guarantees him at
— pi <
and holds the buyer down io v
He sends a
=
—
p\
c
+
e.
Given
new
the seller prefers the
of p
—
Pi
—
=
—
pi
—
c
+
e.
If e
— pi,
u
respectively.
would be
but the
efficient
because refusing to supply gives him pa
>
—
P\
seller
does not want to trade
Again the buyer could wait
c.
=
po
equilibrium the seller will accept this offer and trade, so the payoffs are u^
—
the last day before date 2 and then offer to raise the trade payment to p
=
u
— Po —
c,
>
the seller will not trade, and payoffs (net of investment costs) are
= c — pi >
and u^
c
c,
or he can give up
c,
contract. Thus, in equilibrium the buyer will offer a no-trade
Finally, in case (v) trade
u^
po
can either supply
this offer, the seller
production and take the new contract to enforce a payment of pi
=
— c>
least pi
—pQ. Consider the following strategy of the buyer.
the good and refer to the initial contract to get a payoff of pi
payment
contract the
renegotiation offer to the seller on the very last day before date 2, raising
the no-trade payment io p
u'^
initial
-|-
until
c.
In
po and
respectively.
Comparing Proposition
1'
with Proposition
1
in
Hart and Moore two differences can
be observed:
1.
In case
(iii),
yields q
=
if
u
<
and p
Q
<
c
=
po.
pi
—
po, a
Hart-Moore contract
Renegotiation
is
is
not renegotiated and
not necessary because the buyer,
who
doesn't want to trade can prevent inefficient trade unilaterally, guaranteeing himself
u^
2.
=
-po >
c
In case (vi),
-pi.
if
option contract
pi
is
—
po
>
u
>
to
p
=
u
a Hart-Moore contract
not. In this case trade
buyer would veto trade. Thus,
payment
c,
4-
in
is
efficient,
is
renegotiated while an
but without renegotiation the
equilibrium the seller will offer to lower the trade
po and payoffs are u^
=
v
-\-
pq
—
c
and u^
=
—po-
What
investment incentives are given by the option contract? Using Proposition
date 2 payoffs of the buyer and the
u^ = -/3+
{
seller are
-Po
in
(i), (ii)
c-pi
in
(iii)
V
(
= — cr +
whereas social welfare
in
(i), (ii),
in
(iii), (iv), (vi)
is
in
cr
+
V
Using these expressions
it is
—
c
(i) - (iii)
in (iv)
-
(vi)
possible to give a heuristic argument to explain
best can be achieved with an option contract. This argument glosses over a
of technical points, but
is
nevertheless instructive and captures the
main
formal result to be presented in the following section. Briefly put, the idea
First,
how
the
number
intuition of the
is
the following:
note that the private marginal returns of the buyer's investment coincide with
the social marginal returns of his investment in
it is
(v)
in (v)
c
w — — /? —
first
po
<
[pi-c
in (iv), (vi)
— Po —
the
given by:
and u
v-pi
1'
assumed that
all
seller
possible cases (for sake of exposition
the following derivatives are well-defined):
in(i)-(iii)
°
du^ _ _
f
80 ~ ~'^\ll
Why? The
all
in (iv)-(vi)
^ g^
- 80
^'^
•
has the right to decide whether or not trade takes place. Thus
if it is
necessary to renegotiate, then the renegotiated price will follow his costs. So the price
is
independent of the buyer's valuation and therefore independent of his investment. Hence,
the buyer's payoff equals social welfare minus a constant (which depends only on the
seller's cost
and the
price,
right incentives to invest
This
is
but not on the buyer's investment). This gives him just the
no matter how po and pi are chosen.
not true for the
coincide only in cases
private return
is
(i),
— ^^ >
case (v) the social return
to underinvest.
seller.
(ii),
(iv),
Private and social marginal returns of his investment
and
(vi).
In case
(iii)
the social return
an incentive to overinvest.
0,
so there
is
is
— |^ >
while the private return
To give the
is 0,
On
but the
the other hand, in
which gives an incentive
seller the right incentives to invest, it is
8
is
thus necessary to
—
show, that by choosing pi
ca^es
and
(iii)
such that on average the
(v)
The idea why
there exist real
>
Pi -~Po
k,
numbers
k,
k,
such that
if
pi
is 0,
so
if
— po =
pi
i^
he
the private marginal return of his investment
return
if
equal to
trade
so
1,
"option price"
little.
—
then Prob{(iii) or (vi)} = l. In cases
the sellers investment
is efficient.
if
pi
it is
—
po
=
Since u(-) and
simple:
is
po
'^
k,
and
(i)
(v) the private
the seller
is
— g^ which
is
may
first
if
(iii)
and
(vi)
efficient is smaller or
is
induced to overinvest. Hence, by varying the
suspect that there exists
the desired incentive to choose his
bounded
equal to the social marginal
much
possible to induce the seller either to invest too
Consequently, one
are
marginal return of
In cases
all.
However, the probability that trade
/:
c(-)
then Prob{(i) or (v)} = l, and
not invest at
will
is
the respective probabilities of
fix
has just the right incentive to invest.
seller
should be possible
this
we can
po appropriately
k'
a.
^
[k, k]
or to invest too
which gives the
seller
best investment level.
Let us briefly explain the difference to Hart and Moore. Under a Hart-Moore contract
and
private
marginal returns of investments coincide
social
in cases (i)
the buyer's incentives are fine but the seller's marginal return
In case (vi)
it
is
just the other
buyer's investment does not pay
the fact that in general
and
(vi)
precise
so he will underinvest.
has the right incentives, but the
seller
Hart and Moore's underinvestment result stems from
— po
impossible to choose pi
to develop a formal
such that the probabilities of (v)
argument which makes the intuition given above
and which highlights some further important properties of option contracts.
Consider the investment decision of the
signed at date
0.
By
Proposition
U^{a,po,k)
where
case (v)
Options, Efficient Investments, and the Role of
Reneogtiation
now going
are
off.
(iv). In
both vanish at the same time.
3
We
it is
way round. The
is 0,
-
fc
=
pi
—
po
is
1'
=
his
-cr
seller if
an option contract (po,Pi) has been
expected payoff
+ po+ f
Jq
[k
-
the "option price". Clearly, U^{-)
is
given by
c{uj
is
,
a)]^ du
,
(5)
well-defined and continuous in
all
arguments. Given the option price the
The
that maximizes U^{-).
set of
seller's
maximizers
problem
is
to find
an investment
level
always non-empty (by boundedness of
is
the cost function) and since po enters the problem only as an additive constant will not
depend on
po- In general there is
We
for every possible k.
we simply
Uniqueness of the
ensure that the
is
will discuss this issue in
more
be an unique maximizer
will
detail below, for the
time being
stipulate uniqueness as an additional assumption.
Assumption
result
no presumption that there
There
1
seller's
first
is
a unique optimal investment level, a{k), for all k.
investment choice for
all
possible option prices
best investment levels are implementable.
More
sufficient to
is
precisely our
main
the following.
Proposition 2
//
Assumption
1
holds then there exists an option contract
{po,Pi) which implements efficient investm,ents
13' ,
a'
Furthermore, any
.
divi-
sion of the ex-ante surplus can be achieved via {po,pi).
Proof: Since costs are always positive
which implies a{0)
=
0.
we have
that for
all cr,po,
U^{cr,pQ,0)
= —a + po
Next, since costs are uniformely bounded there exists k such that
h
yk >
U^{cr,po,k)
Let a
=
a{k).
By
d'{k) is
continuous in
a €
a]
[0,
the
k.
= -a + po +
suppose a'
>
a.
To
Now
c{u,a)du
maximum theorem we know
Thus,
it
(6)
.
that Assumption
follows from the intermediate value
can be implemented by choosing k G
that a' G [O,^].
-
k
see this, take any pair of
[0, k\
first
appropriately.
1
imphes that
theorem that any
It
remains to show
best investment levels (/3',cr') and
consider the functions
f{a)
= -^'-a+ f
Jo
[v{u;, /3')
-
c{u, a)]+du
h{a)
= -/3'-a+ f
[v{u,
I3-)
-
c(cj,
(7)
and
Jo
10
a)]du
.
(S)
Note that a
/(^')
^
— argmax
/1(a)
and that a' G argmax /(a). Thus we have h{a) > h{a') and
Combining these two
/(^)-
inequalities yields:
f{a)-h{a)<f{a')-h{a').
However, since production costs are non-increasing
f{a)
is
-
=
h{a)
non-increasing in a. But this
is
I
-
[c{u, a)
a
in
(9)
for all
u
seller to
follows that
v{u, ^)]+du;
a contradiction to (9) and a'
Given the option price k* that induces the
it
choose a'
it
(10)
>
a.
follows immediatelly from
the argument presented in Section 2 that the buyer's optimal choice
is /3*.
Finally, to share
the expected surplus as desired, (poiPi) can be chosen arbitrarily as long as pi
— po =
k'.
Q.E.D.
Assumption
1 is
used in the proof of Proposition 2 only to guarantee that the
optimal investment level
it
is
is
continuous in the option price. Even without this requirement
always possible to induce the
option price. However,
may happen
would have
if
seller to invest
Assumption
1 fails,
there
that there exists no k such that a-{k)
scheme
to use a randomization
investment of the
Thus, Assumption
seller.
seller's
that by varying the option price
it is
little
may be
=
or too
much by
varying the
a discontinuity in a{k)^
i.e.
it
a*. In this case the initial contract
between
(e.g.
1 is
too
k_
and k) to induce
efficient
a continuity requirement needed to ensure
possible to "finetune" the investment incentives of
the seller without using randomization devices.
We
holds.
have refrained from stating explicit assumptions which ensure that Assumption
The reason
for
proceeding this way
is
simply that
general assumptions which guarantee this property.
To
that there
may be
problem.
Suppose that production costs are always
option price that
is
a non-concavity in the
sufficiently low to
chooses a close to zero.
Let us suppose
it is
a.
To
ct
also a global
investments the option
concave in
Then
=
a local
may become
valuable.
it
rule out the possibility that there
11
seller
is
and consider an
never receives a return
if
he
of the seller's utility function.
may happen
If this is
meaningful,
function due to the following
strictly positive
maximum
maximum. Now,
difficult to state
see the difficulty involved, note
seller's utility
imply that the
is
it is
1
that for sufficiently large
the case the
seller's utility is
a second global
maximum
at
non-
some
investment
strictly positive
would be necessary to state conditions which ensure
level, it
that the set of states of the world in which the seller receives a strictly positive payoff
from the option
is
not increasing "too
feist" in a.
Formulating such a requirement
degree of generality, would have obscured the main point we wished to make,
the seller's maximization problem
is
well-behaved a simple option contract
is
viz.
in
any
that
if
sufficient to
achieve efficient investments.
However, the following example
seller's utility
function
is
Suppose that the
holds.
strictly
illustrates that there are natural cases in
concave
seller's cost
in
function
=
c(u;,o-)
where c{a)
seller's
is
cr,
is
utility
is
which clearly implies that Assumption
1
given by
c{ct) -u;,
twice difFerentiable, and satisfies
expected
which the
c(-)
>
(11)
0, c'(-)
<
0, c"(-)
>
Thus, the
0.
given by
.mm[l,3^]
U
= —a + Po +
[k
I
—
c{cr)
u]
du
Jo
= -a + po + mm[l,—-]-k- -mm[l,-—]^I
c[cr)
c{a)
(12)
.
^y^j
Taking the derivative with respect to a one obtains
easy to see from this expression that for sufficiently small k the optimal investment
It is
is <t(/:)
=
and
To obtain an
Then
it
for k
>
c(0) the derivative
interior solution let us
follows
from
strict
the unique solution to the
Proposition
high.
it is
1,
independent of k and simply given by
assume that
convexity of
FOC
is
c(-)
c'{a{k))
=
c'(0)
< —2 and
linv^oo
that the optimal investment level
2 for all such k
>
c(0).
we allowed production
is
—2.
given by
if
i
is
in
sufficiently
cost to be identical equal to zero for
possible to state an assumption that guarantees that the seller's problem
12
>
Consequently, as
the optimal investment level will be independent of ^
Finally, since
c'(cr)
is
a;
=
0,
strictly
concave
in
cr
for all
/:
>
This condition
0.
c"(-)
inequality (15) holds
If
characterized by the
1
>
2!^^
(15)
.
clearly the case that cr[k)
it is
uniquely defined for
is
k and
all
>
order condition for utility maximization whenever cr{k)
first
Thus, by Proposition
is
it
is
possible to implement
first
0.
best investments without any
further assumption on the buyer's valuation function.
Returning now to the general setting,
Renegotiation seems to be very important
vation concerning the role of renegotiation.
for the option contract to work.
First of
us finally point out an interesting obser-
let
all,
it
is
necessary to achieve efficient trade.
Secondly, renegotiation of an option contract yields a price which
buyer's valuation, thus giving
him the
nuity assumption, by choosing pi
is
independent of the
right incentives to invest. Finally,
—po appropriately
it is
under our
conti-
possible to finetune the respective
probabilities such that the renegotiated price gives the seller the correct incentive to in-
However,
vest.
Therefore,
it
is
it
not clear whether renegotiations occur that frequently in reality^".
may be worthwhile
to note that there are interesting circumstances in which
never necessary to renegotiate an option contract.
it is
Suppose that the costs of the
v{uj,
•)
—
c{uj,
•)
strictly decreasing in
is
welfare are always
moving
the seller's point of view,
become worse
a unique
u G
in the
it is
for the buyer.
[0, 1],
private returns
the
same
u
same
=
uj.
) >
v{lj,
c{uj,
•)
=
c{u!{i3',a'),a'),
and only
if c(a;, •)
set of states of the
world
<
in
'
In particular,
if
and only
i.e.
and
(v) of Proposition
the contract
is
1'
seller's
his
1.
lj.
even
if it
Suppose we
The
iff u;
seller's
may
fix
the
<
investment yields
u{l3',a').
But
this
investment coincide. Furthermore,
his subordinate before he
is
investment yields a social return.
(the only cases in which there
13
social
Note that there must be
<
if u;
interpreted as an ownership contract
owner always has to renegotiate with
and
=
k' equals the costs of the seller in the
k', or, equivalently,
which the
seller's utility
social perspective,
given that both parties invested efficiently.
if
k', cases (iii)
from a
if
that w{ijJ,-)
the state of the world gets better from
illustrated in Figure
Thus, the private and social marginal returns of
k
If
also getting better
is
u and assume
This means that the
direction:
This case
such that
option price k' such that k'
marginal state
seller are increasing in
is
we would not
can take a decision.
if
renegotiation)
e.xpect that the
c{co,/3')
v{iv,a*)
Figure
must have zero
1: Efficient
Proposition 3 Suppose
tiahle,
Investments without Renegotiation
probability, since u(a;,
renegotiation in equilibrium. This
c(u,a)
is
is
>
/?*)
<
c(a;,(T*) iff c(cj,cr*)
k".
Thus, there
is
no
stated formally in the following proposition:
and c{u^a) are continuously
that v{u^j3)
increasing in
UJ
1
Co{/3',a')
u and
w{ij,l3,a)
=
—
v{u},/3)
differen-
c{u!,cr) is strictly
decreasing in u. Furthermore, assume that the seller's maximization problem
strictly concave.
is
ments
Proof:
first best levels
Without
>
if
there exists an option contract (pi,Po) that imple-
of investment and trade without renegotiation}^
loss of generality
iv{uj, 13, cr) is strictly
c('i',c")
Then
decreasing in
and only
if cj
<
lu
we only consider the case
then there exists a
iZ'{j3,a).
The
FOC
u:{(3,
in
a) 6
which a' G
[0, 1]
such that
for the social welfare
(0,a-).
u(cj, /3)
maximizing a'
If
—
is
given by
'^^''"'^
dc{io,a')
da
/o
=
1
(16)
under the stated conditions a Hart-Moore contract with pi — po = k' will
implemented the first best without renegotiation if v{uj,P') is decreasing in w. Without such an
additional assumption a Hart-Moore contract will not achieve that goal; in particular in the situation
shown in Figure 1 the Hart-Moore contract would be renegotiated for sufficiently high uj.
^^It is easy to check that
also
14
Chose k*
=
Then
c{u}{^'^cr'),a').
Given that the
cides with (16).
the
FOC
seller's
for the seller's
problem
is
strictly
maximization problem coinconcave k' thus implements
best investments. Furthermore,
first
v{uj,l3')-c{iJ,(T-)>Q
Thus, cases
(iii)
and
^
u<CJ{(3',a')
^
c{u,a')<k'.
cannot occur, so there
(v) of Proposition 1'
is
(17)
no renegotiation.
Q.E.D.
4 Conclusions
We
have shown that
plemented
if
in the
model
derinvestment
effect.
arrangement. The
i.e.
and Moore
if
and
However,
first
it
best can be achieved
if
one of the parties, here the
he can decide unilaterally whether or not trade takes place.
then vertical integration
is
if
first
best
is
not feasible
strictly better
more general
result in
but that
0,
after the state of the world has materialized.
convincing arguments
14),
On
if
the other
both parties
Grossman and Hart (19S6)
the impact of different ownership structures on efficiency. However, they
contract on the level of trade (q) at date
1,
seller, gets
than seperate ownership.
had to impose an "incomplete contracts assumption", saying that
date
an un-
relationship specific investments are non-
may perform
clearly a special case of the
who analyzed
Thus,
does have an impact on the form of the contractual
have control. Thus our results suggest that
This
best investments can be im-
of the state of the world alone does not yield
hand. Hart and Moore have demonstrated that the
verifiable,
first
the courts can observe whether or not the seller supplied the good.
unverifiability of investments
control,
of Hart
why
this
one would wish to replace
assumption
it
is
it is
in
is
impossible to
possible to contract on
it
at
Although Grossman and Hart give
sensible (see in particular their footnote
by a more basic assumption.
which has received considerable attention
it
For a special example,
both the economic and the
legal literature)
Hart and Moore's and our results show, that the superiority of one ownership structure
to another can
be established by just referring to unverifiability, without assuming any
other source of contract incompleteness.
15
References
AghiON,
p.,
DewaTRIPONT, M. and
Unverifiable Information" mimeo,
Chung, T.-Y.
(1991):
S.
(1989):
"Renegotiation Design with
Studies, Vol. 58, 1031-1042.
and O. Hart
of Vertical
Rey
MIT.
"Incomplete Contracts, Specific Investments and Risk Sharing"
Review of Economic
Grossman,
P.
of Ownership: A Theory
and Lateral Integration" Journal of Political Economy, Vol. 94, 691-
(1986):
"The Costs and Benefits
719.
Hart, O. and
J.
Moore
(1988):
"Incomplete Contracts and Renegotiation" Econo-
metrica, Vol. 56, 755-785.
HermaLIN, B. and M. Katz (1991): "Contracting between Sophisticated Parties: A
More Complete View of Incomplete Contracts and Their Breach" Working Paper
No. 91-165, University of California
Moore,
J.
(1990):
at Berkeley.
"Implementation, Contracts, and Renegotiation in Environments
with Symmetric Information" in Advances in Economic Theory, Sixth World
Congress, ed. by
Williamson, O.E.
J. -J.
(1985):
Laffont,
Cambridge University Press, forthcoming.
The Economic
Free Press.
16
Institutions of Capitalism
New
York:
The
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