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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
MODELING
INEFFICIENT INSTITUTIONS
Daron Acemoglu
Working Paper 06-01
December 27, 2005
Room
E52-251
50 Memorial Drive
Cambridge,
MA 021 42
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract=873688
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JAN
2 5 2005
LIBRARIES
Modeling
Inefficient Institutions*
Daron Acemoglu^
December
2005
27,
Abstract
Why do inefficient — non-growth enhancing—institutions emerge and persist?
This paper
develops a simple framework to provide some answers to this question. Political institutions
determine the allocation of political power, and economic institutions determine the frame-
work
for
policy-making and place constraints on various
power, the
elite,
fer resources
policies.
Groups with
political
choose policies to increase their income and to directly or indirectly trans-
from the
The
rest of the society to themselves.
baseline
model encompasses
ma-
various distinct sources of inefficient pohcies, including revenue extraction, factor price
nipulation and political consolidation. Namely, the elite
extract revenue from other groups, to reduce their
fiting
from changes
power.
The
elite's
in factor prices,
demand
pursue
inefficient policies to
for factors,
thus indirectly bene-
and to impoverish other groups competing
for political
preferences over inefficient policies translate into inefficient economic
institutions. Institutions that
the elite
may
can
restrict inefficient policies will in general not
may manipulate economic
institutions in order to further increase their
The exception
facilitate rent extraction.
emerge, and
is
when
income or
commitment (holdup) problems,
worse than the elite would like them to be
there are
and regulations are
from an ex ante point of view. In this case, economic institutions that provide additional
security of property rights to other groups can be useful. The paper concludes by providing
a framework for the analysis of institutional change and institutional persistence.
so that equilibrium taxes
Keywords:
Political
Economy,
Institutions,
Commitment, Holdup,
Social Conflict,
Economic Development, Taxation, Property Rights, Regulation.
JEL Numbers:
*I
H2, NIO, N40, 01, OlO, P16.
thank Alexandre Debs
for
suggestions and excellent research assistance and
Timothy
Besley,
Gerard
Padro-i-Miquel, Torsten Persson, James Robinson and Pierre Yared for comments.
^Dept. of Economics, Massachusetts Institute of Technology, E52-3S0b, 50 Memorial Drive, Cambridge,
MA
02142, U.S.A.; daron@mit.edu; http://www.mit. edu/"daron/
1
Many
ment
economists and social scientists have recently emphasized the importance of governpolicies,
important
economic, political and legal institutions, and more broadly, the organization
There
of society.-'
still
Introduction
for
also
is
mounting evidence that various
economic growth.^ Nevertheless, despite important theoretical advances, we
lack an organizational
ticular, if institutions
or end
institutional features are indeed
up with
framework to analyze the determinants of
matter
(so
institutions that
much)
for
institutions.^ In par-
economic performance, why do societies choose
do not maximize economic growth or aggregate economic
welfare? This paper discusses potential answers to this question.
The main
meaning
focus
on modeling the emergence and persistence of
is
institutions that
of the paper
is
do not maximize the growth potential of a
inefficient institutions,
society.^
The purpose
not to provide a survey but to construct a relatively simple unified model
that illustrates both various issues already raised in the existing literature and a
new mechanisms
(i)
what type
tional frameworks;
and
allocations.
of
that appear to be important in understanding inefficient institutions.
To understand why
stand:
number
inefficient institutions
of equilibrium policies
(ii)
This
cient institutions will
emerge and
persist,
we
first
and allocations emerge within
need to under-
different institu-
the preferences of different individuals and groups over these policies
will
enable us to derive induced preferences over institutions.
emerge and
persist, in turn,
when groups
Ineffi-
that prefer the inefficient
(non-growth enhancing) policies that these institutions generate are sufficiently powerful.
^For general discussions, see North and
and Weingast
^See,
Thomas
North (1981), Olson (1982), North
and Acemoglu et al. (2005).
Knack and Keefer (1995), Mauro (1995), Barro (1999),
(1973), Jones (1981),
(1989), Eggertsson (2005), Dixit (2004),
among
others, the empirical evidence in
Hall and Jones (1999), Acemoglu et
al. (2001, 2002) or Persson (2005).
•^Austen-Smith and Banks (1999) and Persson and Tabellini (2000) are excellent introductions to recent
advances in political economy.
weaker definition of "inefficiency" would be Pareto inefBciency, whereby a set of instituwould be Pareto inefficient if a different set of institutions would make everybody better off. This
definition, though important for certain theoretical analyses, is too weak in the context of political economy discussions, since one set of institutions may enrich a particular narrow social group, while causing
stagnation or low growth for the society at large, and we may wish to refer to this set of institutions as
"^A potentially
tions
"inefficient"
and when other
more
social
arrangements that compensate these powerful groups, while reaching
efficient allocations,
In this paper,
model, which
is
I
cannot be found.
provide one example of such an approach.
I
start with a simple baseline
then enriched to discuss a number of mechanisms that lead to the emergence
and persistence
and
of inefficient policies
institutions.
The model
workers, elite producers and non-elite (middle class) producers.
includes three groups:
The
latter
two groups
have access to investment opportunities with varying degrees of productivity.
policies in the
dimensions.
in society.^
over
model are taxes imposed on producers.^ There are two
The
first is political institutions,
different institutional
which govern the allocation of de jure power
This power determines, for example, which groups (or individuals) have control
fiscal policies.
Economic
The key
To
institutions,
start with,
I
suppose that the
on the other hand,
have de jure
elite
relate to the constraints
and
political
power.
rules governing
economic interactions. They include, among other things, enforcement of property
rights,
entry barriers, regulation of technology, and the set of contracts that can be enforced.^
In the model, restrictions on expropriation, taxation
and
redistribution, or the ability to
regulate technology, correspond to economic institutions.
The model
1,
is first
used to highlight various sources of inefficiencies
Revenue extraction: the group
in
power
class producers in order to extract resources
^This should be interpreted
eis
—the
elite
—
will set
in policies:
high taxes on middle
from them. These taxes are distortionary. This
an example standing
for
many
other forms of distortionary ways of
transferring resources from one group to another. These include simple violations of property rights (as,
for
example, when land tenure
is
removed or
assets are expropriated
from certain groups), entry barriers
(used to indirectly transfer resources from more efficient to less efficient producers or to manipulate factor
prices as
we
will see below), or other distortionary policies, for
order to depress the prices paid for certain agricultural products
of the use of
marketing boards
in
example, the use of marketing boards
(e.g.,
in
see Bates (1981), a classic analysis
Ghana and Zambia)
^See Acemoglu and Robinson (2006a) and Acemoglu et
al.
(2005) for the distinction between de jure
and de facto political power.
^Throughout I retain the assumption that pohtical and economic groups coincide, thus all members of
"the elite" will have the same preferences over economic policies and will somehow be able to coordinate
their policy actions.
in this
In practice
paper (though the model
who
"the elite" are
is
a key question, on which I am remaining agnostic
has an important effect on
will illustrate that the productivity of the elite
the efficiency of equilibria).
^Naturally, the distinction between economic and political institutions is somewhat arbitrary. For example, restrictions on taxes and expropriation are interpreted as "economic institutions" here, though they
clearly require limits on the political
power of certain groups.
source of inefficiency results from the absence of non-distortionary taxes, which imphes that
the distribution of resources cannot be decoupled from efficient production.^
2.
Factor price manipulation: the group in power
may want
to tax middle class pro-
ducers in order to reduce the prices of the factors they use in production. This inefficiency
arises
because the
elite
and middle
taxing middle class producers, the
for themselves.
3.
class
producers compete for factors (here labor).
ensure lower factor prices and thus higher profits
elite
-^^
Political consolidation:
to the extent that the political
depends on their economic resources, greater middle
power and endanger
order to impoverish
Although
By
their future rents.
them and
The
power of the middle
class
class profits reduce the elite's political
elite will
then want to tax the middle class in
consolidate their political power.
-^^
three inefficiencies in policies arise because of the desire of the ehte to
all
extract rents from the rest of the society, the analysis reveals that of the three sources of
inefficiency, the
revenue extraction
is
typically the least harmful, since, in order to extract
revenues, the elite need to ensure that the middle class undertakes efficient investments. In
contrast, the factor price manipulation
the
is
elite to directly
and
impoverish the middle
political consolidation
class.
An
mechanisms encourage
interesting comparative static result
that greater state capacity shifts the balance towards the revenue extraction mechanism,
and
thus,
by allowing the
®Many models
man
in
elite to
extract resources
more
efficiently
from other groups,
the literature emphasize the revenue extraction mechanism. See,
among
may
others, Gross-
Grossman and Kim (1995), McGuire and Olson (1996). The costs of redistributive taxation
in models of democracy are also related (e.g., Romer (1975), Roberts (1977), Meltzer and Richard (1981)).
See also Besley and Coate (1998) for a discussion of inefficient redistribution because of limits on fiscal
(1991),
instruments.
may impose entry
models in which there is a conflict between
agricultural and capitalist producers, or between users of old and new technologies, for example, Krusell
and Rios-Rull (1996), Parente and Prescott (1999), Bourguignon and Verdier (2000), Nugent and Robinson
(2002), Galor et al. (2003), and Sonin (2003). The discussion of the taxation policies and migration and
occupational controls towards blacks in South Africa in Feinstein (2005) provide a clear example of the
factor price manipulation mechanism.
^'The mechanism of political consolidation is most closely related to Acemoglu and Robinson (2000a,
2006b), where a ruler may block technological change in order to increase the probability of staying in
power. In that model, the reason why technological change may threaten the ruler is that it erodes its
incumbency advantage. See also Robinson (2001), Rajan and Zingales (2000) and Bueno de Mesquita et al.
(2003). Empirical evidence related to the political consolidation mechanism from various historical contexts
is discussed in Acemoglu and Robinson (2000a).
"^This mechanism
is
most
closely related to
barriers in order to affect factor prices.
It is
Acemoglu
(2003a), where incumbents
also related to
improve the allocation of resources.
Additional inefficiencies arise when there are "commitment problems" on the part of the
elites, in
the sense that they
may
renege on policy promises once key investments are made.
Following the literature on organizational economics,
With holdup,
more
taxes are typically higher and
are likely to be important, for example,
when
I
refer to this as
distortionary.
a holdup problem.
Holdup problems,
in turn,
the relevant investment decisions are long-
term, so that a range of policies will be decided after these investments are undertaken.
The
inefficiencies in policies translate into inefficient institutions. Institutions
determine
the framework for policy determination, and economic institutions determine both the limits
of various redistributive policies
and other
rules
transactions and productivity of producers.
and regulations that
In the context of the simple
associate economic institutions with two features: limits on taxation
regulation on the technology used by middle class producers. ^^
inefficient policies
imply that there
institutions. In particular, they
for
will
may
middle class producers or they
class producers.
preferred by the
be reasons
in
model
here,
redistribution,
The same forces
for the elite to
may
I
and
that lead to
choose inefficient economic
prefer to block technology adoption by middle
Holdup problems, which imply equilibrium taxes even higher than those
elite,
create a possible exception, and
their
may encourage
own
the
elite to
may
be more
use
This
future policies (taxes).
suggests that economic institutions that restrict future policies
economies
and
economic
not want to guarantee enforcement of property rights
economic institutions to place credible limits on
in
affect the
likely to arise
which there are more longer-term investments and thus more room
for
holdup.
The model
also sheds light
on the conditions under which economic institutions
courage or block technology adoption.
If
the source of inefficiencies in policies
extraction, the elite always wish to encourage the adoption of the
nologies by the middle class. However,
when the source
price manipulation or political consolidation, the elite
^^More
generally, these correspond to various rules
is
revenue
most productive tech-
of inefficiencies in policies
may want
dis-
is
factor
to block the adoption of
and arrangements that put constraints on
fiscal
and
regulatory policies of governments, and shape the set of contracts and technology choices available to firms.
more
efficient technologies, or at
the very least, they would choose not to invest in activities
that would increase the productivity of middle class producers. This again reiterates that
when
the factor price manipulation and political consolidation mechanisms are at work,
more
significantly
outcomes can
inefficient
While economic institutions regulate
emerge.-'^
fiscal policies
and technology
choices, political
institutions govern the process of collective decision-making in society.
model, the
to
make
elite
have de jure
political power,
which means that they have the formal right
policy choices and influence economic decisions.
in the institutional
In the baseline
To understand the
inefficiencies
framework, we need to investigate the induced preferences of different
groups over institutions. In the context of political institutions, this means asking whether
the elite wish to change the institutional structure towards a more equal distribution of
political power.
The same
forces that
that the answer to this question
is
make
the
elite
choose inefficient policies also imply
no. Consequently, despite the inefficiencies that follow,
the institutional structure with elite control tends to persist.
The framework
stitutions.
also enables
me
Concentrating political power in the hands of the
(may even be
"efficient"), if
middle
However, a change
could
class).
make
may have
in-
limited costs
the elite are sufficiently productive (more productive than the
which
may have
in the productivity of the elite relative to the
previously functioned relatively well,
new economic environment.
institutions in response to the
Finally,
elite
and inappropriate
middle class
a different distribution of political power more beneficial. In this case, existing
institutions,
the
to discuss issues of appropriate
I
^'^
Yet there
change
in
is
become inappropriate
no guarantee that there
will
be a change
in
environment.
present a framework for analyzing changes in political institutions.''^
ical institutions
to
Polit-
regulate the allocation of de jure political power, as in the example of
^^The framework in this paper
Segura-Cayuela (2006),
is
applied to the inefficiency of institutions in an open economy setting in
'^How a given set of institutions that may first increase but then retard economic growth is also discussed
Acemoglu (2003a) and Acemoglu et al. (2003).
-'^This framework builds on my previous work with James Robinson, but applies these ideas to the
environment considered here which contains richer economic interactions. See in particular Acemoglu and
in
Robinson (2000b, 2001, 2006a).
constitutions or elections determining the party in government. There
power than
groups
this tj'pe of de jure power, however. Certain
existing system, for example,
by solving
their collective action
may be
is
more
able to disrupt the
problem and undertaking
demonstrations, unrest, protests, revolutions or military action. Each group
possess de facto political power even
when excluded from de
to pohtical
may
therefore
jure political power.
In this
context, middle class producers, even though they have no formal say in a dictatorship or
an oligarchic
society,
may sometimes have
system or at
least to
demand some
changes in political institutions
sufficient
de facto
concessions from the
may emerge
political
elite.
power
to
change the
Under these circumstances,
as an equihbrium outcome.
They
are useful as
a way of committing to future allocations, because, by affecting the distribution of de jure
power
political
in the future,
they shape future policies and economic allocations. Such a
commitment may be necessary when the current
elite
to a shift in the distribution of de facto political
concessions within a given political system
institutions take place
power
are less likely
elite are
power and when
limited.
in response
their ability to
in the future).
when
The
make
Consequently, changes in political
forced to respond to temporary changes in de
power by changing the pohtical system (and thus the distribution
facto political
political
when the
is
need to make concessions
of
de jure
analysis also shows that changes in political institutions
political stakes are higher, because, in this case, the elite will fight
and
use repression to defend the existing regime. Rents from the natural resources or land tend
to increase political stakes
state capacity,
may
create
The
and thus contribute to
which makes redistribution more
dynamic
rest of the
is
how
and
of the elite.
for a given
sequence of
policies.
The
rest of the
paper
these policies are determined. Section 3 analyzes the revenue extraction,
factor price manipulation
and
problems and distortions
in
emergence of
stakes
organized as follows. Section 2 presents the basic economic model
and characterizes the equilibrium
investigates
Interestingly,
efficient, also increases political
by increasing the longevity of the dictatorship
costs
paper
institutional persistence.
inefficient
political consolidation
mechanisms, and also discusses holdup
the process of technology adoption.
economic
Section 4 analyzes the
institutions, while Section 5 discusses
emergence and
Section 6 presents a model of endogenous
persistence of inefficient political institutions.
institutional change
and
institutional persistence. Section 7 concludes.
Baseline Model
2
2.1
Environment
Consider an
infinite
horizon economy populated by a continuum
agents, each with a discount factor equal to
good denoted by
y.
The expected
utility of
(3
<
There
1.
agent j at time
is
1
+ ^e + ^m
of risk neutral
a unique non-storable final
is
given by:
oo
Ui
= Eo^P'4,
(1)
t=0
where
M
G
Cj
denotes the consumption of agent j at time
operator conditional on information available at time
Agents are
supply their labor
denoted by
e,
The
in three groups.
inelastically.
who
initially
first
There
is
are workers,
a total mass
will use j to
and Ej
the expectations
is
t.
whose only action
1
of workers.
in the
The second
hold political power in this society. There
Finally, there are 9"^ "middle class" agents,
class producers are
t
is
model
is
a total of
denoted by m. The sets of
elite
the
6'^
is
to
elite,
elites.
and middle
denoted by S^ and S'^ respectively. With a shght abuse of notation,
I
denote either individual or group.
Each member
of the elite
and middle
class has access to production opportunities,
represented by the production function
yi
where
A;
denotes capital and
Cobb-Douglas form
The key
is
difference
/
adopted
= ^{AinkiY-^iiir,
1 — a
labor. Capital
is
between the two groups
A"^.
assumed to depreciate
elite
is
new
in their productivity.
agent
is A"^
in
Productivity of the two groups
they are engaged in different economic activities
old versus
fully after use.
The
for simplicity.
us assume that the productivity of each
middle class agent
is
(2)
(e.g.,
To
start with, let
each period, and that of each
differs, for
example, because
agriculture versus manufacturing,
industries, etc.), or because they have different
human
capital or talent.
On
the policy side, there are activity-specific tax rates on production, r^ and r™, which
are constrained to be nonnegative,
instruments
total
income
(in particular,
(rent) of
R
i.e.,
>
t^
and
>
0,
>
no lump-sum non-distortionary
There are no other
0.
taxes).
T™ >
>
and T^
Let us also introduce a parameter
In addition there
(p
lump-sum
of the states to penetrate
is
e
[0, 1],
which measures how much of the tax revenue
When
</>
=
1
we can think
4>
=
0,
Let us also assume that there
t.
the ability
state capacity
is
limited
all
it
does
tax revenue
of a society with substantial state capacity that
The government budget
is
T- + e-^rr +
and
i.e.,
relations in society (though
able to raise taxes and redistribute the proceeds as transfers.
constraint
a
0.^^
and regulate the production
so in a highly "reduced-form" way).
when
is
transfers targeted towards
can be redistributed. This parameter, therefore, measures "state capacity,"
gets lost, whereas
fiscal
from natural resources. The proceeds of taxes and revenues from
natural resources can be redistributed as nonnegative
each group, T"*
r'"
is
6'^T^
<cp
maximum
a
fividj
[
This prevents the most productive agents
+
R.
(3)
scale for each firm, so that
in the
/^
<
A for
economy from employing the
lidj<l,
j
entire
labor force. Since only workers can be employed, the labor market clearing condition
/
all
is
(4)
JjeS^uS"^
with equality corresponding to
full
employment. Since
0^
there can never be
full
+
e'"
<
l^
<
A, (4) implies that if
(ES)
\,
A
employment. Consequently, depending on whether Condition (ES)
holds, there will be excess
demand
or excess supply of labor in this economy. Throughout,
^^The assumption that taxes and transfers are nonnegative are standard
does not make them innocuous). The non-negativity of transfers
will play
in
the literature (which, naturally,
an important
role in the analysis
by forcing redistributive policies to be distortionary. Although this structure of fiscal instruments can be
motivated as restrictions imposed by "economic institutions", the most compelling reason for assuming this
structure is that it is a tractable reduced-form formulation, which captures potential inefficiencies that will
arise because of informational problems in richer settings (e.g., Mirrlees (1971)).
I
assume that
9^
<\A
and
the
number
is
adopted only
for
<
(Al)
|,
A
which ensures that neither of the two groups
Assumption (Al)
9""
will create excess
demand
for labor
by
itself.
convenience and simplifies the notation (by reducing
of cases that need to be studied).
Economic Equilibrium
2.2
I first
characterize the economic equilibrium for a given sequence of taxes, {T^, t/"}j^q
(the transfers
do not
affect the
a sequence of wages {wt}^^^
{N'^t],£5=u5-}
„,
J t=0,l,...,oo
^
economic equilibrium).
An
economic equilibrium
^, and investment and employment levels for
is
all
^"^'^ *^^^^ given {rt^,Tl"}^^ox-,oo ^^^^ {^«}i=o,i,...,oo. all
^
j
defined as
producers,
producers
-^
K.
choose their investment and employment optimally and the labor market
Each producer
(firm) takes wages,
adjustment costs and
full
clears.
denoted by Wt, as given. Finally, given the absence of
depreciation of capital, firms simply maximize current net profits.
Consequently, the optimization problem of each firm can be written as
maxi^(AO°(A;/)^-'^ {ll^ - w^l - H,
where
j
G 5^ U
S'™.
This maximization yields
r
i\
K=
=0
e[0,A]
A number of points are worth noting.
is
{\-rifl'^A^i, and
(.5)
if i^t
> Y^(l-Tfy/M^'
if^,
= ^(l-r/y/M^-
First, in
equation
(6),
(6)
.
the expression a{l—Tiy^°'A^/ (1
the net marginal product of a worker employed by a producer of group
above this amount, this producer would not employ any workers, and
she would prefer to hire as
equation
(5) highlights
in physical capital
many
workers as possible
(i.e.,
j.
If
if it is
up to the maximum,
the wage
is
below, he or
A).
Second,
the source of potential inefficiency in this economy. Producers invest
but only receive a fraction
(1
—
7f ) of the revenues.
discourage investments, creating potential inefficiencies.
Therefore, taxes
—
a)
Combining
(i)
If
(4),
equilibrium wages are obtained as follows:
excess supply of labor and Wt
is
Condition (ES) does not hold, then there
equilibrium wage
is
Wt
=
The form
elite
with
Condition (ES) holds, there
If
(ii)
(6)
min
(j^-{l \i
wage
of the equihbrium
and middle
demand exceeds
—a
class producers,
"excess
is
r/)l/"A^
0.
demand"
for labor
- tH'^^aA
-^(1
—
i
is
=
a
and the
(7)
.
/
Labor demand comes from two groups, the
intuitive.
and when condition (ES) does not hold,
available labor supply, so the market clearing
wage
will
their total labor
be the
minimum
of their net marginal product.
One
interesting feature, which will be used below,
not hold, the equihbrium wage
producers, so either the
elite or
is
the middle class will
= -^(l-r;)(i-°)/"A^ /"
1 - a
Jj^s-
The equilibrium
is
that
summarized
lidj
output
make
+ -^{l-Tl"Y'-''^/"A'^ f
1
a
Then
^, the equilibrium takes the following form:
0,
and
if
sequence, factor
Suppose Assumption (Al) holds.
Condition (ES) does not hold, then Wt
demands
are given by (5) and (6),
3
Now
I
elite's
for a given
(8)
if
sequence of taxes
Condition (ES) holds, then
given by
(7).
and aggregate output
policies. In this section, political institutions
desired policies.
R.
Given the wage
is
given by
(8).
Inefficient Policies
the elite" in the sense that they allow the
the
is
use the above economic environment to illustrate a
inefficient
+
in the following proposition (proof in the text):
{tj^,t/"}j^q
=
l{dj
Jj^s^
1
Wt
zero profits in equilibrium.
is
Proposition
J
when Condition (ES) does
equal to the net productivity of one of the two groups of
Finally, equilibrium level of aggregate
yt
is
The main
elite to
number
of distinct sources of
correspond to "the dictatorship of
decide the policies, so the focus will be on
(potentially inefficient) policy will be a tax on middle
10
though more generally,
class producers,
As discussed
or entry barriers.
to inefficient policies;
(2)
be three mechanisms leading
Factor Price Manipulation; and (3)
Consohdation.
Political
To
in the introduction, there will
Resource Extraction;
(1)
correspond to expropriation, corruption
this could
illustrate
each mechanism in the simplest possible way,
I
will focus
parameter space and abstract from other interactions. Throughout,
an upper bound on taxation, so that
may
institutional, or
arise
t^^
< f and
r^
<
where f
f,
I
<
on a subset of the
assume that there
1.
is
This limit can be
because of the ability of producers to hide their output or
shift
into informal production.
The timing
of events within each period
is
as follows:
ments are made. This removes an additional source of
problem whereby groups
once
power may
has been produced. Holdup
it
To
in
start with,
strategies are only
I
focus on
seize all of the
holdup
output of other agents in the economy
(MPE)
Perfect Equilibria
strategies are independent of past taxes
and investments
of this economy, where
this context, this
(since there
maximize the
In the dictatorship of the elite, policies will be chosen to
is
set; then, invest-
inefficiency related to the
dependent on payoff-relevant variables. In
a political equilibrium
taxes are
be discussed below.
will
Markov
first,
is full
means that
depreciation).
Hence,
elite's utility.
given by a sequence of pohcies {r/, tI^,TI",T^, Tf}^^^
^
^
(satis-
fying (3)) which maximizes the elite's utility, taking the economic equilibrium as a function
of the sequence of policies as given.
More
specifically, substituting (5) into (2),
we obtain
elite
a
-(l-rf)^/"A^
1-a
with wt given by
square brackets
wage. Total per
receive.
Then
of {rf, r/",
elite,
(7).
is
Wt
it
+
consumption as
T:,
(9)
This expression follows immediately by recalling that the
the after-tax profits per worker, while the second term
elite
consumption
is
given by their profits plus the
the political equilibrium, starting at time
T^,T^, T/Jj^q
^
^
f
=
0, is
is
first
term
in
the equilibrium
lump sum
transfer they
simply given by a sequence
that satisfies (3) and maximizes the discounted utility of the
Et=o/?*c^
11
The determination
the
MPE
(9).
We now
full
capital depreciation, this
is
simphfied further by the fact that in
problem
is
simply equivalent to maximizing
characterize this political equilibrium under a
number
of different scenarios.
Revenue Extraction
3.1
To
with
of the pohtical equihbrium
highlight this mechanism, suppose that Condition (ES) holds, so wages are constant at
zero.
have
This removes any
=
It
It is
\
effect of taxation
Also assume that
for all producers.
straightforward to see that the
redistribute
all
on factor
>
(j)
elite will
(for
example,
</)
=
also
and
will
!).
never tax themselves, so
government revenues to themselves, so T/"
of the
we
In this case, from (6),
prices.
=
T/"
=
r/^
0.
=
0,
Consequently
taxes will be set in order to maximize tax revenue, given by
=
Revenuet
—^r.^^fl - r,'")(i-°)/"A'"A^'" + R
at
time
t,
into (2)
facedownwhere the
and multiplying
producers and a fraction
it
(f)
first
term
is
is
It is
would require
r^"
elite at
=
0.
=
9"'
A and
for (5)
middle class
is
maximized by
simply
t["
=
a.
the peak of their Laffer curve. In
However, the output-maximizing tax
not an equilibrium because, despite the distortions, the
At the root
/"*
The second term
clear that tax revenues are
the tax rate that puts the
tax rate to increase their
If
obtained by substituting for
of tax revenues can be redistributed.
contrast, output maximization
rate
is
by t^, and taking into account that there are
the revenues from natural resources.
In other words, this
(10)
-a
I
elite
would prefer a higher
own consumption.
of this inefficiency
is
a limit on the tax instruments available to the
elite.
^^
they could impose lump-sum taxes that would not distort investment, these would be
preferable. Inefficient policies here result from the redistributive desires of the elite coupled
with the absence of lump-sum taxes.
It is
also interesting to note that as
a
increases, the extent of distortions are reduced,
since there are greater diminishing returns to capital
""See
and investment
will
not decline
much
the discussion in footnote 16 and the further analysis and discussion in Besley and Coate (1998).
12
in response to taxes.
Even though
taxation
^®
r/"
= a
may become
is
the most preferred tax for the ehte, the exogenous hmit on
binding, so the equihbrium tax
r^ = T^^
for all
t.
ticular,
a
as
is
= mm{a,f}
(11)
In this case, equilibrium taxes depend only on the production technology (in par-
how
distortionary taxes are) and on the exogenous hmit on taxation. For example,
decreases and the production function becomes more linear in capital, equilibrium
taxes dechne.
This discussion
is
summarized
in the following proposition (proof in the text):
Proposition 2 Suppose Assumption (Al) and Condition (ES) hold and
unique
3.2
I
political equilibrium features
r^"*
= t^^ = min {a, f}
for all
>
0,
then the
t.
Factor Price Manipulation
now
investigate
how
inefficient policies
can arise
in order to
highhght this mechanism in the simplest possible way,
let
that there are no direct benefits from taxation for the
elite.
us
manipulate factor
first
prices.
To
=
so
assume that
(f)
There are indirect
benefits,
however, because of the effect of taxes on factor prices, which will be present as long as the
equihbrium wage
is
positive. For this reason,
hold, so that equilibrium
wage
is
given by
I
now suppose
that Condition (ES) does not
(7).
Inspection of (7) and (9) then immediately reveals that the elite prefer high taxes in
demand from
order to reduce the labor
possible.
The
the middle class, and thus wages, as
desired tax rate for the elite
the equilibrium tax
is
r™
=
t^^'^
=
f
for all
Proposition 3 Suppose Assumption (Al)
thus r/"
is
t.
(5) implies
that
d'^
1.
In k{ / dr^ da
=
13
r/"
=
as
Given constraints on taxation,
therefore have (proof in the text):
holds, Condition (ES) does not hold,
then the unique political equilibrium features
^Mo:re explicitly,
We
=
much
t-^^^'^
1/ (a'^ (l
=
f for
- r/]] >
0.
all
t.
and
(p
=
0,
This result suggests that the factor price manipulation mechanism generally leads to
higher taxes than the pure revenue extraction mechanism. This
price manipulation
mechanism, the objective of the
much
elite is to
because, with the factor
reduce the profitability of the
as possible, whereas for revenue extraction, the elite
middle
class as
middle
class to invest
and generate revenues.
It is
also
worth noting that,
the pure revenue extraction case, the tax policy of the ehte
from the middle
is
class,
but
also doing so indirectly
it is
is
would
like
differently
the
from
not only extracting resources
from the workers, whose wages are
being reduced because of the tax policy.
The
rate
is
role of
</>
=
also needs to be emphasized. Ta:x;ing the middle class at the highest
clearly inefficient.
the elite?
The answer
Why
is
there not a more efficient
way
of transferring resources to
relates to the limited fiscal instruments available to the elite (recall
the discussion in footnote 16). In particular,
=
implies that they cannot use taxes at
to extract revenues from the middle class, so they are forced to use inefficient
all
of increasing their consumption, by directly impoverishing the middle class.
subsection,
I
discuss
how
means
In the next
the factor price manipulation mechanism works in the presence
of an instrument that can directly raise revenue from the middle class. This will illustrate
that the absence of any means of transferring resources from the middle class to the
is
not essential for the factor price manipulation mechanism (though the absence of non-
distortionary
3.3
I
elite
lump-sum taxes
is
naturally important).
Revenue Extraction and Factor Price Manipulation Combined
now combine
the two effects isolated in the previous two subsections.
By
itself
the factor
price manipulation effect led to the extreme result that the tax on the middle class should
be as high as possible. Revenue extraction, though typically another motive
for
imposing
taxes on the middle class, will serve to reduce the power of the factor price manipulation
effect.
The reason
is
that high taxes also reduce the revenues extracted by the
the economy beyond the peak of the Laffer curve), and are costly to the
To
elite
(moving
elite.
characterize the equilibrium in this case again necessitates the maximization of (9).
14
This
As
simply the same as maximizing transfers minus wage
is
before, transfers are obtained from (10), while
(ES) holds and there
same
wages are given by
each
(7).
elite
producer.
When
Condition
excess supply of labor, wages are equal to zero, and
is
we obtain the
results as in the case of pure resource extraction.
The
zero,
bill for
interesting case
is
the one where (ES) does not hold, so that wages are not equal to
and are given by the minimum
that the
elite will
two expressions
of the
not tax themselves and will redistribute
in (7).
all
Incorporating the fact
the revenues to themselves,
the maximization problem can be written as
max
-
-A^
l-a
1
r+
wt
l-a
r™(l
-
^^'")(i-«)/"^"^/j»^"T
^^
(12)
subject to (7) and
geie
l^
The
first
term
in (12)
is
Equation (13)
receive.
class producers
the
is
=
A
elite's
gmj^m^-^^
+
if
(1
-
and
T^^y/'^A"'
(13)
>
A'.
(14)
net revenues and the second term
is
the transfer they
the market clearing constraint, while (14) ensures that middle
employ as much labor as they wish provided that
their net productivity
is
greater than those of elite producers.
The
solution to this problem can take two different forms depending on whether (14)
holds in the solution.
profits
and
their only
If it
w = aA^/ {1 —
does, then
income
and
a),
elite
producers make zero
derived from transfers. Intuitively, this corresponds to the
is
case where the elite prefer to let the middle class producers undertake
activities
elite
and maximize tax revenues.
generate revenues both from their
producers. In this case
I
If,
w=
on the other hand,
a).
of the profitable
(14) does not hold, then the
own production and from taxing
— T"^y^'^A"^/ (1 —
a{l
all
the middle class
Rather than provide a
full
taxonomy,
impose the following assumption:
om
A"
which ensures that the solution
Intuitively, this condition
>
will
0(1
-
q)(i-")/"/1"^—
(A2)
,
always take the latter form
(i.e.,
(14) does not hold).
makes sure that the productivity gap between the middle
15
class
and
elite
producers
not so large as to make
is
themselves (recall that
always
when (A2)
problem simply
1_^
/„
=
I
Tj'"
-
so
1,
=
0"^
a(l
—
9"
if
=
and
=
A''
A"", this condition
is
all elite
-
a),
and the
a
+R
„,:i-rn^/"A-A,
(15)
employ A employees, and from
(13),
-
producers
r™)^''"^'"' r/"/(l
maximize
to choosing r/" to
rl^){^-'^)l<^A'^r6'^
.
.
have used the fact that
1
will
(1-A^^)/^-.
The maximization
The
<
we have Wt
holds,
down
boils
-t["(1
.
V-
where
a)<^~°'/"
zero profits
satisfied).''^
Consequently,
elite's
-
</>(!
make
attractive for the elite to
it
first
is
of (15) gives
interesting feature
always
than
less
manipulation.
1,
is
that «;(A,^^,a,0)
which
Moreover, k
is
always
is
less
than
oo.
This implies that
the desired tax rate in the case of pure factor price
(A,(9^, a,
</>)
is
strictly greater
than a/{\
—
a), so that r/"
is
always greater than a, the desired tax rate with pure resource extraction. Therefore, the
factor price manipulation motive always increases taxes above the pure revenue
level
maximizing
(beyond the peak of the Laffer curve), while the revenue maximization motive reduces
taxes relative to the pure factor price manipulation case. Naturally,
greater than f, the equilibrium tax will be f,
*
It is also
this level of tax
+
ll
why
which plays no
becomes more
this condition
is
K(A,^^Q,</))'
not to hold,
an
role here) to write the objective of
/{I - a)e^. The maximum of
a)('^-<^)/°'A'^e'^\/{l
a)e^. When it does not hold,
r"* = 1, we have w = Q and U"^ (t'" = 1) = aA^Xj (1 —
r"')(i-")/'*,4'"(l
-
I'')
max C/2
establishing that (A2)
is
(r'")
>
C/^ (r'"
=
first
agent as
this expression
a), so
sufficient for the elite to prefer
r'"'^^''
(j)
in-
declines.
use (13) (and drop the R term,
{ctA'^ / (1 — a) — w) l'^ + 0r'"(l —
when
(14) holds
let the value be maxT-m C/2 (r™).
1)
16
elite
'
^
/
beneficial (generates greater revenues), but
sufficient for (14)
is
i.e.,
interesting to look at the comparative statics of this tax rate. First, as
creases, taxation
'^To see
if
U^ = 4>all Note that when
is
when Assumption (A2) holds
= aA^Xj (1 -
a)
> U\
a tax policy that yields positive profits
for
them.
This might at
comes
first
less costly,
appear paradoxical, since one
4>
importance of revenue extraction, and as commented above,
raises the
in this case, revenue extraction
elite to
among
expected that as taxation be-
taxes should increase. Intuition for this result follows from the observation
that an increase in
the
may have
is
a force towards lower taxes
move beyond the peak
of the Laffer curve).
(it
makes
it
more
Since the parameter
costly for
is
related,
other things, to state capacity, this comparative static result suggests that higher
state capacity
wih translate into lower taxes, because greater state capacity enables the
elite to extract
revenues from the middle class through taxation, without directly impover-
ishing them. In other words, greater state capacity enables
more
efficient
forms of resource
^°
extraction by the groups holding political power.
Second, as 9^ increases and the number of
The reason
for this effect is
this discussion
is
that
producers increases, taxes also increase.
again the interplay between the revenue extraction and factor
price manipulation mechanisms.
becomes more important
elite
When there are more elite producers,
One
relative to gathering tax revenue.
when the
factor price manipulation effect
typically be greater inefficiencies. Finally, an increase in
a
is
reducing factor prices
interesting imphcation of
more important, there
raises taxes for exactly the
will
same
reason as above; taxes create fewer distortions and this increases the revenue-maximizing
tax rate.
Once again summarizing the
analysis (proof in the text):
Proposition 4 Suppose Assumptions (Al) and (A2)
and
(/)
>
0.
Then
hold. Condition (ES) does not hold,
the unique political equilibrium features r/"
=
r*"*^^^ as
all t.
Equilibrium taxes are increasing in 9^ and a and decreasing in
3.4
Political Consolidation
I
now
given by (16) for
0.
discuss another reason for inefficient taxation, the desire of the elite to preserve
their political power. This
to always
remain
in
mechanism has been absent
power.
To
illustrate
it,
so far, since the elite were
the model needs to be modified to allow
^°This is a very different argument for why greater state capacity
than the standard view, for example, espoused in Evans (1995).
17
assumed
may
be good for economic outcomes
for
endogenous switches
For now,
later.
let
power permanently
middle
class will
us assume that there
from the
shifts
is
a probability pt in period
the middle class. Once they
elite to
pursue a policy that maximizes their own
exogenous, the previous analysis
this probability
Institutional change will be discussed in greater detail
of power.
is
still
endogenous. Here
applies. Interesting
I
will use
the trade-offs and assume that this probabihty
utility.
t
come
When
that political
to power, the
this probability
economic interactions
is
when
arise
a simple (reduced-form) model to illustrate
is
a function of the income level of the middle
class agents, in particular
p,
where
is
I
= p(^-cne[0,i],
have used the fact that income
continuous and differentiable with
class producers are richer, they
p'
is
>
(17)
0,
which captures the
have greater de facto
may
may be more
political power.
the middle
This reduced-form
when the middle
class
successful in solving their collective action problems or they
increase their military power.
This modification implies that the
may no
longer be optimal.
recursively,
class
when
fact that
formulation might capture a variety of mechanisms. For example,
are richer, they
Let us assume that p
equal to consumption.^^
is
and denote
it
To
fiscal
policy that maximizes current consumption
investigate this issue
by V^ (E) when they are
in
we now
write the utility of elite agents
power and by V^ (M) when the middle
power. Naturally, we have
in
^^
subject to
"r
+(5[{\-p,)V^{E)
I
(7), (13), (14)
V^ {E) and V^ (M) not
and
(17),
with
pt
= p {^{l -
+ p,V^{M)]
/
r^f'^A'^l^e"'
-
Wtl'^O''').
as functions of time, since the structure of the problem
I
wrote
makes
it
clear that these values will be constant in equihbrium.
The
first
the same
observation
fiscal
policy
is
is
that
if
the solution to the static problem involves
cj"
=
0,
then
optimal despite the risk of losing power. This implies that, as long
as Condition (ES) does not hold and (A2) holds, the political consolidation
^'Alternatively, one can assume, with qualitatively identical results, that
class relative to that of the elite that matters for political power.
18
it is
mechanism does
the income of the middle
not add an additional motive for inefficient taxation.
To
see the role of the political consolidation mechanism, suppose instead that Condition
=
(ES) holds. In this case, Wt
and the optimal
static policy
is
r/"
= r^^ = min {a, f}
discussed above and implies positive profits and consumption for middle class agents.
as
The
dynamic maximization problem then becomes
a
+/3 [V^ (E)
{
The
/le X
an
first-order condition for
-
<t)
It is
when
1
_
r"^
n-
'-
<j)
a
clear that
p'(-)
>
1
— T^
when
r^"^
0,
=
V^ (E) — V^ (M) >
they get to tax the
Intuitively, as
=
elite
/
\1
<t>
^m(-i
_
m\(l-a)/a
(T
—a
(1
-
is
=
Am \am
\
,
TT'-f'^A'^e'^X
V" (M))]
{V (E) -
= t^^ = min{a,f}
V (M)) =
as long as
as above.
'
0.
of the transfers.
However,
V^ {E) - V^ {M) >
immediate since when the middle
now not
^
'
J
J
min{a,r}
all
"I
be expressed as
0.
That
class are in power,
^^
with the factor price manipulation mechanism, the
elite
tax beyond the
to increase their revenues, but to consolidate their
These high taxes reduce the income of the middle
is
d]
i
{V {E) -
r;'")^/"A'"0'"A)
we obtain r™
and receive
Consequently, there
power.
0,
the case
peak of the Laffer curve, yet
political power.
r
interior solution can
r^^ > r^^
is
i
-p{y^{1-
+ /3^V
p' (•)
I
a higher probability that the
elite
class
and
their political
remain in power
in the
future, enjoying the benefits of controlling the fiscal policy. ^^
An
interesting comparative static
V^ (M)
increases,
is
and the tax that the
that as
R increases,
elite sets increases as well. Intuitively,
power receives the revenues from natural resources, R.
more
the gap between
When R
V^ [E] and
the party in
increases, the elite
become
willing to sacrifice tax revenue (by overtaxing the middle class) in order to increase
the probability of remaining in power, because remaining in power has
valuable.
^^More
taxes.
More
greater state capacity, also increases the gap between
V^ {E)
This contrasts with the results so far where
interestingly, a higher
specifically,
cp,
V* (E)
i.e.,
is
R
now become more
had no
effect
given as the solution to (18), while the expression for
equation (24) in Section 6.
^^This result is similar to that in Acemoglu and Robinson (2006b) where a ruhng ehte
beneficial technological change in order to increase the probability of political survival.
19
on
V^ (M)
is
may want
given by
to block
and V^ (M) (because
this enables the
group in power to raise more tax revenues) and
thus implies a higher tax rate on the middle
Intuitively,
class.
when
there
is
no
political
competition, greater state capacity, by allowing more efficient forms of transfers, improves
the allocation of resources. But in the presence of political competition, by increasing the
political stakes,
it
Summarizing
leads to greater conflict and
political replacement.
sumption (Al) and Condition (ES) hold and
3.5
I
=
> T^^
T^""
policies.
this discussion (proof in the text):
Proposition 5 Consider the economy with
r/"
more distortionary
for all
t.
This
rate
tax;
is
>
</'
Suppose also that As-
then the political equilibrium features
0,
increasing in
R
and
(p.
SuBGAME Perfect Versus Markov Perfect Equilibria
have so
far focused
In this case, however,
restrictive.
MPE.
coincide with the
discuss
why
MPE
on Markov perfect equilibria (A4PE). In general, such a focus can be
This
it
can be proved that subgame perfect equilibria (SPE)
will not
be true
in the
next subsection, so
are a subset of the
SPE. Loosely speaking, SPEs that are not Markovian
supported by some type of "history-dependent punishment strategies"
dependence, SPEs
will coincide
In the models analyzed so far, such
the SPE. Intuitively, each individual
maximize
useful to briefly
the case here.
it is
for such history
it is
is
If
there
is
be
no room
with the MPEs.
punishment strategies are not possible even
infinitesimal
and makes
Therefore, (5) and (6) determine the factor
profits.
.
will
its
in
economic decisions to
demands uniquely
in
any
equilibrium. Given the factor demands, the payoflFs from various policy sequences are also
uniquely pinned down. This means that the returns to various strategies for the
independent of history.
Consequently, there cannot be any
characterized above. Therefore,
^^A formal proof
footnote.
A
history
denote the set of
all
we
SPEs other than the
MPE
have:^^
of this proposition requires additional notation, so
is
elite are
defined as the complete
possible histories of play
list
up to
t
—
1,
The essence of the proof is that, since each producer is
commands according to (5) and (6) at the time t for all
20
I
only provide a sketch in this
in the game. Let Tl*~^
and denote a particular history by /i'~^ G Ti*~^.
of actions
up to a certain point
infinitesimal, they will always choose their factor
/i*~'
€ H*~^. This implies that the maximization
Proposition 6 The
3.6
MPEs
Lack of Commitment
The models
characterized in Propositions 2-5 are the unique SPEs.
— Holdup
discussed so far featured
(lack of
the model;
if
commitment
commitment
by the
to taxes
this corresponds to the situation
from organizational economics,
Holdup
full
elites.
Using a term
without any
''holdup''.
to taxes or policies) changes the qualitative implications of
expropriation (or taxation) happens after investments, revenues generated by
investments can be ex post captured by others. These types of holdup problems are likely
when the key investments
to arise
and implemented
are long-term, so that various policies will be determined
after these investments are
The problem with holdup
is
made (and
sunk).
commit
that the elite will be unable to
to a particular
tax rate before middle class producers undertake their investments (taxes will be set after
investments). This lack of
inefficiency.
To
commitment
illustrate this possibility,
the timing of events such that
then the
elite set taxes.
first
amount
will generally increase the
I
consider the
same model
and
as above, but change
individual producers undertake their investments and
The economic
equilibrium
is
unchanged, and
determine factor demands, with the only difference that
(6) still
of taxation
in particular, (5)
r"^
and
t'^
now
and
refer to
"expected" taxes. Naturally, in equilibrium expected and actual taxes coincide.
What
is
different
is
the calculus of the ehte in setting taxes.
into account that higher taxes
investment decisions, this
to tax at the
for all
maximum
would discourage investment. Since, now, taxes are
effect is absent.
is
in the
MPE,
a unique
the
MPE
elite will
where
r/"
set after
always want
= t^^ =
f
This establishes (proof in the text):
t.
is
a unique political equilibrium with
t^ = t^^ = r
t.
It is clear
above.
As a result,
rate, so in all cases, there
Proposition 7 With holdup, there
for all
Previously, they took
that this holdup equilibrium
is
more
inefficient
than the equilibria characterized
For example, imagine a situation in which Condition (ES) holds so that with the
problem of the
elite is
independent of history and establishes the
21
result.
original timing of events (without holdup), the equilibrium tax rate
the extreme case where f
=
1
Now
1.
and the middle
class stop producing.
In this model,
holds and f
up
=
This
it is
than
To
f.
the middle class producers.
= a
and the middle
r'"
= Q
as long as the history consists of r"'
there
is
any other action
With
class producers invest zero.^^
—
a)^^~"^''°'j4'"A&'"/ (1
r'"
in contrast,
=
1,
promise a
the complete set of actions taken
is
the elite raise no tax revenue from
—
class producers invest according to (5)
= a
=
1
and the middle
this strategy profile, the elite raise a tax revenue of
a) in every period, and receive transfers worth
-
aO*^-"^/"^'"A^™.
(19)
they deviate at any point, the most profitable deviation for them
and they
with
and investments have been consistent
in the history, the elite set r'"
-a(l
If,
elite (credibly)
room
is
Instead, consider the following trigger-strategy combination:
always set r"*
(f>a{l
game
MPE,
In the
elite
If
is
to set
will raise
- a)(^-"'/"^"A^'".
-^(1
—
1
The
to (20), which requires
j S
(20)
a
trigger-strategy profile will be an equilibrium as long as (19)
2^More formally,
5"
and
all s
is
example where Condition (ES)
illustrate this, consider the
the
(5).
positive economic
is
the only SPE, since there
is
groups whereby the
different
to that point (recall footnote 24).
with
and there
naturally very costly for the elite as
is
MPE
no longer true that the
Recall that the history of the
1.
=a
their tax revenues.
all
an implicit agreement between
different tax rate
r/"
Consider
a.
In contrast, with holdup, the equilibrium tax
class producers.
well since they lose
for
without holdup,
by the middle
activity
r/"
=
r^ =
is
let
<t—
/3
>
1
—
history h^-'^he such that
1.
r™ = a
Then, the trigger strategy
V
and j4 = (1 - q)^^" A"", and if /i*"
^®Some authors, for example, Greif
we have (proof
a. Therefore
is
greater than or equal
in the text):'^
=
i
-
1
profile in question
is
as follows:
^'"^ then rf
=
for all s
1
and
kf
<
=
and ki
(1
if
-
q)^''"
/i'"^
=
A"^
for all
/i'~^ r/"
=a
0.
(1994), also view differences between the MPE and the SPE as corresponding to "institutional differences," since different equilibria create different incentives for individual
agents (and are supported by different "beliefs").
I
find
it
more transparent to reserve the term
tions" for arrangements that determine the economic or political rules of the
policies or distribution of political
power) rather than using this term also
a given set of rules.
22
game
(i.e.,
limits
"institu-
on
fiscal
for the equilibria that arise for
Proposition 8 Consider the holdup game, and suppose that Assumption (Al) and Condition (ES) hold
where
=a
r/"
and f
for all
=
Then
1.
for
/3
>
1
— a,
there exists a
subgame
perfect equilibrium
t.
An important implication
of this result
that in societies where there are greater holdup
is
problems, for example, because typical investments involve longer horizons, there
is
room
for
coordinating on a subgame perfect equilibrium supported by an implicit agreement (trigger
strategy profile) between the elite and the rest of the society.
Technology Adoption and Holdup
3.7
Suppose now that taxes are
subsection
is
set before investments, so the source of
absent. Instead, suppose that at time
t
=
holdup
in the previous
before any economic decisions or
policy choices are made, middle class agents can invest to increase their productivity.
particular,
r
is
suppose that there
is
and the resulting productivity A"" applies forever
Once investments
ments
in
in
This investment
is
made once
^'^
after.
technology are made, the game proceeds as before. Since invest-
technology are sunk after date
in Propositions 2-5 above.
t
=
0,
the equilibrium allocations are the
Another interesting question
would prefer to commit to a tax rate sequence
The
The function
a cost V [A^) of investing in productivity A^.
non-negative, continuously differentiable and convex.
In
at time
i
is
whether,
=
0.
if
same
they could, the
analysis of this case follows closely that of the baseline model,
and
I
as
elite
simply state
the results (without proofs to save space):
Proposition 9 Consider the game with technology adoption and suppose that Assumption
(Al) holds. Condition (ES) does not hold, and
features r/"
time
t
=
^^The
0,
=
t^^^^
=
f for
then they would
Moreover,
all t.
still
choose r/"
fact that technology choices are
them from the investments
in
fc,
made
if
4>
=
the
Q,
then the unique political equilibrium
elite
= ^fpm =
could commit to a tax sequence at
^^
once, or at any rate,
which are made
in
every period.
23
more
infrequently, partly distinguishes
That
this
unique SPE. In
at time
t
=
0.
MPE
the unique
is
quite straightforward.
is
The reason
only objective of the
is
for
Once
they could commit
if
reduce the middle
elite is to
class'
labor
demand,
again, the
MPE
is
identical to before.
=
As a
result, the first-order condition
extraction case, recall that the equilibrium
this
is
also the unique
their technology decisions, there
to create history-dependent
static
optimum
elite prefer.
If
elite
r™ = t^^ = min{a,f}. With
SPE. Once the middle
Nevertheless, this
is
this,
the same
class producers have
left,
and
it
made
impossible
is
different
than the
not necessarily the allocation that the
could commit to a tax rate sequence at time
choose lower taxes. To illustrate
(it is
future periods. In the pure revenue
punishment strategies to support a tax rate
for the elite. ^^
the
is
all
no history-dependent action
is
(21)
i.
the constant tax rate that they will face in
arguments as before,
is:
-^-^(i-OV«
—p —a
i.
is
no
us next consider the pure revenue extraction case with Condition (ES)
let
r'(^-)
r'"
so they have
middle class producers.
an interior solution to the middle class producers' technology choice
where
the
it is
as follows: in the case of pure factor price manipulation, the
interest in increasing the productivity of
satisfied.
also intuitive that
the ehte would choose exactly this tax rate even
fact,
For contrast,
It is
t
=
0,
they would
suppose that they can commit to a constant tax rate
straightforward to show that they will in fact choose a constant tax rate even without
this restriction,
of the elite
is
but
this restriction saves
on notation). Therefore, the optimization problem
to maximize tax revenues taking the relationship between taxes and technology
as in (21) as given. In other words, they will solve: max(?!>T"'(l -r'")(^-")/"yl"'A6''"/ (1
The
subject to (21).
-
a)
constraint (21) incorporates the fact that (expected) taxes affect
technology choice.
The
first-order condition for
an
interior solution
a
^^The
fact that
1
each middle class producer
possible to create a strategy profile
can be expressed as
- r™
is
where middle
infinitesimal
dr'"
is
class producers
24
important here.
would
Otherwise,
collectively deviate
it
from
would be
(5).
where dA^/dr"^ takes into account the
t
=
0.
effect of future taxes
This expression can be obtained from (21)
on technology choice at time
as:
1
1(1- t"^)(i-'^)/'»
_
f%A^)
dr^ ~ ~l- (5l-a
dA""
This imphes that the solution to this maximization problem
min{a,f}.
in order to
If
they could, the
elite
would
commit
like to
'^
satisfies r"^
=
r^"^
< t^^ =
to a lower tax rate in the future
encourage the middle class producers to undertake technological improvements.
Their inability to commit to such a tax policy leads to greater inefficiency than in the case
without technology adoption. Summarizing this discussion (proof in the
text):
Proposition 10 Consider the game with technology adoption, and suppose that Assumption (Al)
r/"
=
and Condition (ES) hold and
T^^
=
min
{a, f} for
all
they would prefer to commit to
An
important feature
is
If
t.
r"^'^
</>
>
0,
then the unique political equilibrium features
commit
the elite could
<
to a tax policy at time
that in contrast to the pure holdup problem where
/3
>
1
—
class producers invest only once at the beginning, there
is
frequent investments by the middle class, so that there
they deviate from the promised
on future
4
The previous
is
that, since
middle
policies.
is
When
is
{(3
>
1
— a),
but also
a credible threat against the ehte
such implicit agreements
fail
to prevent
greater need for economic institutions to play the role
policies.
Inefficient Economic Institutions
analysis shows
which possesses
could
no possibihty of using history-
tax rates low. Such agreements not only require a high discount factor
of placing hmits
SPE
This illustrates the limits of implicit agreements to keep
strategies.
the most inefficient policies, there
0,
a, recall Proposition 8), with the tech-
nology adoption game, the inefficiency survives the SPE. The reason
if
=
t^^.
prevent the additional inefficiency (when
dependent punishment
t
how
inefficient policies
emerge out of the desire
political power, to redistribute resources
towards themselves.
the implications of these mechanisms for inefficient institutions.
25
Since the
I
of the elite,
now
discuss
elite prefer to
implement
class
inefficient policies to transfer resources
and the workers) to themselves, they
from the
rest of
the society (the middle
will also prefer inefficient
economic institutions
that enable and support these inefficient policies.
To
illustrate the
main economic
(1) Security of
tutions:
interactions,
property rights; there
I
consider two prototypical economic insti-
may be
constitutional or other limits on the
extent of redistributive taxation and/or other policies that reduce profitability of producers'
In terms of the
investments.
model above, we can think
of this as determining the level
of f.^^ (2) Regulation of technology, which concerns direct or indirect factors affecting the
productivity of producers, in particular middle class producers.
As pointed out
work
in the introduction, the
for the determination of policies,
main
role of institutions is to provide the frame-
and consequently, preferences over institutions are
derived from preferences over policies and economic allocations. Bearing this in mind,
us
now
To
simplify the discussion, for the rest of the analysis,
discuss the determination of economic institutions in the
section,
I
and
model presented
in particular,
let
here.
throughout this
MPE.
focus on
Security of Property Rights
4.1
The environment
time
t
=
0,
is
the same as in the previous section, with the only difference that at
level in the interval [0,f'^], thus creating
do
so, i.e.,
The next
whether they prefer f
=
to
some
an upper bound on taxes and providing greater
security of property rights to the middle class.
like to
f^
before any decisions are taken, the elite can reduce r, say from
The key question
f -^ or f
is
whether the
elite
would
< r^
three propositions answer this question:
Proposition 11 Without holdup and technology adoption, the
The proof
of this result
is
elite prefer
f
=
f^
immediate, since without holdup or technology adoption.
^^A difficult question, which is being sidestepped here, is how such upper bounds on taxes or security of
property rights are enforced while the distribution of political power remains unchanged. For this reason,
as noted above, limits on taxes may be considered to be related to political institutions as much as to
economic
institutions.
26
putting further restrictions on the taxes can only reduce the ehte's utihty.
sition implies that
benchmark
if
economic institutions are decided by the ehte (which
This propothe natural
is
since they are the group with poHtical power), they will in general choose not to
provide additional security of property rights to other producers. Therefore, the underlying
economic institutions
The
will
support the
results are different
when
the timing of taxation decision
is
inefficient policies discussed above.
there are holdup concerns.
To
suppose that
illustrate this,
after the investment decisions (so that there
the holdup
is
problem), and consider the case with revenue extraction and factor price manipulation
combined. In this case, the
would
elite
commit
like to
to encourage the middle class to undertake greater investments,
role for
economic institutions
f^
in order
this creates
a useful
to a lower tax rate than
and
(to limit future taxes):
Proposition 12 Consider the game with holdup and suppose Assumptions (Al) and (A2)
hold, Condition (ES) does not hold,
than f^ the
elite prefer
,
The proof
of holdup the
is
f
=
t'^'^^
and
4>
>
0,
then as long as
given by (16)
is less
.
again immediate. While t'~^^^ maximizes the
MPE involves r =
7-'^'^^^
f^ and the
,
elite
elite's utility, in
the presence
can benefit by using economic institutions
to manipulate equilibrium taxes.
This result shows that the
elite
may
provide additional property rights protection to
producers in the presence of holdup problems. The reason
librium taxes are too high even relative to those that the
economic
commit
institutions, the elite
may approach
elite
that because of holdup, equi-
would
prefer.
By manipulating
their desired policy (in fact,
it
can exactly
to the tax rate that maximizes their utility).
Finally, for similar reasons, in the
the
is
elite will
economy with technology adoption discussed above,
again prefer to change economic institutions to restrict future taxes:
Proposition 13 Consider the game with holdup and technology adoption, and suppose
that Assumption (Al) and Condition (ES) hold and
elite prefer
f
=
t^^.
27
</>
>
0,
then as long as r'^^
< f^
,
the
As
before,
when we
may not be
look at SPE, with pure holdup, there
a need for changing
economic institutions, since credible implicit promises might play the same
f3
>
1
— Q
shown
as
However, parallel to the results above,
in Proposition 8).
technology adoption game,
role (as long as
SPE and MPE
coincide, so a change in
in the
economic institutions
is
necessary for a credible commitment to a low tax rate (here t^^).
Regulation of Technology
4.2
Economic
institutions
may
environment
also affect the
For example, by providing infrastructure or
directly the technology choices of producers.
protection of intellectual property rights, a society
its
producers. Conversely, the elite
may want
may improve
to block,
technological improvements of the middle class. "^^
have an interest
technology adoption or more
for
i.e.,
the technology available to
take active actions against, the
Therefore the question
in increasing the productivity of the
is:
do the
middle class as much as possible?
Consider the baseline model. Suppose that there exists a government policy g G
which influences only the productivity of middle class producers,
A"^
(1)
>
A"^
(0).
Assume
that the choice of g
and has no other influence on payoffs (and
Will the
will
elite
always choose g
=
I,
is
made
at
in particular,
t
it
=
i.e.,
A^ = A^
{0, 1},
(g),
with
before any other decisions,
imposes no costs on the
elite).
increasing the middle class producers' productivity, or
they try to block technology adoption by the middle class?
When
would
like
the only mechanism at work
is
revenue extraction, the answer
is
that the elite
the middle class to have the best technology:
>
Proposition 14 Suppose Assumption (Al) and Condition (ES) hold and
=
elite
and the the
The proof
effect
on the
elite
always choose ^
=
then
w
1.
follows immediately since g
elite's
0,
=
1
increases the tax revenues and has no other
consumption. Consequently, in this case, the
elite
would
like
the produc-
^°The decision to "block" technology adoption may also be considered a "policy" rather than an "economic
The reason why it may be closer to economic institutions is that it influences the set of options
available to economic agents, and is plausibly slower to change than certain fiscal policies, such as taxes
or government spending. See Acemoglu and Robinson (2006b) for a more detailed discussion of the elite's
institution".
incentives to block technology.
28
ers to
there
be as productive as possible, so that they generate greater tax revenues.
is
no competition between the ehte and the middle
and when the middle
in the political arena),
class
is
class (either in factor
more productive, the
Intuitively,
markets or
elite
generate
greater tax revenues.
The
situation
is
different
when
the elite wish to manipulate factor prices:
Proposition 15 Suppose Assumption (Al)
and f <
I,
then the ehte choose g
Once again the proof
from the middle
class
is
policy for the
when
it is
class
elite.
straightforward.
is
With f <
1,
labor
=
0,
demand
high enough to generate positive equilibrium wages. Since
elite,
({)
0.
of this proposition
taxes raise no revenues for the
from the middle
=
holds. Condition (ES) does not hold,
and
their only objective
and wages as much as
possible.
is
to reduce the labor
=
This makes g
(p
=
0,
demand
the preferred
Consequently, the factor price manipulation mechanism suggests that,
within their power, the
elite will
choose economic institutions so as to reduce the
productivity of competing (middle class) producers.
The next
of the elite
is
proposition shows that a similar effect
is
in operation
when
the political power
in contention (proof omitted).
Proposition 16 Consider the economy with
sumption (Al) and Condition (ES) hold and
political replacement.
(;6
=
0,
then the
Suppose
elite prefer
g
=
In this case, the elite cannot raise any taxes from the middle class since
differently
there
is
also that As0.
(p
=
0.
But
from the previous proposition, there are no labor market interactions, since
excess labor supply and wages are equal to zero. Nevertheless, the elite would like
the profits from middle class producers to be as low as possible so as to consolidate their
political
power. They achieve this by creating an environment that reduces the productivity
of middle class producers.
Overall, this section has demonstrated
how
the
elite's
preferences over policies, and in
particular their desire to set inefficient policies, translate into preferences over inefficient
non-growth enhancing
—economic institutions.
When
there are no holdup problems, intro-
ducing economic institutions that limit taxation or put other constraints on policies provides
29
no benefits to the
However, when the eUte are unable to commit to future taxes (be-
elite.
may be
cause of holdup problems), equilibrium taxes
the
and
elite,
in this case, using
too high even from the viewpoint of
economic institutions to manipulate future taxes may be
beneficial. Similarly, the analysis reveals that the elite
may want
to use economic institu-
tions to discourage productivity improvements by the middle class. Interestingly, this never
happens when the main mechanism leading
stead,
elite
when
may want
political consolidation effects are present, the
analysis characterized the equilibrium under "the dictatorship of the elite," a set
power to the
political
all
to have "the dictatorship of the middle class,"
makes the key policy decisions
as the decisive voters).
(this
i.e.,
If 9^
+
9"^
<
is
democracy
pursue policies to maximize their own income. "^^
I
now
briefly discuss the possibility of
of the two groups,
is
more
It is
efficient
and whether
elite
in
alternative
which there
a switch from the dictatorship of the
clear that
is
voting
elite to
whether the dictatorship of the
depends on the
relative
democracy
one
elite or
numbers and productivities
more
efficient
depends on
will first characterize the equilibrium
under these
control or
democracy. Hence, this section
alternative political institutions.
An
then the majority are the workers, and
1,
will
that of middle class
producers.
a system in which the middle class
they
of these two alternative regimes.
elite
could also be a democratic regime with the middle class
Finally, another possibility
over different policy combinations.
policies in
revenue extraction. In-
Inefficient Political Institutions
of political institutions that gave
is
is
to discourage or block technological improvements by the middle class.
5
The above
and
factor price manipulation
to inefficient policies
Moreover,
is
for part of the analysis in this subsection, I
simplify the discussion by assuming that
$'^
so that the
^'More
number
generally,
of middle class
we could consider
to Chapter 4 in
9'
elite
< i
producers
(A3)
is
the same, and they are in the
various different political institutions as represented
functions giving different weights to the
Appendix
and
=
elite,
bj'
social welfare
the middle class and the workers (see, for example, the
Acemoglu and Robinson
(2006a).
30
^^
minority relative to workers.
Dictatorship of the Middle Class
5.1
With the
dictatorship of the middle class, the political equilibrium
tatorship of the
analysis. Instead, let
manipulation.
with the roles reversed. To avoid repetition,
elite,
me
identical to the dic-
is
not provide a
will
I
focus on the case, combining revenue extraction and factor price
The analog
of
Assumption (A2)
is:
A^>ct>{l-af''°'^l'^A^~.
Given
this
and
will redistribute the proceeds to themselves,
and moreover, the same analysis as above
;^coM
>
g^g
0,
g-^gj^ i^y (-22) for
ah
elite
=
0,
hold. Condition (ES) does not hold,
=
t^
t.
this equilibrium to the equilibrium
apparent that the
A^
T/
then the unique political equilibrium with middle class control features
Comparing
to
=
T^"
i.e.,
most preferred tax rate as
gives their
Proposition 17 Suppose Assumptions (Al) and (A3)
(/)
(A4)
assumption, a similar proposition to that above immediately follows; the middle
class will tax the elite
and
full
under the dictatorship of the
equilibrium will be more efficient
and 9^, and the middle
class equilibrium will
when A^ and
be more
efficient
9'^
elite, it is
are large relative
when
the opposite
is
the case.
Proposition 18 Suppose Assumptions (A1)-(A4)
with the dictatorship of the
it is
elite
hold, then aggregate output
than the dictatorship of the middle
higher under the dictatorship of the middle class
Intuitively, the
if
A^ >
if
A^
> A^ and
A^
group in power imposes taxes on the other group (and since
these taxes are equal) and not on themselves, so aggregate output
with greater productivity
^^ Otherwise, there is
tions about parties
class
and
is
in
power and
is
higher
is
is
higher
9"^
=
9^,
when the group
spared from distortionary taxation.
no median voter and the analysis of
political procedures.
31
political equilibrium requires further
assump-
Democracy
5.2
Under Assumption (A4), workers
and have the power
are in the majority in democracy,
to
tax the eUte and the middle class to redistribute themselves. More specifically, each worker's
consumption
wages and
is cj"
=
transfers.
Wt
+ T^
Workers
,
with Wt given by
will
the transfers from
problem
to
determine
rnaxu;^
+
with Wt given by
before,
(3),
{T^
,
r/" T^" T/"
,
,
,
T^}^^q
f^'^'^T-
straightforward to see that the workers will always set Tl"
It is
As
that workers care about equilibrium
then choose the sequence of policies
that satisfy (3) to maximize YLt^o
for
(7), so
we obtain that democracy
will solve
=
T/
=
Substituting
0.
the following maximization
policies:
-^
[t/"(1
-
7-^"^)(l-«)/«yl"^^m^m
^ ^e^^ _
^e-)(l-a)/a^ep^ej
^
j^
(7).
when Condition (ES)
holds, taxes have no effect on wages, so the workers
tax at the revenue maximizing rate, similar to the case of revenue extraction for the
will
elite
above. This result
is
stated in the next proposition (proof omitted):
Proposition 19 Suppose Assumption (Al) and Condition (ES) hold and
unique political equilibrium with democracy features
Therefore, in this case democracy
control, since
it
is
imposes taxes on both
more
r/"
inefficient
=
Condition (ES) does not hold and wages are positive.
by taxing the marginal group they are reducing
their
= r^^ =
min
than both middle
The same
groups.''^
r/
(f)
is
>
0,
{a, f}.
and
class
not the case, however,
we may expect workers
to ultimately
elite
when
In this case, workers realize that
own wages.
In fact, taxes always
reduce wages more than the revenue they generate because of their distortionary
^^Naturally, in this case
then the
become entrepreneurs, and
be ameliorated. See Acemoglu (2003a).
^'*To see this, suppose there is only one group with productivity A. With a tax rate of
effects.
this
^^
extreme
inefficiency to
a (1
—
r)
'
"
A/
(1
—
a),
and
in
R, so the total consumption
addition there
of a worker
derivative of this expression with respect to r
1
J.
which
is
—
.-
is
per worker transfer equal to (pr (1
'"''"
—
_ 7-) -|=
cj"
is
(1
^
ry
[q (i
is
^(l-2a)/Q
^^r-(l-^)
Ut
always negative, implying that c^
is
maximized
32
at
r
== 0,
t,
the wage
is
— ry """ " A/ (1 — a) +
The
^pr] / {\ - a) + R.
establishing the claim.
j
As a
workers
result,
example,
specifically, for
- rpy/^A"" = A^
(1
only tax the group with the higher marginal productivity. More
will
or
A^ >
if
A^,
r™ = a and
(1
-
we
will
=
have r/
af/°'A'^
>
0,
and
Therefore,
A''.
r/" will
we
be such that
have:
Proposition 20 Suppose Assumption (Al) and (A4) hold and Condition (ES) does not
hold.
=
T;^
Then
in the
and
0,
= r^"
r/"
Qf)V"^™ > A^.
(1
-
r^e)i/«^e
Most
this
If
will
< A^ we
A""
^ ^m
Qj.
be such that
^De
^^
will
^^^
(^i
(1
have
-
r^^^y/^A""
r^'"
=
is
is
not obvious
is
=
if
A^ >
=
r^''
we
= a
will
have
and
(1
-
be such that
will
_ ^y/^A^ > A\
from the analysis so
The only
far.
that workers prefer to set zero taxes on the less productive group,
proved in Appendix
A
The
(included in the working paper version).
wages are determined by the marginal productivity of the
for this is that
A'^,
A" or r^'"
and r^
0,
of the proof of this proposition follows directly
part that
and
unique political equilibrium with democracy,
less
intuition
productive of
the two entrepreneurial groups, and positive taxes on this group will reduce wages by more
than the gain
The most
in
tax revenues (by a similar argument as in footnote 34).
interesting implication of this proposition
comes from the comparison of the
case with and without excess supply. While in the presence of excess labor supply, democ-
racy taxes both groups of producers and consequently generates more inefficiency than the
dictatorship of the elite or the middle class,
less distortionary
that
there
is
no excess supply,
than the dictatorship of the middle class or the
when Condition (ES) does not
wages and are therefore
5.3
when
elite.
it is
The
in general
intuition
is
hold, workers understand that high taxes will depress
less willing to
use distortionary taxes. ^^
Inefficiency of Political Institutions and Inappropriate Institutions
Consider a society where Assumption (A4)
control
is
more productive
(i.e.,
•^^This is similar to the reasons
societies (see
Acemoglu
moglu (2003a),
is
(2003a)).
is
satisfied
and A^ <
A^
so that middle class
generates greater output). Despite this, the elite will have
why workers (democracy)
Another reason
for
are less in favor of entry barriers than oligarchic
democracy
to be
more
efficient,
emphasized
in
Ace-
that policies that differentially affect the productivity of different groups will lead to a
misallocation of talent.
33
no
incentive, without
class.
some type
of compensation, to relinquish their
In this case, political institutions that lead to
more
power to the middle
inefficient policies will persist
even though alternative political institutions leading to better outcomes
One
possibility
perhaps the
elite
such deals are
is
a Coasian deal between the
elite
and the middle
can relinquish political power and get compensated
in general
not possible.
To
discuss
why (and why
exist.
For example,
class.
in return.
However,
not), let us distinguish
between two alternative approaches.
First, the elite
type of solution
may
will
relinquish
run into two
power
in return for a
difficulties,
they have political power, the middle class
transfers. ^^
the
elite,
(ii)
will
such promises
have no incentive to keep on making such
the middle class will have to impose similar taxes on
Second, the
not be credible, and once
will
since there are no other, less distortionary, fiscal instruments, to
political institutions will not
class.
(i)
promise of future transfers. This
efficient in the first place.
may relinquish power
elite
Such a solution
of holding political
be as
is
in return for
itself,
compensate
so that the alternative
^''
a lump-sum transfer from the middle
also not possible in general, since the net present value of the benefit
power often exceeds any transfer that can be made. Consequently, the
desire of the elite to
implement
institutions that enable
them
inefficient policies also implies that
to pursue these policies. Thus, in the
they support political
same way
as preferences
over inefficient policies translate into preferences over inefficient economic institutions, they
also lead to preferences towards inefficient political institutions.
institutions can
change from the "ground-up"
Another interesting question
is
"appropriate" for a while, but then
later.
I
will discuss
how
political
in Section 6 below.
whether a given
set of
economic institutions might be
become "inappropriate" and
costly for
economic activity
This question might be motivated, for example, by the contrast of the Northeast-
ern United States and the Caribbean colonies between the 17th and 19th centuries.
Caribbean colonies were clear examples of
societies controlled
by a narrow
elite,
The
with po-
3^See Acemoglu (2003b).
is when there are holdup problems and manipulating economic institutions was not
with them. In this case, there can be significant gains from changing political institutions.
^^The exception
sufficient to deal
34
litical
power
in the
monopoly
up the majority of the
of plantation owners,
and few
rights for the slaves that
population.'^® In contrast, Northeastern
made
United States developed as
a settler colony, approximating a democratic society with significant political power in the
hands of smallholders and a broader
centuries, the
Caribbean
certainly richer
were among the richest places in the world, and almost
many
other more democratic
they lagged behind the United States and
which took advantage of new investment opportunities, particularly
raises the question as to
whether the same
institutions that encouraged the planters to invest
and early 18th centuries then became a
baseline
an economy
in
relatively high
elite will
both the 17th and 18th
in
States,^" starting in the
and commerce. ^^ This
The
While
and more productive than the Northeastern United
late 18th century,
societies,
societies
set of producers. ^^
political
and
A^
is
elite are in
power, Condition (ES) does not hold,
relatively small to start with.
The above
class. Nevertheless,
be relatively small since A"^
Consequently, the dictatorship of the
elite
may
is
However,
if
at
economy
in the
is
output
will
be relatively
and the distortion
class.
This
is
reminiscent of the
Caribbean.
relative to A^, the situation changes radically.
class,
small, A'^
generate greater income per capita than
some point the environment changes
impose high taxes on the middle
cp is
Imagine
small.
an alternative society under the dictatorship of the middle
planter elite controlling the
lines.
analysis shows that the
high, because the elite will undertake the right investments themselves,
will
in the 17th
barrier to further growth.
choose a high tax rate on the middle
on the middle class
and economic
and generate high output
model used above suggests a simple explanation along these
which the
in industry
The
so that A"^ increases substantially
elite, still in
power, will continue to
but now these policies have become very costly
because they distort the investments of the more productive group. Another society where
3^See, for example, Beckford (1972)
and Dunn (1972).
^®See, for example, Keyssar (2000).
40
Although the wealth of the Caribbean undoubtedly owed much to the world value of its main produce,
sugar, Caribbean societies were nonetheless able to achieve these levels of productivity because the planters
had good incentive to invest in the production, processing and export of sugar. See Eltis (1995) and
Engerman and Sokoloff (1997).
''^See, for example, Acemoglu et al. (2002) or Engerman and Sokoloff (1997).
/
35
the middle class have political power will
now generate
significantly greater output.
This simple example illustrates how institutions that were
that did not generate
the society to
fall
much
may have
why
inefficient institutions
need an equilibrium model of institutional change.
useful to
jure political power
political
power
is
right to set taxes
draw a
determined by
is
it
The
with a revolution.
of de jure
I
far in the
and de facto
political power.
De
in the discussion of
elite.
problem among
to overthrow the existing regime
of the
middle
in particular,
class).
an existing regime or threatens
harmed
its
members and gather
and to monopolize
sufficient
political
if)
substantially. In particular,
class
comes to power, there
''^The model here heavily builds on
and Robinson (2000b, 2001, 200Ga).
power
is
de facto
power
power (establish a dictatorship
in the process.
I
political
is still
costty,
Moreover,
and
in the
assume that following a violent
utility.
Let us assume that the dictatorship of the middle
and once the middle
political
In each period, with probability q the middle class solve the
However, violently overthrowing the existing regime
overthrow, the elite receive zero
state
when a group
change as resulting from the interplay
each middle class agent incurs a cost of
process, the elite are
is
political power.
the hands of the
collective action
them the
facto political power, which
Imagine a society described by the baseline model above where de jure
initially in
De
In the basehne model, de jure
model (except
to
we
persist,
such a model. ^^
simplest example of de facto political power
will conceptualize institutional
and de facto
briefly discuss
institutions.
and poses a military challenge
to organize itself
emerge and
since the political institutions give
elite,
and determine the economic
political consolidation).
now
political institutions.
hands of the
in the
I
distinction between de jure
comes from other sources, did not feature so
manages
even encouraged growth) later caused
Institutional Change and Persistence
better understanding for
It is first
(i.e.,
substantially behind other economies.
6
To develop a
distortion or
initially "appropriate"
my
class, if established, is
will
an absorbing
never be any further institutional
previous work with James Robinson. See in particular Acemoglu
36
change.
With probabihty l — q, the middle
the state at time
t
by the tuple
G {H, L} denotes the
level of threat (high or low)
against the regime controlled by the
elite.
the middle class amass de facto political power, the elite need to respond in
since letting the middle class overthrow the existing regime
some way,
The
them.
can respond in three different ways:
elite
(i)
concessions, such as reducing taxes on the middle class, etc.;
(iii)
they can use repression, which
to the middle class.
Throughout
the state
political power. Also denote
denotes whether the ehte or
where Pt €
Sf
for
no de facto
{E,M}
(Pf,St),
the middle class are in control, and
When
class has
st,
I
when
St
=
I
focus on
they can make temporary
(ii)
they can give up power;
MPE.
//
for the elite as
MPE,
In a
a whole.
maximize
which were characterized above. So the interesting actions take place
so that the
Let us
main motive
I
power. Since Condition (ES)
themselves, set a tax of
r*^
is satisfied,
= t^^
T^
(r)
at the tax rate r,
=
tpr {1
and n^
j facing the tax rate r.
of the middle class,
—
on the
(r)
= a (1 —
OiA!^Xl {\
the
elite
—
,
given by (11).
Q.'),
class
is
in
(1
—
A^X/
let
the
all
us introduce the following
a) as the tax revenue raised from group j
(1
—
a) as the profit of a producer in group
we have
,
is
when the middle
M to indicate a value function under the dictatorship
Then, using
V'^{M) =
where t^^
r)
satisfied,
every period, and redistribute
elite in
A^d^X/
ry^'"''"'
is
= H.
the above analysis shows that they wiU not tax
revenue to themselves. To write the resulting value function,
notation:
in the state St
revenue extraction.
calculate the value of a middle class agent
first
their utility,
assume throughout that Condition (ES)
for inefficient policy is
falling
strategies are only a function of
L, the elite will set the policies that
Moreover, to simplify the discussion,
excessively costly
but manages to prevent the regime from
assume that repression costs
this section,
so
costly,
is
is
and the second
TT™ (0)
^~
The
is
first
+
(r^ (t^^)
^
term
'
^_
in the
+
R)
le""
^-^
,
,
numerator
is
,
(23)
-
their
own
revenues,
the distribution from the revenue obtained by taxing
and from natural resources. The term
37
1
—
/3
provides the net present discounted
value of this stream of revenues. Similarly, the value of an elite producer in this case
ye ^M)
What
about the dictatorship of the
=
-y^.
is
(24)
Let us write this value recursively starting in
elite?
the no threat state:
V"" {E, L)
=
+l3{l-q)V'^
(r^^)
tt'"
This expression incorporates the fact that,
most preferred
elite will follow their
recurs with probability
three possibilities. Let us
of political
—
I
policy, r"'
— t^^
What happens when
q.
and T"^
St
power by making concessions
=
H)
(25)
The low
0.
= HI As
threat state
noted above, there are
elite
in the high threat state.
class
{E,
during periods of low threat, the
by investigating whether the
start
first
denote the highest possible value to the middle
V^
MPE,
in the
+ pqV^
{E, L)
can prevent a switch
For this purpose,
under the dictatorship of the
let
us
elite
by
{E, H). Then, the condition for concessions within the given political regime to prevent
action by the middle class
simply
is
(E,
t/'"
where
^
recall that
is
holds, the elite could
H) >
V""
[M] -
(26)
V,
the cost of regime change for the middle
make
sufficient concessions to
class.
When
this constraint
keep the middle class happy within the
existing regime.
Therefore, to determine whether concessions within the dictatorship of the
sufficient to satisfy the
middle
the best concession that the
middle
t/'"
class,
(E,
H) =
tt'"
where V"^{E,L)
right
hand
side.
r,mfr,rr,
y {E,H)
r'"
i.e.,
=
=
(0)
0,
bj^
Combining
/^
(
1
-
elite
=
+ [r
given
is
r"
g) TT^
class,
we simply need
can do
is
to adopt a policy that
r^^, and T'"
(r-^^)
+ R)
=
/e^^
(T^ (r^^)
+ (3{l-q)
expression (25), with
(27)
and
(t^^)
+
(25),
(1
to calculate
we
R)
V"^{E,H). Note that
most favorable
for the
1 9"". Therefore,
V"" {E, L)
V^{E,H)
be
+ pqV'''
replacing
{E,
H)
(27)
V"^{E,H) on the
obtain:
- ^ (1 -
?)) [vT- (0)
^^—^^
38
+
is
elite will
+
(T^ (t^^)
+ R)
/g^]
(28)
This
maximum
the
is
credible utiHty that the ehte can promise the middle class within
The reason why they cannot
the existing regime.
commitment problems. As
class only in the state Sj
them
and
in the state St
in the
=
=
makes
(28)
H. Even
it
them
give
greater utihty
the state
middle
they promise to make further transfers or not tax
if
=L
St
because of
clear, the elite transfer resources to the
L, these promises will not be credible (they cannot
MPE, when
is
arrives, the elite will
commit
to them),
choose their most preferred
policy of taxing the middle class and transferring the resources to themselves. ^^
If
given this expression, (26)
making concessions within the
prefer such concessions.
To
satisfied,
is
middle
can prevent a violent overthrow by
elite
investigate this issue,
They
class, since this will give
we
first
will clearly not follow the
more than
not necessarily
need to determine the exact
sufficient utility to
most preferable policy
prevent an overthrow.
such that V"^ {E, H)
Instead, the elite will choose a policy combination (7"", f^, T'", f^
J
V^ (M) — ip,
may
existing regime. Nevertheless, the elite
concessions that the elite will make.
for the
then the
=
they will make the middle class just indifferent between overthrowing the
i.e.,
regime or accepting the concessions. The value of such concessions to the
by similar
elite is,
arguments, given by:
(3{l-q) U'
=
V^ {E, H)
(0)
+ (r-
(r^^)
+ R)
+(1-/3(1-
/e^)
q))
\tt^
[t^)
+T
(29)
Whether the ehte
make
will
these concessions or not then depends on the values of
Another alternative
other options available to them.
there
is
a threat from the middle
cost of this strategy for the elite
y^(0,
St)
Such repression
class.
is
is
the use of repression whenever
is
always
the cost they incur in the use of repression,
the value function to the ehte
it
the only
effective, so
uses repression and the state
is S(.
fi.
By
Denote
standard
arguments, we can obtain this value by writing the following standard recursive formulae:
V' (O, H)
=
V (O, L) =
tt'
tt"
(0)
(0)
^^If instead of the
+
+
(T"^ (r«^)
(T'" (r^^)
MPE, we
+
R) /9^
-
fi
+R)/9"' + p{l-q)V'
will
q)
V
(O, L)
(O, L)
+ pqV
+ pqV
(O,
H) and
(O, H). These two
consider the SPE, the ehte can promise a greater value to the middle class,
this; once the state st =
on their promises. See Acemoglu and Robinson (2006a)
but again there
+ P {1 -
be limits to
39
L
arrives, the elite will
for
an analysis of the
have an incentive to renege
SPE
in
a related game.
when using the
expressions incorporate the fact that,
repression strategy, the elite will
always choose their most for preferred policy combination, and
=
St
H
Consequently, for the
=
when
Combining these two equations, we obtain:
to defend their regime.
ye ^o^H)
use repression
will
+
^^ (0)
(7--^
+ R)
(^^^)
/^"^
-(1-/3(1-9))^
^3Q^
elite to prefer
concessions,
needs to be the case that V^ {E, H)
it
>
V'{0,H).
Finally, the third alternative for the elite
as given
by
make concessions
only
change
is
less
to allow regime change,
than
V'^
(in fact limited concessions)
only happen
will
V^ (M)
Evidently,
(24).^^
is
when
in the latter case
with probability
(26) does not hold.
regime change to take place, we need V^ (M)
{E,H), since
and obtain V^ (M)
q.
they
Therefore, regime
In addition, for similar reasons, for
> V^ [0,H). Note
that
all
of the values
here are simple functions of parameters, so comparing these values essentially amounts to
comparing nonlinear functions of the underlying parameters.
Putting
elite
all
these pieces together and assuming for convenience that
opt against repression,
we obtain the
when
indifferent the
following proposition:
Proposition 21 Consider the above environment with potential regime change and suppose that Condition (ES) holds. Then there are three different types of political equilibria:
1.
If (26)
holds and V^ {E,
H) > V^
remains the dictatorship of the
of
r"*
= T^^
to ensure V""
2.
If
,
T^
=
and T"*
0,
{E,H) = V"" (M) -
(26) holds but
St
=
L, the elite set their
most preferred policy
and when
St
= H,
concessions sufficient
When
elite.
=
{O, H), in the unique equilibrium the regime always
V,
i.e.,
V^E,H) <
the
elite
they adopt the policy (f'^,T'',f^,f'\
V''{0,H), or
if
(26) does not hold
V^ {0,H), then the regime always remains the dictatorship
set their
most preferred policy
of
use repression against the middle
'''*By
construction, this
have to incur the cost
is
t™
make
= t^^
,
r*^
=
and T'"
of the elite.
=
0,
and
The
and when
V {M)
elite
St
<
always
= H,
they
class.
always better
for the
middle class than a violent overthrow, since they do not
tp-
40
change.
T'"
does not hold and V^ (M)
If (26)
3.
=
0,
When
St
=
and when
> V^
L, the elite set their
=
st
H, the ehte
how
This proposition illustrates
most interesting case
most preferred policy of r™
the
elite
is
elite
r^^, t^
=
and
The
is
equihbrium institutional change as a result of
Why
would the
elite give
up
their
the de facto political power of the middle class, which threatens
with a violent overthrow
The
class.
The reason
=
various different institutional equilibria can arise.
the elite voluntarily relinquishing political control.
dictatorship?
equilibrium institutional
is
voluntarily pass political control to the middle class.
where there
is 3,
(O, H), then there
—an outcome worse than the dictatorship of the middle
then prevent such a violent overthrow by changing political institutions
to transfer de jure pohtical
political institutions as
power to the middle
This transfer exploits the role of
class.
a commitment device (a commitment to a
different distribution of
de jure political power), and acts as a credible promise of future policies that favor the
middle class (the promise
and thus the
is
credible, since institutional
change gives de jure
political
right to set fiscal policy in the future to the middle class).
This discussion highlights that institutional change has two requirements:
(i)
cessions within the existing regime are not sufficient to appease the middle class;
repression
is
sufficiently costly for the elites to accept
The comparative
more
costly,
ye
is
(o,
power
i.e., // is
statics of
H) - V^ (M) =
increasing in
R
and
(p.
^'^
(0)
-
^'
i^n +
more
likely.
(^" {r^n + R)
This implies that when
from natural resources, V^ (M)
is
R
is
> V^ {0,H) becomes
(ii)
that
regime change.
regime change are also interesting.
higher, institutional change
that con-
First,
when
repression
is
Moreover:
/O"-
-{l-P{l-q))f^
high, so that there are greater rents
less likely,
to use repression rather than allowing institutional change.
and the ehte now prefer
Similarly, greater 0,
which
corresponds to greater state capacity, has the same impact on institutional equilibrium,
since greater state capacity enables greater tax revenues in the future. This implies that,
as already suggested
by the
results in subsection 3.4, greater state capacitj^,
leads to less distortionary pohcies, also increases political stakes and
41
which typically
makes the use
of
repression by the elite the
institutional change
violated,
class. ^^
making
it
R
change, greater
more
and
less likely, since
difficult for
repression
concessions and institutional change, they
more
do not make
cp
they also make (26) more likely to be
is
between repression and institutional
while
likely,
may encourage
This analysis also illustrates the conditions
is
ov
the elite to use concessions to appease the middle
the trade-off for the elite
make
R
Nevertheless, increases in
hkely.
unambiguously
when
Therefore,
more
when
the trade-off
is
between
institutional change.'*^
Persistence
for institutional persistence.
the natural course of things and something unusual, the success of the middle class in
solving their collective action problem and amassing de facto political power, creates the
platform
middle
for institutional
change. However, even the possibility of collective action by the
can use costly methods to defend the existing
class is not sufficient, since the elite
when
regime. Therefore, institutions will be more persistent
up the
right to determine policies in the future,
significant distributional conflict
tax revenues are important
between the
(i.e.,
which
elite
will in
turn be the case when there
and the middle
when
power and have the means to use
forces
and
who
force to maintain the existing political institutions.
The
first is
between economic
an interaction between economic and pohtical
Suppose that economic institutions impose a low
f.
This implies that control
of fiscal policy will generate only limited gains, reducing political stakes,
have
less
and the
reason to use repression in order to defend the existing regime.
institutional persistence might be
i.e.,
currently hold political
also suggests the possibility of interesting interactions
institutional equilibria.
institutions.
example because
political stakes are high,
alternative institutional arrangements are costly for those
The model
class, for
is
high 0) or because rents from natural resources, R, are
high. Therefore, a set of political institutions will persist
when
the elite are unwilling to give
more
of an issue in societies
elite will
Consequently,
where economic institutions
^^In particular, (26) can be written as:
V"" {E,
and
H) - V" (M) + ^ = P{l-q)[ir"' (t«^) -
increases in
'^^This
is
R
and
<p
similar to the
make
(tt'" (0)
+
{T" (r«^)
+
R)
/e"^)] / (1
-
/?)
+
i/)
>
this constraint less likely to hold.
non-monotonic
effect of inequality
(2006a).
42
on democratization
in
Acemoglu and Robinson
*^
enable those with political power to capture greater rents.
When
nous (as
the ability of the middle class to solve their collective action problem
used above to illustrate the political consolidation
in the iriodel
be a further interaction between economics and
effect),
is
endoge-
there will
In particular, suppose that the
politics.
probability q that the middle class will be able to pose an effective threat to the regime
endogenous and depends on the
profits of the
middle
In this case, the elite realize
class.
that the richer are the middle class, the greater the threat from
power
political
is
them
When
in the future.
very valuable, for example because tax revenues or rents from natural
resources are high, the elite will wish to "overtax" the middle class to impoverish
and
to reduce their political power.
persistence by
making
it
more
These higher taxes
difficult for
will, in turn,
interesting interaction, this time between inefficient policies
This paper developed a simple framework to investigate why
Economic
straints
persist. Political institutions
institutions, in turn, determine the
on
policies.
increase institutional
This suggests another
elite.
and
institutional persistence.
Concluding Remarks
7
emerge and
them
the middle class to solve their collective action
problem and mount challenges against the dictatorship of the
institutions
is
Groups with
political
—the
policy-making and place con-
for
elite
transfer resources from the rest of the society to themselves.
duced preferences over institutions, depending on
—non-growth enhancing
shape the allocation of political power.
framework
power
inefficient
how
—choose
policies in order to
Consequently, they have in-
institutions
map
into policies
and
economic outcomes. This methodological approach therefore necessitates a baseline model
in
which preferences over
The bulk
model
is
rich
policies
can be studied.
of the paper analyzed such a baseline model.
enough to encompass various
Though
relatively simple, this
These
distinct sources of inefficient policies.
include revenue extraction, factor price manipulation and political consolidation. According
to the revenue extraction
^'''This is
and
mechanism, the
related to the result in
to consolidate
when
it
elite
pursue
inefficient policies to extract
Acemoglu and Robinson (2006a) that democracy
is
revenue
less likely to
emerge,
emerges, in agricultural societies where the political stakes are high for the
43
elite.
from other groups. The factor price manipulation mechanism impUes that the eUte seek to
reduce the
demand
for factors
from other groups
in order to indirectly benefit
from changes
in factor prices. Finally, political consolidation implies that to increase their political
the
elite
elite's
may
wish to impoverish other groups that are competing for political power. The
preferences over inefficient policies translate into inefficient economic institutions.
Consequently, institutions that can restrict inefficient policies will typically
Instead, the elite
income or
(e.g.,
power,
may
fail
to emerge.
choose to manipulate economic institutions to further increase their
The exception
facilitate their rent extraction.
when
is
there
is
a holdup problem
because there are investments that involve long horizons), so that equilibrium taxes
and regulations are worse than the
this case,
elite
would
like
from an ex ante point of view.
economic institutions that place limits on future
policies
In
and provide additional
security of property rights to other groups can be useful.
The paper
also provided a
tutional persistence.
framework
The key mechanism
for the analysis of institutional
for institutional
change
without de jure political power. The model shows how the
political institutions in order to
important result from
make
this analysis
is
is
insti-
challenges from groups
may be
elite
change and
forced to change
concessions in response to these challenges.
that,
when
political stakes are high, for
example,
because of large rents from natural resources or the importance of tax revenues, the
will
be unwilling to make such concessions and
deal with outside challenges.
likely to persist.
political institutions:
if
There
The paper
1.
number
While the model featured three
coalitions.
One
of coalitions
2.
also highlights a
of the
between
most major areas
is
also
may be
and
an interesting interaction
economic institutions limit
reduce political stakes, change in political institutions
elite
prefer to use repression in order to
In this case, existing (potentially inefficient) political
economic institutions are more
between economic and
may
The
policies
and thus
easier.
of important areas for future research:
distinct groups,
for the
it
sidestepped issues of political
theory of political economy
is
the analysis
different social groups.
Relatedly, as noted in the Introduction, to
44
map
a model
like this to reality,
one
needs to
know who
"the elite" are. However, the concept of the ehte
is
both abstract and
a shorthand for a variety of groups that are able to capture political power.
of the elite often changes in practice,
how such changes may occur
The
3.
and a dynamic model
is
The
identity
necessary for understanding
in practice.
discussion of inappropriate institutions also raised questions related to insti-
tutional flexibility.
While the discussion here focused on
important dimension
is
whether a given
changing rapidly in the face of changes
tutions flexible
and whether
inefficient institutions,
set of institutions are flexible,
in the
i.e.,
another
capable of
environment. Which features makes
institutional flexibility matters for
insti-
economic performance are
also interesting areas for future research.
4.
The model presented
here features only hmited intertemporal interactions. Introduc-
ing capital accumulation (without
This
will
ering
is
one important area of investigation.
enable both an analysis of dynamic taxation and also of questions related to
inefficiencies
5.
depreciation)
full
The
change as the economy becomes
class of
more reahstic
models used
policies.
for political
richer.
economy
also
Although taxes here stand
Most importantly, such a generahzation
and equilibrium mix of
6.
In the model,
investigation
is
is
is
likely to lead to
new and
will allow a discussion of the
policies in the context of political
government policy
need to be enriched by consid-
for various different distortionary
redistributive policies, explicitly allowing for these policies
results.
how
richer
"optimal"
economic interactions.
purely redistributive. Another important area of
the interaction of the rent-seeking and efficiency-enhancing roles of govern-
ments.^^
7.
Last, but not least, there
persistence.
In practice, there
institutions (e.g., switches
is
is
much more
that needs to be done on institutional
a mixture of frequent changes in certain dimensions of
from dictatorship to democracy), associated with relative persis-
tence in other dimensions (such as the political power of different groups or the inefficiency
of various economic institutions).
Constructing dynamic models that can shed light on
See Acemoglu (2005) for an attempt in this direction.
45
these issues
is
a major area
for future research.
46
Appendix A: Proof of Proposition 20
8
Here
I
prove that in a democracy workers will always set a zero tax rate on the
Without
ductive group.
Q^
=
=
Q<^
such that
is
=
The
A" and denote
Q.
- r'")V"A™ >
(1
the
first case,
wt
A^ >
note that workers can adopt two different strategies, either choose a pohcy vector
First,
the
on the case where
loss of generahty, focus
less pro-
a(l
-
(1
-
T^fl'^A^ or such that
(1
-
r'^fl'^A^
<
(1
- r^f'^A^
In
producers have lower net productivity and thus the equilibrium wage
elite
T^fl'^A'l
(1
-
=
a), while in the second Wt
a{\
-
-
r'^f/^'A'^/ (1
a).
payoffs to the workers from the two strategies are:
=
WUt'^,t')
-^- {I - T^f'' A'
1
(31)
—a
+-^r^(l
—
r'=)(i-«)/"A^ (1
_
A^)
a
1
+ -^r"^(l —a
1
r'^)^^-'''^l'^A"'\6.
and
= -^-(l-r"^)'/"A'"
\ — a
WHt'^^t')
+ -^t\1 1
—a
(32)
r'=)(^-")/"A^A^
+ -^r'"(l \ — a
which incorporate the fact that the more productive group
the less productive group will employ the remainder
The proof
Second,
I
Step
max^m,^e
will consist of
^2
steps. First,
will
prove that in this case r^
1:
To show that the
W^
{t"", t")
To obtain a
ists
two
>
max^m_^.
first
W^
=
I
will
>
strategy
is
preferred
,
first
strategy
is
preferred.
it
is
sufficient
to
show that
(r'", t^).
is
not the case.
(1
^r\ {jm^^e^ fo^ ^^ {t"^ ^t'') that Satisfy
(1
X9)
0.
contradiction, suppose this
- f^y/^A"" <
_
workers.
-
(1
This implies that there ex-
r'^f/'^A'^
-
r"^)V"A"T
<
>
(1
- r^)^/M" and
(i
_
Consider two cases. First, the constraint on the problem maxT-m^-e W"^
so that (1
(l
employ A^ workers, while
will
show that the
(f"\f") G argmax^m_^eVF2^r™,r") subject to
(^m^^e)
— A^
1
r"^)^-")/"^"^
- fy/^A^. But
r'^f/'^A^
{t^,t~'^) is slack,
in this case, the derivative of (32)
47
with respect
to r"'
is
L_
1
which
is
this case
negative for
is
Therefore,
r"*
=
—a
(1
_
^n,)(l-2a)/a^^
[
we must have the
Then suppose
^^^T^
+
(pAd
> A"
constraint tight,
— f")!/"^™ =
that (1
(1
-
first
f'=)i/°A'^ in (31)
Then
strategy.
and
(32),
-^(1
—
WUr^'^r-e) =
,
J
i.e.,
—
[i
(1
we
-
— al —
(i
_
f<=)i/«^e_
and consider the pohcy vector
f'^y/'^A'',
-
=
f"^)i/"^m
r"')i/"A""
>
(1
-
and thus
r'^)^''"^',
— f^yl^j\^ =
have:
f^
-£)'/" ^^
;(i
f^
-
< (l-f^)l/"^^
substituting for the relationship (1
a
\
1
- 0A^)|
contradicts {l-f'^f/°'A'"
(f™, f^ -e), which clearly satisfies the constraint (1
corresponds to the
(1
r™, implying that the optimal tax rate on middle class producers in
all
This combined with A'^
0.
l
+e
+
-i'- ef'^'A^ (1 -
\e)
—
+ --^^-
— al —
1
- f^f'^A^xe
r-(i
f^
and
—a
\
+-^^>
Since A"^
W^
{f^^f^
Step
W^
A",
—
2:
(r"^, t')
e)
it
must be that
> W^
(f'^,f^),
Given the
=
-^— (1
1
-(1
—a
> f^
f"*
,
—
-(1
- T^yi^A^
>
Using the fact that \9
I
-
1,
the problem of the workers
r^^/" A'+-^TH\-T''f^-°'^'"A^
—a
1
(1
is
to
the constraint
is
—
1
—a
slack, the first-order condition
(1
-
r^f-^^'^y-A^
[
48
(1
- 0A^)l <
J
\e)
^
0,
1.
- A0)+-^r'"(l-r'")(i-°)/"A'"A6'
1 — a
with respect to r^
+
i^^i^r^
(pXd
-
maximize
subject to
If
(1
XO, as e
which leads to a contradiction, establishing Step
result in Step
-
^
- ry/^A'xe +
is
and r^
>
0,
with complementary slackness, which again yields
in the proposition. If the constraint is tight,
The
first-order condition for the
(1
-T-^
-Of
=
0.
=
0,
and hence r™
then substituting for
maximization of this expression
- r^)<^-^"'/M4^r<= +
1
which again implies r^
r*^
{
(1
49
,
as claimed
we obtain
is
-</,))<
(/)
This establishes the claim in Step
of the proposition.
it,
=a
0,
J
2,
and completes the proof
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1
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7
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