ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E04−3

Tax Competition and Regional Trade Union

by
OGAWA Hikaru
TAMAI Toshiki

September 2004

ECONOMIC RESEARCH CENTERSCHOOL OF ECONOMICSNAGOYA UNIVERSITYTAX COMPETITION AND REGIONAL TRADE UNIONOGAWA Hikaru∗
TAMAI Toshiki∗∗

Abstract
The conventional wisdom in the tax competition literature is that the
optimal capital tax rate for local government is zero when head taxes on
immobile residents are available. However, the zero tax-rate is incompatible with the phenomenon that we actually observe. In this paper, we
depart from the full employment tax competition model and present amodel of a tax competition with a regional trade union to explain the
behavior of local government choosing a non-zero tax rate. Furthermore,
it turns out that local governments are likely to overprovide public goods
when the trade union’s preferences are characterized by a high elasticity
of substitution between wage and employment rates.

[Keywords] tax competition, regional trade union, unemployment[JEL Classification Code] H21, H72, J51* Associate Professor, School of Economics, Nagoya University,
email:ogawa@soec.nagoya-u.ac.jp** Graduate Student, School of Economics, Nagoya University
email:d030106d@mbox.nagoya-u.ac.jp1

1

Introduction

One clear result in the tax competition literature is that when head taxes on
immobile residents are available, the optimal capital tax rate for local government is zero1 . The essential reason for this is that capital taxation results infiscal externalities through interregional capital mobility, while a head tax onresidents does not [Wildasin (1989)]. However, a zero tax-rate is incompatible
with the phenomenon which we actually observe. In most countries, local governments use a capital tax even if resident taxes are available. Furthermore,competition among states and local governments is sparked by using tax andregulatory policies on capital [Kenyon and Kincaid (1991)].
These non-zero tax competitions which result in a positive tax rate on capital can be described within the traditional framework by assuming that headtaxes are exogenously constrained in their use, or are for use up to a suﬃcientlevel. In this case, local government uses both a resident head tax and a capitaltax, with the result that the local public goods will be underprovided due tofiscal externalities. We also observe that local government subsidies (levies negative taxation on) capital. For instance, local governments have given special
treatment to capital in various ways to attract the owners of capital. These
local policies have really provided subsidies to mobile capital so that capital inflows increase the welfare of residents. The traditional literature has not clearly
explained what incentive local government has in setting a non-zero tax rate,
when it is not constrained from using a head tax2 . What this paper stresses
as the reason why tax competition models cannot explain local governments’practice of setting non-zero capital tax rates is that the behavior of governments
is analyzed in the framework of a perfect labor market.
More recent studies, notably Lejour and Verbon (1996), Fuest and Huber(1999), Boadway et al. (2002), Lozachmeur (2003), Leite-Monteiro et al. (2003),
and Sato (2004) have departed from the assumption of full employment in theirfiscal competition analyses. While the causes of unemployment diﬀer between
1 There is a large body of research on interregional tax competition. A partial list includes
Zodrow and Mieszkowski (1986), Wilson (1986), and Wildasin (1989). See Wilson (1999) and
Wildasin and Wilson (2003) for a general review of the tax competition model.
2 The exceptions are Coates (1993), DePater and Myers (1994) and Ogawa (2000).

2

the analyses of Lejour and Verbon (1996) and Fuest and Huber (1999), theyboth analyze the implication of unemployment for the welfare-eﬀect of tax coordination in the tax competition model. By assuming an other cause of unemployment, Boadway et al. (2002) and Sato (2004) examine the non-full employment model of interregional tax competition. They incorporate a job-searchand recruiting-friction model into the tax competition framework to examine
the eﬃciency of local tax settings. Lozachmeur (2003) and Leite-Monteiro etal. (2003) examine how fiscal competition aﬀects the choice of unemployment
insurance and the eﬃciency of equilibrium, with, the former analysis focusing
on capital mobility and the latter on labor mobility.
The aim of this paper is diﬀerent from those cited above, but we follow
them in agreeing that the labor market is imperfect; however, we postulatethat it is imperfect in the sense that unemployment exists due to a regional
trade union. In our analysis, we can obtain the result that local government
chooses non-zero tax rates on capital even if taxation on residents is available.
This result supports the possibility that local governments use the capital tax
as a strategic policy variable, and that they choose ineﬃcient tax rates. In
the second part of this paper, we analyze the eﬃciency of local public goods
provision when the head taxes on residents are restricted to use. It turns outthat local governments tend to overprovide public goods when the trade union’s
preferences are characterized by a high elasticity of substitution between wage
and employment rates.
This paper is organized as follows. Section 2 introduces the model. We
incorporate an imperfect labor market into a standard tax competition framework. In section 3, we then consider the local government policies. The policy
alternatives are viewed in the context of a tax competition framework with labormarket imperfections, and we show that local government has an incentive tochoose a non-zero tax rate on capital. In section 4, we compare the decentralized equilibrium with the Pareto optimal condition to examine the eﬃciency of
local public goods provision. Section 5 oﬀers concluding remarks.

3

2

The Model

Technology. The model is one of tax competition among small regions witha regional trade union. There are n small regions, denoted by subscript i =1, 2, ..., n. In each region i, there are immobile residents, and the regional population is denoted by Ni . To simplify the notation, we normalize as Ni = 1
without any loss of generality.
The economy has a fixed stock of capital, K̄, which is perfectly mobile among
regions. Denoting the amount of capital located in region i as Ki , the total
supply of capital is fixed at K̄ such that
K̄ =

n
X

Ki =

i=1

n
X

θi K̄.

(1)i=1

We here assume that residents in region i own the fraction θ i ∈ (0, 1) of the capital stock in the economy. The production of private goods requires using capitaland labor with constant returns to scale technology, Yi = F (Ki , Li ) = Li f (ki ),where Li is the amount of labor and ki ≡ Ki /Li . In the following analysis, we
use the Cobb-Douglas type of technology represented by F (Ki , Li ) = Kia L1−a,iwhere 0 < a < 1.
Local government. Local government provides local public goods, gi , whichyield benefits to residents. Private goods can be used as an input to produce
local public goods, and units can be chosen so that the public goods provision
in region i can be measured in terms of units of private goods. The budget
constraint on local government requires that the cost of providing local public
goods must be equal to the sum of the revenue from capital (unit) tax, τi Ki ,and the head tax levied on residents, hi . Thus, the budget constraint is
gi = τi Ki + hi .

(2)

Firms. Profit-maximizing input decisions implyr + τi = f 0 (ki ) = akia−1 ,4(3)wi = f (ki ) − f 0 (ki )ki = (1 − a)kia ,(4)where r is the market net return on capital, τi is the unit tax rate on capital, andwi is the wage rate. Competition among regions is expressed by the assumptionthat each local government takes r as given. Equation (3) implicitly defines
ki = k(τi ) withki0 (τi ) ≡

1
∂ki
1
=
= 00
< 0.
∂τi
f (ki )a(a − 1)kia−2(5)

Regional trade union. In each region, there is a single trade union. Following
Corneo and Marquardt (2000) and Imoto (2003) among others, we assume thatthe union pursues two goals: high wages and high rate of employment. A
regionally monopolistic trade union bargains over wages and the employment
rate by accounting for the labor demand determined by (3) and (4). Formally,
the optimization problem for the union is to maximize the objective function of
the wages and the employment rate represented by
Vi = [βi (wi − w̄i )σ + (1 − βi )(1 − µi )σ ]

1/σ

,

(6)

subject to(1 − µi ) =

µ

w̄i
wi

¶1/a

,

(7)

where −∞ < σ < 1 and βi ≥ 0. (7) is obtained by using (4). In (6) and (7),w̄i denotes the competitive wage, and 1 − µi (= Li ) represents the employment
rate in region i3 .

The particular shape of the convex indiﬀerent curves generated by a CES
objective function depends on the value of σ. As σ → −∞, the substitution
between wages and employment is impossible in the limit for the union. The
CES utility function becomes the Cobb-Douglas function for σ = 0, so that theunion’s objective function has a constant unit elasticity of substitution. In thelimiting case of σ → 1, the indiﬀerence curves become a straight line so thatwages and employment are perfect substitutes.
3 Thus, the unemployment rate is µi = 1 − Li since we have assumed Ni = 1.

5

The first-order condition is

dVi
dwi

=
×

1/σ−1

[βi (wi − w̄i )σ + (1 − βi )(1 − µi )σ ]!
Ãµ ¶σ/a
w̄
1
−
β
1
i
i
= 0,
βi (wi − w̄i )σ−1 −
a
wi
wi

(8)

which is written as4(1 − βi )(1 − µi )σ = aβi (1 − (1 − µi )a )σ−1 ((1 − a)kia )σ .

(9)This yields the unemployment rate schedule µi (ki ) with
µ0i (ki ) ≡Li (1 − Lai )
dµi
aσ
=−
.
a
a
dki
σ(1 − Li ) + aLi (σ − 1)
ki

(10)

From (5) and (10), we can obtain the eﬀects of local tax changes on theunemployment rate as follows:

Lemma. The eﬀects of a tax rate change on changes in the unemployment
rate are classified into three scenarios5 .
Scenario 1: σ < 0. µ0i (ki ) < 0, so that µi increases as τi increases.
Scenario 2: σ = 0. µ0 (ki ) = 0, so that µi has no relationship with τi .
Scenario 3: 0 < σ < σ̂ ≡ a/(1/Lai − (1 − a)). µ0 (ki ) > 0, so that µi decreases
as τi increases.
The decision to attract investment by reducing tax rates is often motivatedby the concern of fighting unemployment and enhancing job creation. This casecorresponds to Scenario 1. However, it might be also the case that capital andlabor has strong substitute relationship, and that capital expels labor from the
4 Notice that, in this model, full employment equilibrium as examined in the traditional
tax competition model can be described by assuming βi = 0, since we obtain µi = 1 as βi = 0
in (9).
5 We might consider a fourth scenario, i.e., the case of σ̂ ≤ σ < 1. However, we exclude thiscase from the following analysis since the second-order condition for the union’s optimization
problem is not satisfied. See Appendix for the second-order condition.

6

job market job. It is in Scenario 3 that invested capital raises the unemployment
rate.
Households. In each region, there are immobile residents with quasi-linear
preferences ui = xi + v(gi ) defined over consumption of a private numeraire
good, x, and a local public good, g, where v 0 ≡ dv/dgi > 0, v 00 ≡ d2 v/dgi2 <0. The residents are classified into two types of workers: employed (j = e)and unemployed (j = u). Since we have assumed identical individuals in theregion, all employed and unemployed workers earn a return from capital and aretaxed by the local government. Unemployment is seen as just an unfortunate
accidentjust an accident for each worker, in which those fortunate enough to be
employed receive wages while the jobless workers earn no wage income. Thus,
the budget constraints of the employed and unemployed workers are given by
xji =

3

½

wi + rθi K̄ − hirθi K̄ − hi

if j = e.
if j = u.

(11)

Equilibrium

The local government i maximizes the utilitarian form of welfare in its region,
Wi = µi uui + (1 − µi )uei , subject to (2) and (11). (2) can be rewritten by
gi = τi (1 − µi )ki + hi . Formally, the maximization problem is given bymax
τi ,hiWi=µi uui + (1 − µi )uei=

(1 − µi )[f (ki ) − ki f 0 (ki )] + rθi K̄ − hi + v(τi (1 − µi )ki + hi ),subject to µi (ki ) and ki (τi ). Since the head tax is a local government choicevariable, the first-order conditions for hi will be∂Wi= v 0 (gi ) − 1 = 0
∂hi

(12)

As for the optimization of the capital tax rate, τi , (5) and (10) permit us toestablish the eﬀect of a change in τi as follows:

7

∂Wi
∂τi

=

−µ0i (ki )ki0 (τi )wi − ki (1 − µi )+v 0 (gi ) [(1 − µi )ki + τi ki0 (τi ) (−µ0i (ki )ki + (1 − µi ))](13)

To derive the optimal capital tax rate for local government when a head tax isavailable, we evaluate equation (13) at τi = 0. Substituting τi = 0 and v 0 (gi ) = 1
into (13), we have∂Wi|τ =0 = −wi µ0i (ki )ki0 (τi )
∂τi i

(14)

From (14), the equilibrium capital tax rates when a head tax is available areclassified into three possible scenarios.
Scenario 1 (σ < 0). τi < 0 since µ0i (ki ) < 0.
Scenario 2 (σ = 0). τi = 0 since µ0i (ki ) = 0.
Scenario 3 (0 < σ < σ̂). τi > 0 since µ0i (ki ) > 0.
Summarizing the results we have the following.
Proposition 1. Assume that local governments can impose a head tax
on immobile residents. When σ < 0 (µ0i (ki ) < 0), local governments provide
subsidies on capital, τi < 0. If σ = 0 (µ0i (ki ) = 0), then they choose a zero tax
rate, τi = 0. If 0 < σ < σ̂ (µ0i (ki ) > 0), they impose a tax on capital, τi > 0.
Since local governments use the capital tax rate as a policy variable, capitalis ineﬃciently allocated across the region, except for the case of σ = 0. The
basic argument that local government chooses a non-zero tax rate on capitalcan be made as follows: when σ < 0 (Scenario 1), an increase in ki accompanied
by a reduction in τi decreases µi since µ0i < 0. That is, a reduction in the tax
rate has a positive impact on the residents’ welfare in region i, so that local
government chooses a negative tax rate on capital. Scenario 2 is the simplest
one. When σ = 0, the capital tax rate has no impact on the amount of capital
available in the region, and that it does nothing to raise the employment rate.
8

Therefore, local government does not use the capital tax as a policy variable,
τi = 0. When 0 < σ < σ̂ (Scenario 3), the reduction in the tax rate increases
ki . However, in this case an increase in ki raises µi since µ0i > 0. Residents are
deprived of their jobs as local government decreases the capital tax rate so as
to attract capital. In this case, local government chooses a positive tax rate toprotect jobs6 .

4Eﬃciency

Now we consider the eﬃciency of local public goods provision when the governments are restricted to using the head tax on residents.
From (13), we havev 0 (gi ) ==ki (1 − µi ) + µ0i ki0 wi
ki (1 − µi ) − µ0i ki0 τi ki + τi ki0 (1 − µi )³´r+τi
1 − ηi ²i 1−aaτi,
1 + ²i + ηi ²i

(15)

where
ηi ≡

ki
d(1 − µi )aσ(1 − Lai )=,dki(1 − µi )σ(1 − Lai ) + aLai (σ − 1)(16)∂ki τi∂τi ki(17)

is the elasticity of the employment rate with respect to the capital located in
the region, and²i ≡is the capital demand elasticity with respect to the tax rate. When the labormarket is perfect, ηi = 0, (15) is reduced to the conventional result of underprovided public goods, v 0 (gi ) = 1/(1 + ²i ) > 1. However, if the labor market
is not perfect and local governments are restricted from imposing a head tax
on residents, we obtain the following result from (15) and Lemma obtained in
6 As referred in the previous footnote, the model corresponds to the traditional tax competition model with full employment when βi = 0. In this case, µ0i = 0, so that local government
chooses a zero-tax rate on capital, τi = 0.

9Section 3.
Proposition 2. When σ ≤ 0, the local government chooses an ineﬃciently
low capital tax rate. However, when σ > 0, the local government might choose
an ineﬃciently high tax rate on capital. Specifically, as σ approaches σ̂, local
government is likely to choose an ineﬃciently high rate of capital tax.
Proof. Assume we are on the left-side of Laﬀer curve, 1 + ²i (1 + ηi ) > 0.
When σ ≤ 0, µ0i ≤ 0 and ηi ≥ 0. Using ²i < 0 and ηi ≥ 0, from (15), we havev 0 (gi ) > 1. Next, we consider the case of σ > 0 (ηi < 0). Public goods are
overprovided when1 − ηi ²iµ

1 − a r + τiaτi¶

< 1 + ²i (1 + ηi ),which can be rewritten as−ηi >From (16), we have

−ηi

=
=

aτi
≡ ηˆi ∈ (0, 1).
(1 − a)r + τi

(18)

aσ(1 − (1 − µi )a )σ(1 − (1 − µi )a ) + a(1 − µi )a (σ − 1)a−.
a(1−µi )a (σ−1)
1 + (1−(1−µi )a )σ−

We now define σ̃ ≡ a(1 − µi )a /[1 + a − (1 − µi )a ], which satisfies σ̂ > σ̃. Then
we obtainlim (−ηi ) = 1.

σ→σ̃

(19)

Therefore, (18) holds as σ → σ̂. The range of σ that leads local government tochoose an ineﬃciently high tax rate is formally given by σ̃ ≤ σ < σ̂. □Proposition 2 implies that when the labor market is perfect or capital inflow
brings about new jobs, local public goods are undersupplied. However, capitalstrongly substitutes for labor, and that capital inflow induced by the capital tax
10rate reduction eliminates jobs in the region, local government might choose an
ineﬃciently high tax rate.
The sources of ineﬃciency can be identified by two kinds of externalities;(i) positive (fiscal) externality and (ii) negative externality. In our model, thelocal government ignores the external eﬀects of its tax change on the otherregions’ tax revenue [Wildasin (1989)]; although a tax increase in region i aﬀects
region j’s fiscal budget as tj (∂[(1 − µj )kj ]/∂ti ), local government i does nottake that into account. The existence of fiscal externality leads to an undertaxation on capital since it causes positive externality, tj (∂[(1 − µj )kj ]/∂ti ) =−τj ki0 (τi )(1 − µj )(ηj + 1) > 07 .

In an environment of an imperfect labor market there is a second sourceof ineﬃciency that might cause negative externality. When local government ichanges its capital taxation it aﬀects the well-being of the residents of the otherregion j through the expected wage income in region j, but does not accountfor this external eﬀect in its decision-making. The external eﬀect is expressedas∂(1 − µj )wj= −ki0 (τi )wj (1 − µj )(ηj + a)kj−1 .
∂τi

(20)

As long as ηj ≥ 0, ∂[(1 − µj )wj ]/∂τi > 0 and an increase in the tax rate causes
positive externality. However, when ηj + a < 0 an increase in capital tax ratecauses negative externality on the other region j, and in cases where the negative
externality dominates the positive (fiscal) externality, the equilibrium tax ratewould be set at an ineﬃciently high level.

5

Concluding Remarks

By incorporating the behavior of a regional trade union to examine the eﬀects oflabor market imperfection on the equilibrium of the tax competition model, we
present a revised model in which local government deviates from a zero capitaltax. Moreover, the overprovision of public goods might prevail when capital
inflow induced by the capital tax rate reduction eliminates jobs in the region.
7 Notice that η

j + 1 > 0 for all σ < σ̂.

11The key point made by our results is not concerned with the existence of
unemployment (see the case of σ = 0), but rather with how the labor demand
react to capital inflow through a reduction in the capital tax rate. In an environment where the economy contains preferences or a technology that brings abouta labor demand reduction when capital moves into the region, local government
tends to impose a positive tax on capital and to overprovide public goods.
Although our model is very general in some respects, it must be noted thatthe eﬃciency results achieved here rely on a variety of simplifying assumptions.
However, it should also be noted that some of our assumptions could be relaxedwithout changing the main result of this paper. Specifically, although we derive
our propositions by characterizing the preferences of a trade union using the
CES utility function, we can also derive the same result if we assume a CES
production function and a Cobb-Douglas utility function for the trade union.

Appendix
Given the first-order condition represented by (9), the second-order condition is
given by(1 − β)(1 − µi )σaµa(σ − 1) + (a + σ)[1 − (1 − µai )]1 − (1 − µi )a

¶

< 0,

which can be rewritten asσ<a(1 − µi )a≡ σ̄i .
1 + a − (1 − µi )a(21)

Taking a logarithm for (9), we haveln a + ln β + (σ − 1) ln[1 − (1 − µi )a ]+σ[ln(1 − a) + a ln ki ]=ln(1 − β) + σ ln(1 − µi ). (22)The diﬀerentiation of (22) with respect to ki and 1 − µi yields
ηi∙¸
σ[1 − (1 − a)(1 − µi )a ] − a(1 − µi )a= aσ.
1 − (1 − µi )a
12

(23)

From (23), we obtain the features that ηi > 0 if σ < 0 and ηi = 0 if σ = 0.
aa(1−µi )Furthermore, ηi < 0 if 0 < σ < 1−(1−a)(1−µa ≡ σ̂i . Although we might be ablei)to consider the case of σ ≥ σ̂, we can disregard this case since it contradicts thesecond-order condition; as that condition requires σ < σ̄i , σ ≥ σ̂i does not holdsince σ̄i < σ̂i .

Acknowledgement
Hikaru Ogawa is greatful to the Shikishima foundation, the Japan Society for
the Promotion of Science, and the Japan Center for Economic Research for theirfinancial support.

Reference
Boadway R, Cuﬀ K, and N Marceau (2002), Interjurisdictional competition forfirms, International Economic Review 43, 761-782.
Coates D (1993), Property tax competition in a repeated game, Regional Science and Urban Economics 23, 111-119.
Corneo G and M Marquardt (2000), Public pensions, unemployment insurance,and growth, Journal of Public Economics 75, 293-311.
DePater J and G Myers (1994), Strategic capital tax competition: a pecuniary
externality and a corrective device, Journal of Urban Economics 36, 66-78.
Fuest C and B Huber (1999), Tax coordination and unemployment, International Tax and Public Finance 6, 7-26.
Imoto S (2003), An example of nonlinear endogenous business cycle model:build in the trade union, Economics Letters 81, 117-124.
Kenyon AD and J Kincaid (1991). Competition among States and Local Governments: Eﬃciency and Equity in American Federalism, The Urban Institute Press, Washington, D.C.
13

Lejour AM and HA Verbon (1996), Capital mobility, wage bargaining, and social insurance policies in an economic union, International Tax and Public
Finance 3, 495-514.
Lozachmeur JM (2003), Fiscal competition, labor mobility, and unemployment,
FinanzArchiv 59, 212-226.
Leite-Monteiro M, Marchand M, and P Pestieau (2003), Employment subsidy
with capital mobility, Journal of Public Economic Theory 5, 327-344.
Ogawa H (2000), Imperfect capital mobility and local government behaviour
in a two-period economy, Bulletin of Economic Research 52, 151-166.
Sato Y (2004), Tax competition and search unemployment, Discussion paper
No.04-1, Department of Economic Environment, Graduate School of Environmental Studies, Nagoya University.
Wildasin DE (1989), Interjurisdictional capital mobility: fiscal externality anda corrective subsidy, Journal of Urban Economics 25, 193-212.
Wildasin DE and JD Wilson (2004), Capital tax competition: Bane or Boon?,
Journal of Public Economics 88, 1065-91.
Wilson JD (1986), A theory of inter-regional tax competition, Journal of Urban
Economics 19, 296-315.
Wilson JD (1999), Theories of tax competition, National Tax Journal 52, 269304.
Zodrow RG and Mieszkowski P (1986), Pigou, Tiebout, property taxation, andthe underprovision of local public goods, Journal of Urban Economics 19,
356-370.

14