Title

Lobbying and tax competition in an oligopolistic
industry: a reverse home-market effectAuthor(s)Kato, Hayato

Citation

Spatial Economic Analysis. 13(3) P.276-P.295

Issue Date 2018-02-09
Text Version author
URL

http://hdl.handle.net/11094/81777

DOI

10.1080/17421772.2018.1425477

rights
Note

Osaka University Knowledge Archive : OUKA
https://ir.library.osaka-u.ac.jp/
Osaka University

Lobbying and Tax Competition in an Oligopolistic Industry: A Reverse Home Market Effect

Hayato Kato

Abstract This paper studies tax competition between two asymmetric countries for an
oligopolistic industry with many firms. Each government sets its tax rate strategically tomaximize the weighted sum of residents’ welfare and political contributions by owners offirms. It is shown that, if the governments care deeply about contributions and trade costs
are low, the small country attracts a more than proportionate share of firms by setting alower tax rate. The well-known home market effect, which states that countries with a larger
market attract a more than proportionate share of firms, may be reversed as a result of tax
competition by politically-interested governments.
KEYWORDS: Tax competition; economic geography; reverse home market effect; lobbying
JEL CLASSFICATION: F15; F22; H20; H30

Hayato Kato, Faculty of Economics, Keio University, Tokyo, Japan. Email: hayato.kato2@gmail.com.
The author wishes to thank Taiji Furusawa, Jota Ishikawa and Yoichi Sugita for their invaluable suggestions. Thanks also go to Rainold Borck, Masahiro Endoh, Ben Ferrett, Naoto Jinji, Jie Ma, Kaz
Miyagiwa, Michael Pflüger, Pascalis Raimondos, Martin Richardson, Tony Venables, Alan Woodland, Ian Wooton and seminar and conference participants at the ATW2014 Perth, the ETSG2014
Munich, Hosei, Kyoto and Hitotsubashi. This work extends the second chapter of the author’s
Ph.D. dissertation submitted to Hitotsubashi University. The author acknowledges financial support from Grant-in-Aid for JSPS Research Fellows (JP13J03694) and MEXT-Supported Program
for the Strategic Research Foundation at Private Universities (JPS1391003).

1

1

Introduction

As economic integration proceeds, the world has witnessed a huge expansion of international
trade of goods and movement of factors. The acceleration of international capital mobility isparticularly noteworthy. In the post-war period, foreign direct investment (FDI) has grown
more rapidly than international trade (WTO, 2013); in the period from 1970 to 2014, FDI
flows increased 22.2-fold, or 2.2 times faster than trade (van Marrewijk, 2017, Ch.9). In
response to this trend, a number of countries have engaged in competition for mobile firms,
and this competition has been accelerating since the late 1990s (OECD, 1998). A particularly
notable observation is that small countries such as Ireland, Singapore and Estonia tend toundertake a more aggressive reduction in corporate tax rates than large countries such as
France, Japan and the U.S.1 By looking at statutory corporate tax rates from 1982 to 2006,
OECD (2007) concluded that large-sized OECD countries in terms of GDP continue to levy
corporate taxes at higher rates than small-sized OECD countries.2
The theory of tax competition in economic geography, i.e., imperfectly competitive modelsof trade and location, tells us that the positive relationship between country size and tax
rates results from the agglomeration advantage of large countries (Kind et al., 2000; Ludema
and Wooton, 2000; Andersson and Forslid, 2003; Baldwin and Krugman, 2004; Borck andPflüger, 2006).3 Large countries offer larger markets, which attract firms seeking to savetransportation costs of goods. This agglomeration tendency generates taxable rents thatallow large countries to set their tax rates higher than small countries while keeping industries.
However, some small countries with low tax rates have succeeded in attracting a huge
inflow of FDI into export-oriented industries where increasing returns to scale prevail, which
contradicts the prediction of the theory of tax competition in economic geography. For in1
The statutory corporate tax rates of these countries in 2013 were 12.5% (Ireland), 17% (Singapore), 21% (Estonia), 33.33% (France), 38.01% (Japan), and 40% (U.S.). Source: KPMG, Corporate tax rates table: http://www.kpmg.com/global/en/services/tax/tax-tools-and-resources/
pages/corporate-tax-rates-table.aspx
2
In addition to statutory tax rates, several studies find that small countries have a low effective tax rate,
defined as the ratio of taxes paid divided by profits. Grubert (2000), for example, examines the effect of theeffective tax rate on U.S. outward FDI in 60 countries between 1984 and 1992 and finds that small, open andpoor countries decreased their effective tax rates the most. In the context of Europe, Elschner and Vanborren(2009) report that the countries accounting for 10% or more of the total GDP of the EU27 have the highest
effective tax rates. However, it is fair to say that empirical studies are inconclusive as to whether effective
corporate tax rates in small countries are actually lower than those in large countries: see Devereux and
Loretz (2013) for an extensive survey.
3
Baldwin and Okubo (2014) obtain similar results in a heterogeneous firm model. This conclusion depends
on static settings of the game (simultaneous or sequential game), with which most of the studies deal. Kato
(2015) examines a tax game with an infinite time horizon and shows that rather than the initial condition,
whether governments commit to their policies is crucial for the consequence of tax competition.

2

stance, since the late 1970s, Ireland has hosted a number of multinational manufacturingfirms mainly in the computer, instrument engineering, pharmaceutical, and chemical industries, and these firms account for a large proportion of employment and output (Barry andBradley, 1997). In Irish manufacturing, the major target of which is foreign markets, foreign
multinational firms accounted for 91% of Ireland’s tradable exports in 2009.4 As for Singapore, policies including low tax rates and the liberalization of capital markets were basicallyfor the purpose of export-oriented industrialization, which turned out to be successful inattracting increasing-return industries such as electronics and biotechnology (Cahyadi et al.,2004). In recent years, by undertaking pro-market reforms after the end of Soviet control,
Estonia has established a competitive tax system and grown manufacturing exports rapidly
owing to the inflow of FDI in recent years (UNCTAD, 2011).
In order to explain the above observations, we examine tax competition between two
asymmetric countries for an oligopolistic industry. We then argue that the experience of
these countries can be attributed to the political bias of governments. It is worth stressing
three distinct features of the present model. First, unlike many previous studies that adopt
monopolistic competition with the Dixit-Stiglitz preference, we choose a model of oligopolisticcompetition as in Haufler and Wooton (2010) and Thisse (2010). This is because we can analyze a pro-competitive effect, i.e., goods’ prices being dependent on the number of firms, andcan furthermore obtain interior spatial outcomes (or partial agglomeration of firms), which
are in many cases hard to get in monopolistically competitive models. Second, two countries
are asymmetric in that population and capital endowments are larger in one country than in
another. Asymmetric country size allows us to investigate the relationship between country
size and tax rates. Third, capital owners engage in lobbying to extract favorable tax policies
from governments. Based on the political economy approach adopted by (Grossman andHelpman, 1994, 1995), the objective of governments is formulated in a way that they consider not only their domestic residents’ welfare, but also the political contributions by capitalowners when deciding their tax rate.5 Consequently, the resulting tax rates and distributionof firms are biased in favor of the interests of capital owners, which seems plausible in modern
society, where political pressure by firms influences policy decision-making processes.
Since the world today has experienced a huge reduction in trade barriers, tax policies
4“Foreign-owned firms accounted for 91% of Ireland’s tradeable exports in 2009; Food & drink exports fell
15%,” Finfacts Business News Centre, November 25, 2010; http://www.finfacts.ie/irishfinancenews/
article_1021094.shtml
5(Grossman and Helpman, 1994, 1995) rely on the common agency approach developed by Bernheim andWhinston (1986) and analyze trade policies in perfectly competitive models. More recent works apply thepolitical economy approach to the analysis of trade policies in imperfectly competitive models. See Chang(2005) and Bombardini (2008) for monopolistic competition and Paltseva (2014) for oligopolistic competition.

3

rather than trade policies are becoming a major concern for multinational companies indeveloped countries. The experience of Northern Ireland shows a case where lobbying may
determine tax policies. In 1997, the U.K. government started transferring some powers
from central to regional bases, which is a process known as devolution. Three parts of the
U.K., Scotland, Wales and Northern Ireland, were allowed to have a local assembly, butthey had to follow the corporate tax rate set by the central government. Business leadersin Northern Ireland, the region with the smallest population among the three, lobbied for afurther devolution of corporation tax-setting powers, claiming that a reduction in taxes was
the fastest way to stimulate the local economy.6 Northern Ireland eventually achieved thedevolvement of powers in 2014, and now plans to set the corporate tax rate much lower thanthe U.K.-wide rate.7
Another example can be found in the debate over the Common Consolidated Corporate
Tax Base (CCCTB) discussed in the European Commission. The CCCTB is aimed at (partially) harmonizing corporate tax system in EU, i.e., creating a single set of rules to calculate
profits of multinational firms. The proposal has been opposed mainly by small countries with
low tax corporate rates such as Ireland and Estonia (Arbak, 2008). In particular, Irelandbased multinational firms have lobbied the Irish government to support its position against
the proposal.8
The main result of our analysis is as follows. If two governments are mainly concernedwith contributions by their domestic capital owners, and the cost of shipping goods abroad
is low, tax competition leads firms in the large country to relocate to the small country. The
result implies that the home market effect (Helpman and Krugman, 1985), meaning that acountry with larger domestic demand hosts a more than proportionate share of firms, could
be reversed when considering a non-cooperative policy game between politically-interested
governments.9
To understand the intuition of the result, we look at the interests of capital owners in eachcountry who receive the after-tax profits of firms. Increasing taxes not only directly decrease
after-tax profits, but also indirectly affects them through changes in before-tax profits because
6“Leaders unite to lobby for NI corporation tax,” BBC News, November 30, 2010; http://www.bbc.
com/news/uk-northern-ireland-11863434
7“Northern Ireland welcomes cut to corporation tax,” Financial Times, November 24, 2015; https://www.ft.com/content/3b7757e0-91dd-11e5-94e6-c5413829caa5
8“Government believes EU corporate tax reforms will fail,” The Irish Times, August 17, 2017; https://www.irishtimes.com/business/government-believes-eu-corporate-tax-reforms-will-fail-1.
3188978
9
The reversal of the home market effect is obtained by several studies, including Robert-Nicoud andSbergami (2004), Yu (2005), Behrens and Picard (2007), and Wiberg (2011). However, they do not consider
policy competition, which is the focus of our analysis.

4

of the relocation of firms. The direct negative effect of taxes on after-tax profits clearlymotivates capital owners in both large and small countries to seek a lower tax rate, but
the impact of the indirect effect is different between the two asymmetric countries. If one
country increases its tax rate, some firms move to the other country. Such relocation reduces
domestic competition and in general raises the before-tax profits of the firms remaining in
the tax-raising country. This indirect positive effect on before-tax profits mitigates the direct
negative effect more effectively for firms in the large country than for those in the small
country. Since firms in the large country can take advantage of their rich domestic market
without incurring trade costs, they gain more from reduced competition in their domestic
market than do firms in the small country.
Thus, the overall negative effect of the increased tax rate on after-tax profits is more
pronounced in the small country, so that capital owners there are more eager to lower theirtax rate than are those in the large country. The resulting political pressure pushes the small
country to lower taxes more than the large country so that the small country may host agreater share of firms for its size. Our results are roughly consistent with the above-mentioned
observation.
A few exceptions in the literature obtain the reversal of the home market effect.10 Satoand Thisse (2007) and Miyagiwa and Sato (2014) introduce mechanisms that weaken themarket-size advantage of the large country. In Sato and Thisse (2007), agglomeration of firms
raises wages owing to a labor market-crowding effect, while in Miyagiwa and Sato (2014),
firms in a country face an entry cost that is increasing in accordance with the number offirms there. They show that the small country attracts more than a proportionate share offirms by setting a higher tax rate than the large country, which is opposite to our results.
Borck et al. (2012) consider external scale economies and characterize the conditions underwhich the small region, starting from the situation where it hosts all firms, prevents therelocation of firms to the large region. They show that the small region may defend its
industry by choosing a lower tax rate because it attempts to keep offering its residents highwages resulting from external local scale economies. While these previous studies modify thetechnology side, our model generalizes the form of government objectives while keeping thetechnology side as simple as possible.
This study is also related to the literature on tax competition in public finance.11 Using
10

In the literature on bidding for a single multinational (Haufler and Wooton, 1999), Ma and Raimondos(2015) introduce profit shifting motives for location choices and show that the small country may win tax
competition. Ma (2016) adopts the common agency approach and also shows the possibility of the small
country winning the bidding war.
11
Persson and Tabellini (1992), Lockwood and Makris (2006) and Haufler et al. (2008) examine the effectof capital mobility on tax rates. While they focus on voting mechanisms in perfectly competitive economies,5perfectly competitive models, Bucovetsky (1991) and Wilson (1991) show that the small
country attains a higher capital-labor ratio while charging a lower tax rate. In the context ofcommodity tax competition, Kanbur and Keen (1993) obtain a similar result. Their resultof the importance of being small comes from the fact that the small country faces a higher
elasticity of tax base. The contribution of this study is that it provides another rationale forthe advantage of small countries from different standpoints (i.e., agglomeration, oligopolisticcompetition and political economy) than those of the literature on tax competition using theneoclassical production function.12 In our model, the advantage of small countries resultsfrom their attractiveness to export-oriented firms. As shown empirically by Romalis (2007),
Ireland expands its exports more in capital-intensive industries, which can be subject toincreasing returns. Thus, we believe that our framework better explain the experiences ofsome small countries such as Ireland.
In the literature on tax competition using perfectly competitive models, political aspects
are highlighted by Lai (2014), who, as in our analysis, incorporates the common agency
approach into the standard tax competition model. He shows that the small country may
set a higher tax rate than the large country, unlike the models of Bucovetsky (1991), Wilson(1991) and ours.13 In contrast to his prediction, we investigate the mechanism yielding thepositive relationship between country size and tax rates.
The rest of the paper is organized as follows. Section 2 develops a simple general equilibrium model that induces agglomeration forces. Section 3 formulates tax competition with
political process. Section 4 characterizes the Nash equilibrium tax rates and the industry
allocation. The final section concludes the paper.

our emphasis is on lobbying mechanisms in the imperfect competitive model.
12
If one interprets the size of countries more generally, the advantage of being small could be found in theliterature on market-preserving federalism (Weingast, 1995; Qian and Weingast, 1997). The smaller powerof central government, i.e., the greater level of decentralization, prevents it from arbitrarily intervening
markets, making the country attractive to firms. Although the market-preserving federalism literature andour paper obtain a similar result, they give different implications for how governments should deal withlobbying. The literature emphasizes the autonomy and the independence of each levels of governments frompolitical pressure by any special interest groups. By contrast, our finding suggests that governments subject
to political pressure may take policies favorable to firms.
13
In a companion paper, Lai (2010) deals with tax competition between symmetric countries. Haaparanta(1996) also uses the common agency approach and models governments as lobbyists, By contrast, Lai (2010,2014) and we describe capital owners as lobbyists.

6

2

The Model

The economy consists of two unequal-sized countries, indexed by S (small) and B (big).
Each country has two factors of production; labor and capital. The two countries differ
in size and country S is assumed to have smaller shares of labor and capital. That is,
supposing that the world amount of labor is L and that of capital is K, country S has
LS = σS L and KS = σS K (σS < 1/2), while country B has LB = σB L and KB = σB K,
where σB ≡ 1 − σS .14 L is assumed to be sufficiently large to make the production of thenuméraire good possible and K is larger than two for the sake of consistency with oligopolisticcompetition. Since σi represents the country i ∈ {S, B}’s shares of world population andcapital, it can be interchangeably referred to as market share or capital share. Residents are
divided into two groups: workers and capital owners. Each worker has one unit of labor andeach capital owner has one unit of capital. We assume that the fraction of capital owners
among residents is negligible, and that they hold perfectly diversified portfolios that generate
the return λS rS + λB rB for one unit of capital, where λS ∈ (0, 1) (λB ≡ 1 − λS ) is the shareof capital (or firms) located in country S and ri is the (pre-tax) reward to capital invested
in i.15
There are two industries that produce different homogeneous goods: the modern sector(its quantity denoted by q) and the traditional sector (denoted by qo ). The modern sector ischaracterized by oligopolistic competition. One unit of capital as a fixed plant cost is needed
to set up a modern firm, which is the source of increasing returns. Firms play Cournot
competition in both domestic and foreign markets. By contrast, the traditional sector ischaracterized by perfect competition. We choose the traditional good as the numéraire.
Shipment of one unit of the modern good incurs an additional τ unit of trade costs, while
shipment of the traditional good incurs no such costs.
14
If we allow for the difference in capital-labor ratios, our main results, developed in Section 4, remainunchanged. See Appendix 1 for details.
15
Instead of assuming the ownership structure of firms, we can assume that capital owners invest theircapital in firms that offer the highest returns, i.e., the return is equal to max{rS , rB }. Under this alternative
assumption, the ownership structure is endogenously determined. For more on this point in a related context,
see Ferrett and Wooton (2010).

7

2.1

Demand Side

Resident in country i ∈ {S, B} share common preferences, and consume both the modern
and traditional goods. The utility of an individual in country i, ui , is given by
qi 
qi + qoi .
ui = 1 −2Aggregate utility of residents in country i, Ui , thus becomesQi
Ui = Li ui = 1 −Qi + Qoi ,
2Li

(1)

where Qi ≡ Li qi is the aggregate demand in country i for the modern good and Qoi ≡ Li qoi
is that for the traditional good. Given the price of the industrial good, denoted by pi , utility
maximization yields the (inverse) demand function for the good:pi = 1 − Qi /Li ,(2)

The demand curve in each country has the identical intercept, but its slope is flatter incountry B than in country S. Given the price, the large country demands more than thesmall country.

2.2

Supply SideIn the traditional sector, one unit of L produces one unit of output. Because of costless trade
and the choice of the numéraire, the price of the good in the two countries is equalized tounity. That is, letting poi be the price, we have po,S = po,B = 1. Constant returns to scale
production and the choice of units make the wage rates in both countries equal to the priceof the good, i.e., wS = wB = po = 1.
In the modern sector, after establishment, firms can produce without marginal costs andchoose different quantities to be sold in domestic and export markets. The operating profit
of a firm located in each country is given by:
πS = πSS + πSB ,= pS qSS + (pB − τ )qSB ,πB = πBS + πBB ,= (pS − τ )qBS + pB qBB ,8(3)

where πij denotes the profit of a firm based in i, earned from j, and qij represents the quantity
produced by a firm based in i, sold in j (i, j ∈ {S, B}). Since shipping the modern goods
is costly, trade costs τ > 0 are subtracted from the export price. One unit of capital builds
one firm so that the capital market clearing condition requires that the number of firms incountry S is λS K, and that in country B is λB K ≡ (1 − λS )K. The aggregate demand of acountry is met by the total supply by firms in both countries:
QS = λS KqSS + λB KqBS ,QB = λS KqSB + λB KqBB .
Each firm engages in Cournot competition in both domestic and foreign markets. Substituting the demand functions (2) into the operating profits (3) and taking the first orderconditions (FOCs) with respect to the quantity in both markets yield (see Appendix 2 fordetails):qSS = LS pS ,qSB = LB (pB − τ ),qBS = LS (pS − τ ),qBB = LB pB ,

(4)

where
pi =

1 + τ (1 − λi )K
.
K +1

(5)

The domestic price declines as the share of domestic firms increases and trade costs decrease.
Exporting is profitable for firms as long as the mill price pi −τ is positive. For international
trade to occur, trade costs must not be prohibitively high:τ <τ ≡

1
.
K +1

(6)

This inequality is assumed to hold throughout the analysis.
Substituting the equilibrium prices (5) and quantities (4) into the operating profits (3)gives:σS L [1 + τ (1 − λS )K]2 σB L [1 − τ {1 + (1 − λS )K}]2+,(K + 1)2(K + 1)2
σS L [1 − τ {1 + (1 − λB )K}]2 σB L[1 + τ (1 − λB )K]2
πB =+.
(K + 1)2(K + 1)2
πS =A competitive bidding by capital owners forces firms to earn zero excess profits so that the9operating profits are equal to the factor rewards to capital, i.e., ri = πi .
Although the share of firm λS is endogenously determined in the location equilibrium,
which will be discussed shortly, we treat it as an exogenous variable here in order to illustrate the relationship between the individual firm’s profit and the distribution of firms. The
marginal effect of an increased share of domestic firms on their profit depends on the marketsize:∂πii ∂πij∂πi2τ KLΓi Q 0 for i = S
=
,
+
=
∂λi
∂λi
∂λi
(K + 1)2 < 0 for i = B|{z} |{z}
(7)
<0

>0

where Γi ≡ 1 − 2σi − τ [1 − σi + (1 − λi )K],ΓS Q 0,ΓB < 0.

An expansion of domestic firms makes local competition tougher by declining the domestic
price (∂πii /∂λi < 0), while at the same time, it means a contraction of foreign firms, which
relaxes competition in the foreign market (∂πij /∂λi > 0). For firms in the large country,
the first negative effect always outweighs the second positive effect because changes in thenumber of firms make a stronger impact on profits from the large domestic market than on
those from the small foreign market (|∂πBB /∂λB | > |∂πBS /∂λB |). Thus, the overall effect,∂πB /∂λB , is negative. By contrast, the sign of ∂πS /∂λS is ambiguous. For firms in the small
country, profits from exporting to the large country may be affected more by changes in thenumber of firms than those from the small domestic market (|∂πSS /∂λS | < |∂πSB /∂λS |).
Especially when trade costs are low, a greater number of domestic rivals helps a firm in S toearn higher total profits (∂πS /∂λS > 0). The impact of increased competition on profits isquite different between firms based in the two asymmetric countries.

2.3

Location Equilibrium

Firms attempt to locate in a country that offers the highest profit, implying that the profits
in both countries must be equalized:
πS (λS ) = πB (λB ),as long as λS is in between zero and one. The above location equilibrium condition gives aunique distribution of firms:
λ̃S = σS −(1 − 2σS )[2 − τ (K + 1)]< σS .
2τ K
10

(8)

Taking into account the small size of country S (σS < 1/2) and the regularity condition for
trade costs (6), the second term is negative; therefore, it holds that λ̃S < σS . The firm’sshare in country S is smaller than its market (or capital) share. Namely, the small country
becomes the exporter of capital, while the large country becomes the importer. This result
is the so-called home market effect (Helpman and Krugman, 1985). The intuition behind
this is easy to grasp. Consider, to the contrary, the case in which each country hosts a
share of firms that equals its capital endowment, i.e., λS = σS . Locating in a large market
saves trade costs so that firms there earn more from exporting goods and obtain a higher
total profit (πS (λS = σS ) < πB (λB = σB )). Firms in the small country will move to thelarge country until the profit difference disappears. In equilibrium, the distribution of firms
becomes unequal in order to maintain the equalization of profits.
As can be seen in (8), a reduction in trade costs makes the distribution more unequal(dλ̃S /dτ > 0), and it is possible that all firms relocate to the large country when trade costs
are extremely low. To ensure interior spatial outcomes, trade costs are assumed not to be
too small:τ >τ ≡

2(1 − 2σS ).
K − 2σS + 1(9)Such a lowest level of trade costs in fact exists under the no-black-hole condition τ < τ
excluding the situation where agglomeration forces are too strong. This condition requiresthat country S should not be too small: σ ≡ (K + 1)/[2(2K + 1)] < σS < 1/2. If thecondition σS ≤ σ does not hold, country B always attains full agglomeration for all levels of
trade costs.
Finally, it is also worth mentioning the effect of reducing trade costs on prices. As seenfrom (5), a reduction in trade costs directly lowers the price and indirectly affects it throughchanges in the firm share. Since smaller trade costs magnify relocation from country S tocountry B, i.e., dλ̃S /dτ > 0, the indirect effect of reducing trade costs is negative for the pricein B, while it is positive for the price in S. However, the direct negative effect is dominanteven in country S so that smaller trade costs lead to lower prices in both countries.16

16

To see this formally, we havedpi
∂pi
∂pi dλiK + 2σi − 1
=
+
=
> 0,
dτ
∂τ
∂λi dτ
K +1

where we evaluate λi at the location equilibrium without taxes (λi = λ̃i : (8)).

113

Tax Competition by Politically-motivated Governments

This section introduces taxes and governments into the economy. Tax competition with
political pressure is analyzed in the following three-stage game. First, capital owners in eachcountry form a lobby as a special interest group and choose a contribution schedule that
depends on the domestic tax rate, given the tax rate of the foreign country. Second, eachgovernment receives contributions and non-cooperatively chooses their tax rate to maximize
its objective. Finally, relocation of firms occurs in response to the after-tax profit difference.
We solve the problem backward. The analysis of the first-stage game is delegated to Appendix
3.

3.1

Third-stage Game: Firm Location

The government in country i ∈ {S, B} imposes a lump-sum tax, Ti , on each firm locatedin country i.17 Tax rates are allowed to be negative. The location equilibrium requires theequalization of after-tax profits:
πS (λS ) − TS = πB (λB ) − TB = ρ.
The equilibrium share of firms depends on the tax difference:
λS (TS , TB ) = λ̃S −K +1(TS − TB ),2τ 2 KL(10)where λ̃S is the equilibrium share of firms when there are no governments defined in (8). The
higher the tax rate in a country, the fewer firms locate there. Collected tax revenues, Ti λi Ki ,are redistributed to the domestic residents.

3.2

Second-stage Game: Governments

To describe the objective of the governments, we compute the welfare of workers and capitalowners. From the assumptions that capital owners account for a sufficiently small fraction
17

If a profit tax takes an ad valorem form instead of a lump-sum form, our qualitative results would remainunchanged. This is because basic mechanisms (i.e., government incentives to tax) apply to both forms oftaxation, which will be discussed in the next section.

12

of the population, the welfare of capital owners in country i is simply represented as:
Wic = [λS (πS − TS ) + λB (πB − TB )]Ki
= (λS ρ + λB ρ)Ki
= ρKi .
From the first to the second line, we use the result of the third-stage game, i.e., πS (λS )−TS =πB (λB ) − TB = ρ.18 We assume that tax revenues are redistributed only to workers, notcapital owners. Allowing for transfer to capital owners do not change our main results. See
Appendix 6 for details.
The income of a worker consists of the wage paid to one unit of labor service in the
traditional sector, the redistribution of tax revenue and the endowment of the numéraire.
The individual budget constraint can be written as:pi qi + qoi = 1 + Ti λi K/Li + q o ,where q 0 is the initial endowment of the numéraire good and is assumed to be large enoughto ensure positive consumption of the good. The national budget constraint is obtained byaggregating the individual one across workers. By inserting this national budget constraint
into the aggregate utility (1) and evaluating it at the equilibrium quantities (4) and prices(5), the aggregate welfare of workers in country i is given by:
Wil = (CSi + 1)Li + Ti λi K + Qoi ,where Qoi = Li q o and CSi is the consumer surplus of an individual:2(1 − pi )2
1 1 + K{1 − τ (1 − λi )}
CSi =
=
.
2
2
K +1
The total welfare of residents in country i is thus Wi = Wic + Wil .
The problem of the governments is formulated as in Grossman and Helpman (1994, 1995).
18

Specifically, we substitute λS defined in (10) into πS − TS or πB − TB to get ρ:
TS + TB(TS − TB )2+,
2
4τ 2 L4(2 − τ )2 σS (1 − σS ) + (K + 1)2
where π ≡.
4τ 2 L(K + 1)
ρ=π−Under the alternative ownership structure stated in footnote 13, as we solve the problem backward, we also
have Wic = max{πS − TS , πB − TB }Ki = ρKi in the second-stage game.

13

The governments care about not only the welfare of their residents but also campaign contributions. We assume only capital owners can organize a lobbying group and make contributions C to their domestic government.19 This assumption relies on the argument ofcollective action by Olson (2009): small interest groups (capital owners) can overcome freerider problems more easily than large interest groups (workers) and take collective actions.20
The objective function of the government in country i is:
Gi (Ti ; Tj ) = αi Wi (Ti ; Tj ) + Ci (Ti ; Tj ),where αi denotes the weight that the governments place on their residents’ welfare relative
to contributions.
As a result of the first-stage game analyzed in Appendix 3, we can rewrite the government
objective as follows (ignoring constants):
Gi (Ti ; Tj ) = αi Wi (Ti ; Tj ) + 1 · Wic (Ti ; Tj ),= αi Wil (Ti ; Tj ) + (1 + αi )Wic (Ti ; Tj ).
Because of the presence of the “1”, the government objective is biased toward the interestof capital owners. This problem can be solved backward. Given the distribution of firms
defined in (10), we derive the FOCs of both governments by differentiating Gi with respect
to Ti given Tj :
dWil
dWic
dGi
= αi
+ (1 + αi )= 0 or
dTi
dTi
dTi

1 dGi
dWil
dWic
=
+ βi
= 0,
αi dTidTi
dTi

where βi ≡ (1+αi )/αi is a political weight attached to the interests of capital owners. Solving
the systems of equations yields equilibrium tax rates.

19

We do not allow for cross-border political donations (see e.g., Endoh, 2012 in the context of tariffcompetition). Some large countries, including the US, Canada, the UK, France and Japan, have laws against
foreign donations.
20
On the other hand, if workers are allowed to organize lobbies for taxes on their income (labor taxes), ourresults remain unchanged. To see this, suppose that each government imposes (lump-sum) labor taxes Til on
its workers. The aggregate welfare of workers is modified as:
Wil = (CSi + 1)Li + Ti λi Ki − Til Li .
The quasi-linear preference implies that labor taxes have no effect on industrial goods demand (the demand
curve (2) is unchanged). Therefore, labor taxes do not affect the location equilibrium of firms, which also
implies that capital owners do not have any incentive to lobby for labor taxes.

144Consequence of Tax Competition

We now turn to the analysis of equilibrium tax rates and assume here that the two governments attach an equal political weight βS = βB = β on the contributions. The assumption of common political weight is relaxed in Appendix 8. We impose a restriction
on β so as to satisfy the second-order condition of the maximization problem, such thatβ < β ≡ (4K + 3)/(2K).21

4.1

The Incentives of Governments

We show that (i) country S has a stronger incentive to lower taxes than country B and that(ii) this tendency is strengthened by the political weight β under low trade costs. To see
which country chooses a lower tax rate, we compute the difference of the marginal effect oftaxes on the government payoff as follows:
dWSc
dWSl
+β
−
dTS
dTS



dWBl
dWBc
+β
dTB
dTB


>0

z
}|
{
(1 − 2σS )[6 − τ (2βK + 3)] (TS − TB )[2(3 − β)K + 5]
−
=−
.
4τ
4τ 2 L{z}|<0

Under our assumptions that τ < τ and β < β, the first term is negative, while 2(3 − β)K + 5
in the second term is positive. In equilibrium, where the above formula equals zero, thesecond term must be positive, implying that TS < TB . As we have seen in Section 2.3, if
there are no taxes, firms attempt to locate in the large country to save trade costs. Thislocation advantage gives the large country B room to set higher tax rates, whereas the small
country S has to offer a lower tax rate to offset its location disadvantage. We note that even
if governments did not care about capital owners at all, i.e., β = 1, the small country would
have a lower tax rate.
In equilibrium, where TS − TB < 0 holds, an increase in TS decreases after-tax profits in
21

This is a sufficient condition for the second-order condition. That is, supposing that β < β holds, it holds
that (1/α)d2 GS /dTS = [(2βK + 1)σS − 4(K + 1)]/(4Lτ 2 ) < 0 for all σS ∈ (0, 1/2). An analogous expression
holds for country B.

15

the following way:!
dWScd(ρKS )
∂πS dλS
β
=β
= βKS
−1
dTS
dTS
∂λS dTS|{z} |{z}<0≶0TS − TB 1
= βKS
−
< 0,
2τ 2 L2(11)

where we note (7) for the sign of ∂πS /∂λS .22 Responding to the increased tax rate, firms
in country S move to country B (dλS /dTS < 0). The decreased number of firms in S may
increase the domestic profits of an individual firm remaining there because it makes themarket less competitive. Conversely, the movement of firms from S to B leads to tougher
competition in B and reduces the export profits of a firm remaining in S. Since the export
market is larger than the domestic market, firms in S may raise their total profit a little oreven reduce it as a result of the decreased number of domestic rivals (∂πS /∂λS > 0). Thus,
the increased tax rate always has a negative effect on after-tax profits.
A similar expression holds for country B:!
dWBc∂πB dλB
d(ρKB )
β
−1
=β
= βKB
dTB
dTB
∂λB dTB|{z} |{z}<0<01 TS − TB+= −βKBQ 0.
2
2τ 2 L(12)

In contrast to the case of country S, decreasing the number of domestic rivals always increases
the total profits of a firm in country B (∂πB /∂λB < 0). Because of the large size of country
B, gains from reduced competition in the domestic market B always exceed losses fromincreased competition in the foreign market S. Thus, an increase in TB has an ambiguous
effect on after-tax profits (dρ/dTB Q 0). Especially when trade costs are small, firms become
more sensitive to the increased tax rate, resulting in a greater outflow of firms from B to A.
22

In the text, we use ρ = πS − TS for the sake of explanation. However, as ρ = πS − TS = πB − TB holds,
we note the following:βd(ρKS )
d[(πB − TB )KS ]∂πB dλS
=β
= βKS
dTS
dTS
∂λ dTS| {zS} |{z}
>0


= βKS

16

<0

TS − TB
1−
2τ 2 L2< 0.

In this case, the degree of competition in B is greatly reduced so that the after-tax profit
increases.
When (11) is negative and (12) is positive under low trade costs, as a result of considering
the interests of capital owners, the small country prefers lower taxes, while the large country
prefers higher taxes. As both governments care more about their capital owners, i.e., higher
β (care less about their workers, strictly speaking), their direction of incentives becomes moredivergent and the tax difference widens.

4.2

Tax Rates and Firm Distribution in Equilibrium

We solve the FOCs of both countries as a system of equations for tax rates (see Appendix 4
for details):
Ti∗ =

"
#
βτ
2−τ
τ L(1 − 2σi )Θ∗i
τ KL
τ
−
−
−
,
K + 1 |{z} | {z2} 4(K + 1)
4(K + 1)2 [2(3 − β)K + 5]
(a)
|
{z
} |
{z
}
(b)

(c)

(13)

(d)

where Θ∗i is a positive bundling parameter that includes β, K, σS and τ . Both TS∗ and TB∗
can be positive or negative.
Supposing that the two countries are identical in size (σS = 1/2) and only the big bracket
term in (13) is left, the equilibrium tax rates and the distribution of firms become symmetric.
Each term in the bracket term (partly) represents the consideration of each component of
the government’s objective (see Appendix 5 for details). The first positive term (a) in thebracket comes from a tax-revenue effect, which means that governments can exploit location
rents of incumbent firms. The second negative term (b), which we call a profit-income effect,reflects the fact that governments seek to lessen the direct burden of tax incidence on capitalowners. The profit-income effect is reinforced by the political weight β. The third negative
term (c), resulting from a consumer-surplus effect, reflects the motivation of governments to
attract firms so as to decrease the consumer price.
If the two countries differ in size, the second fractional term (d) in (13), which we call amarket-size effect, appears, and the tax rates and the industrial configuration are no longer
symmetric. The market-size effect incorporates all of the impacts resulting from the differencein market size and modifies the three effects mentioned above. The market-size effect for TS∗
is negative whereas that for TB∗ is positive.23 Owing to the firms’ motives of locating a larger
market for saving trade costs, country B can levy a higher tax rate than country S.
23

Note that Θ∗i and the denominators of the fractional term are positive under β ∈ [1, β).

17The difference in the tax rates is given by:TS∗ − TB∗ = −τ L(1 − 2σS )[6 − τ (2βK + 3)]< 0.
2(3 − β)K + 5(14)

The regularity condition on trade costs (6) ensures that the square bracket in the numeratorof (14) is positive. It turns out that country S always sets a lower tax rate than country B.
Furthermore, a higher political weight in general leads to lower taxes, as shown in Figure 1.
There may be a case where, as the weight gets higher, the large country raises its tax rate if
raising taxes causes massive capital outflow from the country, thereby bringing huge profits
to domestic firms.
Combining the tax differential defined above with the location equilibrium condition (10)gives:
λ∗S = σS −(1 − 2σS )[K + 2 − τ (K + 1)2 − 2(β − 1)K{1 − τ (K + 1)}],
τ K[2(3 − β)K + 5]

(15)

where the denominator of the second term is positive under β ∈ [1, β). Our assumptions
ensure that λ∗S lies between zero and one.
Consider first the case of benevolent governments, i.e., β = 1. It is verified that the
distribution of firms in country S under the lobbying-free governments, denoted by λnS , isgreater than the distribution under no taxes, i.e., λnS > λ̃S , because country S chooses alower tax rate. However, the firm share is smaller than the market share, i.e., λnS < σS ,because of the home market effect. The fact that the home market effect still prevails undertax competition is consistent with previous studies such as Haufler and Wooton (2010).
Consider then the case of politically-biased governments, i.e., β > 1. Whether country
S exports or imports capital depends on the sign of the second term in (15). Let β ∗ be thecritical value that changes the sign:β∗ ≡3K + 2 − τ (K + 1)(3K + 1).
2K[1 − τ (K + 1)]

We can confirm that β ∗ is smaller than the upper bound β when:τ < τ∗ ≡1.
K +2

If the political weight is small (β < β ∗ ) and/or trade costs are high (τ > τ ∗ ), the second
term in (15) is negative, which means that the share of firms in country S is smaller than18

its market share (λ∗S < σS ). Tax competition played by relatively benevolent governments
gives the qualitatively same results as those in the lobbying-free case. Higher trade costs alsopreserve the advantage of the large country by enhancing the incentives of firms to relocate
to the large market to save trade costs.
On the other hand, if the political weight is high (β > β ∗ ) and trade costs are low (τ < τ ∗ ),the direction of capital flow becomes opposite; we can observe a reversal of the home market
effect (λ∗S > σS ). If both governments deeply care about the capital owners, they determine
their tax rates to realize the industrial configuration in favor of profit income owned bycapital owners. As a result, the small country chooses a lower tax rate and imports capitalwhile the large country chooses a higher rate and becomes a capital exporter, contrary towhat the home market effect suggests. For the reverse home market effect to emerge, trade
costs should be small enough for firms in S to make exporting fairly profitable compared toserving the domestic market.
These findings are summarized in
Proposition. Consider tax competition between the politically-motivated governments with
common political weight β ∈ [1, β). Assume that country S is small (σS ∈ (σ, 1/2)) andτ ∈ (τ , τ ) holds. Then two cases may arise:(i) if the political weight is small (β < β ∗ ) and/or trade costs are large (τ > τ ∗ ), country S
hosts a smaller share of firms than its market share (λ∗S < σS ).
(ii) if the political weight is large (β > β ∗ ) and trade costs are small (τ < τ ∗ ), country S
hosts a larger share of firms than its market share (the reverse home market effect: λ∗S > σS ).
In both cases, the tax rate of country S is always lower than that of country B (TS∗ < TB∗ ).
In the case of no taxes, we have seen that a reduction in trade costs lowers prices inboth countries. It can be verified that this generally holds true in this tax-competition case.
However, if the political weight is sufficiently high, freer trade leads to a higher price incountry B (dpB /dτ < 0).24 Lower trade costs accelerate relocation from the large to thesmall country so that the reducing share of firms in the large country may result in a higher
price there.
24

To check this, we havedpS
σS (3K + 2) + 3K 2 + K − 1 − 2βK(σS K + 2σS − 1)
=
> 0,
dτ
(K + 1)(6K + 5 − 2βK)
dpB
(K + 1)(3K + 1) − σS (3K + 2) − 2βK[K + 1 − σS (K + 2)]
=
R 0.
dτ
(K + 1)(6K + 5 − 2βK)

dpB /dτ < 0 holds at β close to β.

19The reversal of the home market effect is illustrated in the range β ∈ (β ∗ , β) in Figure
2. Country S attracts more firms as the governments put more emphasis on the interestsof capital owners.25 The result may explain well the fact that small countries with lower
corporate tax rates have succeeded better in attracting FDI than large countries with higher
rates.26
We relax the assumption of common political weight and consider asymmetric politicalweight in Appendix 8. Since having a higher political weight leads governments to choose
lower tax rates, it is natural to see that if two countries have the same size, the country witha higher political weight attracts a larger share of firms than its market share. If the small
country has a higher weight than the large country, the reverse home market is observedin a wide range of parameters. The central implication of our analysis holds in the general
setting.
Welfare implications are discussed in Appendix 7.

Figure 1.

The equilibrium tax rates and the political weight.

To check this formally, it is verified that dλ∗S /dβ = −Ψd(TS∗ − TB∗ )/dβ > 0 for all τ ∈ (τ , 3/(3K + 4))
where Ψ ≡ (K + 1)/2τ 2 KL > 0. Since τ ∗ < 3/(3K + 4) holds, we have dλ∗S /dβ > 0 when the reverse homemarket effect prevails (β > β ∗ and τ < τ ∗ ).
26
Although many empirical studies on the protection-for-sale model obtain rather low estimates of politicalweight β (Goldberg and Maggi, 1999; Gawande and Bandyopadhyay, 2000), there are several studies thatobtain fairly high estimates of β (Gawande et al., 2012) or report mixed results (McCalman, 2004).
25

20

Figure 2.

5

The equilibrium share of firms and the political weight.

Conclusion

This study has analyzed a tax game between two countries of asymmetric size taking thelobbying activities of capital owners into account. It was shown that if the governments
are sufficiently biased toward the interests of capital owners and trade costs are low, thesmall country attracts a more than proportionate share of firms (the reverse home market
effect). Capital owners lobby for governments in order to raise after-tax profits, which responddifferently to tax changes in the small country compared with those in the large country.
Increasing taxes in the small country always reduces after-tax profits, whereas increasing
taxes in the large country reduces after-tax profits by less or may even raise it. Therefore,
government biased toward capital owners in the small (large) country tend to have lower(higher) taxes. If the political bias is strong and trade costs are low, the tax difference
between the two countries is so wide that the small country hosts a greater share of firms thanits market share. This reverse home market effect provides new insight into the literature of
agglomeration and tax competition, which concludes that the larger market size and/or initial
location advantage are crucial for determining the winner of competition. The implicationthat a smaller market size can be attractive to firms when considering politically-biased
governments may help provide a better understanding of how tax competition works in thereal world.

21

Appendices
Appendix 1:

Capital-labor Ratios

In the text, the country i’s world share of population is equal to its world share of capital.
Our main result is unchanged if we allow the capital-labor ratio to differ between countries.
Let σiL (σiK ) denote the world share of population (capital) in country i ∈ {S, B}. Country S is assumed to be smaller than country B in terms of both population and capital:
max{σSL , σSK } < min{σBL , σBK }.
We focus on the case where the share of population in country S is larger than its shareof capital, i.e., σSL > σSK . As σBL = 1 − σSL and σBK = 1 − σSK hold, the inequality σSL > σSK
implies that σBL < σBK . Combining these two inequalities yield the following relationship:
σBK
σSK
<
1
<
,
σSL
σBL
which states that country S has a smaller capital-labor ratio than country B. Country S issmall in terms of the three measures, i.e., the share of population, the share of capital, andthe capital-labor ratio.
Noting that σiL does enter the profit function of firms but σiK does not, we replace σi in(13), (14) and (15) with σiL . Accordingly, Proposition holds if σi is replaced with σiL . If theconditions in Proposition (ii) hold, we have:σSK < σSL < λ∗S ,λ∗B < σBL < σBK .
Our main result of the reverse home market effect holds for the three measures of country
size.

Appendix 2:

Derivation of Equilibrium Quantities andPrices
We show the details of derivations of (4) and (5) in the text. Only variables for country S
are concerned and symmetric expressions hold for country B. Using the demand function22

defined in (2), the operating profit of a firm in country S defined in (3) can be re-written as:
πS = (1 − QS /LS ) qSS + (1 − QB /LB − τ ) qSB .
The firm chooses qSS and qSB to maximize πS . The FOCs are given by:
dπS= −qSS /LS + 1 − QS /LS
dqSS= −qSS /LS + pS = 0,dπS
= −qSB /LB + 1 − QB /LB − τdqSB= −qSB /LB + pB − τ = 0,
where we assume that dQS /dqSS = dQB /dqSB = 1. Rearranging these terms gives qSS =LS pS and qSB = LB (pB − τ ) as in (4).
The equilibrium price clears the goods market in country S. We substitute the equilibrium
quantities into the market clearing condition to get the equilibrium price:
QS = λS K · qSS + λB K · qBS ,→ LS (1 − pS ) = λS K · LS pS + λB K · LS (pS − τ ),→ 1 − pS = KpS − τ KλB ,1 + τ λB K
→ pS =.
K +1

Appendix 3:First-stage GameAt the first stage of the game between governments and capital owners, capital owners in eachcountry propose a contribution schedule to maximize their payoffs net of the contribution.
The problem of capital owners as a interest group in country i is formulated as:
max Wic (Ti ; Tj ) − Ci (Ti ; Tj ),Ci (Ti ;Tj )s.t. max Gi (Ti ; Tj ) = max [αi Wi (Ti ; Tj ) + Ci (Ti ; Tj )] ≥ Gi ,
Ti

Ti

23

where the second line is a participation constraint of the government in country i and Gi =αi W i is the government’s payoff under no contributions. Following Grossman and Helpman(1995), we assume that the contract between a interest group and a government in one
country is implicit and thus unobservable in the other.
With the participation constraint holding equality, the interest group prefers a tax ratethat maximizes its payoff:
max Wic (Ti ; Tj ) − {Gi − αi Wi (Ti ; Tj )}Ti= max αi Wil (Ti ; Tj ) + (1 + αi )Wic (Ti ; Tj ) .
Ti

The FOC is given by
αi

dWic
dWil
+ (1 + αi )
= 0.
dTi
dTi

Let the tax rate determined by the FOC be Ti∗ = Ti∗ (Tj ). The interest group attempts togive a minimum amount of contributions so as to make their government choose Ti∗ . Thus,
the contribution schedule becomes Ci (Ti ; Tj ) = Wic (Ti ; Tj ) − [Gi (Ti∗ ) − Gi ].
A few comments are in order. As there is only one interest group (i.e., one principal)
in each country, the problem is a special case of the common agency problem analyzed by
Bernheim and Whinston (1986).
Putting a political weight on the welfare of residents, rather than contributions, causes a
conceptual problem, although it does not affect the analysis of the later stages of the game.
In doing so, from Proposition. 1(c) in Grossman and Helpman (1994), the equilibrium tax
rate must maximize the joint profit of the interest group and the government, which is given
as follows:
Wic (Ti ; Tj ) − Ci (Ti ; Tj ) + Wi (Ti ; Tj ) + αi Ci (Ti ; Tj ).
As αi 6= 1 in general, the contribution term Ci does not disappear. It is optimal for theinterest group to set an extreme contribution schedule (Ci = ∞ or −∞) to maximize thejoint payoff, in which case we cannot have interior equilibria and are unable to use the FOC
defined above.

24Appendix 4:

Derivation of Equilibrium Tax Rates

Consider the general case where two countries differ in size and political weight. From the
FOCs (1/αi )dGi /dTi = 0, we obtain the following best response function for each government:σS (2K + 1) − 4(K + 1) + 2σS K(βS − 1)
σS (2K + 1) − 2(K + 1) + 2σS K(βS − 1)
TS −
TB
2
4τ L
4τ 2 L2τ (1 − s)K 2 − (5σS τ − 4τ − 6σS + 4)K + (1 − 2σS )(2 − σS )(2 − τ ) σS K(βS − 1)=−+,4τ (K + 1)
2
(A.1)
σS (2K + 1) + 2K + 3 − 2K(1 − σS )(βB − 1)
σS (2K + 1) + 1 − 2K(1 − σS )(βB − 1)
TS −
TB
2
4τ L
4τ 2 L2σS τ K 2 + (5σS τ − τ + 6σS + 2)K + (1 − 2σS )(σS + 1)(2 − τ ) K(1 − σS )(βB − 1)=−+,4τ (K + 1)2
(A.2)
where (A.1) is the best response function for government S and (A.2) for government B.
Politically-motivated Governments with Symmetric Political Weight.
We first consider
the case where both governments place an equal weight on their contributions. Imposing
βS = βB = β on (A.1) and (A.2) and solving the system of equation, we obtain the following
equilibrium tax rates:


τ KL
2−τ
βτ
τ L(1 − 2σS )Θ∗S
−
,
τ−
−
K +1
2
4(K + 1)4(K + 1)2 [2(3 − β)K + 5]


τ KL
2−τ
βτ
τ L(1 − 2σS )Θ∗B
∗
TB =
−
,
τ−
+
K +1
2
4(K + 1)4(K + 1)2 [2(3 − β)K + 5]TS∗ =Θ∗S ≡ δσS + ,Θ∗B ≡ δ(1 − σS ) + ,δ ≡ −2[4K 2 (K + 1)β 2 − 2K(4K + 5)β + 3K + 4]τ + 4[2βK(3K + 4) − (3K + 2)], ≡ [4K 2 (K + 1)β 2 − 2K(2K 2 − 3)β − (6K 2 + 15K + 8)]τ − 4K(3K + 4)β + 2(6K 2 + 15K + 8),
as given by (13). δ and  can be negative.
Politically-motivated Governments with Asymmetric Political Weight.
In the general casewhere the political weights are different in countries, we get the following equilibrium tax

25

rates from FOCs (A.1) and (A.2):
TS∗∗ =



τ KL
βS τ
2−τ
τ−
−
K +1
2
4(K + 1)

τ L(1 − 2σS )Θ∗∗S−,
2
4(K + 1) [{6 − (βS + βB )}K + 5][2{3 − (βS σS + βB (1 − σS ))}K + 5]


τ KL
βB τ
2−τ
∗∗
TB =
τ−
−
K +1
2
4(K + 1)
τ L(1 − 2σS )Θ∗∗B+,
4(K + 1)2 [{6 − (βS + βB )}K + 5][2{3 − (βS σS + βB (1 − σS ))}K + 5]2
Θ∗∗S ≡ ζσS + ησS + θ,2Θ∗∗B ≡ ζ(1 − σS ) + η(1 − σS ) + ι,

ζ ≡ 4K(βS − βB )(2 − τ )[{6 − (βS − βB )}K + 5],η ≡ −2[{6 − (βS + βB )}K + 5]× [4βS βB τ K 3 + 2{4(βS + βB + βS βB ) − 3(βS + βB )}K 2 . . .
· · · + {(3βS + 7βB − 3)τ + 2(3 − 6βB − 2βS )}K + 2(2 − τ )],θ ≡ −8τ (6βS − 3βB − 4βS βB + βS βB2 )K 4
− [4(31β1 − 29βB − 13βS βB + 2βS βB2 + 2βB2 + 9)τ + 12(βB − 1)(6 − βS − βB )]K 3+ 2[(84βB − 51βS + 9βS βB − 5βB2 − 60)τ + 8βS βB − 93βB − 15βS + 8βB2 + 120]K 2+ [(73βB − 27βS − 123)τ + 2{123 − 8(βS + 6βB )}]K + 40(2 − τ ),ι ≡ θ − 2K(βS − βB )[4τ (βS βB − 9)K 3 + 2{2(βS + βB + βS βB − 30)τ + 3(6 − (βS + βB ))}K 2+ {4σS (σS − 1)(6 − (βS + βB ))(2 − τ ) + (5(βS + βB ) − 135)τ + 2(39 − 4(βS + βB ))}K
+ 40(σS2 − σS + 1) − 10(2σS2 − 2σS + 5)τ ],which are reduced to (13) if βS = βB = β. The tax differential and the resulting distributionof firms become:TS∗∗ − TB∗∗ = −τ L[2τ K{βS σS − βB (1 − σS )} + 3(3σS τ − 4σS − τ + 2)],
2[{3 − (βS σS + βB (1 − σS ))}K + 5]

λ∗∗S = (num)/(den),(num) ≡ 2K[βS σS (σS τ − 2σS + 1) + β2 (1 − σS )(σS τ − 2σS − τ − τ K + 1)] . . .

· · · + (3K + 2)[(2 − τ )σS − 1] + (K + 1)(3K + 1)τ ,(den) ≡ τ K[{6 − (βS σS + βB (1 − σS ))}K + 5].

26

We use λ∗∗S for the simulation analysis in Appendix 7.

Appendix 5:

Three Effects on Tax Rates

We show that the equilibrium tax rates can be decomposed into three effects, namely, theconsumer-surplus effect, the profit-income effect and the tax-revenue effect as explored in
Section 4.2. For the sake of illustration, we restrict our attention to the no-lobbying case andput weights ωCS and ωπ on the corresponding components of welfare:
Wi = ωCS CSi Li + ωπ (πi − Ti )Ki + Ti λi K,i ∈ {S, B}.

Suppose σS = 1/2, where the market-size effect does not emerge, we can compute equilibriumtax rates as follows:ωCS (2 − τ )
ωπ τ
4τ KL
−
τ−
.
TS = TB =K +1
2
4(K + 1)
If the government solely care about the tax revenue, the two weights are zero (ωCS = ωπ = 0)
and only the first term (τ ) in the square bracket remains, which we call a tax-revenue effect.
Clearly, the second term (−ωπ τ /2) and the third term (−ωCS (2 − τ )/[4(K + 1)]) come fromthe after-tax profit income ((πi −Ti )Ki ) and from the consumer surplus (CSi Li ), respectively.
Hence, we name the second term a profit-income effect and the third term a consumer-surplus
effect.

Appendix 6:

Redistribution of tax revenues to capitalownersIn the text, taxes collected from capital owners are assumed to be transferred to workers,
not to capital owners. If we allow for the transfer to capital owners as well as workers, we
obtain the qualitatively same results.
Supposing that in each country, 100 · γ% of tax revenues are redistributed to residents,
while the remaining 100 · (1 − γ)% of them are to capital owners, where γ ∈ [0, 1] represents
an exogenously given share. The aggregate welfare of each group in country i ∈ {S, B} can27be re-written as
Wil = (CSi + 1)Li + γTi λi K + Qoi ,Wic = [λS (πS − TS ) + λB (πB − TB )]Ki + (1 − γ)Ti λi K.
As a result of tax competition, the equilibrium share of firms is given by(1 − 2σS )Φ
,τ ΩKΩ ≡ 2β[2K + 3 − 3γ(K + 1)] + 6γ(K + 1) − 1 > 0,λ∗∗∗
S = σS +Φ ≡ Φ1 β + Φ0 ,
Φ1 ≡ τ (K + 1)[K + 1 − γ(3K + 1)] + 2[γ(K + 1) − 1],Φ0 ≡ γτ (K + 1)(3K + 1) − 2γ(K + 1) − K < 0.
We note that Φ1 > 0 holds if τ > τ ∗∗∗ ≡ min{τ , 1/(K + 1)2 }, where τ ≡ 2(1 − 2σS )/(K −2σS + 1) as defined in the text.
It can be verified that under small trade costs, i.e., τ ∗∗∗ < τ < τ ∗∗∗ ≡ 2/(3K + 1), thefirm share in country S exceeds its market share if the political weight is high:β > β ∗∗∗ ≡ −Φ0 /Φ1 ,→ λ∗∗∗
S > σS ,confirming the reverse-home-market effect. If the political weight is small (β < β ∗∗∗ ) and/or
trade costs are large (τ > τ ∗∗∗ ), country S hosts a smaller share of firms than its market
share, i.e., λ∗∗∗S < σS . The main message of Proposition is unchanged.
It can also be seen that under small trade costs (τ < τ ∗∗∗ ), an increase in γ reduces thethreshold, i.e., dβ ∗∗∗ /dγ < 0. Put it differently, as capital owners get more redistribution(γ ⇓), the reverse-home-market is less likely to be observed (i.e., the required condition istightened: β ∗∗∗ ⇑). As discussed in Section 4.2, once the tax-revenue effect comes in, capitalowners in both countries prefer a higher tax rate. Then the equilibrium tax gap becomesnarrower, reducing relocation from country B to country S.

28

Appendix 7:

Welfare Analysis

This appendix examines welfare implications. We compare the socially desirable outcome tothat under tax competition. We consider a social planner who chooses the industry allocation
λS to maximize the sum of national welfare of the two countries W ≡ WS + WB . The social
planner implements the policy through lump-sum transfers among agents while taking asgiven the equilibrium market prices (5) and quantities (4).
Figure A1 shows the global welfare along with the distribution of firms that attains the optimum λoS , the one under benevolent governments λnS and the one under politically-interested
governments λ∗S . λnS is larger than λoS , meaning that tax competition played by lobbying-freegovernments leads to an excessive tax gap and thus to a more equalized distribution. Thiscan be explained by international externalities resulting from market size asymmetry. Under
lobbying-free governments, country B hosts some fraction of foreign capital from country S
as well as its domestic capital. Thus, the taxes imposed by B affect the reward to capitalcoming from S, as well as the reward to domestic capital. Because there is a negative externality from B to S and a positive externality from S to B, country S chooses a tax ratethat is too low, while country B charges a tax rate that is too high from the global welfare
point of view. The large tax difference generates arbitrage opportunities for capital owners
and consequently yields an inefficiently equalized distribution.
As we have seen in the previous sections, the relationship between λnS and λ∗S is clear:when the governments are heavily biased in favor of capital owners and trade barriers are
low, λ∗S is greater than σS (> λnS ) and the more so, the higher political weight β.
We summarize this as follows:
The equilibrium share of firms where the reverse home market effect is prevailing is moresocially inefficient than that under benevolent governments (λoS < λnS < σS < λ∗S ).

29

Figure A1.

Global welfare.

Derivations.
Quasi-linear preferences imply that the sum of the two countries’ indirect
utilities consists the global welfare as follows (ignoring constants):
W (λS ) ≡ WS (λS ) + WB (λB ≡ 1 − λS )= [σS CSS (λ1 ) + (1 − σS )CSB (λS )]L + [πS (λS ) − TS ]KS + [πB (λS ) − TB ]KB+ TS λS K + TB (1 − λS )K= [σS CSS (λS ) + (1 − σS )CSB (λS )]L+ [{πS (λS ) − TS } − {πB (λS ) − TB }](σS − λS )K + πS (λS )λS K + πB (λS )(1 − λS )K= [σS CSS (λS ) + (1 − σS )CSB (λS )]L + πS (λS )λS K + πB (λS )(1 − λS )K.
From the third line to the forth, we use the fact that πS − TS = πB − TB . Solving the FOCof the social planner’s problem for λS gives the globally optimal level of industry allocation:
λoS = σS −(1 − 2σS )[K + 2 − τ (K + 1)2 ].
τ K(2K + 3)

We can check that the second-order condition trivially holds: d2 W/dλ2S = −τ 2 K 2 L(2K +3)/(K + 1)2 < 0. We have λoS < λnS for all τ ∈ (τ , τ ) and λnS < λ∗S for all τ ∈ (τ , τ ∗ ).
Therefore, when the reverse home market effect is dominant (β > β ∗ and τ ∈ (τ , τ ∗ )), we
order the spatial outcomes in this way: λoS < λnS < λ∗S .
Additionally, we can compute the tax differential to replicate λoS from the location equi-30librium condition (10):K +1 o(T − TBo )2τ 2 KL S
τ L(1 − 2σS )(2 − τ )or TSo − TBo = −,2K + 3λoS = λ̃S −where λ̃S is defined in (8) and the absolute levels of taxation are indeterminate. Comparing
this to the tax differential under benevolent governments gives|TSn − TBn | − |TSo − TBo | =4τ KL(β − 1)(1 − 2σS )[3 − τ (3K + 4)],(4K + 5)[2(3 − β)K + 5]

which is positive when τ ∈ (τ , τ ∗ ) holds.
By noting that d|TS∗ − TB∗ |/dβ = −d(TS∗ − TB∗ )/dβ = Φ(1 − 2σS )[3 − τ (3K + 4)] > 0 forτ ∈ (τ , 3/(3K + 4)) where Φ ≡ 4τ KL(1 − 2σS )/[2(3 − β)K + 5]2 > 0, we have |TSo − TBo | <|TSn − TBn | < |TS∗ − TB∗ | for τ ∈ (τ , τ ∗ ).

Appendix 8:

Asymmetric Political Weight

Our main analysis assumed that the political weight is common to the two governments,
i.e., βS = βB = β. Here, we allow for the asymmetry of the weight and confirm that our
main result of the reverse home market effect still holds. In order to single out the effect ofdifferent political weights, we first analyze the case of symmetric market size, i.e., σS = 1/2.
The equilibrium tax rate in country i ∈ {S, B} is given by:Ti∗∗ =



τ KL
βi τ
2−τ
τ−
−
.
K +1
2
4(K + 1)The profit-income effect, the second term in the square bracket, reflects the asymmetricweight and is stronger as the weight gets higher. The tax differential becomes:TS∗∗ − TB∗∗ = −τ 2 KL(βS − βB ).
[6 − (βS + βB )]K + 5

Since the denominator is positive as long as βi < β holds as we have assumed in the previous
analysis. the tax difference is negative if βS > βB . The government with a higher weight setsa lower tax rate so as to reduce the direct tax burden on capital owners.

31

Since there is no market-size effect and thus only the tax differential matters for theindustrial configuration, the more politically-motivated government choosing a lower tax
rate attracts more firms than its market share:
λ∗∗
S =

1
(K + 1)(βS − βB )+> σS ,
2 2[{6 − (βS + βB )}K + 5]

as long as βS > βB holds.
Having made clear the role of asymmetric political weights, we then consider the mostgeneral situation where both country size and weights are asymmetric. Since it is hard toanalytically characterize the conditions that make the home market effect reversed, we rely
on numerical simulations.
Figures. A2 and A3 show the equilibrium share of firms based in country S (z-axis) for
various levels of political weights along with the horizontal plane representing the country
S’s size: σS = 0.4. Other parameter values are K = 3; τ = 0.25 for Figure A2 and K = 3;
τ = 0.14 for Figure. A3, respectively. The diagonal line linking the north corner to thesouth corresponds to the case of symmetric weight. As βS moves from low to high given a
particular level of βB , the share of firms based in country S increases. Moreover, country
S with a higher political weight is likely to host a more than proportionate share of firms(λ∗∗S > σS ). The emergence of the reverse home market effect remains unchanged in thegeneral situation.

Figure A2.

Equilibrium share of firms when trade costs are high.

32

Figure A3.

Equilibrium share of firms when trade costs are low.

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