POLLUTION MOBILITY, PRODUCTIVITY DISPARITY, AND THE SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS*: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS

Abstract

This paper first develops a model to characterize the equilibrium distribution of polluting and nonpolluting firms and then turns to the larger question of whether the equilibrium distribution is socially optimal. We find that the equilibrium distribution of polluting firms differs from the social optimum when they generate a large amount of stationary pollution and have much higher or lower productivity than clean firms. In these cases, conventional pollution control approaches generally do not bring about an optimal distribution. Consideration of transport costs along with productivity and pollution changes some of the classic results of the new economic geography literature.

Full text

Journal of Regional Science, VOL. 00, NO. 0, 2016, pp. 1–20
POLLUTION MOBILITY, PRODUCTIVITY DISPARITY, AND THE
SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING
FIRMS*
JunJie Wu
Department of Applied Economics, Oregon State University, 213 Ballard Extension Hall, Corvallis,
OR 97330; and Resources for the Future. E-mail: junjie.wu@oregonstate.edu
Jeffrey J. Reimer
Department of Applied Economics, Oregon State University, 213 Ballard Extension Hall, Corvallis,
OR 97330. E-mail: jeff.reimer@oregonstate.edu
ABSTRACT. This paper first develops a model to characterize the equilibrium distribution of polluting
and nonpolluting firms and then turns to the larger question of whether the equilibrium distribution
is socially optimal. We find that the equilibrium distribution of polluting firms differs from the social
optimum when they generate a large amount of stationary pollution and have much higher or lower
productivity than clean firms. In these cases, conventional pollution control approaches generally do
not bring about an optimal distribution. Consideration of transport costs along with productivity and
pollution changes some of the classic results of the new economic geography literature.
1. INTRODUCTION
The impact of a polluting firm on human health and ecosystems, to a large extent, de-
pends on its location. A firm generating air pollution, for example, is likely to affect more
people when it is located in a heavily populated area than in a sparsely populated area.
The spatial distribution of polluting firms is therefore of critical importance for designing
environmental policy (Kohn, 1974). At the same time, the clustering and dispersion of
firms across the landscape may be driven in part by production technology, with agglom-
eration economies playing a role in firm location decisions (Abdel-Rahman and Fujita,
1990; Artz, Kim, and Orazem, 2016).
It is an open question whether the existing spatial distribution of polluting firms
is in any sense ideal. Selected aspects of the seven most air polluting industries in the
United States are reported in Table 1, along with an aggregate of service industries for
comparison. The latter are designated as “clean,” i.e., relatively nonpolluting. The table
reports geographic concentration, productivity, emissions of particulate matter (PM10),
and emissions of volatile organic compounds (VOC). Spatial concentration, productiv-
ity, and pollution vary greatly among the industries. While there may be a relationship
among these characteristics, it is not simple. For example, firms producing petroleum
and coal products have high productivity, moderate spatial concentration, and fairly high
pollution by most measures. Firms producing transport equipment, meanwhile, are rel-
atively concentrated, with moderate levels of productivity and pollution. Service indus-
tries, by contrast, contribute little pollution and have average levels of concentration and
*We thank JRS co-editor Steven Brakman and two anonymous referees for their invaluable com-
ments.
Received: February 2015; revised: August 2015, November 2015; accepted: November 2015.
C
2016 Wiley Periodicals, Inc. DOI: 10.1111/jors.12266
1

2 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
TABLE 1: Firm Concentration, Productivity, and Pollution by Sector, United States
Productivity PM10 (annual VOC (annual Concentration
($ of output per tons per million tons per million (Ellison-Glaeser 1997
Industry (NAICS Code) hour of labor, Mean) $ of output) $ of output) gamma, mean)
Polluting industries less productive than the service (clean) sector
Fabricated metal product
manufacturing (332)
67.0 0.02 0.38 0.022
Nonmetallic mineral product
manufacturing (327)
74.5 1.50 0.39 0.019
Polluting industries with productivity levels similar to that of the service (clean) sector
Paper and allied products
(322)
93.4 0.70 1.18 0.017
Primary metal manufacturing
(331)
96.4 0.86 0.57 0.046
Transport equipment
manufacturing (336)
119.4 0.01 0.19 0.063
Polluting industries more productive than the service (clean) sector
Chemical manufacturing (325) 182.4 0.20 0.86 0.044
Petroleum and coal products
manufacturing (324)
574.7 0.22 1.08 0.028
Service (clean) sector
Service industries (423-722) 104.3 nil nil 0.021
Notes: All data are for 1999. The concentration index was obtained from Thomas J. Holmes and is described
in detail in Holmes and Stevens (2004). Productivity is calculated as output in million dollars, divided by millions
of hours worked using data from the website of the Bureau of Labor Statistics, Labor Productivity, and Costs.
Pollution measurements are from Industry Sector Notebooks, Environmental Protection Agency, various profiles.
productivity. Many other combinations of concentration, productivity, and emissions can
be observed in Table 1.
Anecdotal evidence suggests that in developing countries the degree of spatial con-
centration is even more extreme, while absolute levels of pollution are higher. In China,
for example, the level of pollution in some regions has become so pronounced that own-
ers of some firms are choosing to relocate themselves and their employees away from it
(Burkitt and Spegele, 2013). Pollution, therefore, can be a source of spatial dispersion
even as it is, at other times, a consequence of agglomeration (Cao and Karplus, 2014).
In this paper, we first develop a model to characterize the equilibrium distribution
of polluting firms and then turn to the larger question of whether the equilibrium dis-
tribution is socially optimal. The model accounts for the mobility and level of emissions,
consumer preferences, firm heterogeneity, and other key features of markets, and is used
to address the following questions: (1) Why are firms in some polluting industries spatially
dispersed but concentrated in others? (2) Does the market lead to the optimal spatial dis-
tribution of polluting firms? (3) If not, can traditional pollution control approaches, such
as the polluter pays principle, correct the problem?
Our approach builds on the original work of Ottaviano, Tabuchi, and Thisse (2002)
and Saito, Gopinath, and Wu (2011), including their ways to characterize consumer behav-
ior, producer technology, and trade costs. We extend their work by introducing polluting
firms into the model and by allowing their productivity to differ from that of nonpolluting
firms. We show that the range of possible spatial configurations of firms is greatly en-
larged when we consider the level and mobility of pollution and productivity differences
between polluting and nonpolluting industries. This makes the model more complex but
allows us to replicate some of the situations observed in Table 1.
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 3
Pollution differs in important ways from congestion considered in some economic
geography models (e.g., Fujita and Thisse, 2002, p. 146). First, some firms in our analysis
do not generate pollution, in contrast to the case with congestion, in which every firm
contributes to the problem; we allow for both polluting and nonpolluting firms. Second,
unlike congestion, pollution may be transboundary, meaning that a firm can be outside a
region yet still be contributing to pollution in the region; we allow for both stationary and
transboundary pollution. While it is true that the impact of congestion, such as reduction
in the growth rate of a given region, can propagate to neighboring regions, congestion
itself does not “transport” to neighboring regions as pollution does. Third, in contrast to
congestion, pollution may not be fixed per firm; we allow for both pollution that is fixed
per firm and a more general case in which it varies with output. We show that these three
issues distinguish pollution as a unique problem, which pays a major role in determining
the spatial distribution of firms and its derivation from the social optimum.
We also account for the primary factors that influence entrepreneurs’ location deci-
sions: profit, the cost and availability of goods and services, and environmental amenities
(i.e., a distaste for pollution). We consider the spatial distribution of polluting firms (hence-
forth referred to as dirty firms) as well as nonpolluting firms (henceforth referred to as
clean firms) for two reasons. First, the relocation of clean firms changes the market size
and the number of people exposed to pollution, and second, the locations of dirty and clean
firms are not independent due to scale economies (see, e.g., Henderson, 1977; Delgado,
Porter, and Stern, 2010), knowledge spillovers (Lucas, 1988), and labor market pooling
(Krugman, 1991).
Much progress has been made in modeling the causes of firm agglomeration and dis-
persion (Brakman, Garretsen, and Marrewijk, 2014). Pioneering studies (e.g., Krugman,
1991) generally do not explicitly consider pollution, which differs in important ways from
congestion, as described above. The early literature on spatial pollution (e.g., Tietenberg,
1974) considers the amount of emissions transported from sources (e.g., firms) to monitors
(e.g., population centers), but has the common weakness of taking the location of firms
and households as fixed.
Our study allows for endogenous locational choice by polluting firms and thus con-
nects to empirical and theoretical work on the pollution haven hypothesis, the idea that
jurisdictions with less stringent environmental regulation attract pollution intensive in-
dustries (Markusen, Morey, and Olewiler, 1993; Levinson and Taylor, 2008). Some of
the work does consider agglomeration effects. For example, Elbers and Withagen (2004)
consider ecological dumping and the pollution haven hypothesis with a spatial model of
monopolistic competition and show that pollution can countervail clustering that would
otherwise occur, although they do not examine optimal policy. Zeng and Zhao (2009) show
that agglomeration forces can alleviate the pollution-haven effect, if environmental regu-
lation is more stringent in the larger country. In contrast to previous studies, this paper
focuses on the spatial distribution of polluting firms among population centers, which has
important implications for pollution exposure and damage.
This paper is closely related to a few studies that examine the linkages between
pollution and firm concentration. Copeland and Taylor (1999) develop a two-sector model
to examine the effects of pollution-created cross-sectoral production externalities on trade
patterns, and find that pollution provides a motive for trade because trade can spa-
tially separate incompatible industries. They assume pollution from the industrial sector
damages the environmental capital, which reduces the productivity of agricultural goods
within that region, but pollution is not transboundary. Unteroberdoerster (2001) intro-
duces transboundary pollution into the Copeland and Taylor model and finds that allowing
pollution to be transboundary can change some of Copeland and Taylor’s results. Hosoe
and Naito (2006) also explore the effect of transboundary pollution on trade patterns, but
C
2016 Wiley Periodicals, Inc.

4 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
use a new economic geographic model. In addition, Hosoe and Naito (2006) simulate the
effect of an import tax as the environmental policy on trade patterns. Like Copeland and
Taylor (1999) and Unteroberdoerster (2001), Hosoe and Naito (2006) also assume pollu-
tion reduces agricultural productivity, but does not affect household utility directly. Lange
and Quaas (2007) use an economic geography model to characterize different equilibria
of firm concentrations, and find that the extent of agglomeration is not independent of
pollution. Arnott, Hochman, and Rausser (2008) investigate the optimal combinations
of housing and industry under different tradeoffs of pollution costs and transport costs,
and call for future research that takes into account increasing returns to scale, product
variety, and heterogeneous skills among the population. We incorporate all these features
into our analysis. More importantly, our study differs from all the above by its ability to
explain some of the outcomes in Table 1, which shows multiple dimensions by which eco-
nomic sectors differ across the landscape. Uniquely among these studies, we distinguish
between polluting and nonpolluting firms and allow for productivity differences. We also
explore the optimal distribution of firms and policies to achieve it.
Our study contributes to a large literature documenting the existence of considerable
productivity differences even within narrowly defined industries (Bernard and Jensen,
1999; Aw, Chung, and Roberts, 2000). We explore the implication of productivity dif-
ferences between industries for firm location. Firms within each industry, however, are
assumed to have adopted the most profitable technology, which we take as exogenous.
Our allowance for industrial differences connects our paper to recent economic geography
work by Tabuchi and Thisse (2006), Baldwin and Okubo (2006), Okubo, Picard, and Thisse
(2010), and Saito et al. (2011). We go beyond these studies by allowing for pollution, which
differs from congestion in the three ways already outlined above.
In our analysis we describe how our results nest firm distributions that arise in
existing models, and can represent additional distributions that occur in the real world.
We are unable, of course, to satisfactorily explain all of the differences in concentration,
productivity, and pollution exhibited in Table 1, in part because they also depend on the
spatial distribution of natural endowments and other factors that we do not model in
this paper. Nonetheless, we are able to provide new insights into the spatial patterns of
polluting firms, and contribute to this rapidly evolving literature.
The remainder of this paper is organized as follows. We first present the model and
then apply it to characterize the equilibrium distribution of clean and dirty firms when
they have the same productivity. In a subsequent section we consider the case in which
firms in the clean industry have higher productivity than firms in the dirty industry. A
third general case considers that firms in the dirty industry have higher productivity;
they run cheaply, but have inherently higher levels of pollution. Once we analyze all the
possible market equilibria that arise under these cases, we evaluate whether these are in
any sense socially optimal. Most of the cases outlined in the first part of the paper are not
optimal from a societal point of view. For these cases we derive optimal taxes that induce
a socially optimal distribution of dirty and clean firms.
2. THE MODEL
Consider an economy with two symmetric regions, East (E)andWest(W). We divide
the economy into two sectors, manufacturing (M) and agriculture (A). Sector Mincludes a
dirty (D) manufacturing industry and a clean (C) service industry. Firms in the industries
produce horizontally differentiated goods. Sector Aproduces the homogenous, num´
eraire
good. There are two types of workers in the economy: laborers and entrepreneurs. Laborers
provide labor input for sectors Aand M. They are evenly dispersed between the two regions
and are not mobile. Each entrepreneur owns one firm, which produces a unique good. The
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 5
total mass of firms in industry k(referred to as type-kfirms henceforth), Nk, equals the
number of goods produced by the industry, where k=C,D. Entrepreneurs provide human
capital to their firms and decide where their firms locate, taking into consideration profit,
consumption, and quality of life.
Consumption Decisions
Worker preferences are defined by a quadratic utility function:
U=␣NC
0
qC(i)di +ND
0
qD(j
)dj
−␤−␥
2NC
0
q2
C(i)di +ND
0
q2
D(j
)dj

−␥
2NC
0
qC(i)di +ND
0
qD(j
)dj
2
+qA−D(Z),(1)
where qk(i) is the consumption of the ith good produced by a type-kfirm; qAis the
num´
eraire good; Zis the level of pollution in the region where the consumer lives, D(Z)
is the disutility of pollution, and ␣,␤,and␥are positive parameters. (␣−␥) measures
the substitution between sector Mgoods and the num´
eraire good, and (␤−␥) measures
the degree of product differentiation among sector Mgoods, with (␤−␥)=0 indicating
that varieties are perfect substitutes and consumers care only about total consumption.
We assume ␤>␥, implying that there is consumer love of variety in the aggregate.
Each worker maximizes utility subject to a budget constraint:
maxqC(i),qD(j
),qAUs.t.NC
0
pC(i)qC(i)di +ND
0
pD(j
)qD(j
)di +qA=Y+Y0,(2)
where pk(i) is the price of the ith good produced by type-kfirm, Yis profit from manufac-
turing activity for entrepreneurs and wage for laborers, and Y0is the initial endowment,
which is large enough to ensure some consumption of the type-Agood. Utility maximiza-
tion yields the following demand functions (derived in the online Appendix):
qC(i)=a−dp
C(i)+b(PC+PD),(3)
qD(j
)=a−dp
D(j
)+b(PC+PD),(4)
qA=(y+y0)−a(PC+PD)−b(PC+PD)2+d(PC2+PD2),(5)
where a =␣[␤+␥(NC+ND−1)], b =␥/{(␤−␥)[␤+␥(NC+ND−1)]},d=1/(␤−␥),
Pk=Nk
0pk(i)di,and Pk2=Nk
0p2
k(i)di.Bothaand bare a decreasing function of NCand
ND, suggesting that as the number of competitors increases, the demand for a variety de-
clines at a given price. Thus, the different levels of competition would have an additional
effect on the location decision of firms. To focus on the effect of pollution characteristics on
agglomeration and to keep the analysis tractable, we assume that clean and dirty firms
have the same mass, which is normalized to one ( NC=ND=1). Let Lrepresent the total
mass of laborers in the economy, and ␭Cand ␭Ddenote, respectively, the share of clean and
dirty firms in the East. Then the total masses of population in the east and west equals:
ME=␭C+␭D+0.5Land MW=(1 −␭C)+(1 −␭D)+0.5L.
Substituting (3)–(5) into (1) yields the indirect utility function:
V=a2
d−2b−a(PC+PD)−b
2(PC+PD)2+d
2(PC2+PD2)+Y+Y0−D(Z),(6)
which shows that profit, product variety, and environmental quality all affect utility.
C
2016 Wiley Periodicals, Inc.

6 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
Production Decisions
On the supply side, sector Ais perfectly competitive in both regions, and its production
technology requires one unit of labor to produce one unit of output. The supply of labor for
firms is perfectly elastic in both regions. The choice of sector A’s good as the num´
eraire
implies that the price of labor equals one in both regions.
Sector Mhas increasing returns to scale technology by virtue of a fixed cost compo-
nent. Each entrepreneur owns one firm and provides one unit of human capital for her
firm. Each firm uses human capital as a fixed input and laborers as a variable input.
Thus, type-kfirms’ total cost to produce qr
kunits in region ris (1 +wkqr
k), where wkis
the marginal cost of production. Later we will separately analyze the cases wC=wD,
wC<w
Dand wC>w
D. The productivity difference between the two types of firms is em-
bodied in human-capital differences between the two types of entrepreneurs (Henderson,
2003; Nocke, 2006).1Without loss of generality, we will assume that the firm with higher
productivity has a marginal cost of zero.
A key aspect of pollution is that it varies in its mobility according to the type of
pollution, e.g., atmospheric particulate matter may be more easily transmitted across
regions than VOCs or industrial waste. In the model, each dirty firm contributes ␦units of
pollution to the region where it is located and (␦−ε) units of pollution to the neighboring
region, where 0 ≤ε≤␦. If pollution is stationary, ε=␦. If pollution is highly mobile
or sources of emission are unimportant, ε=0. The total amount of pollution in East
and West equals ZE=␭D␦+(1 −␭D)(␦−ε)andZW=(1 −␭D)␦+␭D(␦−ε), respectively.
We also assume the unit of pollution is normalized such that the marginal disutility of
pollution is one. These assumptions are restrictive and made for simplicity. Later we will
allow the amount of pollution to depend on firm output. We will show that the main
insights from the simpler case carry over to this more general one.
The number of firms is large enough that each firm can ignore its influence on, and
reactions from, other firms. Under product differentiation and trade costs, firms set prices
specific to each region to maximize profit:
max
p
rr
k,p
ro
k
␲r
k=p
rr
k−wkqrr
kMr+p
ro
k−t−wkqro
kMo−Yr
k,(7)
wherek=C,D;r,o=E,W;r= o;p
rr
kis the price of a type-kgood produced in region rand
sold in region r,p
ro
kis the price when produced in region rand sold in the other region, t
is the cost of transporting one unit of any variety from one region to the other, qrr
kis the
demand of a consumer living in region rfor a type-kgood produced in region r,andqro
k
is the demand of a consumer living in region rfor a type-kgood produced in the other
region. Yr
kis the cost of human capital and goes to the entrepreneur as his income. qrr
kand
qro
kare defined by (3) and (4). First-order conditions result in the following prices (see the
online appendix):
pEE
k=2a+b(wD+wC)+bt (2−␭D−␭C)
4(d−b)+wk
2,pEW
k=pWW
k+t
2,(8)
pWW
k=2a+b(wD+wC)+bt (␭D+␭C)
4(d−b)+wk
2,pWE
k=pEE
k+t
2.(9)
1The model assumes that there are inherent productivity differences between clean and dirty firms
(wparameter) that do not vary with agglomeration. In other words, the type of agglomerations modeled
here are scale economies or urbanization economies, rather than inter-industry linkages, which may lead
to the marginal costs to vary with agglomeration. This is an area for future work.
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 7
These equations show that firms with lower marginal cost set lower prices for their
products.
Substituting Equations (8) and (9) into (7) gives the firm’s profit. Free-entry leads to
zero profit in equilibrium. Thus, the income for entrepreneurs in industry kand region r
equals:
Yr
k=p
rr
k−wkqrr
kMr+p
ro
k−t−wkqro
kMo.(10)
That is, any markup over variable costs goes to the owner as the net return to his
human capital. The difference in additional returns for locating in the East, as opposed
to the West, for the two types of entrepreneur equals:
YE
C−YW
C−YE
D−YW
D=−dt(wC−wD)(␭C+␭D−1),(11)
which is positive for (␭C+␭D−1) >0 if and only if wC<w
D. This suggests that firms
with lower marginal cost would gain more in profit by locating in a larger market.
Spatial Equilibrium
Before analyzing the spatial distribution of firms, we first define the equilibrium
concept. A distribution of firms between the two regions is said to be in equilibrium if no
firms have incentives to move to the other region. This can occur only if VE
k=VW
kunless all
type-kfirms have already moved to the high-utility region. Formally, a spatial equilibrium
is defined as follows:
DEFINITION 1. A distribution of firms between the two regions (␭∗
C,␭∗
D)is an equilibrium
if and only if
VE
k=VW
kif 0 <␭∗
k<1
VE
k≤VW
kif ␭∗
k=0
VE
k≥VW
kif ␭∗
k=1
,k=C,D.(12)
To study the stability of equilibrium, we follow a well-established tradition in migra-
tion modeling by assuming that people are attracted to regions that offer higher utility,
with the power of attraction increasing with a region’s size (Fujita, Krugman, and Ven-
ables, 1999; Tabuchi and Thisse, 2006). Formally, we study stability through replicator
dynamics defined by:
·
␭k=␭k(1 −␭k)Vk,k=C,D,(13)
where ·
␭kdenotes the time derivative of ␭k,andVk≡VE
k−VW
k. Like Tabuchi and Thisse
(2006), we assume when firms move, all markets adjust instantaneously. Because the two
regions are symmetric, we assume whenever an agglomeration occurs, it occurs in the
East.
With the specification of dynamics in (13), we can formally define the stability of
equilibrium (see the online appendix for a formal definition). Intuitively, an equilibrium
is stable if, for any marginal deviation from the equilibrium, entrepreneurs’ pursuit of
higher utility will bring the distribution back to the equilibrium in the case of asymptotic
stability, or at least will not bring it farther away from the equilibrium in the case of
neutral stability (Simon and Blume, 1994, pp. 684–686). Lemma 1 in the online appendix
provides the conditions for checking the stability of various types of equilibrium.
With this basic setup, we consider the equilibrium distribution of clean and dirty
firms under different assumptions about their relative productivity.
C
2016 Wiley Periodicals, Inc.

8 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
3. EQUAL PRODUCTIVITY
We first consider the simple case in which clean and dirty firms face equal costs—or
equivalently under our assumptions, have equal productivity. Differences in utility across
regions are derived by substituting (3)–(5) and (7)–(10) into (6). When the two types of
firms are equally productive, the difference in utility equals:
VE
C−VW
C=VE
D−VW
D=␪␭C−1
2+(␪−2ε)␭D−1
2,(14)
where
␪≡dt 2a(3d−2b)−3d(d−2b)+2b2+bL(d−b)t
4(d−b)2,(15)
which is negative if and only if
t>t∗≡ 2a(3d−2b)
3d(d−2b)+2b2+bL(d−b)>0.(16)
Ottaviano et al.’s (2002) classic spatial equilibrium results can be derived from (14)–
(16) as a special case. Specifically, by setting ε=0, (14) reduces to VE
D−VW
D=VE
C−VW
C=
␪(␭D+␭C−1). Because Ottaviano et al. (2002) do not distinguish between clean and dirty
firms, this equation can be further simplified to VE−VW=␪(␭−1), where ␭=␭D+␭C.
Using this equation and the fact that ␪is negative, zero and positive when tis greater,
equal, and less than t*, we can derive Ottaviano et al. (2002)’s result that if t>t*, the
symmetric configuration (␭=1) is the only stable equilibrium; if t<t*, there are two
stable equilibria corresponding to the agglomeration configuration (i.e.,␭=0or␭=2); if
t=t*, any configuration (any ␭∈[0,2]) is a spatial equilibrium.
In contrast to Ottaviano et al. (2002), which shows the importance of transport cost,
this paper highlights the importance of the level and mobility of pollution in determining
the spatial distribution of firms. Specifically, using (14) and Lemma 1, we can prove the
following:
PROPOSITION 1. Suppose dirty and clean firms are equally productive.
(i) If ε<␪,(␭∗
C,␭∗
D)=(1,1) is the only stable equilibrium.
(ii) If ε=␪, any distribution of firms is a stable equilibrium if ε=␪=0; if ε=␪= 0,any
distribution where ␭C=␭Dis a spatial equilibrium, but unstable.
(iii) If ε>␪,anypointon␪(␭C−0.5) +(␪−2ε)(␭D−0.5) =0is a stable equilibrium.
Proof: The proof of Proposition 1, as well as the proofs of all subsequent propositions,
is given in the online appendix.
Recall that εmeasures the difference in the amount of pollution that a polluting
firm contributes to its own region and the neighboring region. It equals zero if pollution
is perfectly mobile, and equals the total amount of pollution from a dirty firm if pol-
lution is perfectly stationary. Proposition 1 states that if pollution is highly mobile, or
each polluting firm does not release much pollution if pollution is stationary such that
ε<␪, both dirty and clean firms fully agglomerate in the East. To understand the in-
tuition behind this result, note that ∂(VE
D−VW
D)/∂␭C=∂(VE
C−VW
C)/∂␭C=␪>0. Thus, ␪
can be interpreted as the “agglomeration benefit” generated by a clean firm moving to the
East. This agglomeration benefit disappears when there are no trade costs because ␪→0
as t→0. The impact of a dirty firm moving to the East is ∂(VE
D−VW
D)/∂␭D=∂(VE
C−
VW
C)/∂␭D=␪−2ε, which implies that the agglomeration benefit from a dirty firm is mod-
erated by the associated pollution brought to the East.
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 9
When the location of pollution matters relatively little (ε<␪), the agglomeration
effect dominates the pollution consideration, and a complete agglomeration of both types
of firms is the only stable equilibrium. When the agglomeration benefit generated by a
clean firm moving to the East is completely offset by pollution damage generated by a
dirty firm moving to the East (i.e., ε=␪= 0), any distribution with␭C=␭Dis a spatial
equilibrium. But these equilibria are unstable unless if ␪=0 because a slight deviation
from such an equilibrium will lead to complete agglomeration. Specifically, starting from
any point where ␭C>␭D(␭C<␭D), the trajectory of (14) will approach (1, 1) ((0, 0)) as
t→+∞. However, when ε=␪=0, firms’ incentives to move disappear completely, and
any distribution is a neutrally stable equilibrium.
When the local pollution damage is relatively large and/or the trade cost is rela-
tively small such that ε>␪,any(␭C,␭D)on ␪(␭C−0.5) +(␪−2ε)(␭D−0.5) =0 is a stable
equilibrium, including the symmetric configuration. For asymmetric configurations, the
region with more dirty firms is compensated with a larger market where consumers en-
joy more varieties and lower prices of goods. Bosker et al. (2007) show empirically that
multiple equilibria are present in German city growth after the Second World War and
are more likely to be detected when spatial interdependencies are considered.
This case could be relevant to some of the examples in Table 1. To make this com-
parison, note that values of ␭Dclose to one would correspond to the higher levels of the
Ellison-Glaeser (1997) index in Table 1, while values of ␭Dclose to 0.5 would correspond to
Ellison-Glaeser values closer to zero. With this mind, consider the relationship between
firm concentration and pollution for the three sectors that have a productivity level similar
to that of the service sector. Firms in the transport equipment manufacturing are much
less polluting, but more concentrated than firms in the primary metal manufacturing or
paper and allied products. This is consistent with Proposition 1, in that firms in sectors
that are relatively less polluting are more concentrated.
4. THE CLEAN INDUSTRY HAS HIGHER PRODUCTIVITY
Clean industries may have higher productivity levels when they use a cutting-edge
technology to produce a high-tech product. Dirty industries may have lower productivity
levels when they use a traditional or obsolete technology to exploit a natural resource.
The latter scenario may apply to the fabricated metal and nonmetallic mineral product
industries of Table 1. These industries are notably less productive and are more polluting
than the average service industry. As with the equal cost case, the differences in utility
for entrepreneurs located in the two regions can be derived by substituting (3)–(5) and
(7)–(9) into (6):
VE
C−VW
C=s1␭C−1
2+s2␭D−1
2,(17)
VE
D−VW
D=s3␭C−1
2+s4␭D−1
2,(18)
where s1=s,s2=s−m−2ε,s3=s−2m,ands4=s−3m−2εwith:
s≡bdt (2d−b)wD
4(d−b)2+␪,m≡dtwD
2.(19)
From Equations (17) and (18), we can derive the following results.
PROPOSITION 2. Suppose dirty firms are less productive.
(i) If ε≤(s−2.5m),(␭∗
C,␭∗
D)=(1,1) is a stable equilibrium.
C
2016 Wiley Periodicals, Inc.

10 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
(ii) If ε>(s−2.5m),(␭∗
C,␭∗
D)=(1,␭)is a stable equilibrium, where
␭=
ε+0.5m
2ε+3m−s<1(20)
Proposition 2 shows that when clean firms are more productive, they agglomerate in
one region, while the distribution of the dirty firms depends on the level and mobility of
pollution. When each dirty firm produces a low level of pollution, or a high level of mobile
pollution, they also agglomerate in the East. However, when each dirty firm produces a
sufficiently high level of stationary pollution, they disperse between the two regions. The
larger the pollution differential ε, the more dispersed dirty firms are between the two
regions. To see this note that when (2m-s)>0and␭<0.5, (∂␭/∂ε)>0; when (2m-s)<0and
␭>0.5, (∂␭/∂ε)<0. Thus, ␭become closer to 0.5 as εincreases.
To better understand these results, consider an initial distribution where clean and
dirty firms are divided equally between the two regions (␭C=␭D=0.5). Now suppose a
clean firm moves from the West to East. This increases the variety of sector Mproducts in
the East. Consequently, the prices of the manufactured goods decrease, and the demand
increases in the East. Higher production levels reduce the average costs for firms in the
East because of their increasing-returns-to-scale production technologies. This will lead
to higher profit for firms in the East and attract more firms to the region. In equilibrium,
all clean firms locate in the East. This outcome is similar to the “black hole” condition
in Krugman and Venables (1995) and Fujita et al. (1999): the region with the larger
initial share of the manufactured sector will attract the whole sector because of product
differentiation and increasing returns.
The “black hole” would also attract all dirty firms to the East if they differ little
from clean firms. However, when a dirty firm generates a large amount of pollution and
pollution damage is mostly limited to the region where it is located, dirty firms tend
to disperse between the two regions. This occurs because as more dirty firms move to
the East, the pollution damage will increase in the East, but decrease in the West. The
migration will stop when the higher environmental quality in the West completely offsets
the cost-of-living advantage in the East.
Given the level of pollution, dirty firms also disperse between the two regions when
they have much lower productivity than clean firms. Mathematically, ε>(s−2.5m)holds
when wDis large enough because
(s−2.5m)=−
[4(d−b)2+(d−2b)2]dtwD
4(d−b)2+␪,(21)
which is negative when wDis large enough. Because the less productive dirty firms have
lower markups when locating in a larger market, as indicated by Equation (11), they are
more likely to disperse than clean firms. This may explain why the dirty firms in the two
sectors with the lowest productivity in Table 1 (fabricated metal industries, nonmetallic
mineral products) are highly dispersed. Proposition 2 can also explain why the sector that
is more polluting is less concentrated.
As in previous studies, trade costs play a key role in the spatial distribution of firms.
From (21), (s−2.5m)→0ast→0. Thus, condition ε>(s−2.5m) holds when trade costs
are low enough. This implies that dirty firms disperse between the two regions when
the trade cost is low enough. Also, as t→0, then ␭∗
D→0.5, suggesting that the dirty
firms will be highly dispersed between the two regions when the trade cost is minimal.
The result differs from Okubo et al. (2010), who show that agglomeration tends to follow
trade cost reductions. This result also differs from Ottaviano et al. (2002) and Saito et al.
(2011), who show that all firms, both high- and low-productivity firms, agglomerate in
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 11
one region when trade costs are low enough. The difference occurs because when trade
costs are low enough, there are both markup and cost-of-living advantages to be located
in a larger market. Therefore, without pollution, all firms agglomerate in one region with
sufficiently low trade costs. However, with pollution, the region with more dirty firms
will eventually become a less desirable place to live as t→0 because the markup and
cost-of-living advantages both approach zero as t→0. Thus, as t→0, the dirty firms will
divide equally between the two regions if they generate more pollution damage locally.
5. THE DIRTY INDUSTRY HAS HIGHER PRODUCTIVITY
The case in which firms in the dirty industry have higher productivity could reflect a
situation in which labor-saving technologies are available in a high value-added industry.
This situation may apply to petroleum and chemical manufacturing in Table 1, when
compared to clean but relatively low productivity service industries. In such a case, the
differences in utility between the two regions for owners of dirty and clean firms are:
VE
D−VW
D=˜
s1␭D−1
2+˜
s2␭C−1
2,(22)
VE
C−VW
C=˜
s3␭D−1
2+˜
s4␭C−1
2,(23)
where ˜
s1=˜
s−2ε,˜
s2=˜
s−˜
m,˜
s3=˜
s−2˜
m−2ε,and˜
s4=˜
s−3˜
mwith:
˜
s≡bdt (2d−b)wC
4(d−b)2+␪,˜
m≡dtwC
2
(24)
Using equations (22) and (23), we can derive the following:
PROPOSITION 3. Suppose dirty firms are more productive.
(i) If ε<(˜
s−2.5˜
m),(␭∗
C,␭∗
D)=(1,1) is a stable equilibrium.
(ii) If ε=(˜
s−2.5˜
m), the following cases are possible:
(a) If ε<0.5˜
m, (␭∗
C,␭∗
D)=(1,1) is a stable equilibrium.
(b) If ε=0.5˜
m, (␭∗
C,␭∗
D)=(␭,1) is a stable equilibrium for any ␭∈[0,1].
(c) If ε>0.5˜
m, both (0.5,0.5) and (1,1) are equilibrium, but are unstable.
(iii) If ε>(˜
s−2.5˜
m), the following cases are possible:
(a) If ε<0.5˜
m, (␭∗
C,␭∗
D)=(␭,1) is a stable equilibrium, where ␭=(0.5˜
m−ε)/(3 ˜
m−
˜
s)<1.
(b) If ε=0.5˜
m, any point on ␭C+␭D=1is an equilibrium, but stable only if ε>
(˜
s−1.5˜
m).
(c) If ε>0.5˜
m, (0.5, 0.5) is an equilibrium, but stable only if ε>(˜
s−1.5˜
m).
Figure 1 displays some of the results from Proposition 3, which embodies both com-
plete agglomeration of all firms and symmetric dispersion. A comparison of Propositions
2 and 3 reveals that the relative productivity of dirty and clean firms has a significant ef-
fect on their spatial distribution. When the pollution differential is relatively small such
that ε<(˜
s−2.5˜
m), all firms agglomerate in the East, as in Proposition 2. This occurs
because the positive effects of increasing return and cost-of-living advantages associated
with agglomeration dominate the negative effect of pollution concentration.
When the pollution differential is large, but not too large, i.e., (˜
s−2.5˜
m)<ε<0.5˜
m,
the dirty firms still agglomerate in one region, but some clean, less productive, firms
would move to the West to take advantage of higher environmental quality and a less
competitive business environment there. Given the level of pollution differential, condition
C
2016 Wiley Periodicals, Inc.

12 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
FIGURE 1: Types of Stable equilibrium When Dirty Firms Are More Productive.
(˜
s−2.5˜
m)<ε<0.5˜
mholds when clean firms’ productivity is low enough (i.e.,wCis large
enough).
When dirty firms generate a large amount of local pollution and clean firms are not
too unproductive such that ε>max{0.5˜
m,(˜
s−1.5˜
m)}, full dispersion is the only stable
equilibrium. Without pollution, the more productive firms would agglomerate because
it leads to both higher profit (due to higher markups over marginal cost) and higher
utility (from lower prices and more varieties). However, with pollution, the benefits from
agglomeration decrease. The region with more productive firms also suffers more pollution
damage. When the local pollution damage is large enough, the region with more dirty firms
would offer lower utility. In such cases, the symmetric configuration emerges as a stable
equilibrium.
The results in Proposition 3 may correspond to certain situations in Table 1. Two
sectors are more productive than the service (clean) sector: chemical manufacturing and
petroleum and coal products manufacturing. The former is less polluting, but more con-
centrated than the latter. In other words, there is a negative correlation between pollution
and concentration. This is consistent with Proposition 3.
As in the previous case, trade costs also play a key role in the spatial distribu-
tion of firms. Note that max{0.5˜
m,(˜
s−1.5˜
m)}→0ast→0. Thus, ε>max{0.5˜
m,(˜
s−
1.5˜
m)}holds when trade costs are low enough. This implies that the symmetric configura-
tion where both types of firms divide equally between the two regions is the only stable
equilibrium when trade costs are low enough. This occurs because both the markup and
cost-of-living advantages approach zero as t→0. This result is in stark contrast with
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 13
the classic economic geography result that that all firms agglomerate in one region when
trade costs are low enough.
6. OPTIMAL DISTRIBUTION OF FIRMS
So far we have examined the equilibrium distribution of firms between the two
regions. A natural question is: Is the equilibrium distribution socially optimal? To address
this question, we follow Ottaviano et al. (2002) to define the optimal distribution as the
one that maximizes the sum of utilities for all residents in the economy where (a) all
firms price their products at the marginal costs, (b) all dirty firms pay for their pollution
damage, and (c) all entrepreneurs are compensated, using lump-sum transfers from all
residents, for the value of their human capital. Specifically, the optimal distribution of
firms between the two regions, (␭o
C,␭o
D), solves:2
max
(␭C,␭D)TV(␭C,␭D)≡0.5LV E
L+␭CVE
C+␭DVE
D+0.5LVW
L+(1 −␭C)VW
C+(1 −␭D)VW
D
s.t.0≤␭k≤1fork=C,D,
(25)
where VE
L,VE
C,and VE
Ddenote the indirect utility functions of laborers, owners of clean
firms, and owners of dirty firms in the East, respectively, and are defined by:
VE
k=a2
d−2b−awD+(2 −␭C−␭D)t−b
2wD+(2 −␭C−␭D)t2
+d
2w2
D+(2 −␭C−␭D)t2+2(1 −␭D)twD−(␦−ε)␭D+ε+Y0+YE
k−T,(26)
for k=L,C,D.YE
L,YE
C,and YE
Ddenote, respectively, the income of laborers, owners of
clean firms, and owners of dirty firms in the East. Tis the amount of lump-sum transfer
from each resident. VW
kcan be derived by replacing (2 −␭C−␭D)by(␭C+␭D)and(␭D+1)ε
by (␦−ε␭D) in (26). Solving the maximization problem (25) leads to the following:
PROPOSITION 4. Suppose dirty firms are less or equally productive. The optimal distri-
bution of firms is as follows:
(i) If ε≤␳,(␭o
C,␭o
D)=(1,1),
(ii) If ε>␳,(␭o
C,␭o
D)=(1,␭o
D),
where
␭o
D=
ε+2m
4ε+2m−3␳,(27)
␳=t
3{4a−(3d−4b)wD−[2(d−b)+bL]t]}.(28)
Proposition 4 states that when the dirty firms generate little pollution or when
pollution is highly mobile, it is socially desirable to agglomerate all firms into a single
region. When all firms are located in one region, total trade cost and the overall prices of
goods are the lowest. This will lead to more consumption and higher total output. Because
of the increasing returns to scale production technology, the average cost of production is
also the lowest.
2To focus on the spatial distribution of the dirty firms, we assume it is socially desirable for them to
operate, although they generate pollution.
C
2016 Wiley Periodicals, Inc.

14 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
When local pollution damage is large, such that ε>␳, all clean firms should still
agglomerate in the East, while some dirty firms should be located in the less populous
area. Also,
∂␭o
D
∂ε
<0,∂␭o
D
∂wD
<0,∂␭o
D
∂t<0,(29)
indicating that more dirty firms should be located in the less populous area when (1) they
generate a larger amount of stationary pollution, (2) they are less productive, or (3) the
trade cost is higher. As ε→+∞or t→0, ␭o
D→0.25, suggesting that about three quarters
of the dirty firms should be located in the less populous region when the local pollution
damage is extremely high or the trade cost is minimal. Under this distribution, the total
pollution damage is lowest.
PROPOSITION 5. Suppose dirty firms are more productive. The optimal spatial distribu-
tion of firms is as follows:
(i) If ε≤max{˜␳,˜
m}and ␺=t{4a−[2(b+d)+Lb]t−4dwC}<0,then
(a) if ε≤2˜
m+␺,(␭o
C,␭o
D)=(1,1),
(b) if ε>2˜
m+␺,(␭o
C,␭o
D)=(␭o
C,1), where
˜
␭o
C=
ε−2˜
m
␺.(30)
(ii) If ε>max{˜␳,˜
m}or if ␺≥0,(␭o
C,␭o
D)=(1,˜
␭o
D), where
˜
␭o
D=
ε−2˜
m
4ε−2˜
m−3˜␳<1.(31)
When dirty firms generate little stationary pollution, it is optimal for all firms to
agglomerate in one region. When dirty firms generate a moderate amount of pollution
such that 2 ˜
m+␺<ε≤max{˜␳,˜
m}, it is optimal for dirty firms to agglomerate and for
clean firms to disperse. When dirty firms generate a large amount of stationary pollution,
it is optimal for clean firms to agglomerate and for dirty firms to disperse.
7. EQUILIBRIUM VS. OPTIMAL DISTRIBUTIONS
A comparison between the optimal and equilibrium distribution of firms reveals the
following results:
PROPOSITION 6. Regardless of the relative productivity of dirty and clean firms, when ε
is large enough or when t is small enough,
␭∗
D>␭o
D,
and the total pollution damage is higher under the market equilibrium than under the
optimal distribution of firms.
Proposition 6 shows that when dirty firms generate a large amount of stationary
pollution and the trade cost is low, the market equilibrium will deviate from the social
optimum. Thus, the equilibrium distribution of firms can be optimal only when (1) there
is little difference between dirty and clean firms in terms of local pollution, and (2) trade
costs are high. Under these conditions, all firms agglomerate in the East under the market
equilibrium, which is also socially optimal.
As shown in the proof of Proposition 6 in the online appendix, when dirty firms are
less productive than clean firms, (␭∗
C,␭∗
D)→(1,0.5) and (␭o
C,␭o
D)→(1,0.25) as ε→+∞or
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 15
t→0. This suggests that when dirty firms generate a large amount of stationary pollution
or when trade costs are low enough, too many dirty firms locate in the more populous area.
As a result, too many people are exposed to pollution. The total pollution damage is larger
under the market equilibrium than under the optimal distribution, with the difference in
total pollution damage equal to 0.125ε.
Likewise, when the dirty firms are more productive, (␭∗
C,␭∗
D)→(0.5,0.5) and TD
∗→
(1 +0.5L)(2␦−ε)asε→+∞or t→0, compared with (␭o
C,␭o
D)→(1,0.25) and TD
o→[(1 +
0.5L)(2␦−ε)−0.125ε. In this case, both dirty and clean firms are overly dispersed under
the market equilibrium. This also leads to too much pollution exposure and damage under
the market equilibrium.
The discrepancy between the optimal and equilibrium distributions arises because
firms do not consider the pollution externalities they impose on local residents when
making location decisions. As a dirty firm moves from a smaller to larger market, its
pollution will affect more people. The private incentive to move to a larger market is
larger than the social value of moving, causing too many people to be exposed to pollution.
Conversely, even if it is socially desirable for a dirty firm to move to a smaller market, the
firm may not do so because it cannot capture the social benefit of moving (less pollution
damage). This also causes a misallocation of clean firms when they are less productive
than dirty firms.
8. ENVIRONMENTAL POLICY AND FIRM LOCATION
The comparison between market equilibrium and the optimal distribution of firms
reveals that when dirty firms generate a large amount of stationary pollution or when
the trade cost is low, dirty firms are too dispersed spatially, causing too much pollution
damage, regardless of whether they are more or less productive than clean firms. An
important question is: Can traditional pollution control approaches, such as the polluter
pays principle, be used to correct the problem? To address this question, we consider a
pollution tax that forces dirty firms to internalize their pollution damage. Specifically, a
dirty firm located in the East must pay TE≡␶{␦ME+(␦−ε)MW}and a dirty firm located
intheWestmustpay
TW≡␶{␦MW+(␦−ε)ME},where␶is the pollution tax rate, with ␶=1 indicating
each dirty firm pays a pollution tax that equals its pollution damage. A tax rate ␶ois said
to be optimal if it leads to the optimal distribution of polluting firms.
PROPOSITION 7. Suppose ␭o
D<␭∗
D. If dirty firms are less than or equally productive as
clean firms,
␶o=1+2ε(s−3␳−7m)+2m(s−3␳−m)
4ε(ε+2m).(32)
If dirty firms are more productive than clean firms,
␶o=1+2ε(˜
s−3˜␳+4˜
m)−˜
m(4˜
s−3˜␳−2˜
m)
4ε(ε−2˜
m).(33)
(␭o
C,␭o
D)is the only stable equilibrium under the optimal pollution tax.
Proposition 7 reveals that the traditional prescription for pollution control, the pol-
luter pays principle, will generally not lead to the optimal distribution of firms. To
understand the intuition behind this, consider the case where dirty and clean firms have
the same productivity. In this case, m=0, and the optimal tax rate (32) reduces to:
␶o=1+(␪−3␳)
2ε
,(34)
C
2016 Wiley Periodicals, Inc.

16 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
FIGURE 2: Optimal Pollution Tax: Dirty Firms are Less Productive (wD>0).
which indicates that the polluter pays principle will lead to the optimal distribution of
dirty firms only if ␪=3␳.When␪<3␳, the tax rate must be set below one to achieve the
optimal distribution of firms, and vice versa. To understand this result, note that
␪−3␳=−t(␬−t␩),(35)
where
␬≡a(5d2−14db +8b2)
2(d−b)2>0,(36)
␩≡(15d+9bL)(d−2b)2+6b(d2−4b2)+6db2+bL[17b(d−b)+16b2]
12(d−b)2>0.(37)
Thus, ␶o<1 if and only if t<(␬/␩). The intuition behind this result is that when the
trade cost is sufficiently low, the market tends to lead to an overdispersion of dirty firms,
compared with the optimal distribution. The tax rate must be set below one to correct
the over dispersion. On the other hand, when the trade cost is high, the market tends to
lead to an over concentration of dirty firms in the more populous area, compared with the
optimal distribution. The tax rate must be set above one to prevent an over concentration
of dirty firms.
Figure 2 illustrates the optimal tax rate when dirty firms are less productive. Given
the pollution level, for small wDand t,both(s−3␳−7m)and (s−3␳−m) are positive,
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 17
and the optimal tax rate is above one. As wDincreases, both (s−3␳−7m)and (s−3␳−
m)decrease. When wDis large enough, both (s−3␳−7m)and (s−3␳−m) are negative,
and the optimal tax rate is below one. This result reflects that when the dirty firms are
highly unproductive compared with clean firms, they have incentives to move away from
the clean firms to avoid competition. This leads to an over dispersion of dirty firms. The
tax rate must be set below one to correct this tendency.
9. MODEL EXTENSIONS
Above we assumed that each dirty firm causes a fixed amount of pollution damage
to a resident. In this section, we consider an extension of the model in which pollution
damage is proportional to firm output. Specifically, suppose production of each unit of
output in a dirty firm generates ␦units of pollution in the local region and (␦−ε)units of
pollution to the other region, with 0 ≤ε≤␦. In this case, the total amount of pollution in
the East and West equals
ZE=␦␭DqEE
DME+qEW
DMW+(␦−ε)(1 −␭D)qWE
DME+qWW
DMW,(38)
ZW=␦(1 −␭D)qWE
DME+qWW
DMW+(␦−ε)␭DqEE
DME+qEW
DMW,(39)
where qro
Dis the demand of a consumer located in region rfor the good produced by a dirty
firm located in region o. Equations (38) and (39) show that both the amount of pollution
and the marginal pollution damage a dirty firm generates are endogenously determined.
Substituting the demand functions into (38) and (39), the difference in pollution
between East and West can be derived as
ZE−ZW=−␪C␭C−1
2+␪D␭D−1
2+4␪2␭C−1
2␭D−1
2
−␪2(␭C−␭D)2␭D−1
2,(40)
where ␪C=tdε
2,␪D=dε
2(d−b)[8a−d(8wD+3t)+b(12wD+7t)] and ␪2=dbtε
(d−b). Equation (40)
reduces to ZE−ZW=−␪C(␭C−0.5) when ␭D=0.5. This indicates that even if dirty firms
are equally distributed between the two regions, the two regions still have different levels
of pollution if they have different numbers of clean firms; the region with more clean firms
will have a lower level of pollution. The intuition behind this result is that the region with
more clean firms has a higher level of competition and lower output prices. As a result,
each dirty firm produces less, and therefore generates less pollution.
Using (40), the differences in utility can be derived as:
VC=ˆ
s1␭C−1
2+ˆ
s2␭D−1
2−4␪2␭C−1
2␭D−1
2
+␪2(␭C−␭D)␭D−1
2,(41)
C
2016 Wiley Periodicals, Inc.

18 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
VD=ˆ
s3␭C−1
2+ˆ
s4␭D−1
2−4␪2␭C−1
2␭D−1
2
+␪2(␭C−␭D)␭D−1
2,(42)
where ˆ
s1=s+␪C,ˆ
s2=s−m−␪D,ˆ
s3=s−2m+␪C,and ˆ
s4=s−3m−␪D.
Using (41) and (42), we can prove that the major insights developed in Section 4 still
hold. Specifically, we can prove the following:
PROPOSITION 8. Suppose dirty firms are less productive and generate pollution in
proportion to their output. The distribution of firms in a stable equilibrium is as follows:
(i) If ␽ε<(s−2.5m),(␭∗
C,␭∗
D)=(1,1) is a stable equilibrium, where
␽=d
4(d−b)t(2d−5b)+4(2d−3b)wD−8a.
(ii) If ␽ε≥(s−2.5m),(␭∗
C,␭∗
D)=(1,␭∗)is a stable equilibrium, where ␭∗is the unique
positive solution of 0.5(m+␪C+␪D+␪2)+(ˆ
s4−0.5␪2)␭−␪2␭2=0.
Proposition 8 is the counterpart of Proposition 2 in Section 4 and can be interpreted
in a similar way.
10. CONCLUSIONS
In this paper, we model the locational patterns of polluting firms, taking into account
the level and mobility of pollution, firm heterogeneity, trade costs, and preference for
differentiated products and environmental quality. We find that the equilibrium distribu-
tion of firms is more likely to differ from the social optimum when dirty firms generate a
large amount of stationary pollution and have much higher or lower productivity. In these
cases, conventional pollution control approaches do not bring about an optimal distribu-
tion due to more fundamental forces at play. Specifically, our model offers the following
overarching lessons.
First, the type of pollution matters relatively more than the absolute level of pollution
when explaining the spatial distribution of polluting firms. In particular, what matters
most is whether the pollutant is mobile across regions, or is confined to the immediate
region. When pollution is relatively mobile, it is generally socially desirable for all firms
to agglomerate into a single region. This is unlike the case of congestion in economic
geography models, where the opposite may be socially desirable.
Second, consideration of the role of trade costs along with pollution changes some
of the classic results. For example, the “black hole” result of Krugman and Venables
(1995) and Fujita et al. (1999) no longer holds when pollution is considered. Without
considering pollution, the classic result is that the region with the larger initial share of
the manufactured sector would eventually attract the whole sector when trade costs are
low enough. However, when dirty firms generate a large amount of local pollution, the
region with more dirty firms will become a less desirable place to live, and the dirty firms
tend to disperse, instead of agglomerate.
Third, the locational patterns of polluting firms cannot be fully understood without
considering the productivity differences between dirty and clean firms. For example, the
symmetric distribution where both dirty and clean firms fully disperse is a stable equi-
librium when dirty firms are more productive and generate a large amount of stationary
pollution. Such a distribution can never be an equilibrium when dirty firms are less
C
2016 Wiley Periodicals, Inc.

WU AND REIMER: SPATIAL DISTRIBUTION OF POLLUTING AND NONPOLLUTING FIRMS 19
productive. Note that, while we have taken firms’ heterogeneous productivity as given,
future work may consider situations in which technology choice is endogenous.
Finally, this study shows how conventional policy prescriptions for pollution control
can be inadequate under the more general settings examined here. For example, too many
dirty firms are located in the more populous region when they generate a large amount
of stationary pollution, regardless whether they are more or less productive than clean
firms. This is especially true when trade costs are low. A conventional policy prescription,
such as the polluter pays principle, will generally not bring about an optimal distribution.
In particular, the tax that induces a socially optimal distribution of dirty firms exceeds
the total pollution damage under some conditions, but lies below it in other cases. A topic
for future work may include derivation of policies in the presence of additional distortions
in the economy, including imperfect competition.
Our exploration of the territory between the economic geography and environmental
economics literatures has implications for policymakers who wish to balance environ-
mental goals with continued expansion of the economy. Our results suggest that current
approaches to mediate between these goals may be too blunt. Subtler approaches that
go beyond standard economic geography or environmental policy prescriptions may be
required to bring about an outcome that is sought by policymakers and the public at
large.
REFERENCES
Abdel-Rahman, Hesham and Masahisa Fujita. 1990. “Product Variety, Marshallian Externalities and City Size,”
Journal of Regional Science, 30(2), 165–183.
Arnott, Richard, Oded Hochman, and Gordon C. Rausser. 2008. “Pollution and Land Use, Optimum and Decen-
tralization,” Journal of Urban Economics, 64(2), 390–407.
Artz, Georgeanne, Younjun Kim, and Peter Orazem. 2016. “Does Agglomeration Matter Everywhere? New Firm
Location Decisions in Rural and Urban Markets,” Journal of Regional Science, 56(1), 72–95.
Aw, Be Yan, Sukkyun Chung, and Mark J. Roberts. 2000. “Productivity and Turnover in the Export Market,”
World Bank Economic Review, 14, 65–90.
Baldwin, Richard and Toshihiro Okubo. 2006. “Heterogeneous Firms, Agglomeration and Economic Geography:
Spatial Selection and Sorting,” Journal of Economic Geography, 6, 323–346.
Bernard, Andrew B. and J. Bradford Jensen. 1999. “Exceptional Exporter Performance: Cause, Effect, or Both?”
Journal of International Economics, 47, 1–25.
Bosker, Maarten, Steven Brakman, Harry Garretsen, and Marc Schramm. 2007. “Looking for Multiple Equilibria
When Geography Matters: German City Growth and the WWII shock,” Journal of Urban Economics, 61(1),
152–169.
Brakman, Steven, Harry Garretsen, and Charles van Marrewijk. 2014. “New economic geography: Endogenizing
location in an international trade model,” in Manfred Fischer and Peter Nijkamp (eds.), Handbook of Regional
Science. Heidelberg: Springer, pp. 569–589.
Burkitt, Laurie and Brian Spegele. 2013. “Why Leave Job in Beijing? To Breathe,” The Wall Street Journal,
April 14.
Cao, Jing and Valerie J. Karplus. 2014. “Firm–level Determinants of Energy and Carbon Intensity in China,”
Energy Policy, 75, 167–178.
Copeland, Brian R. and M. Scott Taylor. 1999. “Trade, Spatial Separation, and the Environment,” Journal of
International Economics, 47, 137–168.
Delgado, Mercedes, Michael E. Porter, and Scott Stern. 2010. “Clusters and Entrepreneurship,” Journal of Eco-
nomic Geography, 10(4), 495–518.
Elbers, Chris and Cees Withagen. 2004. “Environmental Policy, Population Dynamics and Agglomeration,” Con-
tributions to Economic Analysis & Policy, 3(2), 1–23.
Ellison, Gless and Edward L. Glaeser. 1997. “Geographic Concentration in U.S. Manufacturing: A Dartboard
Approach,” Journal of Political Economy, 105, 889–927.
Fujita, Masahisa, Paul Krugman, and Anthony J. Venables. 1999. The Spatial Economy: Cities, Regions, and
International Trade. Cambridge: MIT Press.
Fujita, Masahisa and Jacques-Francois Thisse. 2002. Economics of Agglomeration: Cities, Industrial Location,
and Regional Growth. New York: Cambridge University Press.
C
2016 Wiley Periodicals, Inc.

20 JOURNAL OF REGIONAL SCIENCE, VOL. 00, NO. 0, 2016
Henderson, J. Vernon. 1977. “Externalities in a Spatial Context,” Journal of Public Economics, 7, 89–110.
———. 2003. “Marshall’s Scale Economies,” Journal of Urban Economics, 53, 1–28.
Hoel, Michael and Perry Shapiro. 2003. “Population Mobility and Transboundary Environmental Problems,”
Journal of Public Economics, 87(5–6), 1013–1024.
Holmes, Thomas J. and John J. Stevens. 2004. “Spatial Distribution of Economic Activities in North America,”
in J. Vernon Henderson, and Jacques Franc¸ois Thisse (eds.), Handbook of Regional and Urban Economics.
Amsterdam: Elsevier North Holland, pp. 2797–2843.
Hosoe, Moriki and Tohru Naito. 2006. “Transboundary Pollution Transmission and Regional Agglomeration
Effects,” Papers in Regional Science, 85(1), 99–120.
Kohn, Robert E. 1974. “Industrial Location and Air Pollution Abatement,” Journal of Regional Science, 14(1),
55–63.
Krugman, Paul. 1991. “Increasing Returns and Economic Geography,” Journal of Political Economy, 99, 483–499.
Krugman, Paul and Anthony J. Venables. 1995. “Globalization and the Inequality of Nations,” Quarterly Journal
of Economics, 110, 857–80.
Lange, Andreas and Martin F. Quaas. 2007. “Economic Geography and the Effect of Environmental Pollution on
Agglomeration,” The B.E. Journal of Economic Analysis & Policy, 7(1), 1935-1682.
Levinson, Arik and M Scott Taylor. 2008. “Unmasking the Pollution Haven Effect,” International Economic
Review, 49, 223–254.
Lucas, Robert E. 1988. “On the Mechanics of Economic Development,” Journal of Monetary Economics, 22, 3–39.
Markusen, James, Edward R. Morey, and Nancy Olewiler. 1993. “Environmental Policy when Market Structure
and Plant Locations are Endogenous,” Journal of Environmental Economics Management, 24, 69–86.
Nocke, Volker. 2006. “A Gap for Me: Entrepreneurs and Entry,” Journal of the European Economic Association,
4(5), 1542–4774.
Okubo, Toshihiro, and Pierre M. Picard, and Jacques-Francois Thisse. 2010. “The Spatial Selection of Heteroge-
neous Firms,” Journal of International Economics, 82(2), 230–237.
Ottaviano, Gianmarco I.P., Takatoshi Tabuchi, and Jacques-Francois Thisse. 2002. “Agglomeration and Trade
Revisited,” International Economic Review, 43, 409–435.
Ottaviano, Gianmarco I.P. 2012. “Agglomeration, Trade and Selection,” Regional Science and Urban Economics,
43, 987–997.
Polinsky, A. Mitchell. 1980. “Strict Liability vs. Negligence in a Market Setting,” American Economic Review, 70,
363–367.
Simon, Carl P. and Lawrence E. Blume. 1994. Mathematics for Economists. New York City: W.W. Norton &
Company.
Saito, Hisamitsu, Munisamy Gopinath, and JunJie Wu. 2011. “Heterogeneous Firms, Trade Liberalization and
Agglomeration,” Canadian Journal of Economics, 44(2), 541–560.
Tabuchi, Takatoshi and Jacques-Francois Thisse 2006. “Regional Specialization, Urban Heirarchy, and Commut-
ing Costs,” International Economic Review, 47(4), 1468–2354.
Tietenberg, Thomas H. 1974. “Derived Demand Rules for Pollution Control in a General Equilibrium Space
Economy,” Journal of Environmental Economics and Management, 1, 3–16.
Unteroberdoerster, Olaf. 2001,. “Trade and Transboundary Pollution: Spatial Separation Reconsidered,” Journal
of Environmental Economics and Management, 41, 269–285.
Zeng, Dao-Zhi and Laixun Zhao. 2009. “Pollution Havens and Industrial Agglomeration,” Journal of Environmen-
tal Economics and Management, 58(2), 141–153.
SUPPORTING INFORMATION
Additional supporting information may be found in the online version of this article at
the publisher’s web site.
Online Appendix: Proofs of propositions.
C
2016 Wiley Periodicals, Inc.