The Economics of Agglomeration

Abstract

We address the fundamental question arising in economic geography: why do economic activities agglomerate in a small number of places? The main reasons for the formation of economic clusters involving firms and/or households are analysed: (i) externalities under perfect competition; (ii) increasing returns under monopolistic competition; and (iii) spatial competition under strategic interaction. We review what has been accomplished in these three domains and identify a few general principles governing the organization of economic space. Other standard lines of research in location theory are also discussed while several alternative, new approaches are proposed.

Full text

JOURNAL OF THE JAPANESE AND INTERNATIONAL ECONOMIES
10, 339–378 (1996)
ARTICLE NO
. 0021
Economics of Agglomeration*
M
ASAHISA
F
UJITA
Kyoto University and University of Pennsylvania
AND
J
ACQUES
-F
RANC
¸
OIS
T
HISSE
CORE, Universite´ Catholique de Louvain and CERAS–ENPC (URA 2036, CNRS)
Received January 11, 1996; revised August 20, 1996
Fujita, M., and Thisse, J.-F.—Economics of Agglomeration
We address the fundamental question arising in geographical economics: why do
economic activities agglomerate in a small number of places? The main reasons for
the formation of economic clusters involving firms and/or households are analyzed:
(i) externalities under perfect competition; (ii) increasing returns under monopolistic
competition; and (iii)spatialcompetitionunder strategic interaction. We review what
has been accomplished in these three domains and identify a few general principles
governing the organization of economic space. A few alternative, new approaches
are also proposed. J. Japan. Int. Econ., December 1996, 10(4), pp. 339–378. Kyoto
University and University of Pennsylvania; and CORE, Universite
´
Catholique de
Louvain and CERAS–ENPC (URA 2036, CNRS).
 1996 Academic Press, Inc.
Journal of Economic Literature Classification Numbers F12, L13, R12.
1. I
NTRODUCTION
‘‘Nearly half the world’s population and three-quarters of all westerners
live in cities’’ (The Economist, July 29, 1995). This mere, crude fact can no
* Paper prepared for the Trilateral TCER/NBER/CEPR Conference on ‘‘Economic Ag-
glomeration,’’ Tokyo, January 11–12, 1996. The authors are grateful to Simon Anderson and
Vernon Henderson for helpful discussions during the preparation of this article. They also
thank Gilles Duranton, Louis-Andre
´
Ge
´
rard-Varet, Jean-Marie Huriot, Yoshitsugu Kane-
moto, Xavier Martinez-Giralt, Dominique Peeters, Diego Puga, Tony Smith, Tetsushi Sonobe
Takatoshi Tabuchi, and one referee for useful comments. The extended version of this paper
has been published as a CEPR discussion paper.
339
0889-1583/96 $18.00
Copyright  1996 by Academic Press, Inc.
All rights of reproduction in any form reserved.

340
FUJITA AND THISSE
longer be put aside. We are therefore led to raise the following, fundamental
question: why do economic activities tend to agglomerate in a small number
of places (typically cities)?
More precisely, we want to explain why some particular economic activi-
ties choose to establish themselves in some particular places, and what is
the resulting geographical organization of the economy. Intuitively the
equilibrium spatial configuration of economic activities can be viewed as
the outcome of a process involving two opposing types of forces, that is,
agglomeration (or centripetal) forces and dispersion (or centrifugal) forces.
This view agrees with very early work in economic geography. For example,
in his Principes de Ge
´
ographie humaine published in 1921, the famous
French geographer Vidal de la Blache argues that all societies, rudimentary
or developed, face the same dilemma: individuals must get together in
order to benefit from the advantages of the division of labor, but various
difficulties restrict the gathering of many individuals.
1
Among the several questions that are investigated in the literature, the
following ones are central: (i) why are there agglomeration or dispersion
forces? (ii) why do we observe agglomerations formed by different agents?
and (iii) why do regions and cities specialize in different activities? In order
to answer these questions, we must consider a variety of models focusing
on different aspects. Indeed it would be futile to look for the model ex-
plaining the economic landscape of economies at different stages of devel-
opment and in different institutional environments. As mentioned in the
paragraph above, an interesting model of economic geography must include
both centripetal and centrifugal forces. The corresponding spatial equilib-
rium is then the result of a complicated balance of forces that push and pull
consumers and firms until no one can find a better location. As will be seen,
the major models which have been developed do reflect such an interplay.
Though convenient at a high level of abstraction, it should be clear that
the concept of agglomeration used in this paper does refer to different real
world phenomena. For example, one type of agglomeration arises when
restaurants, movie theaters, or shops selling similar products are clustered
within the same neighborhood of a city. At the other extreme of the spec-
trum lies the core-periphery structure corresponding to North–South dual-
ism. Other types of agglomeration can be found in the existence of strong
regional disparities within the same country, in the formation of cities
having different sizes, or in the emergence of industrial districts where firms
have strong technological and/or informational linkages. At this stage, it
is probably not necessary to distinguish between these different entities,
though the intensity of the forces at work is likely to vary according to
the cases.
1
The term agglomeration is less ambiguous than concentration which is used to describe
different phenomena. It has been introduced in location theory by Weber (1909, Chap. 1).

ECONOMICS OF AGGLOMERATION
341
In recent years, a growing number of economists have become interested
in the study of location problems. This is probably best illustrated by the
work of Lucas (1988), Krugman (1991a, 1991b), Becker and Murphy (1992),
among several others, which triggered a new flow of interesting contribu-
tions in the field. No doubt, this increased interest has been fostered by
the integration of national economies within trading blocks such as the
European Union or NAFTA, as well as by its impact on the development
of their regions and cities. As market integration dissolves economic barriers
between nations, national boundaries no longer provide the most natural
unit of analysis. Contrary to a widespread opinion, this question is not new:
it has been raised by some scholars at the outset of what had to become
the European Union (Giersch, 1949). However, the subject matter remains
neglected for a long time despite the suggestions made by Ohlin (1933,
1968, Part III) who proposed to unify interregional trade and location
theory. Connections with the new theories of growth are also under scrutiny.
Indeed cities, and more generally economic agglomerations, are considered
as the main institutions where both technological and social innovations
are developed through market and nonmarket interactions. Furthermore,
city specialization changes over time, thus creating a geographically diversi-
fied pattern of economic development. It seems therefore reasonable to
say that growth is localized, a fact that had been recognized by early develop-
ment theorists, such as Myrdal (1957) and Hirshman (1958).
Thus it is fair to say that the new economic geography, which we will
call geographical economics, is in many respects more rooted in standard
economic theory than the traditional theories of location. As we will see
in the course of this paper, geographical economics has strong connections
with several branches of modern economics, including industrial organiza-
tion and urban economics, but also with the new theories of international
trade and of economic growth and development.
2
This suggests that this
field has high potentials for further developments and that cross-fertilization
can be expected. It has also generated a large flow of empirical studies that
use the modern tools of econometrics, thus leading to more solid conclu-
sions.
As in any economic field, several lines of research have been explored
in geographical economics. The earliest line was initiated by von Thu
¨
nen
(1826) who sought to explain the pattern of agricultural activities sur-
rounding many cities in pre-industrial Germany. More generally, von Thu
¨
-
nen’s theory has proven to be very useful in studying land use when eco-
nomic activities are perfectly divisible. Despite his monumental
contribution to economic thought (Samuelson, 1983), von Thu
¨
nen’s ideas
2
References to potential connections with various field of economics can be found in the
extended version of the paper published as the CEPR Discussion Paper 1344.

342
FUJITA AND THISSE
languished for more than a century without attracting widespread attention.
Yet, Alonso (1964) succeeded in extending von Thu
¨
nen’s central concept
of bid rent curves to an urban context, in which a marketplace is replaced
by an employment center (the Central Business District). Since that time
urban economics has advanced rapidly.
However the von Thu
¨
nen model has several limitations. Indeed the
following question suggests itself: why is there a unique city in von Thu
¨
nen’s
isolated state? Or a unique Central Business District in most urban eco-
nomic models? This is likely because increasing returns are at work in
the design of trading places or in the production of some private goods.
Conceding the point, Lo
¨
sch (1940) argued that scale economies in produc-
tion are essential for understanding the formation of economic space, and
built a spatial model of monopolistic competition involving increasing re-
turns. Similarly Koopmans (1957, p. 157) claims that:
without recognizing indivisibilities—in the human person, in residences, plants,
equipment and in transportation—urban location problems down to the smallest
village cannot be understood.
The assumption of nonincreasing returns has indeed dramatic implica-
tions for geographical economics. Under nonincreasing returns and a uni-
form distribution of resources, the economy reduces to a Robinson Crusoe
type, where each individual produces for his/her own consumption (back-
yard capitalism). Each location could thus be a base for an autarkic econ-
omy, where goods are produced on an arbitrarily small scale, except possibly
(as in the neoclassical theory of international trade) that trade might occur
if the geographic distribution of resources was nonuniform. While pertinent,
the unequal distribution of resources seems insufficient as the only explana-
tion of specialization and trade. Furthermore, when capital or labor can
move freely, the neoclassical model of trade does not allow for the predic-
tion of the size of regions when natural resources are uniformly distributed.
We can therefore safely conclude that increasing returns to scale are essential
for explaining the geographical distribution of economic activities.
3
However,
when indivisibilities are explicitly introduced, nonexistence of a competitive
equilibrium in a spatial economy is common, as shown by Koopmans and
Beckmann (1957) and Starrett (1978). Furthermore, as noticed by Dre
`
ze
and Hagen (1978) in a somewhat different context, scale economies in
production have another far-reaching implication for the working of the
economy: the number of market places open at a competitive equilibrium
is likely to be suboptimal. Or, to use a different terminology, spatial markets
3
This statement has sometimes been referred to as the ‘‘Folk Theorem’’ of geographical
economics because it has been rediscovered several times by various scholars (see Scotchmer
and Thisse, 1992, for a more detailed discussion).

ECONOMICS OF AGGLOMERATION
343
are typically incomplete so that an equilibrium allocation is in general not
Pareto-optimal.
If production involves increasing returns, a finite economy accommodates
only a finite number of firms which are imperfect competitors. Treading in
Hotelling’s footsteps, Kaldor (1935) argued that space gives this competition
a particular form. Since consumers buy from the firm with the lowest ‘‘full
price,’’ defined as the posted price plus the transport cost, each firm competes
directly with only a few neighboring firms, regardless of the total number
of firms in the industry. The very nature of the process of spatial competition
is, therefore, oligopolistic and should be studied within a framework of
interactive decision making. This was one of the central messages conveyed
by Hotelling (1929) but was ignored until economists became fully aware
of the power of game theory for studying competition in modern market
economies (see Gabszewicz and Thisse, 1986, for a more detailed discus-
sion). Following the outburst of industrial organization since the late 70s,
it became natural to study the implications of space for competition. New
tools and concepts are now available to revisit and formalize the questions
raised by early location theorists.
Despite its factual and policy relevance, the question of why a hierarchical
system of cities emerges remains open. In particular, it is a well-established
fact that cities tend to be distributed according to some specific relationship
relating their size and their rank in the urban system (what is called the
rank-size rule). The first attempt to build a spatial theory of the urban
hierarchy goes back at least to the German geographer Christaller (1933)
who pioneered ‘‘central place theory,’’ based on the clustering of market
places for different economic goods and services. Though the theory pro-
posed by Christaller, and developed by Lo
¨
sch, has served as a cornerstone
in classical economic geography, it is fair to say that the microeconomic
underpinnings of central place theory are still to be developed.
The topic is difficult because it involves various types of nonconvexities
which are even more complex to deal with than increasing returns in produc-
tion. For example, a consumer organizes his shopping itinerary so as to
minimize the total cost of purchases, including transport costs. This problem
is extremely complex: determining the optimal geographical pattern of
purchases requires solving a particularly difficult combinatorial problem,
and finding an equilibrium becomes very problematic (Eaton and Lipsey,
1982). In the same vein, there are often considerable scale economies in
carrying the goods bought by a consumer when shopping. These various
nonconvexities affect demand functions in complex ways which have not
been fully investigated. This is just one example of the many difficulties
one encounters in attempting to construct a general spatial model that
would consider cities of different sizes trading different commodities. It is
therefore no surprise that we still lack such a model since it is well known

344
FUJITA AND THISSE
that economic theory has serious problems in dealing with nonconvexities.
Yet, this turns out to be a real embarrassment because the rank-size rule
is one of the most robust statistical relationships known so far in economics.
A major centripetal force can be found in the existence of ‘‘externalities’’
since the geographical concentration of economic activities can be viewed
as a snowball effect. Specifically, more and more agents want to agglomerate
because of the various factors that allow for a larger diversity and a higher
specialization in the production processes, and the wider array of products
available for consumption. The setting up of new firms in such regions
gives rise to new incentives for workers to migrate there because they can
expect better job matching and, therefore, higher wages. This in turn makes
the place more attractive to firms which may expect to find the types of
workers and services they need, as well as new outlets for their products.
Hence, both types of agents benefit from being together. This process has
been well described by Marshall (1890, 1920, p. 225) in the following quo-
tation:
When an industry has thus chosen a location for itself, it is likely to stay there
long: so great are the advantages which people following the same skilled trade
get from near neighborhood to one another. . . . A localized industry gains a
great advantage from the fact that it offers a constant market for skill. . . .
Employers are apt to resort to any place where they are likely to find a good
choice of workers with the special skill which they require; while men seeking
employment naturally go to places where there are many employers who need
such skills as theirs and where therefore it is likely to find a good market.
More generally, the ‘‘Marshallian externalities’’ arise because of (i) mass-
production (the so-called internal economies which are similar to the scale
economies mentioned above), (ii) the formation of a highly specialized
labor force based on the accumulation of human capital and face-to-face
communications, (iii) the availability of specialized input services, and (iv)
the existence of modern infrastructures. Not surprisingly Marshallian exter-
nalities are the engine of economic development in the new growth theories.
The advantages of proximity for production have their counterpart on
the consumption side. For example, cities are typically associated with a
wide range of products and a large spectrum of public services so that
consumers can reach higher utility levels and, therefore, have stronger
incentives to migrate toward cities. Furthermore the propensity to interact
with others, the desire of man for man, is a fundamental human attribute,
as are the pleasure to discuss and to exchange ideas with others. Distance
is an impediment to such interactions, thus making cities the ideal institution
for the development of social contacts corresponding to various kinds of
externalities (Fisher, 1982, Chaps. 2 and 3).
Before describing the content of the paper, we want to clarify the follow-
ing issue. For many years, the concept of externality has been used to

ECONOMICS OF AGGLOMERATION
345
describe a great variety of situations. Following Scitovsky (1954), it has
been customary to consider two categories: ‘‘technological externalities’’
(such as spillovers) and ‘‘pecuniary externalities.’’ The former deals with
the effects of nonmarket interactions which are realized through processes
directly affecting the utility of an individual or the production function of
a firm. By contrast, the latter refers to the benefits of economic interactions
which take place through usual market mechanisms via the mediation of
prices. For obvious reasons Marshall was not aware of this distinction, and
his externalities turn out to be a mixture of technological and pecuniary
externalities. As a consequence, each type of externality may lead to the
agglomeration of economic activities.
In order to understand how an agglomeration occurs when Marshallian
externalities are present, it is useful to divide human activities into two
categories: production and creation. The former stands for the routine ways
of processing or assembling things (such as the preparation of a dinner
or the working of an assembly line). For an agglomeration of firms and
households to be based on this type of production activity, the presence
of pecuniary externalities is crucial. However human beings enjoy more
pleasure from, and put much value on, creative activities. Furthermore, in
economic life, much of the competitiveness of individuals and firms is due
to their creativity. Consequently, as emphasized by Jacobs (1969), economic
life is creative in the same way as are arts and sciences and, as pointed out
more recently by Lucas (1988, p. 38), personal communication within groups
of individuals sharing common interests can be a vital input to creativity:
New York City’s garment district, financial district, diamond district, advertising
district and many more are as much intellectual centers as is Columbia or New
York University.
In this respect, it is well known that face-to-face communication is most
effective for rapid product development. For example, Saxenian (1994,
p. 33) emphasizes the importance of this factor in the making of the Silicon
Valley as an efficient productive system:
By all accounts, these informal conversations were pervasive and served as
an important source of up-to-date information about competitors, customers,
markets, and technologies. Entrepreneurs came to see social relationships and
even gossips as a crucial aspect of their business. In an industry characterized
by rapid technological change and intense competition, such informal communi-
cation was often of more value than more conventional but less timely forums
such as industry journals.
Given that different people have different skills (by nature as well as by
nurture), the size of such groups also gives rise to significant scale effects.
Furthermore, information and ideas have characteristics of public goods
and, hence, tend to generate spillover effects. In this way, the creative
process itself can lead to strong agglomeration tendencies.

346
FUJITA AND THISSE
Thus an economic agglomeration is created through both technological
and pecuniary externalities, often working together. Recent advances in
geographical economics have mainly concentrated on the Chamberlinian
models of monopolistic competition developed in industrial organization
by Spence (1976) and Dixit and Stiglitz (1977). As will be seen below, this
approach allows one to decipher the working of the pecuniary externalities
discussed above (Krugman, 1991a). Accordingly, the section devoted to
(technological) externalities will concentrate on production or consumption
externalities as they are now defined in modern economic theory, i.e. non-
market interactions. These externalities seem to play an increasing role in
advanced economies, which are more and more involved in the production
and consumption of less tangible goods for which distance matters in a
more subtle way than in less advanced economies. This has been observed
both in high-tech industries (Saxenian, 1994) and in traditional sectors
(Pyke et al., 1990).
The remainder of this paper will elaborate on many of the issues discussed
above. Because of space constraints, we will concentrate on the main issues
only. They will be organized into three themes dealing respectively with
externalities, increasing returns and spatial competition. However progress
in these three areas has not been the same. In particular, the area of
externalities has attracted most attention and, hence, will be discussed first.
For the reasons discussed above, we will limit ourselves to a discussion
of technological externalities. Formally, such externalities often stand for
particular nonconvexities in production or consumption processes. As usual,
assuming a continuum of firms and of households permits us to retain
the assumption of a competitive behavior while circumventing the many
difficulties encountered when nonconvexities are present. In Section 3 we
focus on models of monopolistic competition with increasing returns, and
show how they can serve to illuminate several aspects of the agglomeration
process. One of the most severe limitations of monopolistic competition a
`
la Spence–Dixit–Stiglitz is that price competition is nonstrategic. Yet, as
we saw above, spatial competition is inherently strategic because it takes
place among the few. Intuitively, one can say that this approach aims at
dealing with the strategic externalities generated by the proximity of rival
firms or suppliers in economic space. Despite the real progress made during
the last decade, spatial competition models are still difficult to manipulate
and much work remains to be done in this area. In Section 4 we will review
what has been accomplished and will discuss the corresponding implications
for geographical economics. In Section 5 we identify a few general principles
that seem to emerge from the literature and suggest new lines of research.
4
4
The reader is refereed to the excellent book of Ponsard (1983) for a historical survey of
spatial economic theory.

ECONOMICS OF AGGLOMERATION
347
Before proceeding, one final remark is in order. Contrary to general
beliefs, location problems have attracted a great deal of attention in various
disciplines. In economics alone, the topic has been blooming since the early
90s. Thus we have chosen to be selective. As a result, it is fair to say that
this survey reflects our idiosyncrasies as much as the state of the art. We
owe our apologies to those who have contributed to the field and who feel
frustrated by our choice of menu.
2. E
XTERNALITIES
Models involving externalities describe spatial equilibria under the influ-
ence of nonmarket interactions among firms and/or households. In modern
cities or industrial districts, nonmarket interactions typically take the form
of information exchanges between agents. Since most of the corresponding
models have been developed in urban economics with the aim to explain
the internal structure of cities, we will concentrate on the agglomeration
of various economic activities within a city. However, it should be clear
that the same principles apply to the spatial organization of broader areas
such as regions or nations.
5
The central idea behind the formation of cities has been very well summa-
rized by Lucas (1988, p. 30):
What can people be paying Manhattan or downtown Chicago rents for, if not
for being near other people?
To the best of our knowledge, the first contribution focusing on the role
of interaction among individuals as an explanation for cities is due to
Beckmann (1976). More precisely, the utility of a household is assumed to
depend on the average distance to all households in the city and on the
amount of land bought on the market. In equilibrium the city exhibits a
bell-shaped population density distribution, which is supported by a similarly
shaped land rent curve. Focusing on firms instead, Borukhov and Hochman
(1977) and O’Hara (1977) studied models of firm location in which interac-
tions between firms generate agglomeration.
The basic contribution, in that the key-variables are independent of the
economic system, is due to Papageorgiou and Smith (1983). They consider
a trade-off between the need for social contacts, which is negatively affected
by distance, and the need for land, which is negatively affected by crowding.
5
However, they do not necessarily apply to multinational spaces when different national
governments are present. Such governments have indeed very specific and powerful instru-
ments, such as money or trade policy, that strongly affect the economic environment in which
the agents operate. The study of location problems in the international marketplace is still
in infancy and constitutes a very promising line of research.

348
FUJITA AND THISSE
Initially the preferences are such that the uniform distribution of individuals
over a borderless landscape is an equilibrium. When the propensity to
interact with others increases enough, this equilibrium becomes unstable:
any marginal perturbation is sufficient for the population to evolve toward
an irregular distribution. In this model, cities are considered as the outcome
of a social process combining basic human needs which are not (necessarily)
expressed through the market. It is probably fair to say that this model
captures much of the intuition of early geographers interested in the spatial
structure of human settlements. However, it is important to consider less
general, abstract formulations and to study models based on explicit and
economic forms of interactions.
2.1.
To illustrate more concretely the fundamental mechanism of agglomera-
tion involving both firms and households, we give a brief description of a
model developed by Fujita, Imai, and Ogawa. The agglomeration force is
the existence of informational spillovers among firms (see, e.g., Saxenian,
1994, Chap. 2). An important characteristic of information is its public-
good nature: the use of a piece of information by a firm does not reduce
its content for other firms. Hence the diffusion of information within a set
of firms generates externality-like benefits to each of them. Provided that
the information owned by firms is different, the benefits of communication
generally increase as the number of firms involved rises. Furthermore, since
the quality of information involves distance–decay effects, the benefits are
greater if firms locate closer to each other. Therefore, all other things being
equal, each firm has an incentive to be close to others, thus fostering the
agglomeration of firms. On the other hand, the clustering of many firms in
a single area increases the average commuting distance for their workers
which, in turn, increases the wage rate and land rent in the area surrounding
the cluster. Such high wages and land rents tend to discourage the agglomer-
ation of firms in the same area. Consequently the equilibrium distributions
of firms and households are determined as the balance between these
opposite forces.
Suppose that in a given location space X there is a continuum of firms
that are symmetric in the pattern of spillovers. However, they are different
in the information they own as well as in the goods they produce. Therefore,
each firm gains from the informational spillovers generated by others. Let
a(x, y) be the resulting benefit for a firm at x obtained from a firm at y.
Then, if f(y) denotes the density of firms at each location y [ X,
A(x) ;
E
X
a(x, y)f(y) dy (2.1)

ECONOMICS OF AGGLOMERATION
349
expresses the aggregate benefit that a firm at x can enjoy from the informa-
tion field within the city. Assume also that each firm needs some given
amount of land (S
f
) and of labor (L
f
). Consequently, if R(x) and W(x)
represent the land rent and wage rate prevailing at x, the profit of a firm
located at x [ X is equal to
P(x) 5 A(x) 2 R(x)S
f
2 W(x)L
f
. (2.2)
Next there is a continuum of homogeneous households who seek location
in the same space. The utility of a household is given by U(s, z), where s
represents the land consumption and z the consumption of a composite
good. For simplicity, we assume that the land consumption is fixed and
equal to S
h
. Furthermore, each household supplies one unit of labor and
the composite good is imported at a constant price normalized to one.
Then, if a household chooses to reside at x [ X and to work at x
w
[ X,
his budget constraint is given by:
z 1 R(x)S
h
1 t
h
ux 2 x
w
u 5 W(x
w
),
where t
h
is the unit commuting cost. Since the lot size is fixed, the objective
of a household is to choose a residential location and a working location
which maximize the consumption of the composite good given by
z(x, x
w
) 5 W(x
w
) 2 R(x)S
h
2 t
h
ux 2 x
w
u.
Finally, in line with mainstream urban economics, it is supposed that
land is owned by absentee landlords.
Following the standard approach in land use theory where firms and
households are free to choose their locations, the equilibrium configuration
is determined through the interplay of the firms’ and households’ bid rent
functions (see Fujita, 1989, Chap. 2, for a detailed discussion of this proce-
dure). An equilibrium is then reached when all the firms achieve the same
maximum profit, all the households the same maximum utility, while rents
and wage clear the land and labor markets. The unknowns are the firm
distribution, the household distribution, the land rent function, the wage
function, the commuting pattern, the maximum utility level, and the maxi-
mum profit level.
The case of a linear, unbounded space has been studied by Fujita–Ogawa
and Imai in different papers. They show that the properties of the equilib-

350
FUJITA AND THISSE
rium configuration crucially depend on the shape of the local benefit func-
tion. Consider the following two examples:
6
a(x, y) 5 b exp(2aux 2 yu) (2.3)
and
a(x, y) 5 b 2 aux 2 yu, (2.4)
where a and b are two positive constants, a measuring the intensity of the
distance–decay effect. The former corresponds to a spatially discounted
benefit, while the latter corresponds to a linear benefit.
In the case of a linear benefit, Ogawa and Fujita (1980) and Imai (1982)
show that a unique equilibrium configuration exists for each parameter
constellation. The equilibrium configuration is monocentric, incompletely
mixed or completely mixed. The first (second and third, respectively) con-
figuration occurs, not surprisingly, when a/t
h
is large (intermediate and
small, respectively).
7
Hence multiple centers cannot arise under linear bene-
fit functions. The case of a spatially discounted benefit leads to more possible
cases. Fujita and Ogawa (1982) show that, in addition to the three configu-
rations just mentioned, several other equilibrium configurations may arise.
Examples include a duocentric city, where each business district is seg-
mented into two labor pools associated with the adjacent residential areas;
a city with one central business district and two subcenters; and a system of
three cities, each having its own CBD, or as one city with three subcenters.
Furthermore the solution is not necessarily unique: multiple equilibria occur
over a wide range of parameter values. Finally the city may undergo a
catastrophic structural transition when parameters take some critical values.
Hence these models are successful in explaining several important features
of modern cities such as the endogenous formation of CBDs and subcenters,
as well as the transition from a monocentric city to a polycentric one.
2.2.
In the models above, the firm is considered as a single-unit entity. Conse-
quently they are not able to explain a basic trend observed in the spatial
organization of large cities, that is, the location of firm-units in suburban
6
These two functions can be derived from explicit benefit functions (Fujita and Smith, 1990).
7
This type of externality has been further explored by Kanemoto (1990) who considers
the case where firms can engage into transactions with others. Combining the exchange of
intermediate inputs between firms with indivisibilities in their production creates externalities
similar to those considered by Fujita-Imai-Ogawa. If
t
is the unit transportation cost of the
intermediate goods, Kanemoto then shows that the monocentric configuration is an equilibrium
when the ratio
t
/t
h
is large, a condition similar to that stated above.

ECONOMICS OF AGGLOMERATION
351
areas. For example, many firms (e.g., banks or insurance companies) have
recently moved part of their activities (such as book-keeping, planning,
and employee training) to the suburbs; similar moves have been observed
earlier in the case of industrial activities (cf. Hohenberg and Lees, 1985).
In this case, a firm typically conducts some of its activities (such as communi-
cations with other firms) at the front-office located in the CBD while the
rest of its activities are carried out at the back-office set up in the suburbs.
This problem has been recently tackled by Ota and Fujita (1993). Keeping
the other assumptions of the Fujita–Imai–Ogawa model unchanged, it is
now assumed that each firm consists of a front-unit and a back-unit. Each
front-unit is assumed to interact with all other front-units for the purpose
of business communications, while each back-unit exchanges information
or management services only with the front-unit belonging to the same
firm. Each firm must choose the location of the front-unit and back-unit
so as to maximize its profit. If a firm sets up its front-unit at x [ X and
back-unit at y [ X, the firm incurs an intrafirm communication cost G(x,
y) which depends only upon the locations x and y. As before, each front-
unit needs S
f
units of land and L
f
units of labor; each back-unit requires
S
b
units of land and L
b
units of labor.
In this context, the only change from the previous model is in the profit
function (2.2). A firm having a front-unit at x, a back-unit at y and choosing
a level of contact activity q(x, z) with the front-unit of any other firm at
z [ X has now a profit function defined as follows
P(x, y) 5 A(x) 2 R(x)S
f
2 W(x)L
f
2 R(y)S
b
2 W(y)L
b
2G(x,y).
Assuming that the linear benefit function is linear (see (2.4)) and that
the intrafirm communication cost is linear in distance, Ota and Fujita (1993)
show that no less than eleven different equilibrium configurations are possi-
ble, depending on the values of the various parameters. These configura-
tions are the result of two basic effects: (i) as the commuting cost of workers
decreases, the segregation of business and residential areas raises, and (ii)
as the intrafirm firm communication cost gets smaller, back-units separate
from front-units. The most typical one when intrafirm communication costs
are low involves the agglomeration of the front-units at the city center,
surrounded by a residential area, while back-units are established at the
outskirts of the city together with their employees. Hence the advancement
of intrafirm communication technologies provides a major cause for job
suburbanization. In particular, the recent developments of telecommunica-
tion technologies should play a central role on the new spatial organization
of production.

352
FUJITA AND THISSE
3. I
NCREASING
R
ETURNS
The general principle that lies behind most modern contributions to
geographical economics is that product and/or input differentiation gives
rise to agglomeration forces. This idea is then grafted onto the trade-off
between increasing returns and transport costs highlighted in central place
theory, in order to generate cumulative processes resulting in the formation
of cities and/or industrial districts. In a sense, this corresponds to a revival
of ideas advocated by early development theorists, who used related con-
cepts such as the ‘‘big push’’ of Rosenstein–Rodan (1943), the ‘‘growth
poles’’ of Perroux (1955), the ‘‘circular and cumulative causation’’ by Myr-
dal (1957, Chap. 2), and the ‘‘backward and forward linkages’’ by Hirshman
(1958, Chap. 1).
In this section, our primary objective is to show how simple models of
monopolistic competition may capture agglomeration forces suggested by
some of the authors above. In particular, we will see that a major contribu-
tion of this approach is to uncover some of the economic mechanisms that
underlie the pecuniary externalities evoked in the regional development
literature. As mentioned in the introduction, we retain interpretations based
on product variety in consumption and/or intermediate goods which are
in line with modern theories of growth and international trade.
Consider a population of homogeneous consumers/workers. Each con-
sumes a homogeneous good together with varieties of a differentiated good.
More precisely, when a continuum of varieties of size n is supplied, the
utility of a worker is given by a CES-type utility with 0 ,
r
, 1
U 5 z
a
o
H
E
n
0
[z(g)]
r
dg
J
(1
2a
)/
r
, (3.1)
where the preferences between the homogeneous good (z
o
) and the differ-
entiated goods (z(g)) is of the Cobb–Douglas-type. When 0 ,
r
, 1, it
is well known that
r
measures the degree of substitution between the
differentiated varieties and that a low value for
r
means that consumers
have a strong preference for variety. More important for our purpose, the
utility of each consumer increases with the number n of varieties.
Alternatively, as observed by Ethier (1982), the right-hand side of (3.1)
can be interpreted as the production function of a competitive firm, which
has constant returns in a homogeneous input (z
o
) and a composite of
differentiated intermediate goods (z(g)). However this function exhibits
increasing returns in the number n of specialized intermediate goods used
by this firm while
r
now expresses its desire for employing a greater variety
of intermediate goods in the production of a final good. In other words,

ECONOMICS OF AGGLOMERATION
353
x 5 z
a
o
H
E
n
0
[z(g)]
r
dg
J
(1
2a
)/
r
(3.2)
can be viewed as the ‘‘dual’’ of the utility model (3.1) in the production
sector. The importance of specialized intermediate goods (such as legal
and communication services, nontraded industrial inputs, maintenance and
repair services, finance, etc.) for agglomeration and regional development
is a well-documented fact.
In both interpretations, because of specialization in production, each
differentiated good z(g) is produced by a single firm according to an identi-
cal technology, where the only input is labor. The total amount of labor
L(g) required to produce the quantity z(g) is assumed to be given by
L(g) 5 f 1 az(g), (3.3)
where f is the fixed labor requirement and a the marginal labor requirement.
Clearly, this technology exhibits increasing returns to scale. These firms
choose their mill (f.o.b.) price and their location in a nonstrategic manner
in the spirit of Chamberlin (Spence, 1976; Dixit and Stiglitz, 1977). In
other words, there is free entry and the number of firms producing the
differentiated good/service is very large. Finally, as in von Thu
¨
nen, an
iceberg-type transport cost, in which only a fraction of the good shipped
reaches its destination, is assumed (Samuelson, 1983). These assumptions
put together have a strong implication. Since the impact of a price change
on the total consumption of the differentiated good is negligible (firms are
nonstrategic by assumption), a consumer’s demand can be shown to be
isoelastic. In consequence, because of the multiplicative structure of the
transport cost, the elasticity of an individual demand is the same across
locations, thus implying that the elasticity of the aggregate demand is inde-
pendent of the spatial distribution of consumers. For a firm located at x,
the equilibrium price for its product is then unique and given by
p*(x) 5 aW(x)/
r
, (3.4)
where W(x) is the equilibrium wage prevailing at x (see below for an
example). Thus the equilibrium price is equal to the marginal production
cost, aW(x), times a relative mark-up given by 1/
r
. 1 which rises with
the degree of product differentiation.
Two groups of papers, using variants of the model described above, are
now discussed. In the first group, we focus on models of city formation in
the case of a linear space, using a partial equilibrium approach. In the
second, a two-region economy is considered and the emphasis is on the

354
FUJITA AND THISSE
emergence of a core-periphery structure. Working with more than two
regions (or countries) is known to be complex. We then review some recent
work dealing with the formation of an urban system. In this second group
of papers, the approach is in the spirit of general equilibrium.
3.1.
In the first group, differentiation in consumption and/or intermediate
goods is shown to generate endogeneously a city. This idea was developed
in a series of contributions published in the late 80s, including Papageorgiou
and Thisse (1985), Abdel-Rahman (1988), Fujita (1988; 1989, Ch. 8), Rivera-
Batiz (1988), and Abdel-Rahman and Fujita (1990).
Papageorgiou and Thisse (1985) and Fujita (1988) deal with the following
system of centripetal/centrifugal forces. Firms are attracted by places where
consumers are many because they have a better access to consumers, but
are repulsed by places involving many firms because competition is fierce;
households are attracted by places where sellers are many in order to have
accessibility to a large variety of goods, but are repulsed by places where
households are many because of high land rents. While Papageorgiou and
Thisse use reduced forms, Fujita assumes explicit market interactions and
obtains reduced forms similar to those supposed by the former authors. In
Papageorgiou and Thisse the equilibrium configuration is such that both
distributions of firms and households are bell-shaped when the purchasing
pattern of consumers is dispersed enough, i.e., when the products sold by
the firms are sufficiently differentiated. In Fujita two configurations may
emerge depending on the relative sizes of consumers and sellers: if there are
relatively more (less) consumers than sellers, then most sellers (consumers)
agglomerate while most consumers (sellers) surround them. The equilib-
rium configurations explain here the formation of a downtown area where
people can find a large number of small stores, restaurants, theaters, and
other commercial activities.
On the supply side, it has often been argued that one of the main causes
for industrial agglomeration is the availability of specialized local producer
services, such as repair and maintenance services, engineering and legal
support, transportation and communication services, and financial and ad-
vertising services. Based on this observation, Abdel-Rahman and Fujita
(1990) consider a city with a final good industry and an intermediate good
industry, where the latter supplies a large variety of specialized services to
the former. The production function of a firm belonging to the final good
industry is given by (3.2), where z
o
stands for labor while z(g) represents
a specialized service. Finally, the production function of the service-firms
is as in (3.3). Abdel-Rahman and Fujita then show that the aggregate
production function of the city is given by

ECONOMICS OF AGGLOMERATION
355
X(N) 5 AN
(1
2a1a
r
)/
r
,
where N is the labor force in the city and A a constant depending on the
parameters of the model. Thus, in the aggregate, production in the final
sector exhibits increasing returns in the labor force (the exponent of N is
larger than one). The reason for this result lies in the fact that the number
of specialized service-firms at the free-entry zero-profit equilibrium rises
with N, permitting a finer supply of the intermediate good and the emer-
gence, in turn, of increasing returns at the aggregate level. It is hard here
not to think of Marshall (1890, 1920, p. 225):
The economic use of expensive machinery can sometimes be attained in a very
high degree in a district in which there is a large aggregate production of the
same kind, even though no individual capital employed in the trade be very
large. For subsidiary industries devoting themselves each to one small branch
of the process of production, and working it for a great many of their neighbours,
are able to keep in constant use machinery of the most highly specialized
character, and to make it pay its expense, though its original cost may have
been high.
Furthermore, since labor is homogeneous, the equilibrium wage is com-
mon to both sectors and also increases with the labor force. Indeed, having
more service-firms enhances the productivity of the final sector and, hence,
leads to higher wages in both industries. Nevertheless, increasing N leads
to an expansion of the residential area which in turn yields higher land
rents and transport costs. Thus, in equilibrium, the city achieves a finite size.
Note, finally, that the analysis of Abdel-Rahman and Fujita remains
incomplete in that they assume that both types of firms are located at the
CBD. When the final sector firms are set up at the CBD, it is reasonable
to conjecture that the agglomeration of the service-firms in the CBD is an
equilibrium when the intermediate good is differentiated enough, as in the
consumption models discussed above.
3.2.
The initial objective of the second family of models is to show the possibil-
ity of divergence between two regions, while the neoclassical model of inter-
regional trade based on constant returns necessarily leads to the conver-
gence either under free trade or under perfect mobility of labor or capital.
8
The prototype model has been proposed by Krugman (1991a; 1991b) which
8
Michel et al. (1996) show that new conclusions emerge when production externalities (as
in modern growth theory) and amenities (as in urban economics) are added to the neoclassical
model. In the presence of amenities, the skilled workers may receive different earnings in
equilibrium, while a core-periphery structure similar to Krugman (1991b) may emerge as an
equilibrium outcome when production externalities are at work. Such an approach extends
the neoclassical model following the line of research described in Section 2.

356
FUJITA AND THISSE
triggered subsequent developments in trade and growth, such as Krugman
and Venables (1995a; 1995b), Premer and Walz (1994), Englmann and
Walz (1995), Kubo (1995), and Venables (1996), to mention a few.
9
(a). The basic framework can be described as follows. There are two
regions, two sectors, and two types of labor. As in the foregoing, agglomera-
tion may arise because of preference for variety on the consumption side
or diversity in intermediate goods on the production side. For the sake of
brevity, we deal with the first context only. In (3.1), z
o
stands for a homoge-
neous agricultural good (A-good), produced under constant returns using
one type of labor (A-workers) and sold on a competitive national market
(transport costs are zero). The varieties z(g) correspond to differentiated
industrial goods (I-goods), produced according to (3.3) where L(g)isthe
other type of labor (I-workers) and sold on monopolistically competitive
regional markets (transport costs are positive). The A-workers are immo-
bile, while the I-workers are perfectly mobile. Finally, all workers/consum-
ers have a preference for variety expressed by the utility (3.1).
In this model, the immobility of A-workers is a centrifugal force because
they consume both types of goods. The centripetal force is more involved.
If a larger number of producers are located in a region, the number of
regional products is greater. Then, because firms are mill pricers, the full
equilibrium prices are lower there in comparison to the other region, thus
generating a real income effect for the corresponding workers (who are
also consumers). This, in turn, induces workers to migrate toward this
region.
10
The resulting increase in the number of consumers (5workers)
creates a larger demand for the I-goods in the region, which therefore
leads more firms to locate there. This implies the availability of even more
varieties of the differentiated good in the region in question. In this way,
a circular causation for the agglomeration of firms and workers is generated
through forward linkages (the supply of more varieties of the I-goods in-
creases the workers’ real income) and backward linkages (a greater number
of consumers attracts more firms). Therefore, through these linkage effects,
scale economies at the individual firm level are transformed into increasing
returns at the level of the region as a whole.
Krugman shows that this mechanism may give rise to a core-periphery
pattern in which the whole production of the I-goods is concentrated into
one region, a regional structure considered by Kaldor (1970) as being more
reasonable than the convergence between regions precisely because of the
existence of increasing returns. The core-periphery pattern is likely to occur
when (i) the transportation rate of the I-goods is low enough, (ii) when
9
An earlier analysis that anticipated several aspects of Krugman’s work was developed by
Faini (1984).
10
This effect of product variety on consumer migration was first emphasized in Stahl (1983).

ECONOMICS OF AGGLOMERATION
357
the I-goods are sufficiently differentiated, or (iii) when the share of the
industrial sector in the national economy is large enough. Furthermore,
because of the existence of multiple equilibria, minor changes in the values
of the critical parameters may generate dramatic changes in the equilibrium
spatial configuration. This suggests that history matters (the initial condi-
tions) to explain actual industrial patterns, while circular causation gener-
ates a snowball effect that leads manufacturing firms to be locked-in within
the same region for long periods of time (examples are provided by the
‘‘industrial belt’’ in the United States or the ‘‘banane bleue’’ in Europe).
Note that a broader set of configurations has been obtained by Helpman
(1995) who supposes that the dispersion force is given by a fixed stock of
housing, while all individuals are assumed to be perfectly mobile. It is
then shown that both regions accommodate industrial firms, even though
transportation costs are very low, when the demand for land is high or
when products are close substitutes. However, as in Krugman, industrial
concentration arises provided that the demand for land is low or products
are differentiated enough, but when transport costs are high instead of low.
These results imply that new configurations may emerge when ingredients
from urban economics are added into the model. Indeed land is consumed
by individuals in Helpman while cities are supposed to be ‘punctual’ in
Krugman and subsequent work. Another interpretation of Helpman’s is
that the transportation costs of the A-goods are assumed to be prohibitive
while they are zero in Krugman’s.
(b). A line of research in the spirit of Krugman, exploiting the dual
model, has been pursued by Englmann and Walz (1995) who study growth
in a two-region economy. There are two types of labor, the skilled and the
unskilled; the former are mobile and the latter are immobile. There are
three sectors: the agricultural sector using both types of labor, the industrial
sector where the production function is similar to (3.2) but in which the
homogeneous input is replaced by the two types of labor, and the R&D
sector. Using an endogeneous growth device, these authors suppose that
the R&D sector, where only skilled workers are employed and knowledge
is accumulated, produces intermediate inputs which are nontraded. Hence,
the immobility of the unskilled is a centrifugal force, while the existence
of nontraded inputs is a centripetal force. When technological progress is
localized, Englmann and Walz show that, at the steady-state, the production
of innovations and of the I-good will take place in the region with the initial
advantage in the number of intermediate, nontraded inputs. The reason for
the persistence of leadership lies in the fastest accumulation of knowledge
in the region having the initial advantage, while growth is sustained because
the marginal productivity of the R&D sector does not decrease to zero.
That result provides an explanation for the continuance of a core-periphery

358
FUJITA AND THISSE
structure; it also sheds light on the role of historical accidents that define
the initial conditions of the development process.
However the core-periphery structure is no longer the unavoidable mar-
ket outcome when knowledge spills over the other region. More diversified
patterns of regional development involving interior solutions arise because
the impact of local intermediate inputs is lessened by the transfer of knowl-
edge, which is itself induced by the existence of interregional spillovers.
Furthermore, a developed and rich region might well be less ready to adopt
a new technology, so that the lagging region may ‘leapfrog’ the leading
region as a reaction to a major exogeneous change in technology. This
would suggest that there is no point of no return.
(c). It is well known that results established for two regions are difficult
to extend to the case of an arbitrary number of regions. For this reason,
Krugman (1993) has extended his initial model to a linear spatial economy.
Under the three conditions stated above, he shows that the whole industry
tends to concentrate into a single city whose location need not be at the
center of the segment. Fujita and Krugman (1995) relaxes the assumption
that A-workers are immobile and allow for mobility between regions and
sectors. Furthermore the transportation costs of the A-goods are now posi-
tive. They show that a single city, surrounded by an agricultural area, arises
when varieties are differentiated enough (or when transportation costs are
low) and when the population of workers is not too large. Indeed, if varieties
are close substitutes and/or the population is sufficiently large, an individual
producer has an incentive to locate far away from the city and to sell a
larger output to local consumers. In this case, there is scope for more
than one city. Therefore, the work of Fujita and Krugman provides an
endogeneous determination of the central city as in von Thu
¨
nen but within
the context of a completely closed model.
The endogeneous determination of several cities has attracted the atten-
tion of many scholars but very few results are so far available. In this
respect, a recent contribution by Fujita and Mori (1996a) sheds new light
on this classical problem of geographical economics. These authors show
that, as the population in the national economy increases continuously,
new cities are created periodically because of a catastrophic bifurcation in
the existing urban system. As the number of cities increases, the urban
system approaches a structure where cities are more or less equally distant.
Specifically, starting from one city, population growth leads to a larger
agricultural area. Beyond some threshold, the agglomeration of industrial
firms within a single city is no longer an equilibrium. Some I-workers and
some firms leave the existing city to form a new city located deep in the
agricultural area, together with some A-workers while new firms are also
created. However the size of the existing agglomeration remains large

ECONOMICS OF AGGLOMERATION
359
enough for the other I-workers and firms to stay put. This process keeps
going as the population rises. Thus, exactly for the reason suggested by
Marshall in the quotation given in the introduction, the locations of the
existing cities remain the same though their sizes may vary with the level
of population. Finally, there is intercity trade, in addition to trade between
cities and rural areas, because the goods produced in the different cities
are differentiated and because consumers have a preference for variety.
(d). However only one level of city emerges as the outcome of this
process. What remains to investigate is the fundamental question of the
formation of an urban hierarchy, that is, the construction of an economic
theory of central places. A first step into this direction is taken by Fujita
et al. (1995) who introduce into (3.1) different groups of I-goods, having
each different elasticities of substitution and/or transportation rates. As
the population rises, they show that a (more or less) regular hierarchical
central place system a
`
la Christaller emerges within the economy, in which
‘higher-order cities’ provide a larger number of groups of I-goods. There
is two-way trade between cities, unlike standard central places theory where
trade goes from high-order to low-order cities only. However, as expected,
higher-order cities export more varieties than lower-order cities.
An alternative, original approach to the formation of a system of cities
has been pioneered by Henderson (1974). When the production of a good
involves increasing returns (see 3.1) and takes place in the Central Business
District (see 2.1 and 3.1), Mills (1967) argues that each city has a finite size
because of the commuting costs borne by the workers. Then, assuming a
‘‘market for cities,’’ Henderson shows that cities will be created until no
opportunity exists for a developer or a local government to build a new
one. This corresponds to a free entry equilibrium in which all cities are
identical. Henderson also shows that cities have an incentive to specialize
in the production of traded goods because the production of different goods
within the same city rises commuting costs and land rents. Therefore, if
the traded goods involve different degrees of scale economies, cities will
be specialized in the production of different goods and will export. This
approach explains the existence of an urban system formed by cities having
different sizes, as well as inter-city trade involving different goods (see Hen-
derson, 1987, 1988, for further developments). However, this model does
not permit to predict the location of cities nor does it explain the urban
hierarchical structure. In a sense, Henderson’s and Fujita-Krugman’s ap-
proaches can be viewed as dual: cities have a spatial extension while trans-
portation costs between cities are supposed to be zero in the former, cities
have no dimension but intercity trade is costly in the latter.
Finally, though all the models above use very specific functional forms
and rest on particular market and transport structures, it seems fair to say

360
FUJITA AND THISSE
that they point to the right direction. Therefore, they can be viewed as a
first step toward the still missing theories of regional development and of
central places. More importantly, combining these various approaches, i.e.,
preference for variety on the product market and diversity/specialization
on the input markets, within the same general equilibrium model seems to
be an important and challenging task for future research.
Given what we said in the introduction, one of the main limitations of
the monopolistic competition models lies in the assumption that firms do
not strategically interact (formally this means that we implicitly assume a
continuum of firms). Consequently, it is important to deal with oligopolistic
rivalry, something which is done in spatial competition. However, as will
be seen below, this is not an easy task to accomplish.
4. S
PATIAL
C
OMPETITION
It is now customary to distinguish between two types of models in
spatial competition, i.e., the shopping and shipping models. Roughly
speaking, we have a shopping model when firms charge mill prices while
consumers visit firms and bear the whole transportation costs; in a
shipping model, firms deliver the product and take advantage of the
fact that the customers’ locations are observable to price discriminate
across locations. The former are rooted in the seminal work of Hotelling
(1929) while the latter find their origin in Hoover (1937) and Greenhut
and Greenhut (1975). Shopping models seem to be appropriate to study
competition between sellers of consumption goods while shipping models
would describe better competition between sellers of industrial goods.
11
Strategic interaction is at the heart of these models and space is the
reason for this behavior: competition is localized in shopping models
while shipping models involve oligopolistic competition in spatially sepa-
rated markets. Though shopping and shipping models have different aims,
the analysis shows that they are governed by the same centrifugal and
centripetal forces, thus leading to similar locational patterns under similar
conditions. In particular, high transportation costs are always a centrifugal
force that results in distinct locations. In consequence, we will limit
ourselves to the case of shopping models.
Typically, models of spatial competition assume that the consumer distri-
bution is given. If we introduce a land market and consumer mobility into
the Hotelling model then, as observed by Koopmans (1957, Chap. II.9),
11
In his study of pricing policies followed by business firms in Japan, the United States,
and West Germany, Greenhut (1981) finds that about three-quarters of the firms surveyed
price discriminate.

ECONOMICS OF AGGLOMERATION
361
the locations of firms and consumers become interdependent. Not much
has been done so far and we briefly discussed the few existing contributions.
4.1.
Ever since Hotelling, it has been generally accepted that competition for
market areas is a centripetal force that would lead vendors to congregate,
a result known in the literature as the Principle of Minimum Differentiation.
This principle has generated controversies about the inefficiency of free
competition since it suggests that ‘‘buyers are confronted everywhere with
an excessive sameness’’ (Hotelling, 1929, p. 54).
The two ice cream men problem provides a neat illustration of this
principle. Two merchants selling the same ice cream at the same fixed price,
compete in location for consumers who are uniformly distributed along a
linear segment of length L. Each consumer purchases one unit of the good
from the nearer firm. The consumers are thus divided into two segments,
with each firm’s aggregate demand represented by the length of its market
segment. The boundary between the two firms’ market areas is given by
the location of the marginal consumer who is indifferent between buying
from either firm. This boundary is endogenous, since it depends upon the
locations selected by the firms. Since Lerner and Singer (1937), it is well
known that the unique Nash equilibrium in pure strategies of this game is
given by the location pair
x*
1
5 x*
2
5 L/2
regardless of the shape of the transport cost function. Hence, two firms
competing for clients choose to locate together at the market center, min-
imizing their spatial differentiation. Contrary to a wide-spread opinion, this
result is not driven by the existence of boundaries. To see it, consider a
continuous distribution over the real line. Then, both firms locate back to
back at the median of the distribution. It is our belief that several of the
results presented below could be extended to this framework.
However things become more complex when (mill) prices are brought
into the picture, as in Hotelling’s original contribution. Hotelling considers
a two-stage game where the firms first simultaneously choose their locations
and afterwards their prices. This decoupling of decisions captures the idea
that firms select their locations in anticipation of later competing on price.
The boundary between the two firms’ markets is now given by the location
of the consumer for whom the full prices, defined by the posted prices plus
the corresponding transport costs, are equal (transport costs are linear in
distance). Because of the continuous dispersion of consumers, a marginal
variation in price changes the boundary and each firm’s demand by the

362
FUJITA AND THISSE
same order.
12
For each location pair, Hotelling determines what he thinks
will be the equilibrium prices of the corresponding price subgame. He
includes these prices, which are functions of the locations, into the firms’
profit functions, which then depend only upon locations. These new profit
functions are used to study the first-stage location game. As in the foregoing,
Hotelling finds an equilibrium where the two firms locate at the market
center.
Hotelling’s analysis was incorrect. When the two firms are sufficiently
close, there does not exist an equilibrium in pure strategies for the corre-
sponding price subgame: at least one firm has an incentive to undercut its
rival and to capture the whole market. The study of the location game is
accordingly incomplete. Nevertheless, as established by d’Aspremont et al.
(1979), if the transport costs are quadratic rather than linear, a unique price
equilibrium exists for any location pair. Reconstructing Hotelling’s analysis,
these authors then show that the two firms wish to set up at the endpoints
of the market.
The extreme spatial dispersion is the result of a trade-off where price
competition pushes firms away from each other while competition for mar-
ket area tends to pull them together. To illustrate how this trade-off works,
let P*
1
be firm 1’s profit evaluated at the equilibrium prices p*
i
(x
1
, x
2
)
corresponding to the location pair (x
1
, x
2
) such that x
1
, x
2
. Then, since
P
1
/p
1
5 0, we have
dP*
1
/dx
1
5 (P
1
/p
2
)(p
*
2
/x
1
) 1P
1
/x
1
.
In general, the terms in the right-hand side of this expression can be
signed as follows. The first one corresponds to the strategic effect (the desire
to relax price competition) and is expressed by the impact that a change
in firm 1’s location has on price competition. Since goods are spatially
differentiated, they are substitutes so that P*
1
/p
2
is positive; because
goods become closer substitutes when x
1
increases, p
*
2
/x
1
is negative.
Hence the first term is negative. The second term, which corresponds to
the market area effect uncovered by Hotelling, is positive. Consequently
the impact of reducing the inter-firm distance upon firms’ profits is undeter-
mined. However, when firms are close enough, the first term always domi-
nates the second so that firms always want to be separated in the geographical
space. This implies that the Principle of Minimum Differentiation ceases
to hold when firms are allowed to compete in prices (d’Aspremont et al.,
12
d’Aspremont et al. (1979) have demonstrated that the hypotheses of Hotelling do not
guarantee continuity at the global level. For that it is necessary to replace the assumption of
linear transport costs by one in which transport costs are increasing and strictly convex
in distance.

ECONOMICS OF AGGLOMERATION
363
1983); one may even observe maximum differentiation. In other words,
price competition is a strong centrifugal force.
There is no doubt that Hotelling’s contribution to economic theory, and
in particular to geographical economics, has been fundamental in many
respects. Yet, as such, his analysis is unable to explain the currently observed
agglomeration of shops selling similar goods. The dispersion of firms turns
out to be very sensitive to a particular assumption of the model, namely
that consumers patronize the firm with the lowest full price. Somewhat
ironically when one knows Hotelling’s purpose, the model above corres-
ponds to a very sharp consumer behavior that follows from the fact that
firms are supposed to sell identical goods. On the contrary, dramatically
different results are obtained when consumers behavior is smooth enough,
for example because firms sell differentiated products.
The idea that consumers distribute their purchases between several sellers
is not new in economic geography and goes back at least to Reilly (1931)
who formulated the so-called ‘‘gravity law of retailing.’’ For a long time,
despite their success in empirical studies, gravity models and their exten-
sions, such as the logit, remained somewhat mysterious to the economists
because they did not seem to fit the utility maximization assumption. Psy-
chologists have suggested an alternative model of individual choice which
imputes a random term to utility and makes the consumer’s decision
whether to switch firms probabilistic. The use of such models in economics
has been pioneered by McFadden (1981) and surveyed by Anderson et al.
(1992, Chap. 2).
Thus it is now assumed that consumers are influenced by various tangible
as well as intangible factors at the moment of their choice, and that the
relative importance of these factors may change due to external factors.
This implies that consumers’ purchase decisions are not based solely on
the full prices, but also on firm-specific factors which are typically perceived
differently by different consumers. Such a behavior means that consumers
at the same location do not react in the same way to a firm’s unilateral
change in its strategy. The presumably wide array of factors influencing
consumers’ shopping behavior makes it problematic for a firm to predict
exactly a consumer’s reactions to a reduction in price. In other words, the
firm assigns a probability between zero and one to whether a particular
consumer on a particular date will respond to a price difference by switching
firms. This is modeled by assuming that consumers maximize a random
utility rather than a deterministic utility.
13
Firms implicitly sell heteroge-
neous products and the random term in the consumer’s utility expresses her
matching with firms at the time of purchase. An alternative interpretation is
13
For our purpose, it is worth noting that Anas (1983) has shown that many descriptive
gravity- and logit-type models can be derived from the maximization of a random utility.

364
FUJITA AND THISSE
that consumers like product variety (see Section 3) so that, even if prices
do not vary, they do not always purchase from the same firm over time.
In both cases, the indirect utility of a consumer at x and buying from firm
i can be modeled as
V
i
(x) 5 a 2 p
i
2 t ux 2 x
i
u 1«
ix
i 5 1,...,n, (4.1)
where a is a constant measuring the gross utility of the good and «
ix
a random
variable (with a zero mean) whose realization expresses the matching of
product i with a consumer at x. In the special case of the multinomial
logit (where the random variables «
ix
are independently and identically
distributed according the double exponential), the probability for a con-
sumer at x to buy from firm i is given by the following expression derived
in the econometrics of discrete choices
14
P
i
(x) 5
exp(2p
i
2 tux 2 x
i
u)/e
o
n
j
5
1
exp(2p
j
2 tux 2 x
j
u)/e
i 5 1,...,n, (4.2)
where t is the transport rate and e the standard deviation of the variables
«
ix
(up to a numerical factor). The values of the choice probabilities P
i
(x)
reflect those of the full prices: the higher the latter, the lower the former.
Consequently, the consumer behavior described by (4.2) encapsulates a
tendency to buy from the cheapest shops. Note also that the logit and the
CES are closely related in that both models can be derived from the same
distribution of consumer tastes; the only difference is that consumers buy
one unit of the product in the former and a number of units inversely
related to its price in the latter (Anderson et al., 1992, Chaps. 3 and 4).
The expected demand to firm i is equal to the integral of the choice
probabilities over the market space; it is smooth in prices and locations
when e is strictly positive. However the continuity of profits does not suffice
to restore the existence of an equilibrium. Additional restrictions on the
parameters are necessary. As will be seen, these restrictions can be given
a simple and intuitive interpretation: the relative importance of the transport
costs must be small compared to that of the idiosyncratic components of
the individual preferences (4.1). Formally, this means that e/tL must be
‘‘large enough.’’
Let c be the common marginal production cost. In the case of a simultane-
ous choice of prices and locations by firms, the following result holds true:
14
This formula is well known in classical economic geography but it is usually applied to
describe the flows of commodities and of individuals.

ECONOMICS OF AGGLOMERATION
365
if the choice probabilities are given by (4.2) and if the inequality
e/tL $ 1/2
is satisfied, then the configuration
x
*
i
5 L/2 and p
*
i
5 c 1 ne/(n 2 1) i 5 1,...,n (4.3)
is a Nash equilibrium (de Palma et al., 1985). Therefore, firms choose to
agglomerate at the market center, as Hotelling thought, when their products
are differentiated enough and when transportation costs (or market size) are
low enough. When firms are gathered at the market center, they constitute a
very attractive pole for the consumers who may find there the best product,
as in Fujita and Krugman (1995) discussed in 3.2. However, products must
be differentiated enough for the advantage of being agglomerated to domi-
nate the incentive to move away from the cluster and to charge a higher
price.
When transport costs are low, the benefits of geographical separation
are reduced and prices are lower. Firms then choose to reconstruct their
profit margins by differentiating their products in terms of some nongeo-
graphical characteristics, which may be tangible or intangible. Stated differ-
ently, product differentiation is substituted to geographical dispersion (this
is shown in a partial equilibrium model of spatial competition by Irmen
and Thisse, 1996). In this case, they no longer fear the effects of price
competition (the centrifugal force is weakened by the differentiation of
products) and strive to be as close as possible to the consumers with whom
the matching is the best. Since these consumers are spread all over the
market space, they set up at the market center and, therefore, minimize
their geographical differentiation. This is reminiscent of the market poten-
tial theory, developed by Harris (1954) in classical economic geography,
according to which firms tend to locate where they have the ‘‘best’’ access
to markets where they can sell their product. The difference is that here
the point of highest ‘‘potential’’ corresponds to a Nash equilibrium. Further-
more, firms charge a price equal to marginal cost plus an absolute markup.
Consider now the implications of the logit for the sequential, original
Hotelling duopoly model. Anderson et al. (1992, Chap. 9) have shown the
existence and the uniqueness of a price equilibrium for any location pair
when e/tL is large enough. Using this price equilibrium, these authors are
then able to study the location game. The following results emerge. As
e/tL rises from 0 to 0.062, there is no location equilibrium. For 0.062 #
e/tL , 1.47, there is a symmetric dispersed equilibrium which initially
entails increasing geographical separation of firms. However, when e/tL

366
FUJITA AND THISSE
goes beyond some threshold (around 0.30), the geographical separation
starts to decrease. For 0.76 # e/tL , 1.47, an agglomerated equilibrium
exists along the dispersed one; however the former is unstable while the
latter is stable. Finally, for e/tL $ 1.47 there is a unique equilibrium that
involves central agglomeration.
The intuition behind these results, which is reminiscent of what we saw
with the CES, is as follows. An arbitrarily small amount of heterogeneity
among products/consumers is not sufficient to restore existence because
consumers’ shopping behavior remains very sharp. When existence is guar-
anteed, firms’ market areas overlap, thus making price competition so
fierce that firms want to move apart. Beyond some threshold, the product
differentiation effect tends to dominate the price competition effect and
firms set up closer to the market center because price competition is relaxed.
Finally, for a sufficiently large degree of differentiation, the market area
effect becomes predominant and the agglomeration of sellers is the market
outcome as in the nonprice competition context. In both the simultaneous
and sequential games, the message is the same: agglomeration arises when
price competition is weakened enough.
15
Furthermore, unlike what we observe in the homogeneous product case,
the agglomeration may be socially desirable. The social welfare function
includes both product differentiation benefits and transportation costs in
an entropy-like function where e plays the role of preference for variety.
As e/tL rises, from 0 to 1/2, the inter-firm distance decreases from L/2
(firms are located at the quartiles) to 0 (firms are located at the market
center). When e/tL exceeds 1/2, it is socially optimal for the duopolists to
be located back to back; thus, in this model, the market tends to provide
excessive geographical dispersion (Anderson et al., 1992, Chap. 9). In other
words, spatial competition does not necessarily lead to excessive sameness,
as Hotelling thought.
Another approach, based on the idea of search, is explored by Schulz
and Stahl (1996). Building on early work by Stahl (1982) and Wolinsky
(1983), these authors suppose that the total demand is variable: consumers
have the same reservation price but are uniformly distributed along the
real line. Thus, if consumers have different tastes and are uncertain about
the characteristics of the products on offer, the firms can manipulate the
search cost structure by joining an existing market or by establishing a new
one. The trade-off faced by a firm is as follows: a firm captures a small
market share when setting up in a large market or obtains the whole market
when opening a new one. Since total demand is elastic, a demand externality
arises when more firms are located together because more consumers will
15
Another example is provided by price collusion in the context of a repeated price game
(Friedman and Thisse, 1993).

ECONOMICS OF AGGLOMERATION
367
benefit from economies of scope in searching (that is, the extent of the
product market is endogeneous) and, therefore, will visit the cluster. Such
an externality is obviously a centripetal force.
16
Though collectively several firms may want to form a new market, it may
not pay an individual firm to open a new market in the absence of a
coordinating device. Consequently, a new firm entering the market will
choose instead to join the incumbents, thus leading to an increase in the
agglomeration size. The entry of a new firm creates a positive externality for
the existing firms by making total demand larger. Though price competition
becomes fiercer, it appears here that firms take advantage of the extensive
margin effect to increase their prices in equilibrium.
17
A related idea is explored by Gehrig (1996) when two differentiated
markets are located at the endpoints of a linear segment. Unlike Schulz
and Stahl, Gehrig supposes that the aggregate demand over the two local
markets is fixed. The number of products available in a local market in-
creases with the number of consumers visiting this place, thus reducing the
average matching costs. The attractiveness of market therefore depends
on the size of its clientele. Gehrig then shows that, in such a setting,
an entrant is likely to join one of the existing markets, especially when
transportation costs are low.
4.2.
In the models of spatial competition discussed above, the distribution of
consumers is fixed. Ideally, one would like to make it endogeneous. So far
there have been few attempts to do so because of the complexity of the
problem. Since firms have more market power than consumers, it seems
reasonable to assume that firms locate first, anticipating the subsequent
consumers’ locations and demand functions. When products are homoge-
neous, such a process may reinforce the tendency toward dispersion. Indeed,
when firms are dispersed, consumers pay smaller transport costs on average
and may also pay lower average land prices since the supply of attractive
lots (those close to firms) is greater. The resulting income effect would
increase consumers’ demand for private goods and make geographical
16
Observe that such an externality cannot arise in the standard model of spatial competition
because total demand is fixed. On the other hand, it is at the heart of the monopolistic
competition models through the forward linkage effect.
17
In work in progress, Stahl (1995) develops an alternative shopping model in which trans-
port costs are lump-sum. Indeed, there are often considerable scale economies in carrying
the goods bought by a consumer. In the limit, consumers’ outlays on transportation can be
considered as independent of the purchased quantities. Therefore, if the utility functions are
homothetic, a more distant consumer has a lower income and demands fall in the same
proportion. This leads to much simpler aggregate demand functions and allows Stahl to derive
new results and to extend those in Schulz and Stahl (1996).

368
FUJITA AND THISSE
isolation even more profitable than in the Hotelling model (Fujita and
Thisse, 1986).
However the mere existence of a public facility or of a major transporta-
tion node might be enough to attract firms within the same urban area.
Indeed, other things the same, transportation costs are reduced for consum-
ers who then have higher disposable incomes to buy the composite good
sold by the firms (Thisse and Wildasin, 1992). In other words, the existence
of a pre-existing public facility yields an incentive for agglomeration of firms
and consumers within an urban area.
18
5. C
ONCLUSION
Though the economic analysis of agglomeration is still in infancy, a few
general principles seem to emerge from the results discussed in the forego-
ing, they are briefly discussed in 5.1. We will conclude with some suggestions
for future research in Section 5.2.
5.1.
First, it should be clear that the existence of scale economies at the firms’
level is a critical factor for explaining the emergence of agglomeration.
Indeed the mere existence of indivisibilities in production makes it profit-
able for firms to concentrate production in a relatively small number of
plants producing for dispersed consumers, so that increasing returns to
scale constitute a strong centripetal force. However, we cannot leave the
argument at that. Indeed, the geographical extension of markets, and the
corresponding transportation costs, imply that the entire production is gen-
erally not concentrated in one place. In other words, the spatial dispersion
of demand is a centrifugal force. Therefore, there is a fundamental trade-
off between scale economies and transportation costs in the geographical
organization of markets.
Second, the secular fall in transportation costs often intensifies the ten-
dency toward agglomeration. Although this decrease could have suggested
that firms become indifferent about their location, we have seen in various
models that low transport costs, or more generally trade costs, tend to favor
the formation of geographical clusters or to deter the creation of new ones.
There are at least two reasons behind this phenomenon. First, as transporta-
tion costs decrease, firms have an incentive to concentrate their production
in a smaller number of sites in order to reduce fixed costs, as suggested by
the trade-off mentioned above. Second, as seen in 4.1, low transportation
18
See Fujita and Mori (1996b) who study the formation of port-cities using a monopolistic
competition model similar to those discussed in 3.2.

ECONOMICS OF AGGLOMERATION
369
costs makes price competition fierce, thus inducing firms to differentiate
their products to relax price competition. This in turn leads firms to benefit
from the advantages of ‘‘central locations’’ where, on average, they are the
closest possible to the consumers for whom the matching is best. The
counterpart of that result is that product differentiation is a strong force
toward agglomeration. Behind this result lies the following fundamental
cause: when price competition is relaxed (e.g., price collusion or quantity
competition with a homogeneous product), firms no longer fear the devasta-
ting effects of price competition and the various centrifugal forces discussed
in this paper might well be predominant. In other words, even if products
are potential substitutes, additional forces make them complements. Ag-
glomeration may then emerge as an equilibrium outcome because competi-
tion is overcome by other effects (Matsuyama, 1995; Stahl, 1995). Observe
also that similar arguments apply to labor: wage competition is a centrifugal
force as is price competition, while a better access to a diversified labor
pool for both firms and workers is a centripetal force.
However, it should be kept in mind that the models surveyed in this
paper are still very simple. In richer models integrating more realistic
patterns of migration, new effects might emerge that could more than offset
the direct effects identified above. For example, Puga (1996) shows that a
drastic fall in communication and transportation costs may lead to geo-
graphic dispersion when the mobility costs of workers between regions are
arbitrarily large while the mobility costs between sectors are positive but
finite (unlike Krugman, 1991a, who assumes prohibitive costs). He also
supposes the existence of input/output linkages, as in Venables (1996),
otherwise there would be no agglomeration force. In this context, the ag-
glomeration of firms into a single region intensifies competition on the corre-
sponding local labor market because workers are not spatially mobile.
Though firms can attract workers from the agricultural sector, the latter
effect turns out to be a dominant centrifugal force when transportation
costs are low enough because they are able to supply the other region at
low cost while benefiting of low wages. Mori (1995) obtains comparable
results in a continuous model with a land market: firms are willing to locate
away from cities because of the lower wages they pay in the agricultural
areas and because the supplying costs of the manufactured goods in cities
are low; workers are willing to leave cities because the cost of agricultural
goods is lower and, therefore, real wages are higher in the rural hinterlands
while manufactured goods are available at prices close to those prevailing
in cities. Thus new cities may emerge when the population is large enough,
leading to a more dispersed pattern of economic activities. Finally, using
simulations, Krugman and Venables (1995a) also predict the collapse of the
core-periphery structure and the convergence between regions when trade

370
FUJITA AND THISSE
costs are sufficiently low for reasons similar to those discussed above. They
summarize their results as follows (p. 476):
The world economy must achieve a certain critical level of integration before
the forces that cause differentiation into core and periphery can take hold; and
when differentiation occurs, the rise in core income is partly at peripheral
expense. As integration proceeds further, however, the advantages of the core
eroded, and the resulting rise in peripheral income may be partly at the
core’s expense.
These preliminary findings suggest that there would be no monotonic
relationship between the degree of geographical concentration and the
level of transportation costs. Very high or very low trade costs would favor
the dispersion of economic activities, while agglomeration would emerge for
intermediate values of these costs once the spatial mobility of workers is low.
In other words, the relationship between trade costs and the degree of
geographical concentration of the economy would be U-shaped. More work
is needed to check the robustness of these results, while empirical studies
are required to evaluate their real-world implications.
19
They are indeed
very important since they would suggest that ‘‘incompletely’’ integrated
markets, that characterize most trading blocks, would favor the polarization
of space while full integration would be associated with a large diffusion
of economic activities across regions.
In addition, as discussed in 2.2, low transportation costs may also favor
the delocation of activities that need not be close to other producers and/or
are labor-intensive. More generally, most models in geographical economics
suppose a space homogeneous in terms of ‘‘socio-economic’’ factors. Still,
it is well known that some firms seek a location in areas where the labor
cost is very low because their products can be produced by means of labor-
intensive techniques. Under such circumstances, the fall in transportation
costs can be viewed as a dispersion force that fosters convergence across
countries, as in the neoclassical model. In this perspective, it seems promis-
ing to model the firm as a multi-location agent in the context of the new
theories of the firm. Indeed the way firms organize their activities may
induce particular forms of convergence between various areas since the
choice of a location for a particular activity of the firm may obey different
logics. Clearly, there is a strong need to integrate the agglomeration models
surveyed in this paper with neoclassical models of trade based on compara-
tive advantage in order to study the new international division of labor.
Some preliminary attempts dealing with the tension between agglomeration
19
Note that all these models do not integrate externalities as such discussed in Section 2.
They also assume horizontal, and not vertical product differentiation which permits a better
description of product innovation. The combination of these two factors seems to be essential
for the localized growth of some industries (Saxenian, 1994, Chap. 5), and it is not clear that
the results above would remain the same when they are taken into account.

ECONOMICS OF AGGLOMERATION
371
and factor price equalization can be found in Matsuyama and Takahashi
(1994) as well as in Puga and Venables (1996).
Third, the size of the population is also an important determinant of the
urban structure of the economy. We have seen that more cities are likely
to emerge when the population rises. Indeed, since production is character-
ized by increasing returns to scale, larger markets allows for the entry of
more firms that can serve as a basis for new clusters and a denser urban
pattern. Furthermore, a larger population also permits a better match be-
tween consumers/workers and products/job requirements, as well as a wider
range of intermediate inputs. In the aggregate, this is reflected by a higher
degree of returns to scale on the production side, but also by higher welfare
levels on the consumption side. However this process comes to an end when
the addition of a consumer/worker leads to an increase in transportation and
congestion costs that offset the benefit this individual may derive from
variety. Hence, beyond some threshold, firms and consumers/workers have
an incentive to form a new city. However, in a hierarchical urban system,
a population increase can instead boost the growth of the highest order
cities (for example, think of New York, Paris, Tokyo, but also of some
urban giants in the Third World).
Finally, in many models of geographical economics, there is multiplicity
of equilibria. This is because the agglomeration of economic activities has
the nature of a cumulative, self-reinforcing process and because the emer-
gence of a particular site as a major agglomeration does not only depend
upon the intrinsic features of this site. In other words, history matters for
economic geography in that initial conditions appear to be essential in the
selection of a particular equilibrium. It is then well known that minor
changes in the socio-economic environment occurring at some critical peri-
ods may result in very different geographical configurations. This might
well explain why the location of new agglomerations is difficult to predict.
Furthermore, some equilibria turn out to be socially preferable to
others so that there is scope for regional policy. More precisely, the role
of the government would be here to create the conditions for the ‘‘best’’
equilibrium to arise. Yet it is fair to say that our knowledge of the
underlying dynamics is by far too rudimentary to permit us making
detailed policy recommendations. In addition, even though a spatial
structure might well be inefficient, it is likely to be difficult to change
it because of the lock-in effects associated with existing agglomerations.
Another reason for this inertia, related to Krugman (1991c) and Matsuy-
ama (1995), is the formation of self-fulfilling prophecies about the
development of some areas. Indeed, it seems reasonable to consider
existing cities as focal points that help agents coordinate their spatial
decisions. In such a context, reshaping the urban landscape would then
require major changes in agents’ expectations.

372
FUJITA AND THISSE
Accordingly, we seem to have a putty-clay geography: there is a priori
a great deal of flexibility in the choice of locations but a strong rigidity of
the urban structure once the process of urbanization has started. Those
factors, together or in isolation, could explain why, in many countries
and at different times, many ‘‘planned cities’’ have failed to develop once
governments have stopped supporting most of the urban activities before
some critical mass was reached (exceptions involving massive involvement
of national governments through huge coordination programs include Bra-
silia and Saint Petersburg).
Though more work is called for, it is worth mentioning that these prelimi-
nary results seem to fit well the waves of urbanization observed in Europe
in the 12th century, as well as the process of urban growth that took place
during the Industrial Revolution in Europe and the United States, so well
analyzed by Bairoch (1985) in his masterful economic history of cities.
5.2.
One of the main limitations of most models of geographical economics
is that results seem to heavily depend on strong assumptions made about
the economy; in particular very specific functional forms, like the CES or
the logit, are used in most models. It is reasonable to think that such
simplifying assumptions are needed at an early stage of development of
the theory. However, one should now strive for more robust results. For
example, it might well be possible to extend the CES model by using the
random utility model of monopolistic competition developed in Anderson
et al. (1992, Chap. 6) that permits to retain the idea of symmetry within a
much more general framework. (See also Mirrlees (1995) for another exten-
sion dealing with several goods.) Similarly using an iceberg transport cost
function implies that any increase in the mill price is accompanied with a
proportional increase in transport cost, which seems both unrealistic and
undesirable. It is also known that aggregating local demands across locations
may lead to demand systems that exhibit undesirable features, such as
discontinuities or outward kinks. Still, even if simplifying assumptions are
probably unavoidable, more attention should be paid to the aggregation
problem over space. In the monopolistic competition models discussed in
Section 3, it is not clear what the nonstrategic interaction assumption implies
and one should try to relax it. In spatial competition models (see Section
4), there is clearly a need for more work devoted to the endogeneous
determination of the consumers’ locations and the combination of atomistic
and nonatomistic markets.
There are several important questions which remain on the research
agenda. First more work is called for about the emergence of urban hierar-
chies. Central place theory is probably the main topic in geographical
economics, though very few major results are so far available. There is no

ECONOMICS OF AGGLOMERATION
373
doubt that the problem is hard, but it is too important to be ignored any
longer (insightful suggestions for new developments can be found in Stahl,
1987). In particular, it would be interesting to pursue the comparison of
the self-organization approach advocated by Krugman (1996) to that devel-
oped by Henderson (Becker and Henderson, 1996; Henderson and Mitra,
1996) for whom modern urban landscapes are mold by large agents. Each
approach has its own merits that should be further investigated. In this
perspective, there is a new line of research that emerges in modern economic
theory in which agents have a certain probability to meet, which depends
on socio-economic and geographical factors; when the interaction occurs,
a transaction may happen between the corresponding agents (Kirman,
1996). This type of model might prove to be useful to study the emergence
of market-towns where people meet in order to trade goods or exchange
information.
20
It also seems to be in accord with the self-organization ap-
proach.
Second, the question of regional convergence/divergence has at last re-
ceived the attention it has long deserved, especially in the empirical litera-
ture. However models are still too preliminary to draw strong policy recom-
mendations, and more developments are required. In particular, we do not
know much about the circumstances that lead a region to recover. In the
real world, we observe that some regions are successful in their economic
revival while others seem to decline inexorably. It is not always clear why
such differences arise. Third, the role of infrastructure, emphasized in the
endogeneous growth literature, has not been studied in the new theories
of regional economics. So far we have very few insights about what could
well be a ‘‘good’’ infrastructure policy in the context of a spatial economy.
Building transportation infrastructures is often presented as the main rem-
edy to regional imbalance, but this is a policy in search of a theory. See,
however, Martin and Rogers (1995) for a first attempt to evaluate the
impact of infrastructures on the regional distribution of production in a
model similar to those reviewed in 3.2. Fourth, most models of economic
agglomeration assume a one-dimensional world. Though acceptable as a
first approximation, one should try to go further and to construct more
general models allowing for a second dimension. This creates unsuspected
difficulties in that the metrics proposed in location theory for measuring
distance in a two-dimensional space have different mathematical properties.
Last, all existing models of geographical economics assume full employ-
ment (Zenou and Smith, 1995, is a noticeable exception). Even during the
Golden Sixties, some regions have experienced persistent unemployment.
Nowadays the distribution of unemployment seems to be fairly uneven
20
For general, competitive equilibrium models of marketplace formation, see Berliant and
Wang (1993) and Wang (1993).

374
FUJITA AND THISSE
across regions, even within the same country. We have a very poor under-
standing of these questions, and the appeal to low regional mobility of
workers, though relevant in some cases, seems weak at the main explanation
for regional unemployment disparities. This important economic and social
problem should be given more attention in the future. A possible line of
research would be to integrate concepts of labor economics and of matching
and search models of unemployment into the corpus of geographical eco-
nomics.
R
EFERENCES
A
BDEL
-R
AHMAN
, H. (1988). Product differentiation, monopolistic competition and city size,
Region. Sci. Urban Econ. 18, 69–86.
A
BDEL
-R
AHMAN
, H.,
AND
F
UJITA
, M. (1990). Product variety, Marshallian externalities, and
city sizes, J. Region. Sci. 30, 165–183.
A
LONSO
, W. (1964). ‘‘Location and Land Use,’’ Harvard Univ. Press, Cambridge, MA.
A
NAS
, A. (1983). Discrete choice theory, information theory, and the multinomial logit and
gravity models, Transport. Res. B 17, 13–23.
A
NDERSON
,S.P.,
DE
P
ALMA
, A.,
AND
T
HISSE
, J.-F. (1992) ‘‘Discrete Choice Theory of Product
Differentiation,’’ MIP Press, Cambridge, MA.
B
AIROCH
, P. (1985) ‘‘De Je
´
richo a
`
Mexico. Villes et e
´
conomie dans l’histoire,’’ Gallimard, Paris.
B
ECKER
, G.,
AND
M
URPHY
, K. (1992). The division of labor, coordination costs, and knowledge,
Quart. J. Econ. 107, 1137–1160.
B
ECKER
, R.,
AND
H
ENDERSON
, J. V. (1996). City formation, mimeo, Brown University.
B
ECKMANN
, M. J. (1976). Spatial equilibrium in the dispersed city, in ‘‘Mathematical Land
Use Theory (Y. Y. Papageorgiou, Ed.), pp. 117–125. Lexington Books, Lexington, MA.
B
ERLIANT
, M.,
AND
W
ANG
, P. (1993). Endogenous formation of a city without agglomerative
externalities or market imperfections: market places in a regional economy, Region. Sci.
Urban Econ. 23, 121–144.
B
ORUKHOV
, E.,
AND
H
OCHMAN
, O. (1977). Optimum and market equilibrium in a model of
a city without a predetermined center, Environ. Planning A 9, 849–856.
C
HRISTALLER
, W. (1933). ‘‘Die Zentralen Orte in Su
¨
ddeutschland,’’ Gustav Fischer Verlag,
Jena.
D
’A
SPREMONT
, C., G
ABSZEWICZ
,J.J.,
AND
T
HISSE
, J.-F. (1979). On Hotelling’s stability in
competition, Econometrica 47, 1045–1050.
D
’A
SPREMONT
, C., G
ABSZEWICZ
, J. J.,
AND
T
HISSE
, J.-F. (1983). Product differences and prices,
Econ. Lett. 11, 19–23.
DE
P
ALMA
, A., G
INSBURGH
, V., P
APAGEORGIOU
,Y.Y.,
AND
T
HISSE
, J.-F. (1985). The principle
of minimum differentiation holds under sufficient heterogeneity, Econometrica 53,
767–781.
D
IXIT
, A. K.,
AND
S
TIGLITZ
, J. E. (1977). Monopolistic competition and optimum product
diversity, Amer. Econ. Rev. 67, 297–308.
D
RE
`
ZE
, J.,
AND
H
AGEN
, K. (1978). Choice of product quality: equilibrium and efficiency,
Econometrica 48.

ECONOMICS OF AGGLOMERATION
375
E
ATON
, B. C.,
AND
L
IPSEY
, R. G. (1982). An economic theory of central places, Econ. J.
92, 56–72.
E
NGLMANN
,F.C.,
AND
W
ALZ
, U. (1995). Industrial centers and regional growth in the presence
of local inputs, J. Region. Sci. 35, 3–27.
E
THIER
, W. (1982). National and international returns to scale in the modern theory of
international trade, Amer. Econ. Rev. 72, 389–405.
F
AINI
, R. (1984). Increasing returns, non-traded inputs and regional development, Econ. J.
94, 308–323.
F
ISCHER
, CL. (1982). ‘‘To Dwell among Friends: Personal Networks in Town and City,’’ Univ.
of Chicago Press, Chicago.
F
RIEDMAN
, J. W.,
AND
T
HISSE
, J.-F. (1993). Partial collusion fosters minimum product differenti-
ation, Rand J. Econ. 24, 631–645.
F
UJITA
, M. (1988). A monopolistic competition model of spatial agglomeration: a differentiated
product approach, Region. Sci. Urban Econ. 18, 87–124.
F
UJITA
, M. (1989). ‘‘Urban Economic Theory. Land Use and City Size,’’ Cambridge Univ.
Press, Cambridge, MA.
F
UJITA
, M.,
AND
K
RUGMAN
, P. (1995). When is the economy monocentric? von Thu
¨
nen and
Chamberlin unified, Region. Sci. Urban Econ. 25, 505–528.
F
UJITA
, M., K
RUGMAN
, P.,
AND
M
ORI
, T. (1995). On the evolution of hierarchical urban
systems, Institute of Economic Research, Discussion Paper No 419, Kyoto University.
F
UJITA
, M.,
AND
M
ORI
, T. (1996a). Structural stability and evolution of urban systems, Region.
Sci. Urban Econ., forthcoming.
F
UJITA
, M.,
AND
M
ORI
, T. (1996b). The role of port in the making of major cities: self-
organization and hub-effects, J. Develop. Econ. 49, 93–120.
F
UJITA
, M.,
AND
O
GAWA
, H. (1982). Multiple equilibria and structural transition of non-
monocentric urban configurations, Region. Sci. Urban Econ. 12, 161–196.
F
UJITA
, M.,
AND
S
MITH
, T. E. (1990). Additive-interaction models of spatial agglomeration,
J. Region. Sci. 30, 51–74.
F
UJITA
, M.,
AND
T
HISSE
, J.-F. (1986). Spatial competition with a land market: Hotelling and
von Thu
¨
nen unified, Rev. Econ. Stud. 53, 819–841.
G
ABSZEWICZ
,J.J.,
AND
T
HISSE
, J.-F. (1986). Spatial competition and the location of firms, in
‘‘Location Theory’’ (J. J. Gabszewicz, J.-F. Thisse, M. Fujita, and U. Schweizer, Eds.),
pp. 1–71 Harwood Academic, Chur.
G
EHRIG
, T. (1996). Competing exchanges, Euro. Econ. Rev., forthcoming.
G
IERSCH
, H. (1949). Economic union between nations and the location of industries. Rev.
Econ. Stud. 17, 87–97.
G
REENHUT
, J.,
AND
G
REENHUT
, M. L. (1975). Spatial price discrimination, competition and
locational effects, Economica 42, 401–419.
G
REENHUT
, M. L. (1981). Spatial pricing in the U.S.A., West Germany, and Japan, Economica
48, 79–86.
H
ARRIS
, C. (1954). The market as a factor on the localization of industry in the United States,
Ann. Assoc. Amer. Geograph. 64, 315–348.
H
ELPMAN
, H. (1995). The size of regions, The Eitan Berglas School of Economics, Working
Paper No. 14-95, University of Tel Aviv.
H
ENDERSON
, J. V. (1974). The sizes and types of cities, Amer. Econ. Rev. 64, 640–656.
H
ENDERSON
, J. V. (1987). Systems of cities and inter-city trade, in ‘‘Systems of Cities and

376
FUJITA AND THISSE
Facility Location,’’ (P. Hansen, M. Labbe
´
, D. Peeters, J.-F. Thisse, and J. V. Henderson,
Eds.), pp. 71–119. Harwood Academic, Chur.
H
ENDERSON
, J. V. (1988). ‘‘Urban Development. Theory, Fact and Illusion.’’ Oxford Univ.
Press, Oxford.
H
ENDERSON
,J.V.,
AND
M
ITRA
, A. (1996). The new urban landscape: developers and edge
cities, Region. Sci. Urban Econ., forthcoming.
H
IRSCHMAN
, A. O. (1958). ‘‘The Strategy of Development,’’ Yale Univ. Press, New Haven, CT.
H
OOVER
, E. M. (1937). Spatial price discrimination, Rev. Econ. Stud. 4, 182–191.
H
OTELLING
, H. (1929). Stability in competition, Econ. J. 39, 41–57.
I
MAI
, H. (1982). CBD hypothesis and economies of agglomeration. J. Econ. Theory 28, 275–299.
I
RMEN
, A.,
AND
T
HISSE
, J.-F. (1996). ‘‘Competition in Multi-Characteristics Spaces: Hotelling
Was Almost Right,’’ Discussion Paper No. 1446, CEPR, London.
J
ACOBS
, J. (1969). ‘‘The Economy of Cities,’’ Random House, New York.
K
ALDOR
, N. (1935). Market imperfection and excess capacity, Economica 2, 35–50.
K
ALDOR
, N. (1970). The case for regional policies, Scot. J. Polit. Econ. 17, 337–348.
K
ANEMOTO
, Y. (1990). Optimal cities with indivisibilities in production and interactions be-
tween firms, J. Urban Econ. 27, 46–59.
K
IRMAN
, A. P. (1996). Economies with interacting agents, Games Econ. Behav., forthcoming.
K
OOPMANS
, T. C. (1957). ‘‘Three Essays on the State of Economic Science,’’ McGraw–Hill,
New York.
K
OOPMANS
,T.C.,
AND
B
ECKMANN
, M. J. (1957). Assignment problems and the location of
economic activities, Econometrica 25, 1401–1414.
K
RUGMAN
, P. (1991a). ‘‘Geography and Trade,’’ MIT Press, Cambridge, MA.
K
RUGMAN
, P. (1991b). Increasing returns and economic geography, J. Polit. Econ. 99, 483–499.
K
RUGMAN
, P. (1991c). History versus expectations, Quart. J. Econ. 106, 651–667.
K
RUGMAN
, P. (1993). First nature, second nature, and metropolitan location, J. Region. Sci.
33, 129–144.
K
RUGMAN
, P. (1996). ‘‘The Self-organizing Economy,’’ Basil Blackwell, Oxford.
K
RUGMAN
, P.,
AND
V
ENABLES
, A. J. (1995a), Globalization and the inequality of nations,
Quart. J. Econ. 110, 857–880.
K
RUGMAN
, P.,
AND
V
ENABLES
, A. J. (1995b), ‘‘The Seamless World: A Spatial Model of
International Specialization,’’ Discussion Paper No. 1230, CEPR, London.
K
UBO
, Y. (1995). Scale economies, regional externalities, and the possibility of uneven regional
development, J. Region. Sci. 35, 29–42.
L
ERNER
, A.,
AND
S
INGER
, H. W. (1937). Some notes on duopoly and spatial competition, J.
Polit. Econ. 45, 145–186.
L
O
¨
SCH
, A. (1940). ‘‘Die Ra
¨
umliche Ordnung der Wirtschaft,’’ Gustav Fischer Verlag, Jena.
L
UCAS
, R. E. (1988). On the mechanics of economic development, J. Monetary Econ. 22, 3–22.
M
ARSHALL
, A. (1890). ‘‘Principles of Economics,’’ Macmillan, London (8th ed. published
in 1920).
M
ARTIN
,P
H
.,
AND
R
OGERS
, C. A. (1995). Industrial location and public infrastructure, J. Int.
Econ. 39, 335–351.
M
ATSUYAMA
, K. (1995). Complementarities and cumulative process in models of monopolistic
competition, J. Econ. Lit. 33, 701–729.
M
ATSUYAMA
, K.,
AND
T
AKAHASHI
, T. (1994). ‘‘Self-Defeating Regional Concentration,’’ Cen-

ECONOMICS OF AGGLOMERATION
377
ter for Mathematical Studies in Economics and Management Science, Discussion Paper
No. 1086, Northwestern University.
M
C
F
ADDEN
, D. (1981). Econometric models of probabilistic choice, in ‘‘Structural Analysis
of Discrete Data with Econometric Applications,’’ (C. F. Manski and D. McFadden,
Eds.), pp. 198–272. MIT Press, Cambridge, MA.
M
ICHEL
,P
H
., P
ERROT
, A.,
AND
T
HISSE
, J.-F. (1996). Interregional equilibrium with heteroge-
neous labor, J. Pop. Econ. 9, 95–114.
M
ILLS
, E. S. (1967). An aggregate model of resource allocation in a metropolitan area. Amer.
Econ. Rev. 57, 197–210.
M
IRRLEES
, J. (1995). Welfare economics and economies of scale, Japan. Econ. Rev. 46, 38–62.
M
ORI
, T. (1995). A model of megapolis: the maturing of city systems, mimeo, University
of Pennsylvania.
M
YRDAL
, G. (1957). ‘‘Economic Theory and Underdeveloped Regions,’’ Duckworth, London.
O
GAWA
, H.,
AND
F
UJITA
, M. (1980). Equilibrium land use patterns in a non-monocentric city,
J. Region. Sci. 20, 455–475.
O’H
ARA
, D. J. (1977). Location of firms within a square central business district, J. Polit.
Econ. 85, 1189–1207.
O
HLIN
, B. (1932). ‘‘Interregional and International Trade,’’ Harvard Univ. Press, Cambridge,
MA (revised version published in 1968).
O
TA
, M.,
AND
F
UJITA
, M. (1993). Communication technologies and spatial organization of
multi-unit firms in metropolitan areas, Region. Sci. Urban Econ. 23, 695–729.
P
APAGEORGIOU
, Y. Y.,
AND
S
MITH
, T. R. (1983). Agglomeration as local instability of spatially
uniform steady-states, Econometrica 51, 1109–1119.
P
APAGEORGIOU
, Y. Y.,
AND
T
HISSE
, J.-F. (1985). Agglomeration as spatial interdependence
between firms and households, J. Econ. Theory 37, 19–31.
P
ERROUX
, F. (1955). Note sur la notion de po
ˆ
le de croissance, Economique applique
´
e 7,
307–320.
P
ONSARD
, C. (1983). ‘‘History of Spatial Economic Theory,’’ Springer-Verlag, Heidelberg.
P
REMER
M.,
AND
W
ALZ
, U. 1994. Divergent regional development, factor mobility, and non-
traded goods, Region. Sci. Urban Econ. 24, 707–722.
P
UGA
, D. (1996). The rise and fall of economic agglomerations, mimeo, London School
of Economics.
P
UGA
, D.,
AND
V
ENABLES
, A. J. (1996). The spread of industry: spatial agglomeration in
economic development, J. Japan. Int. Econ. 10, 440–464.
P
YKE
, F., B
ECATTINI
, G.,
AND
S
ENGENBERGER
, W. (1990), ‘‘Industrial Districts and Inter-firm
Cooperation in Italy,’’ International Institute for Labour Studies, Geneva.
R
EILLY
, W. J. (1931). ‘‘The Law of Retail Gravitation,’’ Pilsbury, New York.
R
IVERA
-B
ATIZ
, F. (1988). Increasing returns, monopolistic competition, and agglomeration
economies in consumption and production, Region. Sci. Urban Econ. 18, 125–153.
R
OSENSTEIN
–R
ODAN
, P. N. (1943). Problems of industrialization of Eastern and South-Eastern
Europe, Econ. J. 53, 202–211.
S
AMUELSON
, P. A. (1983). Thu
¨
nen at two hundred, J. Econ. Lit. 21, 1468–1488.
S
AXENIAN
, A. (1994). ‘‘Regional Advantage: Culture and Competition in Silicon Valley and
Route 128,’’ Harvard Univ. Press, Cambridge, MA.
S
CHULZ
, N.,
AND
S
TAHL
, K. (1996). Do consumers search for the highest price? Equilibrium
and monopolistic optimum in differentiated products markets, Rand J. Econ. 27, 542–562.

378
FUJITA AND THISSE
S
CITOVSKY
, T., (1954). Two concepts of external economies, J. Polit. Econ. 62, 143–151.
S
COTCHMER
, S.,
AND
T
HISSE
, J.-F. (1992). Space and competition: a puzzle, Ann. Region. Sci.
26, 269–286.
S
PENCE
, M. (1976). Product selection, fixed costs, and monopolistic competition, Rev. Econ.
Stud. 43, 217–235.
S
TAHL
, K. (1982). Differentiated products, consumer search, and locational oligopoly, J. Indust.
Econ. 31, 97–114.
S
TAHL
, K. (1983). A note on the microeconomics of migration, J. Urban Econ. 14, 318–326.
S
TAHL
, K. (1987). Theories of urban business location, in ‘‘Handbook of Regional and Urban
Economics,’’ (E. S. Mills, Ed.), Volume 2, pp. 759–820. North-Holland, Amsterdam.
S
TAHL
, K. (1995). Towards a microeconomic theory of the retailing sector, mimeo, Universi-
ta
¨
t Mannheim.
S
TARRETT
, D. (1978). Market allocations of location choice in a model with free mobility, J.
Econ. Theory 17, 21–37.
T
HISSE
, J.-F.,
AND
W
ILDASIN
, D. (1992). Public facility location and urban spatial structure,
J. Pub. Econ. 48, 83–118.
V
ENABLES
, A. J. (1996). Equilibrium locations of vertically linked industries, Int. Econ. Rev.
37, 341–359.
VON
T
HU
¨
NEN
, J. H. (1826). ‘‘Det Isolierte Staat in Beziehung auf Landwirtschaft und Nationalo
¨
-
konomie,’’ Perthes, Hamburg.
W
ANG
, P. (1993). Agglomeration in a linear city with heterogeneous households, Region. Sci.
Urban Econ. 23, 291–306.
W
EBER
, A. (1909). ‘‘Ueber den Standort der Industrien,’’ J. C. B. Mohr, Tu
¨
bingen.
W
OLINSKY
, A. (1983). Retail trade concentration due to consumers’ imperfect information,
Bell J. Econ. 14, 275–282.
Z
ENOU
, Y.,
AND
S
MITH
, T. E. (1995). Efficiency wages, involuntary unemployment and urban
spatial structure, Region. Sci. Urban Econ. 25, 547–573.