rent seeking and the provision of public goods
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Rent Seeking and the Provision of Public Goods
Author(s): Mark GradsteinSource: The Economic Journal, Vol. 103, No. 420 (Sep., 1993), pp. 1236-1243Published by: Wiley on behalf of the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2234249 .
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8/9/2019 Rent Seeking and the Provision of Public Goods
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The Economic ournal,
103
(September)236-I243.
?
Royal Economic
Society I993. Published by Blackwell
Publishers, io8 Cowley
Road, Oxford OX4 iJF, UK and 238 Main
Street, Cambridge, MA 02I42, USA.
RENT SEEKING AND THE
PROVISION OF PUBLIC
GOODS*
Mark Gradstein
Public good provision is a
typical example
of market
failure, having served
as
an
argument
for
government
intervention since
the
time of
John
Stuart
Mill
(In Principles fPoliticalEconomy, ook V, Chapter
XI).1 Many economists were
quick
to
recognise
the limits
of
government
intervention and the
corresponding
causes of 'intervention
failure'. One
of
these causes has to do with the
observation that for reasonssuch as pressure by interestgroups (Becker, I983,
i985),
wasteful rent seeking (Tollison,
i982),
legislative failure (Fiorina and
Noll,
I
978),
and
others,
the
government
is
unlikely
to
act
purely
in
the
interests
of the
public.
These
factorsquestion the validity
of
the benefits of
government
intervention relative to decentralised provision. To
resolve
the
ambiguity
pertaining
to welfare
enhancing possibilities
of
intervention,
it
is
interesting
to
depart
from
models
in
which the
government
is
represented
in
a
purely
benevolent manner and
introduce some realistic features into the
underlying
political process.
This
approach
has been
emphasised
in
the
writings
of
the
public
choice scholars
(see, e.g. Buchanan,
i968,
and Buchanan and
Tullock,
I962). Pursuing this line of
inquiry, a related recent paper (Gradstein, I992)
presents
a
preliminary analysis
of
the effect
of
incomplete
information on the
welfarecomparison
between public and private provision of public goods. The
results are quite
surprising: sometimes, even
an extremely uninformed
government performs well
(and frequently even better) relative
to
the
voluntary action of
uninformed individuals.
Incomplete information
is
only
one
among several
reasons
for
the possible inferiority of intervention.
An
alternativelikely reasoninvestigatedin this paper is non-benevolent behaviour
of the
government.
In
this
study,
I
adopt the public choice school
paradigm
of
modelling the
government
in
order
to
compare
its
performance
with that of the market
in
the
standard model of
the
provision
of
public goods. Specifically,
I consider an
economy
consisting
of
jurisdictions
which
provide
local
public goods.
Private
provision
is
represented by the Cournot-Nash
equilibrium
in
individual
voluntary
contributions towards the
provision
of
public
goods,
whereas
public
provision entails
influence costs. Specifically, it is assumed that levels
of the
public goods are determined by rent seeking activities, e.g. lobbying. Thus,
both
allocation
procedures
yield inefficiency,
and the
question
is
which
procedure results
in
a
greater
amount of
inefficiency: private provision
with its
free
riding
incentives,
or
public provision
with its rent
seeking
incentives. The
*
I
would like to thank
two referees
and the
editor, John Hey,
for
their
helpful
comments
and
guidance.
Financial
assistance from the Monaster Research Center is also
gratefully acknowledged.
1
The
public goods
that
we
have in mind are
characterised
by
the absence
of
rivalry
in
consumption;
in
the
particular example presented
here
they
are
pure
local
public goods.
[ I236
]
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8/9/2019 Rent Seeking and the Provision of Public Goods
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RENT SEEKING AND PROVISION OF PUBLIC GOODS
I237
particular modelling adopted is somewhat ad hoc, but nevertheless
provides a
useful frameworkfor the analysis of a
realistic political process by which
public
decisions are
made.
The
results
indicate that
government intervention is
frequently preferred to private provision of public goods. Thus, the
benefits
from improved coordination, which centralisation is likely to bring about, may
exceed the attendant influence
costs. According to the results
obtained,
intervention is advantageous in
large jurisdictions, especially when the number
of these
jurisdictions is small.
In
contrast, private provision can appear
as
welfare superior when jurisdictions are
small,
or
when there are
many
jurisdictions.
I
conclude that
superiority
of
private provision
is not
guaranteed
when the
government displays a forms
of
non-benevolent behaviour.
This
paper takes its perspective from
the growing literature
on
rent seeking,
which
originated
in
the contributions of
Bhagwati (I982), Krueger
(I974),
Posner
(I975)
and Tullock
(I967, I980).
Recent years have witnessed an
increasing interest
in
the subject, as can be illustrated by many studies such
as
Applebaum
and Katz
(1986 a, b),
Hillman
and Katz
(i
984), Katz etal.
( I990),
Nitzan
(i
99
i),
Tollison
(i 982), Ursprung
(
1990).
The
papers of
Katz et al.
( I990), Nitzan (i
99
i), and Ursprung
(
I990) are especially relevant since
they
touch on
the public good aspect of rent
seeking.
The
present contribution can
be considered as an
extension of
their
analyses.
The
novelty
here is
in
presenting
a welfare
comparison
of
two imperfect allocation systems, whereas
the above studies
are
mainly
concerned
with
the extent of
rent
dissipation
in
the
context
of rent
seeking
for
pure
public goods.
I.
DESCRIPTION OF
THE
ECONOMY
Consider an
economy
with
N
=
kn
individuals,
where
k,
k
>
2,
stands for the
number of distinct
jurisdictions, each
of
which is populated by n identical
individuals. There are two types of goods
-
private and public.
Each
individual's initial endowment of the private good is w, and the initial
amount
of the
public goods
is zero.
kjurisdiction-specificpublic goods
can be
produced.
The
production function of each of these goods is assumed to be a
linear
function
of
the
average private good
contribution
in
each
jurisdiction,
a
common
assumption
in
situations where the
population
size is allowed to
vary.
Letting
xi
denote the
amount of contribution made
by
individual
i
to
public
goodj,
and
X,
-
the
amount
of
public goodj,
the
assumption
on the
production
function can be written as
Xj
=
Yi
x0j/n.
Each
jurisdiction
is characterised
by
a different
public good
that the members
of
the
jurisdiction prefer.
In
particular,
the
utility
function of
individual
i
which is identified
with
jurisdiction j (henceforth referred to as individual ij) is assumed to be
quasilinear,
that
is,
v(Xj)
+yi,,
where
yij
is the amount of that individual's
private consumption.
I
make
the
following assumptions
on
v: v'
>
o,
v
<
o,
v(o)
=
o, v'(o)
=
00, v'(oo)
=
O.2
All
these
assumptions
are
quite
standard
-
see
Cornes
and
Sandler
(I986).
Note that the
public goods
here are local
public
goods,
one
possible interpretation
being
in
terms of a
geographical separation
2
This
particular
form
of
utility
function
is
adopted
for
simplicity
of
presentation.
?
Royal
Economic
Society
I993
42
ECS 103
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8/9/2019 Rent Seeking and the Provision of Public Goods
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THE
ECONOMIC JOURNAL
[SEPTEMBER
among
districts populated by competing
constituencies.3This model is
similar
to that of
Ursprung (I990) who
is
also interested in
the political economy of the
provision of
local public
goods.
Pareto efficiency requires maximisation of a
representative individual's
utility
function, v(Xj)
+yi,
subject to the
resource constraint,
knyi1
k(nX,)
-
knw
=
o,
which
yields
E '-1(I)
XE.
(I)
The
Pareto optimal amount
of each good is independent of the population
size
because
of
the
assumptions
made
on
the
production technology.
The
symmetric
Pareto
optimal
allocation
yields
an
individual
utility
of
uE
=
V(XE)
+W_XE. (2)
I
now turn
to the welfare
analysis
of
private
and
public provision
of
public
goods.
II.
WELFARE COMPARISON BETWEEN PRIVATE AND
PUBLIC
PROVISION
OF PUBLIC GOODS
This
section presents
an
analysis of private
provision, public
provision,
and
then performs
a
welfare
comparison between the two. Private
provision is
represented by a Cournot-Nash equilibrium in individual voluntary con-
tributions
towards
the
provision
of
public goods.
The
public provision requires
each
individual
to
participate
in the
provision
of each
public good
on an
equal
basis,
that
is,
the individual tax shares are
equal.
The amount
of
each of
the
public goods produced
is then
determined via
a
lobbying
process,
the details
of
which are
specified
below.
II.
I.
Private
provision
In
the Cournot-Nash
equilibrium
of
the
voluntary
provision
of
public
goods,
individual ij chooses (x0,
ye),
so as to maximise v(X1)+yU, subject to x
+yij
=
w.
(Note
that
an
individual
residing
in
localityj
will
not
make
any
contribution
to
public goods
other
thanj.)
The
Cournot-Nash
equilibrium
amount of
public
good j,j=
I,...,k,
is
seen to be
X;7N
=
vU'
(n)
=
XCN.
(3)
This
amount
decreases
in
n
because
of the free
riding
incentives and is smaller
than
the
socially optimal
amount,
v'1
(I).
The
equilibrium utility
level of each
individual in a symmetric equilibrium is
u
N
=
V(XCN) +w-XCN
Its
derivative with
respect
to
n
is
[VI
(XCN)
-
I]
(dXCN/dfl)
=
(n
I)/lvf(XCN)
<
o,
hence,
this
utility
decreases with
respect
to
the
jurisdiction
size.
3
Some authors (e.g.
Fiorina and Noll
(I978),
and Weingast et al.
(I98I))
have argued that
geographical
separation is likely
to
result
in a political failure due to the pork barrel politics
generated by geographically
based constituencies. Their argument,
however,
is only distantly related to rent seeking.
?
Royal
Economic
Society
I993
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8/9/2019 Rent Seeking and the Provision of Public Goods
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I993]
RENT
SEEKING AND PROVISION
OF PUBLIC GOODS
1239
II.2.
Public provision
In
this
section
I assume that members
of group
j
are compelled
to
participate
on
an
equal basis
in
the provision
of each of the public
goods
that will be
produced in the economy so that individual gs tax share is
i
/kn.
This
assumption
may reflect the
idea that
income tax is used
to finance
the public
goods,
and that individuals
who
earn the same income
are taxed the same,
or
it
may
reflect some other
equity considerations
of
society.
The level of each
of
the public goods
that
gets
to
he
produced
in the economy is determined
by
jurisdiction
lobbying.
Based on this premise, I depart
from the standard
public
goods
literature
in
which
rent
seeking
efforts
or
other 'wasteful'
activities are
absent.4
The incorporation
of
some types
of socially 'non-optimal'
behaviour,
however, may sometimes
better represent the
realistic political
situation.
As is common
in
the rent seeking
literature,
I adopt a particular
function
form which
transforms individual
lobbying
to the distribution
of the tax
burden.
Specifically,
the
probability
p1
that
public
good
j
will
be
produced
is
a function
of the
lobbying
efforts
of group j
relative
to
the total amount of
lobbying. Letting
zU denote the amount
of lobbying
of individual ij,
and
Z1
the
amount
of
lobbying
of
group
j
as a whole,
we have
p1
=
ZJ/Z,
where
Z1
=
Ei
zU,
and
Z
=
Yj
Z1.Public provision
can be
conceived as
a
two stage
game,
the
first stage
of which
is the rent seeking competition among
the
jurisdiction,
and
the second stage is the optimal choice of the victoriousjurisdiction. Proceeding
backwards,
let XArSdenote
the amount
of
public good
j
which
is
optimal
from
the
viewpoint
of
groupjs
members;
the
optimal
level
of
public
goods
other
than
j
from the viewpoint
of these individuals
is
o. (Recall
that a winning group
in
the rent seeking contest
is
entitled to set the
level
of
the
public goods
in
the
economy.)
Assuming
an internal
solution,
XjRS
maximises
v(Xj) +
w
X/k and
is
given
by
XsR
'
/k(
X;s=
Vt-
(I /k)
.
(5)
This is
the amount of public good
j
provided
if
localityj
wins the
rent
seeking
contest; no other public goods are provided in this case. This amount is an
increasing
function
of
k.
The
amount
of a
public good
which
gets
to
be
produced
in
a
victorious jurisdiction
is
larger
than the
efficient one,
and the
amount
of
public
goods produced
in
other
jurisdictions
is less than
what is
required
by social
optimality.
The
expected
utility
of
group
js
individual
member
is
Uj=
p1v XRs)
+w-XjRs/k-z0y.
The amount of
lobbying
is determined
as
a Nash
equilibrium
of
the
resulting game
in
which
individual
zj
seeks
to maximise
his
utility by choosing zU
>
o. Assuming
existence
of
an interior
symmetric
equilibrium,
this
equilibrium
is
characterised
as follows:
V
(XjRJ)
apJ/ZiI
=
0
(6)
or
v(XRS
)Z-Z,/Z2
= I,
j=
I,
...,k.
(7)
4
See
Katz et al.
(I990), Nitzan (i99i),
and
Ursprung (I990),
for related public
goods
models
incorporating
rent seeking.
These
authors do not attempt
to provide welfare comparisons
of the
kind
performed
in
this paper.
?
Royal
Economic
Society I993
42-2
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[SEPTEMBER
Summing
up the
above k
equations
we
obtain
v(Xjs)
(k-i)/Z=
k
(8)
from
which it follows
that the equilibrium
amount
of rent
seeking
efforts
s
Z
=
v[v'-'(
1k)]
(k- i)/k, and the individual rent seeking effort is ZIN =
v[v'-'
(i/k)
]
(k i)
Ink2.
See
also
Katzet
al.
(
I990)
for
thederivation
f
Z.)
This
yields
the
following
level
of an individual's
welfare:
uRS
=
V(XRS)/k+w
-XRS/k-v(XRS)
(k-
)Ink,
(9)
where
XRS
v'-'
(
i/k).
To
ensurean
internal
solution,
URS
must
be
larger
than
w, otherwise
the jurisdictions
would do
better by
not producing
the public
goods
at
all. Hence,
v(XRS) XRSV(XRS)
(k- i)/nk >
o.
(Io)
The
individual's
welfare
is seen
to increase
in
n. This
is the case because
when
jurisdictions
are
more populous,
individuals
in each
jurisdiction
tend to
free
ride
on the rent seeking
efforts
of other
members
of the jurisdiction,
which,
in
turn,
enhances
efficiency.
Furthermore,
duRS
v(XRS)_XRS
v(XRs)
k-2
[v
(XRS)I
f(XRS\
k-
i
dXRS
dk
k
+
n k3 k
v ()
nk2J
dk
where the sign
follows from (i
o).
This,
in
turn,
implies
that
URS
decreases
n
k,
that is, the numberof competingjurisdictionsis adverselyrelated to welfare.In
any
case,
however,
uRS
<
UE, that
is rent seeking
is indeed
socially
wasteful.
II.3.
Privateversus
ublic
provision
Recalling
(4)
and
(9)
the welfare
difference
between public
and
private
provision
of public goods
is
given by
v(XRS)/k-XRS/k
v(XRS)
(k-
i)/nk2
_
V(XCN)
+ XCN.
(II)
Since
URS
is
an
increasing
function
of
n,
and
uCN is a
decreasing
function
of
n,
the expressionin
(i i)
is an increasing function of the population size, which
implies,
once again,
that
public
provision
is welfare
enhancing
relative
to
private
provision
in
a large
economy.
It
follows
from
(3)
that
as
the
jurisdiction
size increases
to infinity,
XCN
decreases
to
zero. This,
in
turn, implies
that
as
n tends to infinity,
(i i)
tends to
[V(XRS)
-XRS
]/k > o, that
is,
when
the
group
size is sufficiently
large, public
provision
always performs
better
than private
provision
does.
Since
URS
is a decreasing
function
of k, and
uCN s a
constant
function
of
k,
it follows
that the larger
the number of
interest groups,
the better
private
provision
performs
relative
to public
provision.5
I
conclude
with
an
illustrative
example,
Let
v(X)
=
Xx,
o
<
ac
<
i.
Then
XE
-
(i/ac)i/(xi),
XCN
=
(n/cx)i(6-x),
and
XRS
=
(il/kac)
(`1); v(XCN)
=
(n/1a)x(x-1)
and
V(XRS)
=
(i
/kx)x/(X-1).
Sub-
stituting these
values
into
(ii)
we can numerically
calculate
the
welfare
difference
for selected
values
of
parameters
oc, k,
and
n.
The
results
are
5 Comparative
statics
of the effect of
n and
k on the extent of
rent dissipation in
a related
but different
contextare presented
n Katz
et al.
(I990)
and Nitzan
i99i).
? Royal
Economic Society
I993
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8/9/2019 Rent Seeking and the Provision of Public Goods
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I993] RENT SEEKING AND PROVISION OF PUBLIC GOODS
I24I
Table
I
Thewelfare ifferentialetweenrivate rovision ndpublicprovision fpublicgoodswith
influencectivityoverwhich ublicgoodtoproduce boldnumbersepresentreferenceor
thepublicprovision)
k\n IO
Io2
I03 I04 Io5
a
=
O-I
2 - 0279 -0-I32
-0-025
oo56 O-II9
3 -o0408 -0-262 -0-I55 -0?074
-OOII
4 -0o473 -0 329 -0o224
-0-I43
-o-o80
5
-05I5 -
0373 -0-267 -oi86 -0-I23
as
=
0-2
2 -0-I50 0025 O-II9
0172
0'201
3 -0o27I
-o-o96
-o0002
0
050
o
o8o
4 -0?340
-o
i66 -0o072 -o0020
0010
ao
=
03 2 - 0075
0-076
0130
01-49 0-I56
3
-
0-206
-
os53
0001
0-020
o0o28
0
04 2 -0-048
0o059
o-o8i
o-o83
oo86
*
The parameters are chosen so as to ensure positive public levels in the public provision case.
presented
in
Table i. This table vividly illustrates our general conclusions,
namely, that private provision is preferable when jurisdictions are small, and
public provision performs
better when there is a small number
of
large
jurisdictions.
III. DISCUSSION AND EXTENSIONS6
Some
assumptions
made
in
this
paper
deserve
a closer look as
they
are the
driving
force
behind
the
results.
First,
there is the
assumption
on
strictly
non-
cooperative
behaviour
of
individuals
-
both
in
their
private provision
of
public
goods
and
in
their rent
seeking
efforts. Were more
'cooperative' equilibrium
concepts
used,
private provision
would
become more
attractive
and
public
provisionmore wastefulsince free riding varies negatively and rent dissipation
varies
positively with cooperative
behaviour.
In
the context
of
private
provision of public goods, several attempts have been made to model the
individual's behaviour
in
a
more
cooperative way than is suggested by
the
Cournot-Nash
paradigm
-
see, e.g. Sugden
(i
984)
for one such
alternative
equilibrium concept.
A
related
line
of research
in
the
public goods
literature
departs
from
the neoclassical tradition
by assuming
that
individuals
make their
contributions to the
provision
of
public goods partly
because of
'egoistic'
motives,
that
is, they
derive
utility
from the act of contribution
as well as from
private and public goods
-
see, e.g. Andreoni (I989)
and
references therein.
Proceeding along
these lines
may
also
increase
the attractiveness
of
private
provision, especially in those circumstances where the 'egoistic' motive is
relatively important.
It is
equally plausible
to
approach
rent
seeking
with the
aid
of
some
kind of
cooperative equilibrium concept
since
lobbying
is
usually
done
by
a
relatively
small number of
(sometimes
well
organised
and
disciplined)
groups
of individuals
-
see Olson
(I982)
who
stresses
the
importance
of the
interest
groups' organisation
for economic
growth.
6
This section has been
inspired by
the referee's
remarks.
?
Royal
Economic
Society
I993
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THE ECONOMIC JOURNAL
[SEPTEMBER
Another
possible extension is to
represent
rent seeking as lobbying
over
shares
of
the public good
(as
in
Ursprung
(I990)). For example,
suppose that
the government
sets the
amount of public good provision, whereas
individuals
attempt
to affect the
distribution of the tax
burden. More precisely,
an
individual's share in public good provision can be affected by rent seeking
individuals with the
assumption that
the individual's tax share
is a decreasing
function
of
his own
lobbying and an increasing
function
of lobbying by others.
A
preliminary
analysis
done by the author
along these lines
indicates that our
main conclusions are
unaffected. A more promising
possibility
is to assumethat
individual
rent seeking
efforts are, at least, partly
an input
in
the provision
function
of
the public
good, as was suggested
in
a related context by Long
and
Vousden (I987).
This seems to be an interesting
line of research
to
pursue
in
future work.
Finally, relaxing the
assumption
of identical individuals may
yield interesting
results as to the effect
of heterogeneity
in
initial wealth
on the welfare
comparison
between
private provision
of
public goods
and
public provision
with
rent
seeking.
In this
case,
both outcomes could
also be
compared
to that
attained by direct voting,
where the
median voter
is
pivotal
in
determining
the
final allocation
of resources.
IV. CONCLUDING
REMARKS
The
main
objective
of this
paper
is
to
approach
the issue
of
government
intervention
in the provision of public
goods
from a positive perspective,
by
introducing
some realistic features
into the underlying political process.
Following the paradigm
developed by the public
choice
school, this study
is
based
on
the
presumption
that
public provision
of
public goods
entails wasteful
rent seeking.
The results
supplement those of
a related work (Gradstein, I992)
which
contains a
preliminary
discussion
of
the
comparison
of
private
and
public provision
of
public goods
when the
government
is uninformed.
In both
cases, public provision frequently outperforms private provision in large
economies.
The amount
of
inefficiency generated by
rent seeking
incentives
is
much smaller here than
in the
context
of rents having
the nature
of
private
goods.7
The
presented
model
illustrates, therefore,
that
in
the case
of
public
goods provision,
rent
seeking
behaviour
does
not
necessarily
impair
the welfare
enhancing potential
of
centralised
intervention.
Ben Gurion
University
Date
of receipt
ffinal
typescript:
March
993
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Since
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the ideal
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organisation
would probably try
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by either
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Almost
universal
existence of the aforementioned
activities
hints at the
unavoidable difficulties
nvolved
in designing
the appropriate
disincentive
system.
K
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Economic
Society
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http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp
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