Influence in Decline: Lobbying in Contracting Industries

&Blackwell Publishers Ltd 2002. Published by Blackwell Publishers, 108 Cowley Road,Oxford OX4 1JF, UK and 350 Main Street, Malden MA 02148, USA. 209

INFLUENCE IN DECLINE:LOBBYING IN CONTRACTING INDUSTRIES

RICHARD DAMANIA*

Recent empirical work suggests that declining industries lobby moresuccessfully for policy concessions than do growing industries. This paperpresents a novel and simple explanation for this phenomenon. It is shownthat an industry in decline is constrained in its ability to raise revenuethrough production and therefore has a greater incentive to protect profitsby lobbying for more favourable treatment. However, greater lobbying onlytranslates into policy concessions if government policy is sufficientlyresponsive to lobby group contributions. The paper further explores thecircumstances under which such government behaviour is likely toeventuate. We show that a self-interested government will always be morereceptive to the demands of lobbyists in declining industries.

1. INTRODUCTION

A SUBSTANTIAL body of empirical literature suggests that declining industries

are generally more successful in forming lobby groups and securing policy

concessions from governments, than are industries in growing sectors of the

economy.1 Theoretically, this finding is somewhat paradoxical and difficult to

explain. Rapidly growing industries, with more resources at their disposal, ought

to be better placed to lobby effectively and garner more favourable treatment

than their declining counterparts.

In a pioneering paper, Hillman (1982) examined protectionist incentives in

declining industries and demonstrated that if an industry’s political weight is

sufficient, tariffs will be introduced to partly compensate the industry for adverse

terms-of-trade shocks. More recent explanations of the lobbying success of old

and declining sectors have focused upon the consequences of entry in a growing

industry. For instance, Grossman and Helpman (1996) suggest that it is the

potential for free riding that makes lobbying more difficult in an expanding

industry. Specifically in a growing industry new entrants will benefit from the

lobbying efforts of incumbents, without contributing to the costs of lobbying. In

ECONOMICS AND POLITICS 0954-1985

Volume 14 July 2002 No. 2

* School of Economics, University of Adelaide, Adelaide 5001, Australia.E-mail: [email protected]

1 The lobbying prowess of declining industries appears to be a robust empirical finding whichemerges from both inter-industry studies of lobbying (El-Agraa, 1987) and more specific industrystudies. Some examples cited in the literature include the policy concessions and protection given tothe agricultural sector in developed countries (Anderson, 1995), textiles in the USA (Dixit andLondregan, 1995).

contrast, Baldwin (1993) argues that firms in growing industries have less

incentive to lobby for concessions since the resulting increased profits would be

eroded by new entrants. Finally, Brainard and Verdier (1997) propose two novel

explanations for the lobbying success of declining industries. First, if capital

markets are imperfect, then growing industries may have less ability to raise

funds for lobbying than declining industries which have access to accumulated

financial reserves. Alternatively, if there are fixed costs associated with the

formation of a lobby group, then growing industries may be too small in their

formative years to be able to cover these fixed lobbying costs.

This paper seeks to outline a hitherto unrecognized mechanism which explains

why declining industries lobby more successfully. It is demonstrated that even

when the special conditions identified in the literature do not hold, the

opportunity costs of lobbying are lower when demand is depressed, so that firms

in declining sectors have a greater incentive to protect their profits by lobbying

more intensively.

The analysis in this paper deals with the case of a polluting industry which

lobbies for less stringent environmental regulations. However, the results apply

more generally to other contexts such as lobbying for trade protection, income

support or tax concessions. For simplicity we consider a symmetric oligopolistic

industry which emits pollution emissions. The firms are assumed to interact for a

finite number of periods over which industry demand varies. Industry growth

and contraction is represented through either monotonically rising or falling

demand. These variations in demand are assumed to be common knowledge to

both firms and the government.

Pollution emissions generated by firms in the industry adversely affect a

widely dispersed subset of individuals in the economy. The government regulates

pollution levels through a tax levied on emissions. Lobbying is introduced into

this framework by drawing on the familiar assumption that a self-interested

government seeks to maximize its chances of remaining in office. Since winning

an election depends on the funds available for campaigning, the government is

assumed to care about the political contributions received from lobby groups.

This allows special-interest groups to influence policy decisions by making

political donations which are linked to the policies proposed by the government.

Accordingly we assume that firms seek to minimize their tax burden, by forming a

lobby group which offers political contributions to the government. Since the

analysis focuses upon firms’ lobbying incentives, the role of an opposing

environmental lobby group is suppressed. This may be justified by assuming

that pollution damage is so widely dispersed that it does not induce the affected

individuals to forma lobby group. In the parlance of Baron (1994) this represents a

particularist policy, where the benefits of a tax concession are concentrated,

while the costs are insufficient to induce individuals to form an opposing lobby.2

210 DAMANIA

2This assumption does not appear to be unduly restrictive and covers policies in a range of contextssuch as trade protection and industry support through subsidies or tax concessions.

&Blackwell Publishers Ltd 2002.

Within this framework we explore the impact of variations in demand on

firms’ incentives to contribute to the lobby group. It is demonstrated that under

certain circumstances, the opportunity costs of lobbying are lower when demand

is depressed so that there is less incentive to free-ride on lobby group

contributions. Intuitively, this reflects the fact that when demand is low the

ability to raise profits through the output market is limited. Hence, firms have a

greater incentive to protect their profits by lobbying for lower taxes. Political

contributions therefore rise when demand is expected to decline.

However, this outcome depends critically upon the manner in which the

payoffs to lobbying vary with political contributions. It is shown that declining

industries lobby more intensively only if the tax set by the government declines

with contributions at a sufficiently rapid rate.3 To see why this condition is

essential to the results, consider an industry with falling demand. Ceteris

paribus, the payoffs from production will be declining over time. However, if

higher political contributions result in a sufficiently low tax rate, then firms can

mitigate the decline in profits by lobbying more intensively. Thus, there is an

incentive to lobby only if higher contributions induce a sufficient decline in taxes.

Since declining industries lobby more aggressively only if the tax set by the

government declines rapidly with contributions, it is essential to inquire whether

such behaviour is consistent with the notion of a self-interested government

which maximizes its utility. Perhaps the most widely used model of self-

interested government behaviour is the political support framework developed

by Grossman and Helpman (1994). Accordingly, we explore the properties of

the equilibrium tax schedule in the political support model.

The political support model assumes that an incumbent government increases

its chances of re-election by maximizing a weighted sum of political donations

and social welfare. Political contributions from lobby groups influence the

government’s decisions because of their many uses, including funding

campaigns, retiring debt from past elections and deterring rivals. In what

follows, we demonstrate that under very general conditions the political support

model yields a tax schedule which induces firms in declining industries to lobby

more intensively. This occurs because political donations vary with taxes and

mirror the profitability of a given tax policy. When demand is depressed, ceteris

paribus, profits are low and firms’ political contributions tend to decline. A

government that values political donations sufficiently has an incentive to limit

the potential decline in contributions by being more responsive to firms and

adopting more favourable policies. This finding has the interesting implication

that the credible threat of lower political contributions makes the government

more receptive to the demands of interest groups in declining sectors.

The formal analysis in the paper is based on a three-stage game, which is

solved sequentially. The first stage represents the political equilibrium in which

firms offer the government a contribution schedule, which is contingent upon the

INFLUENCE IN DECLINE 211

3Formally, the requirement is that the tax schedule (which is declining in contributions) is concave.


tax, given knowledge of demand variations. The government then sets the tax

which maximizes its payoffs. In the next stage firms interact in a Cournot game,

given knowledge of the tax and changes in demand.4

The remainder of this paper is organized as follows. Section 2 outlines the

basic structure of the model, while section 3 deals with the incentives for firms to

contribute to a lobby group. Section 4 analyses the political equilibrium. Finally,

section 5 concludes the paper.

2. THE MODEL

Consider a symmetric homogeneous good duopoly where firms labelled i and j

interact over a known finite period of time.5 Industry demand in period

t 2 ½1, T � is represented by QtðPÞ. Since the analysis is concerned with the

impact of variations in demand, it is necessary to specify certain properties of the

demand function in detail.

Assumption 1. QtðPÞ: <þ ! <þ is a continuous bounded function, 8 t 2 ½1, T �.

Assumption 2. There exists a ~PPt such that QtðPÞ ¼ 0 if and only if P5 ~PPt,

8 t 2 ½1, T �.

Assumption 3. @QtðPÞ=@P < 0; 8 P 2 ½0, ~PPt�, 8 t 2 ½1, T �.

Assumption 2 implies that demand falls to zero when price exceeds ~PPt, while

Assumption 3 merely asserts that the demand function is negatively sloped.

Moreover, for a one-shot Cournot–Nash equilibrium to exist it must be

assumed that a firm’s marginal revenue does not rise with its rival’s output. This

condition is satisfied if (see Shapiro, 1990):

Assumption 4.

@Pt

@q ftþ q f

t@2Pt

@q f 2

t

< 0 8 t 2 ½1, T �,

where Pt is the inverse demand function, q ft is output of firm f ð f ¼ i, j Þ.

To investigate the impact of anticipated growth or decline in the industry we

impose a particular structure upon the movement of demand over time. Let

QtðPÞ � Qtþ1ðPÞ denote that ~PPt 5 ~PPtþ1 and QtðPÞ > Qtþ1ðPÞ 8 P 2 ð0, ~PPtÞ.

Assumption 5. If the industry is experiencing growth in demand then:

212 DAMANIA

4The tax rate having been set in the prior political equilibrium is assumed to be invariant over theoutput stage. As noted by a referee, this implies that the government does not renege on its policy, asis assumed in the Grossman–Helpman model and that the policy is not dependent on the state ofdemand in each period. These issues are discussed in more detail in section 5.

5 For expositional reasons the model deals with a duopoly. However, all the results readily extendto an oligopoly.


QTðPÞ � QT�1ðPÞ � : : : � Q1ðPÞ.

Conversely, if the industry is experiencing a contraction in demand then:

Q1ðPÞ � Q2ðPÞ � : : : � QTðPÞ.

Diagrammatically, if QtðPÞ � Qtþ1ðPÞ, then demand in period (tþ 1) rises either

as a result of an outward shift in the demand function or a pivoting of the

demand curve. Assumption 5 asserts that demand is either consistently rising or

declining over time. It is supposed that these changes in demand are known to all

players. Hence, we model a growing (contracting) industry as one with rising

(falling) demand.

Assumption 6. There is neither entry nor exit in the industry.

Thus, variations in demand are not so large that they induce firms to enter or

leave the industry.6

Having specified the basic assumptions relating to demand, we now outline

the remaining structure of the model. Production of good Qt results in pollution

emissions, denoted Et, which adversely affect a subset of individuals termed

environmentalists. The pollution damage suffered by environmentalists is

defined by the damage function DtðEtÞ. It is assumed that pollution damage

increases with pollution levels at an increasing rate, and that emission damage is

non-cumulative in its impact.7 That is:

@Dt=@Et > 0; @ 2Dt=@E2t > 0 and

@Dt=@Et�i ¼ 0 ðt ¼ 1, : : :, T Þ; ði ¼ 1, : : :, T� 1Þ.

Pollution emissions which are related to production levels are given by:

Et ¼ yQtðPÞ, ð1Þ

where y is the emission coefficient of output.

In order to regulate pollution levels, the government levies a tax on pollution

emissions at a rate t. The tax rate is determined in stage 1 in the political

equilibrium and is held constant over the duration of the output stage of the

game. As is well known, emission taxes provide firms with an incentive to abate

emissions.

Following Conrad (1993) we assume that the cost function, denoted Hf,

contains three distinct components: the production costs (c), the cost of abating

emissions vða f Þ and the tax paid on unabated emissions (t). Specifically:


6As noted by Scherer (1980) this assumption may be reasonable for many industries in themanufacturing sector which have been able to endure secular movements in demand without majorstructural changes.

7 Emission damage is assumed to be non-cumulative, since we wish to focus upon the effect ofdemand changes on lobbying, rather than the complications which arise with dynamic externalitieswhich occur when deposits of pollution cause damage.


Hftðq

ft, c, vða

ftÞÞ ¼ ½cþ ftð1� a f

tÞ þ a ft vða

ftÞgy�q

ft

ð f ¼ i, j Þ; ðt ¼ 1, : : :, T Þ, ð2Þ

where c is the unit cost of production; a f is the degree of pollution abatement

activity; vða f Þ is the unit cost of pollution abatement which depends on the

degree of abatement activity undertaken; t is the tax on unabated emissions and

y is the emission coefficient resulting from output q f. We assume that:

@vt=@at > 0, @2vt=@a2t > 0. Observe that tð1� a f

tÞyq ft represents the tax paid on

unabated emissions, while a ftvða

ftÞyq f

t defines total abatement costs.

In the absence of lobbying, the profits of firm f ¼ i, j, in any period t 2 ½1, T �

are defined as:

P ft ¼ PtðQtÞq

ft �Hf

tðqft, c, vða

ftÞ, tÞ ð f ¼ i, j Þ 8 t 2 ½1, T �. ð3Þ

We begin by solving the final stage of the game in which output levels are

determined. Taking the tax as given, equilibrium output in each period is

determined by the solution to the first-order condition:8

Pt þ@Pt

@q itqft � c ¼ ðtð1� a f

tÞ þ vða ftÞa

ftÞy ð f ¼ i, j Þ 8 t 2 ½1, T �. ð4Þ

Let qnt ¼ q i

t ¼ q jt denote the solution to (4) in a symmetric Cournot equilibrium.

Clearly, firms will choose abatement levels to minimize costs, given knowledge

of the emission tax rate (t) and abatement costs (v). Thus, for a given level of

output, abatement levels are determined by the solution to:

minaft

Hftðq

nt , c, vða

ftÞ, tÞ ¼ ½cþ ftð1� a f

tÞ þ a ftvða

ftÞgy�q

nt . ð5aÞ

The first-order condition is:

dHft

da ft¼

�@vða f

tÞ

@a ft

a ft þ vða f

tÞ � t

�yqn

t ¼ 0 8 t 2 ½1, T �. ð5bÞ

Let at be the solution to equation (5b). Observe that (5b) summarizes the

familiar result that firms abate emissions up to the point where the marginal

costs of abatement ½ð@v=@aÞat þ vðatÞ�, equal the tax rate (t). Note also that with

this formulation of abatement technology, the level of abatement (at) is

independent of output levels. Moreover, unabated pollution emissions from

each firm are now given by:

E ft ¼ ð1� atÞyq

ft ð f ¼ i, j, t 2 ½1, T �Þ. ð5cÞ

214 DAMANIA

8Firms maximize the net present value of profits: P f1 þ dP f

2 þ � � � þ dTP fT (where d is the discount

factor). The first-order condition in period t satisfies

dt@P f

t

@qt¼ dt

�Pt þ

@Pt

@q ftq ft �

@Hft

@q ft

�¼ 0.


Thus, total emissions are:

Et ¼ Eit þ E j

t 8 t 2 ½1, T �. ð5dÞ

For completeness Lemma 1 outlines a useful property of the duopoly. The

proofs are relegated to the Appendix.

Lemma 1.

dqnt

dt< 0,

datdt

> 0.

Lemma 1 summarizes the well-established result, that firms respond to higher

emission taxes by lowering output and raising abatement levels.

3. LOBBY GROUP CONTRIBUTIONS

Having determined the equilibrium in the output stage of the game we now turn

to the political equilibrium in the preceding stage. We begin by specifying the

individually rational contribution levels of each firm to the lobby group, given

its rival’s contribution.

Since taxes adversely affect profit levels, firms have an incentive to form

themselves into a lobby group to persuade the government to lower the tax

burden. Thus, it is assumed that in the contributions stage of the game the firms

jointly offer the government contributions (C), as an inducement to lower the tax

rate. It is supposed that the contribution schedule is offered before the output

game commences and that the resulting tax rate is therefore held constant over

the output stage.9

Let the output stage extend over two periods (i.e. T ¼ 2).10 Then, given the

contribution of a rival firm k ¼ i, j ði 6¼ j Þ, the individually rational contribution

of firm f 6¼ k to the lobby group is defined by:

C f 2 argmax ~PP f � ½P f1 þ dP f

2 � C fðCkÞ�, ð6aÞ

where d ¼ discount factor, CfðCkÞ ¼ contribution of firm f 6¼ k ð f, k ¼ i, j;

i 6¼ j Þ. The associated first-order condition is:11


9We therefore implicitly assume that there exists some commitment device (such as reputationeffects) which prevents the government from reneging on its policy promises. This issue is discussedfurther in Section 5.

10 The argument can be extended to any finite period T > 2.11 Observe that:

d ~PP f

dCf¼

��dP f

1

dq f1

dq f1

dtþdP f

1

da1

da1dt

�þ d

�dP f

2

dq f2

dq f2

dtþdP f

2

da2

da2dt

��dt

dCfþ

�@ ~PP f

1

@tþ d

@ ~PP f2

@t

�dt

dCfþ

@ ~PP@Cf

.

By the Envelope Theorem

dP ft

dq ft¼

dP ft

dat¼ 0.

Furthermore, we employ the usual assumption in this context of Cournot–Nash conjectures withrespect to a rival’s contribution [i.e. @C i=@C j ¼ 0 ði 6¼ j Þ]. This assumption is very widely used indetermining the Nash equilibrium in such cases (e.g. Cornes and Sandler, 1994).


�ydt

dCfðð1� a1Þq

n1 þ dð1� a2Þq

n2Þ � 1 ¼ 0. ð6bÞ

Thus, each firm contributes up to the point where the marginal benefits to the

firm resulting from a lower tax equals the marginal cost of the contribution. Let

CfðtÞ denote the solution to (6b). For future reference we note that a necessary

condition for (6b) to hold is dt=dCf < 0. That is, taxes must decline as political

contributions rise. Intuitively, if higher political contributions do not yield

benefits in the form of lower taxes, firms have no incentive to lobby the

government.

Clearly, the marginal benefits accruing to a firm from a reduction in taxes will

depend on, amongst other things, the level of demand. It follows that

contributions are likely to vary with changes in demand. Proposition 1 below

outlines the circumstances under which falling demand induces firms to increase

their contributions.

Define industry contributions as: CðtÞ ¼ CiðtÞ þ CjðtÞ. Let �CCðtÞ be the

equilibrium industry contribution which satisfies (6b) when there is growing

demand. Let CðtÞ be the equilibrium industry contribution which satisfies (6b)

when there is falling demand. Then:

Proposition 1. Contribution levels in an industry with declining demand exceed

those in an industry with growing demand, if the tax declines sufficiently rapidly

with political contributions [i.e. CðtÞ > �CCðtÞ, if d2t=dC 2 < 0].

Proof. Let ð1� a2Þ �qqn2y ¼ �EE f

2 be the level of emissions of a firm in period 2 under

growing demand and let ð1� a2Þqn2y ¼ E f

2 be the corresponding level of

emissions in period 2 under declining demand. Then the first-order conditions

under growing and falling demand respectively are:

�dtð �CC Þ

dCfðE f

1 þ d �EE f2Þ � 1 ¼ 0 ðIÞ

�dtðC Þ

dCfðE f

1 þ dE f2Þ � 1 ¼ 0. ðIIÞ

Since �qqn2 > qn

2 then ðE f1 þ d �EE f

2Þ > ðE f1 þ dE f

2Þ, thus (I) and (II) imply that:

�dtð �CC Þ

dC f< �

dtðC Þ

dC f. ðIIIÞ

Since dtðC Þ=dC f < 012 it follows that (III) holds with �CC f < C f if d2tðC Þ=dC 2 < 0.

As both firms are symmetric, then

�CC ¼ �CCi þ �CCj < C ¼ Ci þ Cj ifd2tðC Þ

dC 2< 0. &

216 DAMANIA

12As noted earlier, if this were not the case then from (6b) a corner solution obtains with zerocontributions. If higher contributions do not yield any benefits to firms in the form of lower taxes,they have no incentive to lobby.


Proposition 1 reveals that the political contributions of a declining industry

exceed those of an industry facing rising demand, only if the tax schedule set by

the government is concave in contribution levels [i.e. d2tðC Þ=dC 2 < 0]. This

implies that, as contributions increase, the resulting tax declines more rapidly.

Intuitively, when demand is low the ability to raise profits through the output

market is limited. If the tax schedule is concave in contributions, firms can

mitigate this fall in profits by increasing their contributions. Hence, the credible

threat of lower future profits gives firms in declining sectors a greater incentive

to protect their profits by lobbying for lower taxes. Stated differently, the

opportunity costs of lobbying are lower when demand is depressed, so that there

is less incentive to free-ride on lobby group contributions. Political contributions

therefore rise when demand is expected to decline.

However, this outcome relies critically on the unsubstantiated assumption

that the government lowers taxes sufficiently with contributions (i.e. that the tax

schedule is concave in contributions). For completeness it is necessary to explore

whether such behaviour is incentive compatible and consistent with rational

maximizing behaviour by a government. This issue is discussed in greater detail

in the following section.

4. THE POLITICAL EQUILIBRIUM

Perhaps the most widely used recent approach to modelling government

behaviour is the political support framework developed by Grossman and

Helpman (1994). In this section we investigate whether the tax schedule implied

by this model of government behaviour induces greater lobbying by firms in

declining sectors.

In the political support model, an incumbent government is assumed to have

some measure of flexibility in making policy choices. The government values

both social welfare and political contributions (Grossman and Helpman, 1994).

Political contributions are desired because of their many uses, such as funding

campaigns, deterring rivals, etc. Contributions of each firm to the lobby group

are defined by the solution to the first-order condition in (6b) and are contingent

upon the tax rate chosen by the government.

Social welfare, gross of contributions, in any period is given by the sum of

profits, consumers’ surplus, pollution tax revenues, less the damage suffered

from pollution emissions:

WtðtÞ �

ðQt

0

PtðQÞdQt � ðcþ vðatÞyþ ð1� atÞytÞQt

�DðEtÞ þ ð1� atÞytQt ,13 ð7aÞ

where Qt ¼ q it þ q j

t is industry output.


13 Since we are dealing with symmetric equilibria, firm superscripts are ignored for notationalconvenience.


For simplicity let T ¼ 2, then aggregate welfare is:

WðtÞ ¼ W1ðtÞ þ dW2ðtÞ. ð7bÞ

For future reference we define the welfare maximizing level of emission taxes:

tw 2 argmaxWðtÞ. ð7cÞ

The government’s objective function is assumed to be given by a weighted sum

of political contributions and social welfare:

GðtÞ ¼ CðtÞ þ aWðtÞ, ð7dÞ

where CðtÞ ¼ CiðtÞ þ C jðtÞ are political contributions, a is the weight given to

aggregate social welfare relative to political contributions.

A subgame-perfect Nash equilibrium is defined by a set of contribution

schedules, for the lobby group and a tax policy t*, such that: (i) the contribution

schedule is feasible; (ii) the tax t* maximizes the government’s welfare, GðtÞ,

taking the contribution schedules as given. From lemma 2 of Bernheim and

Whinston (1986) the following necessary conditions yield a subgame-perfect

Nash equilibrium fCðt*Þ, t*g:

t* 2 argmaxGðtÞ ¼ CðtÞ þ aWðtÞ, ðSIÞ

t* 2 argmaxP1ðtÞ þ dP2ðtÞ þ GðtÞ, ðSIIÞ

where Pt ¼ PitðtÞ þP j

tðtÞ ðt ¼ 1, 2Þ.

Condition (SI) asserts that the equilibrium tax t* must maximize the

government’s payoff, given the contribution schedule offered by the lobby

group. Condition (SII) requires that t* must also maximize the joint payoff of

the lobby group and the government. If this condition is not satisfied, the lobby

group will have an incentive to alter its strategy to induce the government to

change the tax rate, and capture close to all the surplus. Maximizing (SI) and

(SII), and performing the appropriate substitutions, reveals that in equilibrium

the contribution schedule of the lobby group satisfies:14

dP1

dtþ d

dP2

dt¼

dCðt*Þ

dt. ð8Þ

Equation (8) informs us that, in equilibrium, the change in the lobby group’s

contribution equals the effect of the tax on the payoffs of the lobby group. Thus,

as noted by Grossman and Helpman (1994), the political contribution schedules

are locally truthful. As in Bernheim and Whinston (1986) and Dixit et al. (1997)

this concept can be extended to a contribution schedule that is globally truthful.

This type of schedule accurately represents the preferences of the special-interest

218 DAMANIA

14 It can be shown that first-order condition (6b), which determines contribution levels, impliesequation (8). Thus, Cournot–Nash contribution levels satisfy the conditions for a subgame-perfectequilibrium.


group at all policy points. Moreover, expanding terms on the left-hand side of

(8), dPt=dt ¼ �Et < 0. Hence, dCðt*Þ=dt < 0.

Grossman and Helpman further demonstrate that with one lobby group the

level of political contributions is given by the difference in social welfare when

the tax is set at the welfare maximizing level (tw) and at the political equilibrium

(t*):

CðtÞ ¼ aðWðtwÞ �Wðt*ÞÞ, ð9Þ

where WðtwÞ is welfare at the welfare maximizing tax rate tw and Wðt*Þ is

welfare when the tax is set at t*.

Observe that equation (9) implies that the lobby group exactly compensates

the government for the welfare loss arising from a decline in the tax rate. The

welfare loss is weighted by the factor a to adjust for its importance in the

government’s objective function.

Having defined the equilibrium level of contributions, we now explore the

properties of the implied tax schedule. In the Appendix it is demonstrated that

when contribution levels are declining in the tax rate set by the government, then

the resulting equilibrium tax schedule must be concave in contribution levels.

This result is summarized in the following lemma.

Lemma 2. In a political equilibrium the tax schedule is concave in contributions

(i.e. d2t=dC 2 < 0).

Proof. See the Appendix.

Concavity of the resulting tax schedule can be seen to arise from the truthfulness

property of the equilibrium, which requires that contributions reflect the

profitability of a policy. Thus, contributions will rise, only if they generate

sufficient profits by eliciting a corresponding reduction in taxes.15

Proposition 1 and Lemma 2 combine to suggest the following result.


15 The relationship with the truthfulness condition may be illustrated by the following heuristicargument which is implicit in proposition 2 of Dixit et al. (1997). Consider the simple one-period case.Let P ¼ Pi

þP j. By truthfulness

dPdt

¼dCðt*Þ

dt.

Using Shephard’s Lemma and further differentiating the left-hand side,

d 2Pdt 2

¼ �ð1� aÞy@Q

@tþ yQ

@a

@t> 0.

Since any two functions having the same derivative over a given continuous domain must be identicalup to a constant, and vice versa, then d 2Cðt*Þ=dt 2 > 0. Since C�1ðtÞ ¼ tðC Þ, it follows that

dCðt*Þ

dt¼

�dCðt*Þ

dt

��1

and if d 2Cðt*Þ=dt 2 > 0, then d 2t=dC 2 < 0 [a proof of this latter property is in the Appendix; also seeStromberg (1981), p. 374].


Proposition 2. In a political equilibrium industries with falling demand make

larger political contributions and receive lower taxes than do industries with

growing demand.

Proof. See the Appendix.

Proposition 2 reflects the fact that political donations are truthful in the sense

that they vary with taxes and mirror the profitability of a given tax policy.When

demand is depressed, profits are low and firms’ political contributions tend to

decline. A government which values political donations sufficiently has an

incentive to limit the potential decline in political contributions by adopting

policies which are more favourable to the donor. This finding implies that when

a government is predisposed to interest groups, declining industries which lobby

for policy concessions are likely to gain greater support.

5. CONCLUSIONS

This paper has outlined a new mechanism which explains why industries in

declining sectors often lobby more successfully for policy concessions. An

industry in decline is constrained in its ability to raise revenue through

production. There is therefore a stronger incentive to protect profits by lobbying

for greater policy concessions. However, more intensive lobbying may not

necessarily translate into higher levels of support. The paper therefore examined

the conditions under which greater lobbying by firms induces the government to

grant further policy concessions. It was demonstrated that if a government cares

sufficiently about political donations, it has an incentive to adopt a more

favourable policy towards firms in declining sectors. This is because the prospect

of declining profits provides a credible signal to the government that political

contributions will fall. In order to limit the decline in contributions the

government is induced to adopt policies which raise the firms’ profits.

The existing literature suggests other reasons (e.g., free-riding incentives,

industry size, imperfect credit markets, etc.) why declining industries lobby more

successfully. This paper has attempted to complement these studies by

identifying the primitive conditions under which this result might obtain when

these assumptions do not hold.16 It was shown that declining industries lobby

more successfully than their growing counterparts in the political support model

when the government’s tax schedule is concave in contributions (Proposition 1).

While the requirement that the tax schedule is concave may appear to be

restrictive, it was discovered that this condition is always satisfied in the political

equilibrium (Lemma 2). Thus, the results suggest that while declining industries

have a stronger incentive to lobby for concessions, in a political support context

the government too has a greater incentive to grant concessions to these firms in

order to limit the decline in political contributions.

220 DAMANIA

16 I am grateful to a referee for emphasizing these matters.


The analysis in this paper is based on a number of simplifying assumptions.

Perhaps the most important of these is the assumption that contributions and

the tax rate having been set in the prior political equilibrium, and do not vary

over the output stage as demand changes.17 First, this implies that there is some

tacit commitment device (such as reputation effects) which prevents the

government from reneging on its announced policy.18 More importantly this

assumption implies that policies do not vary with the state of demand in each

period. This simplifying assumption has been made only for reasons of

analytical tractability. It would clearly be useful in future research to allow for

state-dependent policies in a more complicated dynamic control problem, where

both the government and the lobby group sequentially vary their offers in each

period. This is an interesting and important issue which warrants further

research.

APPENDIX

Proof of Lemma 1

qn solves the first-order condition:

Pt þ@Pt

@q itqft � c ¼ ðtð1� af

tÞ þ vða ftÞa

ftÞy. ðA1Þ

Totally differentiate and solve, using (5b):

dqnt

dt¼

ð1� a ftÞy

@2Pt=@q 2t þ 2ð@Pt=@qtÞ

< 0. ðA2Þ

The sign of (A2) follows from the fact that, by Assumption 4, the denominator is

negative, while ð1� a ftÞy > 0. &

Similarly using (5b):

datdt

¼yqt

@2vt=@a2t þ 2ð@vt=@atÞ> 0. ðA3Þ

The sign of (A3) follows from the fact that, by assumption, all terms in the

numerator and denominator are positive. &

Proof of Lemma 2

We begin by noting that since dCðtÞ=dt < 0 by equation (8), then by the

inverse function theorem the inverse of CðtÞ exists and the following properties

hold:


17 I thank a referee for highlighting the importance of this issue.18 This assumption is implicit in the Grossman–Helpman model. Tirole (1992) suggests that many

such models which assume enforceability may be robust to the relaxation of this assumption.


ðiÞ C�1ðtÞ � tðCÞ;

ðiiÞdC

dt¼

1

ðdC=dtÞ;

ðiiiÞd2C

dt 2< ð>Þ 0 ,

d2t

dC 2> ð<Þ 0.19

From (9) the level of contributions necessary to induce lower taxes is:

CðtÞ ¼ aðWðtwÞ �Wðt*ÞÞ. ðA4Þ

Totally differentiating (A4):

dCðtÞ ¼ a�@WðtwÞ

@tdtw �

@Wðt*Þ

@tdt*

�. ðA5Þ

But (7c) implies that @WðtwÞ=@t ¼ 0. Thus:

dCðt*Þ

dt*¼ �a

@Wðt*Þ

@t*< 0. ðA6Þ

Where the sign of (A6) follows from the fact that t* < tw and for a unique

maximum to exist we require thatWðtÞ is concave. Hence, @Wðt*Þ=@t > @WðtwÞ=

@t ¼ 0. Differentiating (A6) further:

d2Cðt*Þ

dt*2¼ �a

@2Wðt*Þ

@t*2. ðA7Þ

Since by assumption @2Wðt*Þ=@t*2 < 0, then d2Cðt*Þ=dt*2 > 0. By property (iii)

of inverse functions stated above, it follows that d2t*=dC 2 < 0. &

Proof of Proposition 2

By Proposition 1: CðtÞ > �CCðtÞ, if d2t=dC 2 < 0. By Lemma 2: d2t=dC 2 < 0. Thus

222 DAMANIA

19 Since property (iii) is perhaps less frequently used than the others, we provide a brief proof.Define cc 2 C � Rþ and tt 2 t � Rþ such that cc ¼ Cðtt Þ. Then the following hold: (1) C�1ðccÞ ¼ tt; (2)ðC�1Þ

0ðccÞ ¼ 1=C 0ðtt Þ; (3) limc!cc C

�1ðcÞ ¼ C�1ðccÞ ¼ tt. For notational brevity primes denote derivatives,and c 2 C. Observe that condition (3) implies that limc!cc t ! tt. Without loss of generality, supposethat C 00ðtÞ < 0, then C 0ðtÞ < C 0ðtt Þ 8 t > tt. Thus using the definition of derivatives:

ðC�1Þ00ðccÞ ¼ lim

c!cc

ðC�1Þ0ðcÞ � ðC�1Þ

0ðccÞ

ðc� ccÞ.

By the substitution theorem for limits,

ðC�1Þ00ðccÞ ¼ lim

t!tt

ð1=C 0ðtÞÞ � ð1=C 0ðtt ÞÞ

ðt� tt Þ< 0,

where the sign follows from the assumption that t > tt and concavity of CðtÞ. Hence, if C 00ðtÞ < 0, thent 00ðCÞ > 0 and vice versa (see also Stromberg, 1981). Alternatively this property may be verified bygraphing a function and its inverse.


CðtÞ > �CCðtÞ. Since dt=dC < 0 by equation (8), then the tax levied in a growing

industry exceeds that in a declining industry. &

ACKNOWLEDGMENTS

The author acknowledges with gratitude the extremely helpful and incisive

comments of two referees and the co-editor Peter Rosendorff. The usual

disclaimer applies.

RICHARD DAMANIA

School of Economics, University of Adelaide

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Influence in Decline: Lobbying in Contracting Industries