Do Lobbying Competition between Foreign Firms and
Domestic Firms Increase or Decrease Tariffs?
CAI Dapeng, Institute for Advanced Research, Nagoya University※
LI Jie, Zhejiang University
1. Introduction
In the field of political economy, a substantial amount of literature is present on how trade
policies emerge as an endogenous outcome of interactions between politicians and organized
interest groups (Rodrik, 1995). So far, the emphasis has been largely on the link between
domestic industry lobbies and politicians that results in policies protecting domestic
companies while placing foreign rivals at a comparative disadvantage. However, this result
may not hold when foreign lobbies are actively involved in influencing policy formulation.
By what magnitude can foreign lobbies influence a country’s trade policy? When do foreign
lobbies reduce trade barriers? This paper attempts to theoretically investigate how lobbying
competition between foreign firms and domestic firms influence a nation’s trade
policymaking.
Lobbying by foreign companies has recently attracted growing attention. Many studies
have evaluated the intensity of foreign lobbying and argue that it has high potential for policy
influence. Mitchell (1995) finds that the contributions from foreign lobbies in the US
accounted for 5.6% of the total corporate political contributions in 1987–88. Hansen and
Mitchell (2000) confirm that foreign firms lobby as intensively as domestic firms. In a
pioneering work using US data, Gawande et al. (2006) show that lobbying by foreign firms
significantly affects tariff structures across industries. They demonstrate that foreign agents’
lobbying expenditures in the US are greater than political contributions by domestic firms and
that the elasticity of the US import tariff with respect to foreign lobbying is almost as large as
with respect to the domestic one. These findings are supported by Stoyanov (2009), who
analyzed Canadian post-NAFTA trade data.
To examine the impact of lobbying, we compare the lobbying equilibrium with the social
optimum. We find that foreign lobbying does not inevitably result in reduced tariff rates. As
compared to the no-lobbying case, the tariff rate under lobbying will be lowered when the
foreign firm is more competitive than the domestic firm under the no-lobbying tariff. This
also happens when (i) the no-lobbying tariff cannot cover the efficiency gap between the
domestic firm and the foreign firm or (ii) the contributions from the domestic lobbies are
lower than that from the foreign lobbies, should both lobbies’ elasticity of contribution with
respect to tariff be identical.
At least partially, our paper explains a ‘rich get richer’ phenomenon in international
intra-industry inequality. Our results suggest that by lobbying the domestic government,
competitive foreign firms can maintain or improve their competitive advantage over their
domestic rivals. This is because the politicians, anticipating more corporate contributions, are
willing to bend trade policies to help the more competitive firms to become more profitable.
Consequently, profitable foreign firms become more profitable by a reduction in tariffs and
domestic firms’ comparative disadvantages are aggravated, ceteris paribus. These results
justify the presumption that foreign firms’ successful influence over domestic politicians has a
detrimental effect on domestic firms. Our study provides further evidence that foreign
lobbying should be closely monitored and restricted.
2. The Model Setting
Consider a duopolistic industry composed of a domestic firm (firm 1) and a foreign firm (firm
2). Both produce a homogeneous product, with outputs being Q1 and Q2 . Firm 2 exports to
the domestic market, the inverse demand curve of which is given by P(q) :    (price
as a function of quantity), where P  0 . The firms have different marginal costs, given by
c1 ( 0) and c2 ( 0) . A tariff  is imposed on exports from firm 2. Let  denote the set
of  from which the domestic government may choose. We bound  such that each 
must lie between a minimum  and a maximum  . In what follows, we restrict attention to
equilibria that lie in the interior of  . Both firms maximize their profits, 1 and  2 :
1  PQ1  c1Q1 ,
(1)
2  PQ2  c2Q2   Q2 .
(2)
We define the domestic social welfare function as the sum of the domestic firm’s profit,
Q1  Q2
consumer surplus ( CS  0
W  1  CS   Q2
Pdq  P(Q1  Q2 ) ) and the tariff revenue:
Q Q2
 0 1
Pdq  PQ2  c1Q1   Q2 .
(3)
Firms lobby to gain or keep a comparative advantage over business rivals or to avoid
comparative disadvantage (Reich, 2007). They contemplate influencing the government’s
decision by offering to politicians (members of government) contribution schedules Ci ( ),
where i  1, 2, and Ci ( )  0 . The contribution schedules are assumed to be differentiable.
Given firms’ contribution schedules, the government chooses  to maximize its objective
function, which has social welfare and the total of contribution receipts as arguments:1
G  W   (C1  C2 ),   0 .
(4)
The resulting payoffs for the two firms are
1  1  C1 ,
(5)
 2   2  C2 .
(6)
We consider a simple three-stage game. In the first stage, both firms simultaneously
determine contribution schedules. In the second stage, government sets a tariff level imposed
We use the following superscripts for notations in equilibrium: ‘0’ for welfare maximizing (no lobbying) and
‘*’ for the common agency game.
1
on firm 2. In the third stage, both firms compete in the domestic market, á la Cournot. We use
backward induction to solve this game.
3. The Common Agency Model
3.1 Third Stage: Cournot Competition
In the third stage, firms choose their outputs to maximize their respective objective functions.
The first-order conditions are given by
PQ1  P  c1  0 ,
(7)
PQ2  P  c2    0 .
(8)
We
assume

that
the
 1 Q
 1 Q1Q2
  2 Q2 Q1
  2 Q2
2
2
1
2
stable
equilibrium
condition
is
satisfied—i.e.
2
2
2
0.
The reaction functions for both firms, denoted by R1 (Q2 ) and
R2 (Q1 ) , are implicitly defined by equations (7) and (8), respectively.
R1 (Q2 )  arg max 1 (Q1, Q2 ; c1 ) , R2 (Q1 )  arg max  2 (Q1, Q2 ; c2 , ) .
Q1 0
Q2 0
Moreover, we assume that outputs of the two firms are strategic substitutes,
P'  P''Qi  0,
i  1, 2,
(9)
which ensures that the slope of each firm’s reaction function is negative—i.e. Ri' (Q j )  0 and
Ri' (Q j )  1 , where i  1, 2, j  1, 2 and i  j (Dixit, 1986). As to the second-order conditions,
we assume  2 1 / Q12  0 and  2  2 / Q22  0 .
Denoting E1 and E2 as the firms’ equilibrium outputs, we note the following:
Lemma 1. (i)
 ( E1  E2 )
P
E1
1
E2
 2
E1
0,
 0 ; (ii)
0 ,
0 ,
0 ,
0 ,
0 ,
c1
c1
c2
c1
c1
c1
c1
 ( E1  E2 )
P
E1

E2
 2
1
E2
 2
0,
 0 ; (iii)
0, 1 0,
0,
0,
0,
0,
0,







c2
c2
c2
c2
c2
 ( E1  E2 )

0,
P

0.
We pause here to consider the optimum tariff chosen by a social planner that maximizes
social welfare (there would be no lobbying and no contributions). To ensure the existence of a
unique interior solution, we assume W is strictly concave in  . The social optimum tariff
level  0 is obtained from
W /    P  PE2 (1  R2 )  E2 (E1  )  c1   R2   E1    0 ,
(10)
 0  P[ E1  E2 (1  R2 )] R2  E2 R2 (E1  ) .
(11)

and equations (7) and (8), and is given by
From Lemma 1, we see that

1
2
 0 . That is, firms’ interests concerning
 0 , whereas


the tariff are conflicting. Next, we consider the outcome of such lobbying behaviours.
3.2
First and Second Stage: Optimal Contributions and the Tariff Level
An equilibrium of the common agency game consists of a set of contribution functions
{Ci ( )}i21 , one for each firm, and a tariff level imposed on firm 2  * , such that for each firm,
the contribution function Ci ( ) and the tariff  * are a best response of firm i to the
contribution function C j ( ), j  i, of the other firm.
Lemma 2. (Bernheim and Whinston, 1986): (C1 , C2 ,  ) constitutes a subgame perfect Nash
equilibrium if and only if the following conditions are satisfied: (i) Ci is feasible for i  1, 2 ;
(ii)

maximizes
G  W   (C1  C2 )
on

;
(iii)

maximizes
1  G  1  C1  W   (C1  C2 ) on  ; (iv)   maximizes  2  G   2  C2  W   (C1  C2 )
on  ; (v) for firm 1, there exists a ˆ   that maximizes G  W   (C1  C2 ) on  such
that C1 (ˆ)  0, i.e. W ( * )  [C1 ( * )  C2 ( * )]  W (ˆ)  C2 (ˆ) ; and (vi) for firm 2, there exists a
 
that
maximizes
G  W   (C1  C2 )
on

such
that
C2 ( )  0,
i.e.
W ( * )  [C1 ( * )  C2 ( * )]  W ( )  C1( ) .
Our model can have multiple subgame-perfect Nash equilibria. In the following analysis,
we restrict our focus to the truthful Nash equilibrium, which is supported by truthful
contribution functions that everywhere reflect the true preferences of the firms. We denote the
truthful contribution functions of the two firms by C1T and C 2T . Formally, the truthful
contribution
functions
take
C2T ( )  max{0,  2 ( )   2 ( )},
the
form
C1T ( )  max{0, 1 ( )  1 (ˆ)}
and
  . To ensure the existence of a unique interior
solution, we assume that the total surplus function, TS ( )  W ( )  [1 ( )   2 ( )] , is strictly
concave in  . We then have the following:
Proposition 1. Suppose  *   0 . (i) Lobbying worsens each lobby’s payoff, i.e.
1 ( * )  1 ( 0 ) and  2 ( * )   2 ( 0 ); (ii) lobbying worsens social welfare, i.e. W *  W 0 .
The optimal  * can be obtained by solving the optimization problem max TS ( ) , and is
expressed by
 *  P[ E1  E2 (1  R2 )] R2  E2
Proposition
2.
R2 (E1  )   E2 [ P  1
2
1
A  (112   21
) 11
Let
(E1  )] R2   PE1 .
  0
( 0),
(12)
1   21 E1E2 ,
where
12
 221   2  2 E2 E1 , and 1   2 1 E12 . The equilibrium tariff that emerges from the
11
common agency game will be lower than the social optimum if  0  c2  c1 
A
1 A
 P(
0

)  c1 ;
otherwise, it will be higher than or equal to the social optimum.
Proposition 2 suggests that the equilibrium tariff will be lower when all affected firms
lobby the government than under the no-lobbying case, as long as the foreign firm is more
competitive than the domestic firm under the socially optimal tariff, i.e.
 0  c2  c1 
A
1 A
 P(
0

)  c1 . In other words, if the social optimum is the starting point, a
tariff reduction is likely to emerge if both the domestic and foreign firms lobby the
government and the foreign firm is more competitive initially. An immediate corollary from
Proposition 2 would be
Corollary 1. When the socially optimum tariff cannot cover the efficiency gap between the
domestic firm and the foreign firm, the equilibrium tariff emerging from the common agency
game will be lower than the social optimum, i.e.  *   0 if  0  c1  c2 .
Next, we focus a special case in which the elasticity of the domestic firm’s contribution
with respect to tariffs is the same as that of the foreign firm at equilibrium. We immediately
have
Corollary 2. Suppose the elasticity of the domestic firm’s contribution with respect to tariffs
is the same as that of the foreign firm at equilibrium. When the domestic firm’s contribution
at equilibrium is lower than the foreign firm’s, the tariff that emerges from the common
agency game would be below the social optimum—i.e. when 1 (  )   2 (  ) ,  *   0 if
C1T ( * )  C2T ( * ), where  i (  ) 


 Ci  ( ) , i  1, 2; otherwise,    .
T

C ( )
T
i

*
0
4. Conclusion
In this study, we find that a foreign firm can strengthen competitive advantage in a domestic
market if it lobbies the domestic government. In other words, firms’ lobbying tends to
reinforce an initial comparative advantage, even in the international market. This happens
primarily because a government that values firms’ contributions would choose to shift
production from the least efficient firm to more efficient ones and thus increase the latter’s
profits by bending trade policy, regardless of firms’ nationality. The increase in profits, under
the truthful Nash equilibrium, will be rewarded completely to the government as
contributions, thus maximizing the government’s payoff. Our results suggest it may be
necessary to restrict firms’ lobbying, as it decreases social welfare and may exacerbate
inequality among firms.
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