'^^^^
28
414
\1l\'S^
I
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
MORAL HAZARD, BORROUING, LENDING AND
RICARDIAN EQUIVALENCE
Julio J. Rotemberg
Working Paper #1931-87
September 1987
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
NOV 12 1987
M»BA»> «d
WORAL HAZARD, BORRQUIING, LENDING AND
RICARDIAN EQUIVALENCE
Julio J. Rotemberg
Working Paper #1931-87
September 1987
MORAL HAZARD. BORROWING. LENDING AND
RICARDIAN EQUIV ALENCE
Julio
.1.
Rotomberg''
September 1987
Abstract
In this paper
I
random payoffs
study privately optimal contracts when individuals face
if
they expend unobservable effort. Full ins\iranre
eliminates the incentive to
work so
it
is
generally
tioI
optimal.
Optimal
contracts which tradeoff insurance and the need to preserve incentives are
studied.
In a simple model
I
show that these optimal contracts can be
implemented using only assets, loans and the
instil
ution of iiankcruptcy
Ricardian equivalence even with with taxes that are a function of income
holds locally but not globally
fails
in
this model.
current tax cuts can easUy lead
to
Where Ricardian equivalence
reductions
in
current
consumption.
'•'
Sloan School of Management, MIT.
discussion and the
NSF
I
wish to tliank Olivier Blanchard for
for financial support.
The existence
taken to mean that Ricardian equivalence must
has lost some of
Yotzu7,uka( 1987)
fail.
This a priori argument
force since the papers of Hayaslii (1986) and
its
.
been
of imperfections in financial mari^ots lias often
They show
that the
wedge between lending and borrowing
rates caused by adverse selection in credit markets does not necessarily
imply a failure of Ricardian equivalence.
markets that has been adduced
to
A different
failure in financial
imply absence of Ricardian equivalence by
Barsky, Mankiw and Zeldes (1986) following on work by Chan (1983),
impossibility,
due
to
moral hazard, of selling human capital.
models income insurance
suceeds
in
is
the
is
In their
not privately provided because an individual
who
Then, government
purchasing insurance would stop working.
instituted linear income taxes provide some otherwise vinavailable insurance
which generally affects current consumption.
One weakness
of these
papers
is
that they do not consider optimal
insurance contracts between individvials, they simply postulate that certain
contracts are available and exclude others^^.
In this
paper
is
it
shown
that in a relatively simple model the existence of optimal contracts,
in the
presence of moral hazard, restores Ricardian equivalence
While moral hazard prevents full insurance,
is
locally.
still
Small government insurance schemes are then simply offset by
possible.
changes
some insurance
even
in
this privately
programs have the effect
optimal contracts.
As
provided insurance.
of
Larger
reducing effort even
a result tax cuts
social
insurance
in the equilibria
accompanied by increases
with
in futiire
taxes that are very progressive (i.e. provide a great deal of insurance)
can, by reducing future effort,
and hence
An
reduce the individual's permanent income
his current consumption.
objection to this line of analysis
is
that such privately supplied
optimal insurance schemes are simply not observed.
The simple example
3
developed
in
paper casts some doubt on
this
this criticism
optimal contract can be implemented using only the
which we observe regularly.
three institutions:
it
In particular,
must be possible
of institutions
implementation requires only
borrow,
to
menu
because the
to lend
and
to
go
In implementing the optimal contract via these institutions the
bankrupt.
paper follows the lead of Gale and Hellwig (1985) who show that debt
contracts with bankcruptcy can be optimal contracts
model of asymmetric information.
In their
observabUity of income which leads
model
it
in
is
a rather different
the costly
to these contracts.
Implementation via these borrowing, lending and bankcruptcy has some
appealing features.
First,
people will be observed borrowing and lending
simultaneously even though interest rates on loans exceed interest rates on
assets.
It
rates that
is
betweeen lending and borrowing
of course the difference
is
viewed as suggesting liquidity constraints as well as the
failure of Ricardian equivalence (Pissarides (1978),
Buiter (1985)).
Second, individuals wUl be genuinely credit constrained, they would
to
borrow more
from doing
individual
so,
is
Not only are they prevented
at the existing lending rate.
no additional borrowing
solvent.
This
is
a
more
is
like
possible even though the
strict version of credit constraint
than the one shown to hold by Gale and Hellwig (1985) since
in their
model,
as in that of Keeton (1979 ch.2) more would be lent, albeit at higher
interest rates.
The paper proceeds
as follows.
optimal contract are presented.
using assets and
in this
liabilities.
In Section
Section
III
is
II
the model and the
devoted
to
implementation
Section IV discusses Ricardian equivalence
model while Section V concludes.
II
I
Their
The model
consider people who
utility in the initial
U(Co)
^
where U
pEU(Ci)
is
a
-
live for
period
is
two periods labeled zero and one.
given by:
k6
(1)
concave function, Cj
is
consumption
expectations conditional on information available
6
is
and
in
the
an indicator variable which takes a value of one
is
in
period
initial
if
effort
E takes
i,
period and
is
expended
zero otherwise.
Effort
is
expended
for the disutility of k,
at the
beginning of period one.
who expend
individuals
income Yg with probability
With probability
tt.
and they earn the same Income
In compensation
effort earn a high level of
(1-tt)
they are unsuccesfull
they would earn without expending effort.
Yj-,
These realizations can be thought
of as uncorrelated across individuals.
As
unobservable while income and consvimption
in
Holmstrom (1979), effort
are observable.
A contract
is
Individuals also have an endowment
specifies transfers
institutions in the initial period,
which depend on the realized
Wq
the first period.
in
between individuals and financial
as well as transfers in period one
level of income.
Equivalently
,
and with some
gain in convenience, one can view them as specifying three levels of
consumption Cq, Cg and
Cj,
which correspond
two possible levels of income respectively.
to the initial
Effort will be
period and to the
expended
if
contract stipulates that:
TTfU(Cg)
-
U(Cb)]
^ k
(2)
the
while
not
will
It
the inequality
If
reversed.
is
Financial intermediaries (which can be thought of as foreigners) are
Such risk neutrality emerges
risk neutral and have a dicount factor R.
naturally
(1985).
If
Thus
the intermediaries are willing to sign any contract whose
Therefore,
gross rate of return equals R.
will
be high
(Wo
-
Judd
the Income uncertainty disappears In the aggregate as In
Is
contracts wLLl be offered which satisfy:
z,
Co)R
the probability that income
if
=
z(Cg
Yg)
-
(l-z)(Cb
+
-
Yb)
(3)
Optimal contracts maximize (1) subject to (3) and the constraint that
effort will be
otherwise
z
effort to be
expended
(I.e.
equals zero.
expended
any contract).
in
I
z
now
equals
-
if
and only
any optimal contract (or even
U(x + Yb)]
-
is
k
assumed
all
that optimal contracts Involve effort
Suppose an individual
Then, by expending effort
values of x.
It
is
is:
(4)
changes by the amount on the LHS
that this change be positive for
throughout
>
reaches period one with assets equal to x.
utility
satisfied;
the absence of
in
to hold
This condition can be interpreted as follows:
expected
is
(2)
if
briefly give a sufficient condition for
This condition which
Vx>0: TT[U(x + Yg)
it)
of (4)
To see
.
I
am requiring
that this implies
sufficient to note that
contracts without effort have z equal to zero in (3) so that optimal
contracts are simply risk free lending contracts.
satisfied,
utility
Hence,
his
if
(4)
is
can be Increased by offering the same size loan and
6
allowing the individual to keep any extra income that
lie
earns by expending
effort.
Given
expending effort
(4)
Expending
costlessly monitored.
is
Suppose effort could be
optimal.
effort would
still
bo optimal but, since
individuals are risk averse and financial intermediaries are risk neutral,
consumption would not depend on whether the effort was succcsfull.
other words
Such
full
have the
Cg would equal C^ and
insurance
is
the individuals would be fuUy insured.
obviously impossible with unobservable effort; we
The optimal contract
will
achieve as much insurance as
possible given the need to induce effort.
(2)
and optimal risk
usvial tradeoff of incentive compatibility
sharing.
In
It
thus
will
is
make the constraint
hold with equality.
Using
and
(2)
(3)
in
(1)
and differentiating, the optimal contract
satifics:
U'(Co){l
-
TT[U'(Cb)/U'(Cg)
-
1]1
=
pRU'(Cb)
(5)
where primes denote derivatives.
Equation (2),
(3)
and
can be
(5)
solved for the three levels of consumption although that will not be done
here.
Ill
Implementi n g the Optimum with Debts, Assets and Ba nkcruptcy
Before implementing the equilibrium with debt and assets
convenient
to interpret the optimal contract in
insurance terms.
This can be done as follows.
it
is
more traditional asset-
The
individual can be
7
thought of as carrying ovpr an amount of risk free assets A equal
Cq)
Consumption
.
in
period one
Cg
=
AR
.
Yg
>
Xg
Cb
=
AR
*
Yb
^
Xb
where the X's can be though
is
to
(Wq"
then:
of as transfers.
By
(3)
these transfers
represent simply an actuarially fair insurance policy since:
irXb
(i-^)Xg
*
=
0-
(6)
Moreover, since as much insurance
relatively low,
Xb
is
Is
provided as possible and Yb
is
positive.
In the debt-assets implementation the individual carries over instead
an amount of assets equal
A'
=
A
the
maximum
D
=
Xb
which
is
A'such that:
Xb/R
+
so that
to
Cb
is
(7)
simply A'B. + Yb-
Debt obligations D, which are defined as
the person owes to the financial intermediary are equal to:
-
Xg
positive
(8)
by the argument given above.
assets and liabilities supports
tlie
optimal contract as long as bankcruptcy
prevents consumption from falling below Cb-
such that individuals
In
This combinations of
Bankruptcy
is
an institution
debt can ask for protection from their creditors,
8
debts are forgiven as long as the individuals's consumption level
This threshold
a certain threshold.
economy consisted
payoffs,
is
here required
to
equal
the legislated threshold
If
.
below
C]-,.
the
If
of ex-ante identical individuals with uncorrelated
such a threshold would be have a certain appeal
avithorities
is
mechanism for forgiving debt
is
to distressed
different,
to legislative
some other
borrowers would have
be
to
implemented.
With bankcruptcy,
when
are fully paid
that they are paid
probability
be
it
is
Yg.
must exceed R.
Yj, while
is
So the gross return on debts
the event
in
when they are
actually paid must
This can be seen by noting that since A equals (Wq-Cq)
R/tt.
difference between A' and
they
Since debts are only paid with
the gross return on debts
tt,
when income
the debts are forgiven
A must equal the amount
exchange for
the
the financial
intermediary gave the indlvidvial
in
payable only in the good state.
Moreover, using (6),
tiie
,
claim of
(7)
D which
and
(8)
it
is
is
readily established that D/(A'-A) equals R/tt.
If
and
is
A
is
positive,
liabilities of
the implementation implies an overlap between assets
(A'-A).
The only reason assets exceed A
period zero
because the financial intermediary has also provided a loan.
overlaps are commonplace as
of the
and
minimum
liabilities
positive.
is
evident from table
of financial assets
for individuals
Maintenance Experiment^.
and
liabilities
who participated
A negative A would be
his other loans.
Even when A
an overlap of assets and
1
which
to the
lists
maximum
Such
the ratio
of assets
the Denver Income
in
Of course, at the optimal contract A need not be
a risk free "senior" loan
intermediary could be sure to collect on even
to
in
is
if
which the
the individual defaults on
negative, A' can be positive thus leading
liabilities
although,
if
A'
is
negative as well
9
only
liabllltips will
be observed.
Before one can say that assets and
it
is
necessary
show
to
individuals would,
in
that
if
liabilities
only assets and
implement the contract
liabilities
the presence of the appropriate
and
select the appropriate levels of assets
liabilities.
were offered,
bankcrupcy threshold,
1
deal first with
the choice of assets then with that of liabilities.
To
whether the optimal
find out
whether, starting
level of assets
would be chosen,
at the optimal allocation individuals
would want
I
ask
to
either increase period zero consumption and reduce assets or viceversa.
Because
bankcrupcy these two decisions are somewhat different and must
of
be treated separately.
Suppose that an individual decided
in
period zero and hold one less unit of A.
Intermediary
fall
by R.
is
consumption by one unit
to increase
not collecting anything on
the bad state,
In
its
loan so consumption would
Similarly in the good state the individual
his obligation so constimption
would
by R.
fall
the
is
fully
paying of
Tht:s the change in utility
Is^:
U'(Co)
-
pR[^U(Cg) + (l-Tr)U(Cb)]
<
U'(Co){l + Tr[U'(Cb)/U'(Cg)-in
pRTr[U'(Cg)-U'(Cb)l
where the
first inequality is
due
-
pRfTTU(Cg)Ml-TT)U(Cb)]
<
(9)
to the fact that
lower In the good state than in the bad, the equality
equation that characterizes optimal contracts (5)
inequality
strictly
is
due
to the
same reason as the
bad for the individual.
The reason
=
,
first.
is
marginal utility
is
is
obtained using the
and the second
So this change
is
that for a given Increase
10
in
consumption
in
expected
It
period zero, optimal contracts provide for a smaller
in
utility in
period one than do pure asset contracts.
worth noting that inequalities such as
is
fall
(9)
have iioon defined as
representing liquidity constraints by both Runkle (1987) and Zeldes (1985).
Zeldes (1985) finds evidence that for relatively poor individuals this
inequality holds strictly while Runkle (1987) using the same
PSID data but
different methods disputes this conclusion.
Now consider reducing consumption
of assets.
period zero and raising the level
in
Since bankcruptcy aUows the individual to consume only
extra assets do not secure increased consumption
so only in the good state.
change
in utility
-U'(Co)
the bad state,
consumption rises by R.
In that state
the
they do
So the
is'':
pTTRU'(Cg)
^
in
Cj^,
=
=
{-pU'(Cb)
*
TTpU'(Cg)[l-TT(l-U'(Cb)/U'(Cg))]}/0
p(l-iT)(-U'(Cb)
*
TT[U'(Cg)-U'(Cb)]l/<^
<
(10)
^ =
1
+
TT[U'(Cb)/U'(Cg)
where the
first equality is
also unatractive.
state
-
1]
obtained using (5)
assets required by the optimal contract
In the strongest possible sense;
worse
This change
This occurs because extra assets are useless
where they must be turned over
strictly
.
to creditors.
is
is
in
thus
the bad
Hence, the level of
the individually rational choice
any deviation makes the individual
off.
Now consider
are only relevant
the choice of liabilities.
if
high income
is
Changes
in
period one debts
realized since none of the debts are
11
paid
Suppose the individual reduces
the bad state.
in
his
consumption
in
period zero and correspondingly carries fewer debts forward so consumption
in the
good state of period one
corresponding change
-U'(Co)
Thus
^
this
Is
in utility
pRU'(Cg)
=
increased by
Using
R/tt.
(5),
the
is:
p(l-TT)[U'(Cg)-U'(Ch)]/<^
makes the individual
strictly
worse
<
off.
This means that
the individual would like to increase his indebtness by one dollar and
consume the proceeds
consumption
have
to
will
This means that the inequality
take place.
be written
would impose a
is
more
zero and
to
the consumption during
wLU be reversed so that
all
the debts would
strict than
It
is
He
this.
worth noting that the
what has been derived, for instance
(1985) in that additional credit wouldn't be extended
any interest rate.
in
z falls
(2)
in
The intermediary would never accept
off.
by Gale and Hellwig
more dollar
Thus
strict credit constraint.
credit constraint
at
Such an increase, however, lowers
period zero.
good state without any change
in the
the bad state.
no effort
tt/R in
The reason
is
that
if
the individual owes even one
the good state, he stops working and the equilibrium
is
destroyed.
In conclusion,
the implementation of the optimal contract has three
empirically relevant features.
For individuals, rates of return on assets
are lower than those on liabilities.
types of instruments.
they are allowed
Individuals nonetheless hold both
Moreover, individuals would
like
to
borrow more than
to.
While the implementation of the optimal contract with assets and
liabilities
appears
in
some ways natural one caveat
is
in
order.
The
12
implementation of the optimal contract
The main
take on more values^.
of simultaneous assets
and
will
be more complex when income can
point of this section
liabilities
that the existence
is
the presence of bankcruptcy
in
simplifies the implementation of the optimal contract.
IV Ricardian Equivalence
In this section
I
consider government tax and transfer schemes which
have an expected present discounted value of
to
depend on the
of
A transfer scheme
.
payments from the government
GqR
+
zGg
where
z is
allow these transfers
1
realization of income so that these transfers can in
principle be distortionary
Gg)
7,ero.
+
(l-z)Gb
is
thus a triplet (Gq,
to individuals
Gj^,
which satisfy:
=
(11)
again the probability that high income
is
earned.
Contracts between financial institutions and individuals are entered upon
after the G's
become known.
consumption Cq, Cg and
Cj,.
They
Now
still
specify the three levels of
for the financial intermediary to be
willing to offer a given contract:
(Wo
*
Go
-
Co)R
which, using,
offer the same
maximize
only
if
(1)
(2)
is
menu
=
(11)
z(Cg
-
Gg
reduces
to
-
Yg)
(3).
+
(l-z)(Ch
is
"
(12)
Yfa)
Optimal contracts
subject to (3) and the condition that z
and
Gfa
So intermediaries are willing
of contracts as before.
satisfied
+
is
equal to zero otherwise.
equal to
Thus,
if
still
it
if
in
and
to
13
equilibrium effort takes place, consumption
intervention.
(4)
unaffected by the government
is
With government transfers, the condition corresponding to
which ensures that effort
Vx>0: TTfUCx+Yg+Gg)
-
Is
U(x + Yb + Gb)
The argument given below
try to earn Yg.
Moreover,
expended
(4)
k
-
1
>
(13)
ensures that
if
(13) holds,
individuals
holds there are exists nonzero government
(4)
if
is:
transfers which are such that (13) holds.
These transfers can have
progressive elements so that, for instance,
Gg can be negative
while
G^
is
positive.
Yet, there are also transfer schemes which prevent (13) from holding.
In the extreme case in which the transfers schemes are such that (13) holds
with the inequality reversed for
taking place.
all
x,
the only equilibrium has no effort
Siippose that even though (13)
This can be seen as follows.
holds with the inequality reversed intermdiaries are offering a contract in
This means that
which effort takes place.
equality.
if
income
So,
is
payments from the intermediary
high than
if
it
is
low.
Suppose
deviating intermediary equalized payments
In the
(2)
good state and raising them
than U'(Cb) the individual
is
is
to the individual are
that,
Yet,
larger
maintaining (3) a
both states by lowering them
bad.
Since U'(Cg)
is
better off with this contract even
somehow be kept working hard.
reversed the individual
in the
in
holds at least with
smaller
if
he can
because (13) holds with the inequality
made even better
off
by giving up
effort.
Hence, intermediaries who offer contracts that involve no effort can take
all
the customers from intermediaries whose contracts require working hard.
Government transfer shemes that eliminate
effort have
Gg
lower than
14
Gb, they are progressive^.
So,
one form of intervention that can have this
a cut in taxes at time zero followed
effect
is
in the
event
by
a small increase in taxes
a large tax
if
Yg
eliminates effort, lifetime income
is
lowered so that consumption at time
ta.x
cut lowers consumption unlike what
zero
falls
Yjj
and
unambiguously.
The
is
realized instead.
Barsky, Manklw and Zeldes regard as the normal case
in
If
this sciieme
which the
progressive income tax raises current
corresponding increase
in a
consumption because
reduces future consumption uncertainty'.
it
15
V Conclusions
This paper has two
presence of assets and
One
foci.
liabilities
show that the simultaneoiis
to
is
together with a certain kind of credit
constraint can Implement an optimal contract.
The other
show that
to
is
RIcardlan equivalence survives at least locally when markets are incomplete
due
to
moral hazard.
which failures
in
One question which
arises
whether other models
is
the credit market are derived from contracting
difficulties can also explain the simultaneous existence of assets
liabilities
in
and whether Ricardian equivalence would survive
in
and
these
models.
It
is
worth stressing that reasons for credit rationing advanced by
Keeton (1979) and Grossman and Weiss (1981) are not very compatible with
the actual contracts that
we
see.
One reason
advanced by Jaffee and Russell (1976),
(1986)
and Yotzuzuka (1987)
is
for credit constraints
Stiglitz
and Weiss (1981), Hayashi
that different otherwise indistinguishable
borrowers have different propensities
to
go bankrupt.
Yet,
if
insurance
contracts were explicitely allowed in this adverse selection model and
individuals were risk averse while intermediaries were risk neutral, any
equUibriiim would include at least some individuals
insured.
In particular,
who would be completely
pooling equilibria would have
everyone while separating equilibria would have
full
full
insurance for
insurance at least for
the worst risks.
Another reason for credit constraints advanced by Keeton (1979) and
Stiglitz
is
and Weiss (1981)
They note
involved.
be tempted
to
is
more related
to this
paper since moral hazard
that as interest rates increase individuals would
undertake investements with higher risk but with lower
16
This induces credit rationing by making rises
expected return.
demand
rates an unprofitable response to excess
in
when
Yet,
for loans.
interest
the
potential actions of individuals affect the variability of returns the
standard debt contract
is
very unappealing.
Instead,
to
induce people to
refrain from adopting needless risk, optimal contracts would specify that
Individuals be penalized
when outcomes which are unusual under more
conservative strategies are observed.
setup
in
Stiglitz
This
is
particularly easy for the
and Weiss (1987) were the risky and safe project differ
only in the probability of the good outcome and in the size of the good
outcome.
To prevent the risky
project from being undertaken
sufficient to reduce consumption to zero
project
It
Stiglitz
income
is
the good outcome of the risky
observed.
may thus be
costly observability of income which lies behind the
Gale and Hellwig (1985) show that
and Weiss (1987) analysis.
is
if
observable only
at a cost,
the optimal contract
actual debt contracts with bankruptcy provisions.
when
is
it
the borrower
is
a risk neutral firm.
As
is
if
identical to
Their model applies only
a result their
inconsistent with joint holdings of assets and liabilities.
model
Such
holdings might well arise, even when the only imperfection
is
is
joint
the costly
observation of income when borrowers are risk averse individuals.
It
if
may be tempting
to
conclude that, whatever the market imperfection,
optimal private contracts have the structure of assets and liabilities
then changes
liabilities
in
taxes which resemble changes
in
people carry over can't have an effect.
paper shows that this intuition
is
the level of assets and
In
some sense
this
only partially right since Ricardian
equivalence does not hold globally.
Therefore, whether Ricardian
equivalence would carry over into a world in which income
is
imperfectly
17
observable
It
model
is
in
Is
an open question.
worth pointing out that Ricardian equivalence holds
this
part because contracts are signed either after the government
institutes balanced
budget transfer schemes or because they are made
contingent on such transfer schemes.
transfer schemes are instituted after
government policy.
(1983) in which
reason he doesn't explain,
in
is
is
government
many contracts have been signed and
This incompleteness
randomness
of course
In practice,
the contracts we observe rarely have clauses that
Yet,
in
make them contingent on
reminiscent of the work of Chan
is
introduced by the government which, for some
not privately insured.
models with simultaneous borrowing and lending there
natural reason why,
when the government
signed contracts, the private sector
governments action.
The reason
is
be able
at least in
to
undo the
some sense, agents
find themselves at corners since there are credit constraints.
is
instituted,
suppose
So,
the government institutes a tax rebate financed by future taxes.
contracts were signed after this program
a
acts after private agents have
will not
that,
is
If
individuals would
simply be able to borrow less and the scheme would have no effect.
contracts are set in stone by the time the scheme
is
individuals would continue to avail themselves of the
allowed to borrow so the allocation would change.
If
instituted,
maximum they are
The general analysis
of
the effect on Ricardian equivalence of letting the government act after
contracts which are not contingent on government actions have been signed
is left
for further reseach.
18
FOOTNOTES
This criticism applies more generally to most of the literature on
1
credit rationing including Jaffee and Russell (197G), Keeton (1979),
In
Stiglitz and Weiss (1981,1987), Hayashi (1986) and Yotzuzul<a (1987).
their models people would like insurance yet only "borrowing" contracts are
considered
am grateful to David Runkle for providing the data on which these
2
I
computations are based.
3
It is worth noting that reduced assets do not reduce the desire to
work. Consumption falls by the same amount in both states so utility falls
This means that
by more in the low state where marginal utility is high.
the difference in utility in the two states actually increases.
Again, the increased assets do not impair effort since the increase in
4
consumption when the good state is realized is actually bigger when more
assets are carried forth.
Such more general optimal contracts are discvissed by Varian (1980) who
5
discusses insurance provided by an optimizing government but whose solution
corresponds to optimal contracts which are privately supplied.
6
Budget balance dictates that the government note that the scheme will
eliminate effort so that Gg becomes immaterial.
The low (or negative)
never
actually
takes
place.
transfer Gg
7
This normal case of course requires that U'" be positive.
19
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