Corporate Tax Systems and the Location of Industry.pdf

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Corporate Tax Systems and the Location of
Industry
Magnus Wiberg∗
April 14, 2010
Abstract
This paper analyzes the effects of different corporate tax systems
on the location of industry within an economic geography model with
regional size asymmetries. Both the North and the South gain indus-
try by adopting a tax regime that produces the lowest tax level. As
the share of expenditures in the North increases, the Nash equilibrium
has this region setting regressive taxes, while the South introduces
progressive taxation. The unilateral welfare-maximizing tax structure
in the North (South) is the regressive (progressive) system when ex-
penditures in the North increase. Welfare in the North (South) is
however maximized if both regions set regressive (progressive) taxes,
while regressive (progressive) taxation in both regions represents a
joint welfare maximizing outcome if the economic size of the North is
higher (lower) than a certain threshold value. As trade is liberalized,
the equilibrium tax regime adopted depends on how profits respond
to lower trade costs. Proportional taxation is never an equilibrium,
neither as regional spending changes, nor as trade is liberalized.
Keywords: Economic Geography; Tax Systems; Corporate Taxation
JEL Classification: F12; H25; R12
∗This paper was written when the author was visiting the Department of Economics,
Harvard University, Littauer Center, 1805 Cambridge Street, Cambridge, MA 02138. Cur-
rent affiliation: Swedish Government Offices. SE-103 33 Stockholm, Sweden. E-mail:
magnus.wiberg@finance.ministry.se. Phone: 0046 737 27 12 24.
1 Introduction and Related Literature
There is an extensive line of theoretical and empirical research which exam-
ines the effects of corporate taxation levels on industry location in an inter-
national setting. At the same time, there are many differing views about
the social and economic impacts of the corporate income tax structure, but
few or no studies of how different tax systems interact with the location
decisions of firms in the international economy. Given that suggestions to
reform the tax structure are regularly made, it appears like an important re-
search direction to consider how corporate tax systems affect the location of
economic activity. The current paper investigates the effects of progressive,
proportional, and regressive corporate taxation on industry agglomeration.
Most countries have a mixture of progressive and regressive taxes, both
because different principles of fairness are applied to different taxes and be-
cause of different levels of government (Graddy et al., 2008). Porcano (1986)
argues that although the U.S. corporate income tax rate essentially is defined
to be progressive at low income levels (up to the first USD 335,000 of tax-
able income), and proportional on taxable income for large firms (producing
a flat tax rate of 35 percent on a corporation’s entire taxable income once it
exceeds USD 18.33 million), effectively it is regressive and very low.1
In fact, local governments generally do not make much effort to apply
progressive taxation principles. The reason is that they are subject to tax
competition—a local government that tries to impose high taxes on capital
might find industry moving to other locations where taxes are lower. Clearly,
this is also a concern at the national level in a globalized economy, since the
international capital can easily migrate to where it is treated more favorably.2
Accordingly, standard principles of international taxation suggest that
the tax burden should fall most heavily on those factors of production which
are least mobile, in order to maximize government income and minimize the
disincentives to economic growth. Hence, there has been a corresponding
shift in the incidence of taxation from capital to labor as governments have
tried to maintain levels of both fiscal revenue and private investment. As a
result, it is not surprising that the main conclusion of the basic tax competi-
tion models states that corporate tax rates will be inefficiently low, leading
1The Baltic countries apply an explicit regressive corporate tax rule.
2The corporate tax in the U.S. is imposed both by the federal government and by most
state governments. Germany’s corporate tax is a joint federal-state tax; the surtax is a
federal tax, and the trade tax is a municipal tax.
2
to an underprovision of public goods.3 This happens because capital or firms
respond immediately to tax differentials and governments engage in race-
to-the-bottom tax competition—corporate taxation is competed downwards.
According to the theoretical predictions of the tax competition literature,
a high and increasing degree of economic integration should lead to severe
pressures on local and national tax policies. Moreover, corporate taxation
should become increasingly more important as a determinant of industry lo-
cation as the extent of economic integration increases, since capital becomes
more sensitive-elastic to tax differentials as trade is liberalized.
However, recent applications of new economic geography models to tax
competition have modified the neoclassical race-to-the-bottom result. In case
of full agglomeration, capital might earn a premium that can be taxed by
local authorities without any distortions. This agglomeration rent makes
the mobile factor quasi-inelastic over a certain range of trade costs, so that
tax rates on capital income might rise in proportion to deepened market
integration.4
The implicit assumption in this literature is that the average tax rate
is independent of the tax base, that is, taxes are taken to be proportional.
Hence, these studies do not take into account aspects of tax structure on the
economic geography; for example, how agglomeration rents might vary with
the specific tax regime. It is therefore crucial to extend the current literature
on corporate taxation and industrial location by considering widely adopted
alternative tax schedules other than the proportional scheme.
This paper analyzes the effects of different corporate tax systems on the
location of industry. Specifically, the paper introduces progressive, propor-
tional, and regressive taxation into a modified version of the economic geog-
raphy model of Martin and Rogers (1995). In that respect, the paper closest
to the present is that of Commedatore and Kubin (2008), who study the
choice between taxing capital according to the residence and source principle
within the Martin and Rogers (1995) setting.
The analysis shows that the relatively larger region (the North) prefers
a regressive tax system for a given shift in regional expenditures, while the
smaller region (the South) benefits from adopting progressive taxation. Both
regions gain industry by adopting a tax regime that produces the lowest tax
3See for example Wilson (1999) for a review of the theoretical tax competition litera-
ture.
4Such argument has for example been made by Ludema and Wooton (2000), Kind et
al. (2000), and Baldwin and Krugman (2004).
3
level. As expenditures in the North increase, the North (South) attracts
more industry compared to the location equilibrium without tax structure by
setting regressive (progressive) taxes. However, welfare in the North (South)
is maximized if both regions set regressive (progressive) taxes. The reason
is that symmetric regional regressive (progressive) taxation, through lower
taxes in the North (South) and higher taxes in the South (North), gives rise
to relatively higher (lower) agglomeration economies in the North. This in
turn decreases prices in the North (South) and saves the transportation cost
facing the North (South) consumers when trade costs have to be paid on a
lower number of goods.
Furthermore, as trade is liberalized, and provided that the North’s share
of regional expenditures is lower (higher) than a certain threshold value, the
North optimally sets regressive (progressive) taxes, while the South prefers
to apply a progressive (regressive) tax scheme. In this case, welfare of the
North is maximized if the South also sets regressive (progressive) taxes, since
this increases the agglomeration economies in the North over and above what
is implied by the Nash equilibrium that prescribes different tax systems in
the North and the South. A combination of tax schedules that maximizes
the location of production in the North (South) is a joint efficient outcome
if the relative endowment of labor of the North is higher (lower) than a
certain critical value. The reason is that an endowment above (below) this
threshold level implies that the North (South) gains (loses) more in terms of
total welfare from agglomeration of production than the South (North) loses
(gains).
It is also shown that a proportional tax system is never an equilibrium;
as to be seen, this tax regime replicates the location outcome without re-
gional tax structures. This is an interesting result considering its widespread
international support and usage.
The paper is organized as follows. The next section presents the economic
geography framework with regional corporate taxation levels, and solves for
the equilibrium location of industry. Section 3 defines the specific struc-
tures of the tax policy instrument; determines industry agglomeration under
progressive, proportional, and regressive tax systems; derives the tax sched-
ules that prevail in equilibrium, and those that maximize regional and joint
welfare. Section 4 concludes.
4
2 The Economic Geography Model
The location model applied builds on the framework of Martin and Rogers
(1995), which is based on the Flam-Helpman (1987) version of the Dixit-
Stiglitz (1977) model of monopolistic competition.
2.1 Assumptions
There are two regions, two sectors and two factors. Specifically, the two
regions, North (N) and South (S), belong to the same country—or federation
of countries—and are endowed with two factors, labor (L) and capital (K).
The regions are symmetric in terms of tastes, technology, openness to trade,
but are separate tax jurisdictions and differ in their factor endowments; the
North is a scaled-up version of the South. Thus the regions may be of different
size, but they have identical capital-labor ratios. In particular, the North’s
endowment of both capital and labor is λ > 1 times the South’s endowment.
The two sectors are referred to as agriculture (A) and manufacturing or
industry (M). The agricultural sector is assumed to produce a homogenous
good under constant returns to scale and perfect competition using aA units
of labor per unit of output. Labor is the only input and this good is chosen
as a numeraire. The manufacturing sector uses both labor and capital to pro-
duce a differentiated good under increasing returns to scale and monopolistic
competition. Following Flam and Helpman (1987), the production of each
differentiated good involves a one-time fixed cost consisting of one unit of K
and a per-unit-of-output cost of aM units of L. The implied cost function of
each industrial firm is therefore given by:
π + waMx,
(2.1)
where π and w are the reward to capital and labor, and x is the firm level
output.
Physical capital can move between regions but capital owners are immo-
bile. Thus, when pressures arise to concentrate production to one region,
capital will move, but its entire reward will be repatriated to its region of
origin. Labor, on the other hand, can move freely between sectors but is
immobile between regions. Total supply of capital and labor in the econ-
omy is fixed, with the nation’s endowments denoted by KW and LW . Since
each industrial variety requires one unit of capital, the share of the nation’s
5
capital stock employed in a single region exactly equals the region’s share
of the national manufacturing sector. Consequently, the North’s share of
industry can be used, i.e., sN ≡
nN
nN+nS
, where nN and nS denote the number
of industrial firms in the North and the South, respectively, to represent the
share of capital employed in the North, and the share of all varieties made
in the North. Then clearly, sS = 1− sN ≡
nS
nN+nS
is the South’s share of the
national manufacturing sector.
Output in the agricultural sector is traded at no cost, while interregional
trade in the differentiated output is subject to an iceberg transportation cost.
Hence, in order to sell one unit of the differentiated good in the other region,
τ > 1 units need to be shipped.
The representative consumer in each region has preferences according to:
U = CµMC
1−µ
A + U(CG),
(2.2)
where µ ∈ (0, 1), CA is consumption of the homogenous good, and U(CG) is
a public utility component derived from public expenditures. Consumption
of manufactures enters the utility function through the index CM , which is
defined by:
CM ≡
(∫ nW
0
ci
σ−1
σ di
) σ
σ−1
,
(2.3)
where nW = nN + nS denotes the large number of industrial varieties con-
sumed, fixed by the nation’s total supply of capital, ci is the amount of variety
i consumed, and σ > 1 is the constant elasticity of substitution between any
two varieties. The utility derived from public expenditures, U(CG), is not ex-
plicitly specified; it depends on the quantity consumed of a publicly provided
good, CG, and has a positive first and a negative second derivative. The gov-
ernment in region j = N,S, publicly provides this private good. Following
Commedatore and Kubin (2008), in total LjCG units of the good have to be
produced in region j. The production function is:
LjCG = C
µ
MGC
1−µ
AG ,
(2.4)
where CAG represents the quantity of the agricultural good, and CMG denotes
the quantity index of the manufactured good (again based on a substitution
elasticity of σ > 1). This specification implies that the shares of government
6
revenues devoted to the manufacturing composite and to the agricultural
commodity do not differ from the private shares given in (2.2).5
Public expenditures are financed by corporate income taxes, and the gov-
ernment’s budget is always balanced. Assume that corporate profits are taxed
according to the source principle, that is, capital is taxed according to where
firms are located.6 Further, let sNj (sSj) denote the share of capital em-
ployed in region j, owned by the representative individual residing in the
North (South), where sNN + sSN = 1 and sSS + sNS = 1.
Total expenditures (private and public) on manufacturing goods in region
j, Ej, equal the share of disposable income devoted to manufactures:
EN = µ
(
wNLN + πNKN −KW
∑
j
tjsNjπj
)
+ µTRN(tN),
(2.5)
and
ES = µ
(
wSLS + πSKS −KW
∑
j
tjsSjπj
)
+ µTRS(tS),
(2.6)
where tj ∈ [0, 1) is the average tax levied on firms or capital located in region
j and paid by the representative capital owner residing in j. KW
∑
j tjsNjπj
(KW
∑
j tjsSjπj) is the total tax payments of citizens belonging to region
N (S) who own capital employed in both regions N and S. TRN(tN) =
KW tNπN (TRS(tS) = KW tSπS) denotes the tax revenues of region N (S);
7
i.e., the public expenditure component, since the government’s budget is
always balanced.
2.2 The Economic Equilibrium
The unit factor requirement of the homogenous good is one unit of labor
(aA = 1). This good is freely traded and since it is also chosen as a numeraire,
5This assumption is made for algebraic convenience and does not affect the results.
The reason is that government revenues do not enter the location condition, that capital
employed in the North must earn the same after-tax rate of return as capital in the South,
and therefore do not affect the location equilibrium.
6All results hold under the assumption of taxation according to the residence principle,
since this does not change the structure of the location condition.
7TRN (tN ) = KW tNπN (sNN + sSN ) = KW tNπN and TRS(tS) = KW tSπS(sSS +
sNS) = KW tSπS .
7
pA = w = 1 in both regions.
Maximizing (2.2), subject to (2.3) and the budget constraint, to obtain
the (private and public) demand function in region j for variety i of the
differentiated good:
ci =
p−σ
i Ej
∫ nW
k=0
pjk
1−σdk
,
(2.7)
where pi is the price of variety i. Profit maximization yields:
8
p =
σ
σ − 1
waM ,
(2.8)
and
p∗ =
σ
σ − 1
τwaM ,
(2.9)
for each differentiated commodity sold in the home and export market, re-
spectively. Without any loss of generality, let aM =
σ−1
σ
,9 then using w = 1
to obtain the pricing rules for firms in the manufacturing sector: p = 1 and
p∗ = τ .
Since physical capital is used only in the fixed cost component of industrial
production, the reward to capital is the Ricardian surplus of a typical variety,
i.e., the operating profit of a variety. With a fixed capital stock and free entry,
the reward to capital will be bid up to the point where the entire operating
profit goes to capital. Under Dixit-Stiglitz competition, the operating profit
is the value of sales divided by σ; that is, πj =
xj
σ
, where xj is the scale of
production of a representative industrial firm in region j.10
National expenditures (private and public) on manufacturing goods, EW ,
are written as:
8Differentiating the profit function, Πi = pici(pi) + p∗i c
∗
i (p
∗
i ) − π(1 + t) −
waM (ci(pi) + c∗i (p
∗
i )τ), where c
∗
i (p
∗
i ) is the foreign demand for industry i products, with
respect to pi and p∗i , using σ ≡ −
pi
ci(pi)
∂ci(pi)
∂pi
≡ − p
∗
i
c∗i (p
∗
i )
∂c∗i (p
∗
i )
∂p∗i
, solving for the optimal
prices gives (2.8) and (2.9).
9This assumption is made for algebraic simplicity and does not affect any of the results,
since aM does not enter the location condition. aM = σ−1
σ < 1, because σ > 1, implies
that less than one unit of labor is needed to produce one unit of the differentiated good.
10Free entrance implies that pure profits are eliminated. Employing the profit function
from note 8 for a typical manufacturing firm in region j, w = 1, aM = σ−1
σ
, p = 1, p∗ = τ ,
and xj ≡ cj + c∗jτ gives πj =
xj
σ .
8
EW = µ
(
LW + πWKW −KW
∑
j
tjπj
)
+ µ
∑
j
TRj(tj),
(2.10)
where πW =
xW
σ
= EW
KW σ
(the corresponding expression in Baldwin et al.
[2003], without taxation, is µEW
KW σ
). Using this condition in (2.10), andKW
∑
j tjπj =
∑
j TRj(tj),
11 yields EW = µ
(
LW +
EW
σ
)
, which implies that:12
EW =
σ
σ − µ
µLW .
(2.11)
Combining sEj ≡
Ej
EW
, where sEj represents the share of national expen-
ditures of region j, and sEN = 1−sES , with (2.11) solves for the expenditures
in region j:
Ej = sEj
σ
σ − µ
µLW .
(2.12)
The domestic and foreign demand function for industry i products, and
the optimal prices give the reward to capital or the operating profit in equi-
librium:13
πN =
xN
σ
=
µ
σ
(
EN
nN + φnS
+
φES
φnN + nS
)
,
(2.13)
and
πS =
xS
σ
=
µ
σ
(
φEN
nN + φnS
+
ES
φnN + nS
)
.
(2.14)
11From (2.5) and (2.6) it follows that KW tNsNNπN +KW tSsNSπS and KW tSsSSπS +
KW tNsSNπN represent the aggregate tax payments by capital owners in the North and
the South, respectively. Hence, total (national) tax payments are KW tNπN (sNN +sSN )+
KW tSπS(sSS + sNS) = KW
∑
j tjπj . Moreover, it can also be deduced from note 7 that
∑
j TRj(tj) = KW tNπN (sNN + sSN ) +KW tSπS(sSS + sNS) = KW
∑
j tjπj Accordingly,
total tax payments and tax revenues in (2.10) cancel out, and therefore do not affect the
location equilibrium.
12With the residence principle, the total tax burden on capital owners residing in region
j is identical to the tax revenues of j. Hence, in this case, EW = µ
(
LW + EW
σ
)
and
consequently (2.11) still apply.
13Using the expressions for the demand functions in xjσ ≡
cj+c
∗
j τ
σ
, and p = 1, p∗ = τ
yields (2.13) and (2.14).
9
τ 1−σ ≡ φ ∈ [0, 1] is a measure of the freeness of interregional trade, where 0
corresponds to infinite trade barriers and 1 represents free trade. Substituting
(2.12) into (2.13) and (2.14) to obtain:
πN = aµLW
(
sEN
sN + φ(1− sN)
+
φ(1− sEN )
φsN + (1− sN)
)
,
(2.15)
and
πS = aµLW
(
φsEN
sN + φ(1− sN)
+
(1− sEN )
φsN + (1− sN)
)
,
(2.16)
where a ≡ µ
σ−µ .
With perfect capital mobility and when manufacturing production takes
place in both regions, the location condition requires that capital employed
in the North must earn the same after-tax rate of return as capital in the
South: πN(1− tN) = πS(1− tS). Given (2.15) and (2.16), the distribution of
industry solving this condition is:
sN =
sEN (1− φ2)− φ(υ − φ)
(1− φ)(υ − φ− sEN (υ − 1)(1 + φ))
,
(2.17)
where υ = 1−tS
1−tN
and υ ∈ R++∀tj ∈ [0, 1). Clearly, 0 < υ < 1 holds when
capital in the South is taxed at a higher rate than capital in the North, while
υ > 1 is fulfilled when the North applies a relatively higher corporate tax
rate. Let υ = 1 (i.e., no regional tax rate difference) and differentiate (2.17)
with respect to sEN :
∂sN
∂sEN
υ=1 =
1 + φ
1− φ
> 1,
(2.18)
which demonstrates the home market effect (Krugman, 1980). Thus sN in-
creases more than proportionate to sEN for φ ∈ (0, 1), and this effect becomes
stronger as trade barriers are reduced (so-called home market magnification,
due to Krugman [1991]). This means that even if one region is just slightly
larger than the other, it will obtain the entire manufacturing industry if
transaction costs are sufficiently low.
To illustrate the effect of regional corporate taxes on the geographical
equilibrium, differentiate (2.17) with respect to υ:
∂sN
∂υ
= −
sEN (1− sEN )(1 + φ)2
(φ− υ + sEN (υ − 1)(1 + φ))
2 < 0,
(2.19)
10
for sEN ∈ (0, 1). (2.19) implies that the location of manufacturing activities
in the North is decreasing (increasing) in the corporate tax rate of the North
(South). By differentiating (2.19) with respect to φ and sEN it is clear that
the sign of the derivatives is ambiguous and depends on the relative sizes
of sEN , φ and υ. Within this framework, like in Commedatore and Kubin
(2008), there are no agglomeration rents that the larger region can tax away:
holding everything else constant, a lower tax rate in region j increases the
share of industry in j.
The welfare of a representative individual is a function of the income
devoted to manufactures and the price index prevailing in the region of res-
idence. Given (2.2), the indirect utility functions are (see Appendix A.1 for
details):
VN(υ) = lnµ+ ln(1 + µa) +
µ
σ − 1
ln (sN + (1− sN)φ) ,
(2.20)
VS(υ) = lnµ+ ln(1 + µa) +
µ
σ − 1
ln (sNφ+ (1− sN)) ,
(2.21)
for an agent in the North and the South, respectively. VN > VS if and only
if sN >
1
2
.14 Moreover, it is straightforward to verify that ∂VN
∂sN
> 0 and
∂VS
∂sN
< 0. Consequently, individual welfare increases in the number of firms
located in the agent’s region, since this leads to a decrease in consumer prices
of manufactures and saves the transportation cost facing the consumer when
trade costs have to paid on a lower number of goods. The total welfare of
region j can be expressed as Wj = LjVj. This means that
∣∣∣∂WN
∂sN
/∂WS
∂sN
∣∣∣ ≶ 1 if
λ ≶ sN+(1−sN )φ
sNφ+(1−sN )
> 1, where λ = LN
LS
> 1 since the North has relatively more
labor (and capital).15 Thus, if the relative number of citizens in the North
is lower (higher) than this threshold level, the South (North) loses (gains)
more in terms of total welfare than the North (South) gains (loses) from
agglomeration in the North.
It can further be established that ∂VN
∂υ
< 0 and ∂VS
∂υ
> 0. Hence, increasing
the corporate tax rate of the North (South) decreases individual welfare in
14VN − VS
=
µ
σ−1 (ln (sN + (1− sN )φ)− ln (sNφ+ (1− sN )))
=
µ
σ−1 ln
(
sN+(1−sN )φ
sNφ+(1−sN )
)
> 0 if sN + (1− sN )φ > sNφ+ (1− sN ), i.e., if sN > 12 .
15
∣∣∣∂WN
∂sN
/∂WS
∂sN
∣∣∣ = λ sNφ+(1−sN )
sN+(1−sN )φ ≶ 1 if λ ≶
sN+(1−sN )φ
sNφ+(1−sN ) , where
sN+(1−sN )φ
sNφ+(1−sN ) > 1 if sN >
1
2 .
11
the North (South). The reason is that a higher tax rate in region j decreases
the number of industrial firms in j, which raises the price index in this region.
With the geography model specified, it is now time to analyze how dif-
ferent corporate tax structures affect the location equilibrium.
3 The Tax Policy Equilibrium
Thus far, no assumption has been made on the structure of the regional
tax policy instrument. In the following, industry agglomeration will be de-
termined under progressive, proportional, and regressive corporate tax struc-
tures, where the structure itself is taken to be exogenously given. This makes
it possible to derive the tax systems that prevail in equilibrium, and those
that maximize regional and joint welfare.
3.1 Assumptions
Assuming that the corporate income tax function, tj(πj), is continuous in
πj, the tax system is progressive (regressive) if t
′
j(πj) > 0 (t
′
j(πj) < 0). In
addition, given two tax functions, t1j(πj) and t2j(πj), such that t
′
1j(πj) >
t′2j(πj) > 0 (t
′
1j(πj) < t
′
2j(πj) < 0), the tax structure implied by t1j(πj) is
interpreted as more progressive (regressive) than that implied by t2j(πj).
16
Under the proportional tax system, on the other hand, the average tax rate
remains constant regardless of the profit level; hence, tj(πj) = tj and t
′
j = 0.
Denote the progressive, proportional, and regressive tax schedule of region
j by tP,j(πj), tPL,j, tR,j(πj), respectively, and let ω ≡
t′i,S(πS)
t′i,N (πN )
for any tax
system i = P, PL,R.
Consider then the following two-stage game. In the first stage, firms
relocate between regions in response to the level of economic integration (φ)
and the relative shares of total expenditures (sEN ), i.e., the relative economic
strength of the North. In the second and final stage, πj is realized, taxes,
tj(πj), are exogenously set, and υ =
1−tS
1−tN
is determined. A subgame perfect
16In reality, taxes may be locally progressive over some ranges of income and regressive
over others. The degree to which such taxes could then be deemed to be globally progres-
sive or regressive over the whole domain of the income distribution needs to depend on
the relative weights respectively attached to local progressiveness or regressiveness over
the various income ranges. For simplicity, corporate taxes are assumed to be globally
progressive or regressive.
12
equilibrium of this game is solved by backward induction. In the final stage,
the distribution of industry, sN , is exogenously given by the equilibrium in
the first stage; that is, profits are a function πj(sEN , φ, sN), where sN is
exogenous.
From the perspective of the first stage, and through backward induction,
firms in region j must take the second-stage equilibrium into account when
relocation decisions are made. Hence, the first-stage equilibrium is affected
by the realization of υ. Consequently, (2.17) can be reproduced as:
sN = f (sEN , φ, υ) ,
(3.1)
where υ = f (tN(πN), tS(πS)), υ = f (tN , tS(πS)), υ = f (tN(πN), tS) or υ =
f (tN , tS) depending on the tax structures.
3.2 Tax Structure and Increased Spending
Taking the total derivative of (3.1) with respect to sEN to obtain:
∂sN
∂sEN
=
∂f
∂sEN
+
∂f
∂υ
(
∂υ
∂tN
∂tN
∂πN
∂πN
∂sEN
+
∂υ
∂tS
∂tS
∂πS
∂πS
∂sEN
)
,
(3.2)
where
∂f
∂sEN
> 0 if firms relocate to the larger region as the share of national
expenditures of this region increases (which is assumed throughout the rest
of the paper), ∂f
∂υ
< 0 by (2.19), ∂υ
∂tN
=
1−tS
(tN−1)2
> 0, ∂υ
∂tS
= − 1
1−tN
< 0, ∂πN
∂sEN
=
aµLW
(
1
sN+φ(1−sN )
−
φ
φsN+(1−sN )
)
> 0 and ∂πS
∂sEN
= aµLW
(
φ
sN+φ(1−sN )
−
1
φsN+(1−sN )
)
<
0. Thus the sign of the second term on the right-hand side of (3.2) is solely de-
termined by the sign of ∂tN
∂πN
≡ t′N(πN) and ∂tS
∂πS
≡ t′S(πS); i.e., whether the tax
system in region j is progressive, proportional or regressive. It can be shown
that ∂υ
∂tN
∂tN
∂πN
∂πN
∂sEN
+ ∂υ
∂tS
∂tS
∂πS
∂πS
∂sEN
≷ 0 if t′S(πS)sN + t
′
N(πN)(1− sN)υ ≷ 0.17
Progressive Taxation in the North and the South
Assuming that both regions apply progressive taxation, noting that t′P,j(πj) >
0, the second term on the right-hand side of (3.2) becomes negative, and
therefore ∂sN
∂sEN
<
∂f
∂sEN
. Hence, introducing symmetric progressive taxation
17 ∂υ
∂tN
∂tN
∂πN
∂πN
∂sEN
+ ∂υ
∂tS
∂tS
∂πS
∂πS
∂sEN
=
aµLW (1−φ2)(t′S(πS)(1−tN )sN+t′N (πN )(1−tS)(1−sN ))
(tN−1)2(1−sN (1−φ))(φ+sN (1−φ))
≷ 0 if
t′S(πS)(1−tN )sN+t′N (πN )(1−tS)(1−sN ) ≷ 0; that is, if t′S(πS)sN+t′N (πN )(1−sN )υ ≷ 0.
13
slows down the agglomeration process in the North, as compared to the
location equilibrium without corporate tax structure. On the one hand, the
equilibrium location of manufacturing production in the North is increasing
in its share of national expenditures; this direct effect is captured by the first
term,
∂f
∂sEN
, on the right-hand side of (3.2) and represents the agglomeration
effect without corporate tax systems. On the other hand, as sEN increases,
πN increases while πS decreases. This increases tN and decreases tS with tax
progression in both regions, in turn increasing υ, thereby making it relatively
less beneficial to produce in the larger region. Consequently, sN decreases
by (2.19), so the agglomeration of firms in the North slows down compared
to the equilibrium without corporate tax structure. This indirect location
effect is associated with the second term on the right-hand side of (3.2), and
captures the agglomeration effect from the regions’ tax regimes.
Regressive Taxation in the North and the South
Consider instead the case where both regions set regressive taxes: t′R,j(πj) <
0. Under this combination of tax regimes, the second term on the right-hand
side of (3.2) becomes positive, implying higher agglomeration economies in
the larger region compared to the location equilibrium without corporate
tax structure, i.e., ∂sN
∂sEN
>
∂f
∂sEN
. As the North’s share of total expenditures
increases, πN increases and πS decreases. With regressive taxation, tN de-
creases while tS increases, which decreases υ, thus increasing sN by (2.19). In
other words, higher expenditures in the North, via a higher profit of the rep-
resentative North firm and a lower profit of the typical South firm, increases
the relative corporate taxation in the South under a symmetric regressive
tax system. This increases the agglomeration of firms in the North over and
above what is captured by the term
∂f
∂sEN
.
Proportional Taxation in the North and the South
In contrast, if both regions apply a proportional tax system, where t′PL,j = 0,
the effects of expenditures on the location equilibrium, through profits and
taxation, are eliminated. Accordingly, in this case, equation (3.2) reduces to
∂sN
∂sEN
=
∂f
∂sEN
, i.e., the location equilibrium without tax structure.
14
Progressive Taxation in the North and Regressive Taxation in the
South
Suppose that the regions are subject to different tax regimes, where initially
the North has a progressive system, i.e., t′P,N(πN) > 0, while the South
applies a regressive scheme, that is, t′R,S(πS) < 0. Then the second term on
the right-hand side of (3.2) becomes positive, implying that ∂sN
∂sEN
>
∂f
∂sEN
,
if t′R,S(πS)sN + t
′
P,N(πN)(1 − sN)υ < 0; in other words, if
sN
1−sN
> − υ
ω
. The
intuition behind this inequality can be explained in the following way. First,
for a low tax progression in the North and a high tax regressiveness in the
South—i.e., for a high absolute value of ω—the progressive tax rate in the
North increases by a relatively smaller factor in response to a higher πN when
sEN increases compared to the increase in tR,S(πS) following from a lower πS.
This increases the relative incentives to relocate production to the North.
Second, the location effect of increased taxation in the North is diminished
by a higher sN , that is, as the market-access advantage of producing in the
larger region increases. For higher sN , the rate decreases at which profits
in the North increase relative to the fall in profits in the South, following
higher spending. This further reduces the increase in the North’s tax rate,
and makes it even more beneficial to relocate production to the North. To
see this, note that ∂πN
∂sEN
/ ∂πS
∂sEN
= −1−sN
sN
, which decreases in absolute value as
sN increases.
Third, the location effect of higher taxes in the North is also reduced by a
low υ. For lower tP,N(πN) and higher tR,S(πS) (a low υ), higher taxes in the
North affect υ and ultimately sN at a relatively slower rate. This can be seen
by observing that
∂υ
∂tP,N (πN )
/
∂υ
∂tR,S(πS)
= − 1−tR,S(πS)
1−tP,N (πN )
= −υ, which decreases
in absolute value when tP,N(πN) is lower and tR,S(πS) higher. Therefore,
∂sN
∂sEN
>
∂f
∂sEN
is satisfied for a high absolute value of ω, high sN , and low υ.
Regressive Taxation in the North and Progressive Taxation in the
South
Assume instead that the North has a regressive tax structure (where t′R,N(πN) <
0) and the South has a progressive system (that is, t′P,S(πS) > 0). Then
∂sN
∂sEN
>
∂f
∂sEN
if
sN
1−sN
< − υ
ω
. That is, the North attracts relatively more pro-
duction compared to the location equilibrium without tax structure for low
sN , high υ and low |ω|. As intuition might suggest, for a highly regressive
15
taxation structure in the North and a low progressiveness in the South (i.e.,
for low |ω|), the regressive tax rate in the North decreases by a large amount
when πN increases in response to a higher sEN , while the progressive tax rate
of the South falls relatively less as πS decreases following higher sEN . This
induces firms to relocate from the South to the North at a higher rate than
what is captured by the term
∂f
∂sEN
.
The location effect is reinforced by the relative regional size (sN). An
equilibrium with a less capital-abundant North (low sN) increases the rate
at which the profit of the representative Northern firm increases relative to
the decrease in the operating profit of the typical Southern firm, as a result
of the shift in sEN . This accelerates the relative fall in the North’s tax rate,
and increases the relocation from the South to the North. Again, this is seen
by noting that ∂πN
∂sEN
/ ∂πS
∂sEN
= −1−sN
sN
, which increases in absolute value as sN
decreases.
Moreover, the location effect is also strengthened by a relatively higher
taxation in the North (high υ). Intuitively, a higher tR,N(πN) relative to
tP,S(πS) increases the rate at which lower taxes in the North affect υ and
ultimately sN , compared to the effect of taxation in the South on υ and sN .
This is evident since
∂υ
∂tR,N (πN )
/
∂υ
∂tP,S(πS)
= − 1−tP,S(πS)
1−tR,N (πN )
= −υ, which increases
in absolute value when tR,N(πN) increases relative to tP,S(πS).
Proportional Taxation in the North and Progressive Taxation in
the South
Consider then the case where the North applies a proportional tax system
(i.e., t′PL,N = 0) and the South sets progressive taxes (where t
′
P,S(πS) >
0). Clearly, the second term on the right-hand side of (3.2) reduces to
∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂sEN
< 0, which implies that ∂sN
∂sEN
<
∂f
∂sEN
. Since t′PL,N = 0, the
effect of expenditures on the location equilibrium, channeled through North-
ern profits and taxation, is eliminated. By contrast, increasing sEN decreases
the operating profit of the representative Southern firm, which in turn, with
tax progression, decreases the corporate tax rate levied on firms located in
the smaller region. As a result, firms will relocate to the North at a relatively
slower rate as sEN increases.
16
Proportional Taxation in the North and Regressive Taxation in the
South
Again, let the North set proportional taxes (t′PL,N = 0), while the South levies
regressive taxes (t′R,S(πS) < 0). Thus the second term on the right-hand
side of (3.2) becomes ∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂sEN
> 0, and it follows that ∂sN
∂sEN
>
∂f
∂sEN
.
t′PL,N = 0 eliminates the effect of sEN on sN via πN and tPL,N . However,
as the North’s share of expenditures increases, πS falls, increasing regressive
taxation in the South which increases the number of firms relocating from
the South to the North.
Progressive Taxation in the North and Proportional Taxation in
the South
Under the assumption of progressive taxation in the North (t′P,N(πN) > 0)
and a proportional system in the South (t′PL,S = 0), the second term on
the right-hand side of (3.2) equals ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂sEN
< 0, hence ∂sN
∂sEN
<
∂f
∂sEN
.
t′PL,S = 0 implies that taxation of capital in the South does not affect the
location of industry as sEN increases. Since t
′
P,N(πN) > 0, corporate taxes in
the North are raised through higher operating profits of Northern firms as
sEN increases. This decreases the agglomeration benefit of producing in the
North and slows down the relocation of firms to the larger region, relative to
the case without corporate tax systems.
Regressive Taxation in the North and Proportional Taxation in the
South
Let the North set regressive taxes (i.e., t′R,N(πN) < 0) and the South adopt a
proportional tax regime (t′PL,S = 0). Then the second term on the right-hand
side of (3.2) becomes ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂sEN
> 0, and ∂sN
∂sEN
>
∂f
∂sEN
. Proportional tax-
ation in the South does not affect the location of industry as sEN increases.
The regressive tax regime in the North, however, implies that tR,N(πN) de-
creases as πN increases when expenditures of the North rise, leading to higher
agglomeration economies in the larger region.
17
Equilibrium Tax Regimes
It is straightforward to show that the North always attracts more industry
by setting a regressive tax schedule, while the South prefers a progressive
system. Intuitively, both regions gain industry by applying the tax regime
that produces the lowest tax level. As sEN increases, πN and πS increases
and decreases, respectively. This decreases both tR,N(πN) and tP,S(πS), since
t′R,N(πN) < 0 and t
′
P,S(πS) > 0. The lower tax rate in the North (South) in
turn gives rise to higher (lower) agglomeration economies in the North, and
therefore makes it more (less) profitable to relocate to this region. Hence,
the unique Nash equilibrium in pure strategies has the North applying a re-
gressive tax regime and the South choosing a progressive schedule. As noted
above, this outcome has ∂sN
∂sEN
≷
∂f
∂sEN
if
sN
1−sN
≶ − υ
ω
. Thus, the tax pol-
icy equilibrium may imply higher as well as lower agglomeration economies
compared to the location equilibrium with no tax structure. Which region
attracts relatively more industrial production depends on the tax regressive-
ness of the North relative to the tax progressiveness of the South (ω), on the
relative regional tax level (υ), and on the relative capital abundance of the
North (sN).
However, the North (South) gains relatively more production if both re-
gions set a regressive (progressive) tax system, than if the North (South)
solely applies regressive (progressive) taxation. The reason is that a regres-
sive (progressive) taxation in the South (North) increases (decreases) the
agglomeration economies in the North over and above what is implied by the
Nash equilibrium. The intuition for this is as follows. As sEN increases, πS
(πN) decreases (increases) which, with regressive (progressive) taxation in the
South (North), leads to a higher relative tax rate in the South (North) than
in the Nash equilibrium. This increases (decreases) the benefit of establishing
production in the North, compared to the case where the North (South) solely
sets regressive (progressive) taxes. Mathematically, the location effect of both
regions applying regressive (progressive) taxation is captured by the second
term on the right-hand side of (3.2), which always is positive (negative) when
the regions adopt a regressive (progressive) tax system; hence ∂sN
∂sEN
>
∂f
∂sEN
(
∂sN
∂sEN
<
∂f
∂sEN
)
for all parameter values. In contrast, in the Nash equilibrium,
the second term on the right-hand side is positive (negative) and ∂sN
∂sEN
>
∂f
∂sEN
(
∂sN
∂sEN
<
∂f
∂sEN
)
if and only if
sN
1−sN
< − υ
ω
(
sN
1−sN
> − υ
ω
)
. If the North (South)
18
sets regressive (progressive) taxes, while the South (North) adopts propor-
tional taxation, this term reduces to ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂sEN
> 0
(
∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂sEN
< 0
)
,
which clearly is lower (larger) than the second term on the right-hand side
of (3.2) if both regions would apply regressive (progressive) taxation.
As shown in Subsection 2.2, individual welfare of region j increases in the
number of firms located to j (i.e., ∂VN
∂sN
> 0 and ∂VS
∂sN
< 0), since more industrial
production leads to a decrease in consumer prices of manufactures, and saves
the transportation cost facing the consumers residing in j. Accordingly, as
sEN increases, the unilateral welfare-maximizing tax structure in the North
(South) is the regressive (progressive) system. Welfare of the North (South)
is, however, maximized if both regions adopt a regressive (progressive) tax
structure, since this gives rise to the largest (smallest) agglomeration in the
North.
Note that
∣∣∣∂WN
∂sN
/∂WS
∂sN
∣∣∣ ≶ 1 if λ ≶ sN+(1−sN )φ
sNφ+(1−sN )
. This means that the South
(North) loses (gains) more in terms of total welfare than the North (South)
gains (loses) from agglomeration in the North, provided that the relative
number of citizens in the North is lower (higher) than a critical value. There-
fore, absent compensating interregional transfer payments, if the relative en-
dowment of labor of the North is lower (higher) than this threshold, any com-
bination of tax systems that maximizes the location of firms in the smaller
(larger) region represents a joint efficient outcome. Hence, progressive (re-
gressive) taxation in both regions represents a joint welfare maximizing out-
come, because this maximally increases the location of firms to the smaller
(larger) region relative to the equilibrium without tax systems.
The main results so far are summarized in:
Result 1: As the share of expenditures in the North increases, the Nash
equilibrium has this region adopting a regressive tax system, while the South
applies a progressive tax schedule. The unilateral welfare-maximizing tax
structure in the North (South) is the regressive (progressive) system, when
expenditures in the North increase. Welfare of the North (South) is maxi-
mized if both regions set regressive (progressive) taxes.
Consider next how the location of industry is affected by regional inte-
gration under the progressive, proportional, and regressive tax systems.
19
3.3 Tax Structure and Liberalized Trade
Taking the total derivative of (3.1) with respect to φ to obtain:
∂sN
∂φ
=
∂f
∂φ
+
∂f
∂υ
(
∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
+
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
)
,
(3.3)
where ∂f
∂φ
> 0 if firms relocate to the larger region as trade is liberalized
(which is assumed throughout the rest of the paper), ∂f
∂υ
< 0 by (2.19), ∂υ
∂tN
=
1−tS
(tN−1)2
> 0, and ∂υ
∂tS
= − 1
1−tN
< 0. ∂πN
∂φ
= −aµLW (1−sN)
(
sEN
(sN+φ(1−sN ))2
−
1−sEN
(φsN+(1−sN ))2
)
≷
0 and ∂πS
∂φ
= aµLW sN
(
sEN
(sN+φ(1−sN ))2
−
1−sEN
(φsN+(1−sN ))2
)
≶ 0 if sEN ≶
(sN (1−φ)+φ)2
(sN (1−φ)+φ)2+(1−sN (1−φ))2
>
1/2.18 The relation ∂πN
∂φ
> 0 and ∂πS
∂φ
< 0 is the main focus of the following
analysis; all results are however reported and discussed for the case ∂πN
∂φ
< 0
and ∂πS
∂φ
> 0. Assuming that ∂πN
∂φ
> 0 and ∂πS
∂φ
< 0, ∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
+ ∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
≷
0 if t′S(πS)sN + t
′
N(πN)(1 − sN)υ ≷ 0.19 As before, let ω ≡
t′i,S(πS)
t′i,N (πN )
for any
tax system i = P, PL,R.
Progressive Taxation in the North and the South
Let both regions adopt progressive taxation (t′P,j(πj) > 0), which means that
the second term on the right-hand side of (3.3) becomes negative, imply-
ing ∂sN
∂φ
< ∂f
∂φ
and lower agglomeration economies in the North compared
to the equilibrium without tax structure. The direct effect of trade liber-
alization is captured by the first term on the right-hand side of (3.3), ∂f
∂φ
.
This term is assumed to be positive, which implies that firms relocate to
the North as trade costs are lowered, an effect mediated via the home mar-
ket magnification effect. The second term on the right-hand side represents
the indirect effect of trade liberalization, channeled through profits and tax-
ation. Intuitively, as trade is liberalized, πN increases while πS decreases,
which increases the progressive corporate tax rate in North and reduces the
progressive taxation in the South, making it relatively less profitable to lo-
cate to the North. In contrast, if ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, the second term
18
sEN
(sN+φ(1−sN ))2
−
1−sEN
(φsN+(1−sN ))2
≶ 0 if sEN ≶
(sN (1−φ)+φ)2
(sN (1−φ)+φ)2+(1−sN (1−φ))2 .
19 ∂υ
∂tN
∂tN
∂πN
∂πN
∂φ +
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ = −
aµLW (t′S(πS)(1−tN )sN+t′N (πN )(1−tS)(1−sN ))
(tN−1)2
(
sEN
(sN+φ(1−sN ))2
−
1−sEN
(φsN+(1−sN ))2
)
≷
0 if t′S(πS)(1−tN )sN+t′N (πN )(1−tS)(1−sN ) ≷ 0; that is, if t′S(πS)sN+t′N (πN )(1−sN )υ ≷
0.
20
on the right-hand side becomes positive, and consequently ∂sN
∂φ
> ∂f
∂φ
, so the
agglomeration economies in the North instead increase. Hence, the share of
expenditures of the North, that is, how operating profits respond to trade
liberalization—∂πN
∂φ
> 0 and ∂πS
∂φ
< 0 or ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0—is essential
to the analysis of how lower trade costs affect taxation and the location of
industry.
Regressive Taxation in the North and the South
Suppose that the regions set regressive taxes, where t′R,j(πj) < 0. Then the
second term on the right-hand side of (3.3) becomes positive, and ∂sN
∂φ
> ∂f
∂φ
.
When φ increases tR,N(πN) and tR,S(πS) decreases and increases, respectively,
via higher πN and lower πS. Lower relative regional taxation in the North
makes it more beneficial to produce in the larger region, increasing the loca-
tion of industry in the North over and above what is captured by the term
∂f
∂φ
. On the other hand, given that ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, the second term on
the right-hand side instead becomes negative, and hence ∂sN
∂φ
< ∂f
∂φ
holds.
Proportional Taxation in the North and the South
Consider proportional taxes in both regions (t′PL,j = 0). In this case, (3.3)
reduces to ∂sN
∂φ
= ∂f
∂φ
. The reason is that symmetric proportional taxation
eliminates the effects of trade liberalization on the location of industry by
shutting down the channels through which profits affect the regions’ tax rates.
Clearly, this also holds for ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0.
Progressive Taxation in the North and Regressive Taxation in the
South
Let the regions be subject to different tax regimes. Specifically, let the North
apply progressive taxation, t′P,N(πN) > 0, while the South sets regressive
taxes, t′R,S(πS) < 0. Then the sign of the second term on the right-hand side
of (3.3) is positive, and consequently ∂sN
∂φ
> ∂f
∂φ
, if t′R,S(πS)sN + t
′
P,N(πN)(1−
sN)υ < 0. Thus
∂sN
∂φ
> ∂f
∂φ
if
sN
1−sN
> − υ
ω
.20 The rationale for this inequality
is laid out in Subsection 3.2. Reiterating the arguments developed there: for
20Note that this holds under the assumption of ∂πN
∂φ > 0 and
∂πS
∂φ < 0. Otherwise, if
∂πN
∂φ < 0 and
∂πS
∂φ > 0, then
∂sN
∂φ >
∂f
∂φ if
sN
1−sN < −
υ
ω .
21
a low progressiveness in the North, and a highly regressive taxation struc-
ture in the South (i.e., for a high |ω|), the tax rate in the North increases
by a relatively smaller factor when πN increases in response to a higher φ,
compared to the increase in the tax rate of the South as πS decreases when
trade costs fall. This induces firms to establish more production in the North
than what is captured by ∂f
∂φ
. The effect is reinforced by the relative regional
size of the North (sN), since a higher sN decreases the rate at which profits
of North firms increase relative to the decrease in the profits of South firms
as trade is liberalized; this slows down the relative increase in the North’s
tax rate, and further increases the relocation of firms from the South to the
North. This can be seen by noting that ∂πN
∂φ
/∂πS
∂φ
= −1−sN
sN
, which decreases
in absolute value as sN increases. The location effect is also strengthened by
a relatively lower taxation in the North (a low υ), because a lower tP,N(πN)
relative to tR,S(πS) decreases the rate at which higher taxation in the North
affects υ and ultimately sN , compared to the effect of higher taxation in
the South on υ and sN . Once again, this becomes clear by observing that
∂υ
∂tP,N (πN )
/
∂υ
∂tR,S(πS)
= − 1−tR,S(πS)
1−tP,N (πN )
= −υ, which decreases in absolute value as
tP,N(πN) decreases relative to tR,S(πS). To summarize,
∂sN
∂φ
> ∂f
∂φ
is satisfied
for high |ω|, high sN , and low υ, provided that ∂πN
∂φ
> 0 and ∂πS
∂φ
< 0 holds.21
Regressive Taxation in the North and Progressive Taxation in the
South
Assume that the North adopts a regressive tax structure (i.e, t′R,N(πN) < 0),
whereas the South sets progressive taxes (t′P,S(πS) > 0), leading to the second
term on the right-hand side of (3.3) becoming positive, and ∂sN
∂φ
> ∂f
∂φ
, if
sN
1−sN
< − υ
ω
.22 In other words, the North attracts more production compared
to the equilibrium without tax structure if sN is low, υ is high and |ω| low.
Following the arguments made in Subsection 3.2, when the regressiveness of
the tax system in the North increases and the progressiveness of taxes in
the South decreases (for low |ω|), tR,N(πN) decreases relatively more when
πN increases following a higher φ, compared to the fall in tP,S(πS) as πS
decreases when trade costs become lower. The relatively lower tax rate in
21If, on the other hand, ∂πN
∂φ < 0 and
∂πS
∂φ > 0 is satisfied, then
∂sN
∂φ >
∂f
∂φ holds for low
|ω|, low sN , and high υ.
22This holds under the assumption that ∂πN
∂φ > 0 and
∂πS
∂φ < 0. If
∂πN
∂φ < 0 and
∂πS
∂φ > 0,
then ∂sN
∂φ >
∂f
∂φ if
sN
1−sN > −
υ
ω .
22
the North increases the relocation of firms from the South to the North by
more than what is implied by the equilibrium without tax systems; hence
∂sN
∂φ
> ∂f
∂φ
. This location effect becomes stronger for smaller sN , because a
less capital-abundant North (low sN), increases the rate at which profits of
Northern firms increase relative to the decrease in the operating profit of a
typical Southern firm in response to a shift in φ; this accelerates the relative
fall in tR,N(πN) and increases the relocation of production to the North. To
see this, note that ∂πN
∂φ
/∂πS
∂φ
= −1−sN
sN
, which increases in absolute value as
sN falls. This location effect is also reinforced by a relatively higher taxation
in the North (high υ): higher tR,N(πN) relative to tP,S(πS) increases the
rate at which taxes in the North affect υ and ultimately sN , compared to
the effect of taxation in the South on υ and sN . As in Subsection 3.2, this
can be illustrated by observing that
∂υ
∂tR,N (πN )
/
∂υ
∂tP,S(πS)
= − 1−tP,S(πS)
1−tR,N (πN )
= −υ,
which increases in absolute value when tR,N(πN) increases relative to tP,S(πS).
Hence, provided that ∂πN
∂φ
> 0 and ∂πS
∂φ
< 0 holds, ∂sN
∂φ
> ∂f
∂φ
is satisfied for
low |ω|, low sN , and high υ.23
Proportional Taxation in the North and Progressive Taxation in
the South
Let the North apply proportional taxation (i.e, t′PL,N = 0) and the South
set progressive taxes (where t′P,S(πS) > 0). This means that the second term
on the right-hand side of (3.3) reduces to ∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
< 0 and, as a result,
∂sN
∂φ
< ∂f
∂φ
. The proportional tax system of the North eliminates the effects
of trade liberalization on sN mediated through the operating profit and the
tax rate of the North. In contrast, lowering trade costs decreases the South
firms’ profits, in turn decreasing the progressive tax rate in the South, which
slows down the agglomeration activity in the larger region. If, on the other
hand, ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, then ∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
> 0 holds and thus ∂sN
∂φ
> ∂f
∂φ
.
Proportional Taxation in the North and Regressive Taxation in the
South
Suppose again that the North is subject to proportional taxation (t′PL,N = 0),
while the South levies regressive taxes (t′R,S(πS) < 0). This implies that the
second term on the right-hand side of (3.3) reduces to ∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
> 0,
23If ∂πN
∂φ < 0 and
∂πS
∂φ > 0 is satisfied,
∂sN
∂φ >
∂f
∂φ holds for high |ω|, high sN , and low υ.
23
so ∂sN
∂φ
> ∂f
∂φ
. Since t′PL,N = 0, taxation in the North does not affect sN
as φ increases. However, t′R,S(πS) < 0 raises the tax rate in the South as
πS decreases when φ increases, and this makes it more attractive for firms
to establish production in North.
If ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0 is satisfied,
∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
< 0 and ∂sN
∂φ
< ∂f
∂φ
.
Progressive Taxation in the North and Proportional Taxation in
the South
Consider progressive taxation in the North (t′P,N(πN) > 0) and a proportional
tax system in the South (t′PL,S = 0), such that the second term on the right-
hand side of (3.3) becomes negative, ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
< 0, from which it follows
that ∂sN
∂φ
< ∂f
∂φ
. Clearly, in this case, as trade costs become lower, taxation in
South does not affect the location of industry. Still, as profits in the North
increase when trade is liberalized, tP,N(πN) increases, thereby decreasing the
agglomeration economies in the North.
If ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0 holds,
∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
> 0 and ∂sN
∂φ
> ∂f
∂φ
.
Regressive Taxation in the North and Proportional Taxation in the
South
Assume that the North adopts a regressive tax regime (t′R,N(πN) < 0) and the
South applies proportional taxation (t′PL,S = 0), thereby reducing the second
term on the right-hand side of (3.3) to ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
> 0, implying that ∂sN
∂φ
>
∂f
∂φ
. The proportional tax rate of the South eliminates the location effect of
trade liberalization, channeled through operating profits and taxation in the
South. Regressive taxation in the North decreases tR,N(πN) via higher πN as
φ increases, which increases the location of firms to the North over and above
what is captured by the term ∂f
∂φ
. If ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
< 0,
and ∂sN
∂φ
< ∂f
∂φ
.
Equilibrium Tax Regimes
Again it can be verified that the North attracts more industrial production by
setting regressive taxes, while the South receives more industry from levying
progressive taxes. As pointed out in Subsection 3.2, both regions optimally
adopt tax regimes that give rise to the lowest tax level. When trade costs
24
become lower, the profit of the representative North firm increases and the
profit of the typical South firm decreases. With a regressive (progressive)
system, this reduces taxation in the North (South) and increases (decreases)
the agglomeration of firms in the North, compared to the equilibrium without
tax structure. Therefore, when trade is liberalized, the Nash equilibrium
in pure strategies prescribes the North applying a regressive tax schedule,
while the South adopts a progressive system. As shown in Subsection 3.2,
this equilibrium has ∂sN
∂φ
≷ ∂f
∂φ
if
sN
1−sN
≶ − υ
ω
. Accordingly, the direction of
the agglomeration relative to the location outcome with no tax structure,
depends on the degree of tax regressiveness of the North in relation to the
progressiveness of taxes set in the South (captured by ω), the relative regional
taxation level (υ), and the relative capital abundance of the North (sN).
The North (South) attracts more industry given that the South (North)
also applies regressive (progressive) taxation. Given regressive (progressive)
taxes in the South (North), as φ increases, πS (πN) decreases (increases).
This in turn increases taxation in the South (North), making it relatively
more beneficial to establish production in the North (South), compared to
the case where the North (South) solely sets regressive (progressive) taxes.
Formally, this location effect is captured by the second term on the right-
hand side of (3.3), which always is positive (negative) when both regions set
regressive (progressive) taxes, implying that ∂sN
∂φ
> ∂f
∂φ
(
∂sN
∂φ
< ∂f
∂φ
)
for all
parameter values. Given the Nash strategies followed by the two regions,
the second term on the right-hand side is positive (negative) if and only if
sN
1−sN
< − υ
ω
(
sN
1−sN
> − υ
ω
)
. If the North (South) adopts regressive (progres-
sive) taxation, and the South (North) sets proportional taxes, the right-hand
side of (3.3) reduces to ∂f
∂υ
∂υ
∂tN
∂tN
∂πN
∂πN
∂φ
> 0
(
∂f
∂υ
∂υ
∂tS
∂tS
∂πS
∂πS
∂φ
< 0
)
, which is lower
(larger) than the right-hand side of (3.3) if both regions would apply re-
gressive (progressive) taxation. By contrast, if ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, it is
straightforward to show that the North always attracts more industry by
adopting a progressive tax regime, and the South prefers the regressive tax
system. In this case, the Nash equilibrium has the North setting progressive
taxes and the South levying regressive taxes, while the optimal outcome for
the North (South) is having both regions applying progressive (regressive)
taxation.
Since the welfare of region j is increasing in the number of firms located
in j, the unilateral welfare-maximizing tax structure of the North (South),
25
as trade is liberalized, is the regressive (progressive) system. Welfare of
the North (South) is however maximized if both regions apply regressive
(progressive) taxation. Given that ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, as trade costs
become lower, the unilateral welfare-maximizing tax regime of the North
(South) is the progressive (regressive) system. And the North’s (South’s)
welfare is maximized if both regions set progressive (regressive) taxes.
∣∣∣∂WN
∂sN
/∂WS
∂sN
∣∣∣ ≶ 1 if λ ≶ sN+(1−sN )φ
sNφ+(1−sN )
, which implies that the South (North)
loses (gains) more in terms of total welfare than the North (South) gains
(loses) from agglomeration in the North, provided that the relative number
of citizens in the North is lower (higher) than the threshold. Therefore, as
in Subsection 3.2, in the absence of interregional transfers, if the relative
endowment of labor of the North is lower than the critical value, a tax com-
bination that maximizes production in the South (North) is a joint efficient
outcome. Hence, progressive (regressive) taxation in both regions represents
a joint welfare maximizing outcome. The reason is that this combination
of tax systems minimizes (maximizes) the agglomeration economies in the
larger region.
The main results of Subsection 3.3 can be summarized in the following
way:
Result 2: As trade is liberalized, the Nash equilibrium has the North adopting
a regressive tax system, while the South sets progressive taxes. As trade costs
fall, the unilateral welfare-maximizing tax structure in the North (South) is
the regressive (progressive) system. The North’s (South’s) welfare is, how-
ever, increased if the South (North) also adopts regressive (progressive) tax-
ation. This holds if ∂πN
∂φ
> 0 and ∂πS
∂φ
< 0. If ∂πN
∂φ
< 0 and ∂πS
∂φ
> 0, the Nash
equilibrium prescribes progressive taxes in the North, while the South sets
regressive taxes. The unilateral welfare-maximizing tax system in the North
(South) is the progressive (regressive) regime as trade is liberalized. Welfare
of the North (South) is, however, maximized if both regions apply progressive
(regressive) taxation.
Proportional taxation is never an equilibrium, neither as regional spend-
ing changes, nor as trade is liberalized. If both regions set proportional taxes,
the agglomeration and welfare effects of higher spending and liberalized trade
are eliminated since, in this case, taxes are invariant to changes in profits,
which channel the effects of expenditures and trade costs on taxes and the
26
distribution of industry. This means that the tax policy equilibrium reduces
to the location equilibrium without regional tax regimes, i.e., ∂sN
∂sEN
=
∂f
∂sEN
and ∂sN
∂φ
= ∂f
∂φ
. That is, symmetric proportional regional taxation implies that
the tax structure does not contribute to the location of production over and
above what is given by the market-access advantage, transportation costs,
and the relative regional tax level.
4 Conclusions
The tax competition literature focuses on how tax levels affect the location
of factors of production. In doing so, this line of research assumes that the
average tax rate is independent of the tax base; that is, taxes are taken to be
proportional. Hence, these studies do not take into account how the economic
geography might vary with the specific tax structure. In filling that gap, this
paper has analyzed how different corporate tax systems affect the location
of industry, recognizing that the system itself has important implications for
the agglomeration of firms.
Using a standard model of new economic geography with asymmetric-
sized regions, both regions gain industry by adopting the tax regime that
produces the lowest tax level. This implies that in equilibrium, the regions
apply different tax regimes, and such a combination does not coincide with
the joint welfare maximizing outcome.
As the share of expenditures in the North increases, the North optimally
sets regressive taxes, while the South adopts a progressive tax system. The
North (South) gains relatively more production if both regions set regressive
(progressive) taxes, compared to if the North (South) solely applies regres-
sive (progressive) taxation. As trade is liberalized, and provided that the
North’s share of regional expenditures is lower (higher) than a certain thresh-
old value, the North optimally sets regressive (progressive) taxes, while the
South prefers to apply a progressive (regressive) tax scheme. A combina-
tion of tax schedules that maximizes the location of production in the South
(North) is a joint efficient outcome provided that the relative endowment of
labor of the North is below (above) a critical level. Furthermore, propor-
tional taxation is never an equilibrium; the proportional tax policy outcome
replicates the location equilibrium without tax regimes.
27
References
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29
A Appendix
A.1 Derivation of (2.20) and (2.21)
The indirect utility function of a representative agent in region j with pref-
erences given by (2.2) is:
Ej
(
R nW
k=0 pjk
1−σdk)
−µ
σ−1
. Using w = 1, πWKW =
xWKW
σ
and normalizing LW to unity without loss of generality to obtain the repre-
sentative individual’s net earnings devoted to manufactures:
Ej = µ (1 + πWKW ) = µ
(
1 + xWKW
σ
)
.
xWKW
σ
= xNnN+xSnS
σ
= πNnN +
πSnS. Substituting (2.12) into (2.13) and (2.14) gives: πNnN + πSnS =
µ
(
asEN (nN+nSφ)
(nN+nSφ)
+
a(1−sEN )(nNφ+nS)
(nNφ+nS)
)
= µa, which yields:
Ej = µ(1 + µa).
(A.1)
Solving for the price index prevailing in the North and the South, respec-
tively:
(∫ nW
k=0
pNk
1−σdk
) −µ
σ−1
= (nN + nSφ)
−µ
σ−1 = (sN + (1− sN)φ)
−µ
σ−1 ,
(A.2)
and
(∫ nW
k=0
pSk
1−σdk
) −µ
σ−1
= (nNφ+ nS)
−µ
σ−1 = (sNφ+ (1− sN))
−µ
σ−1 .
(A.3)
Substituting (A.1), (A.2) and (A.3) into the indirect utility function and
taking the logarithm of the resulting expression to obtain (2.20) and (2.21).
30