Intermediate goods and the spatial structure of an economy

Abstract

We develop a monopolistic competition model of spatial economy in which manufacturing requires a large variety of intermediate goods. The economy yields two types of monocentric configurations: an integrated city equilibrium (I-specialized city equilibrium) when transaction costs of intermediate goods are high (low). In the former, both manufacturing and intermediate sectors agglomerate in a single city. In the latter, the city is specialized in the provision of intermediate goods. When the economy is in an integrated city equilibrium, it is in a primacy trap such that population growth alone never leads to the formation of new cities.

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Regional Science and Urban Economics 31 (2001) 79–109
www.elsevier.nl/locate/econbase
Intermediate goods and the spatial structure of an
economy
a,b
*
Masahisa Fujita, Nobuaki Hamaguchi
aInstitute of Economic Research, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
bInstitute of Developing Economies, Wakaba 3-2-2, Mihama-ku, Chiba 261-8545, Japan
Received in revised form 15 August 2000; accepted 10 October 2000
Abstract
We develop a monopolistic competition model of spatial economy in which manufactur-
ing requires a large variety of intermediate goods. The economy yields two types of
monocentric configurations: an integrated city equilibrium (I-specialized city equilibrium)
when transaction costs of intermediate goods are high (low). In the former, both
manufacturing and intermediate sectors agglomerate in a single city. In the latter, the city is
specialized in the provision of intermediate goods. When the economy is in an integrated
city equilibrium, it is in a primacy trap such that population growth alone never leads to the
formation of new cities.
 2001 Elsevier Science B.V. All rights reserved.
Keywords: City formation; Intermediate goods; Primacy trap; Monopolistic competition
JEL classification: R12; F12; 014
1. Introduction
In this paper, we develop a monopolistic competition model of a spatial
economy in which manufacturing requires a large variety of intermediate goods. In
our model, cities are formed in a continuous location space due the agglomeration
forces that arise from the vertical linkages between the manufacturing and
*Corresponding author. Tel.: 181-75-753-7122; fax: 181-75-753-7198.
E-mail address: fujita@kier.kyoto-u.ac.jp (M. Fujita).
0166-0462/01/$ – see front matter
PII: S0166-0462(00)00066-1
 2001 Elsevier Science B.V. All rights reserved.

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M. Fujita, N. Hamaguchi / Regional Science and Urban Economics 31 (2001) 79–109
intermediate-good sectors. The dispersion forces, in contrast, arise from the
demand for the manufactured goods by the agricultural workers who are spatially
dispersed due to the necessity of land input. In this context, we examine the role of
the variety of intermediate goods and their transport costs in shaping the spatial
structure of the economy.
From a methodological viewpoint, our model is not completely new. In fact, our
model is closely related to the spatial economy model of Fujita and Krugman
(1995), called F–K model hereafter. In the F–K model, the agglomeration forces
for city formation arise from the love for variety on the consumer side. In contrast,
in the present model, the agglomeration forces arise from the product variety in
intermediate goods. Therefore, the present model is essentially dual to the F–K
model. For several reasons, however, we claim relevance of the present work in
explaining the formation of cities in the real world.
First, on the empirical side, although the love for variety in consumer goods
may play an important role in city formation, casual observations suggest that the
accessibility to a large variety of intermediate goods (such as producer services
and specific inputs) seems to play an even more important role in the formation of
both specialized cities and mega cities. In particular, many metropolises in
developed countries have been experiencing a new cycle of growth since the early
1980s (The Economist, 1995). The resurgence of these cities seems to be largely
due to the growth of intermediate good sectors. In trying to concentrate in their
core-competence and to save overhead costs, firms in most industries are
increasingly utilizing the externally-provided goods and services. In particular, in
many developed countries, the demand for specialized producer services has
grown rapidly, which includes both non-professional and professional services
(financial services, legal services, information system management, advertising,
accounting, insurance, personnel training, management consultancy, etc.). For
example, between 1970 and 1990, employment in the producer service industries
in the United States, Japan, and Germany expanded annually 4.77, 4.29, and
2.55%, respectively, while total employment grew at much lower rates (Sassen,
1994).
Intermediate good and service firms create a tacit knowledge in cooperation
with final good manufactures. Since such a knowledge is communicated most
commonly on the face-to-face basis, interactions between suppliers and users are
quite sensitive to distance, while manufactured goods are much easier to transport.
Thus, intermediate good firms tend to anchor their users. However, in developed
countries, intermediate good and service firms in large cities are able to cater to
1
1For the increasing use of externally-provided intermediate goods and services, there exist other
reasons such as to avoid dealing with unions and for flexibility in hiring and firing. Our model in this
paper is limited in the sense that the separation of the intermediate sector from the manufacturing sector
is assumed a priori, and we focus on the spatial implications of such an industrial structure. The
simultaneous determination of both the industrial structure and spatial structure is left for future.

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M. Fujita, N. Hamaguchi / Regional Science and Urban Economics 31 (2001) 79–109 81
their customers over the long distance owing to the well-developed transportation/
communication infrastructure. Hence, their users can be dispersed. For example,
based on 1991 data, 47.2% of the total sales of producer services in Japan
originated in Tokyo (Statistic Bureau, 1992). Furthermore, as is well-known,
London and New York City are international centers of finance, insurance, real
estate and other producer services.
On the other hand, in developing countries, all kinds of non-agricultural
production tend to be heavily concentrated in primate cities. For example, in
Thailand, 1990 data shows that 40% of manufacturing jobs is in Bangkok and the
additional 32% is in the five provinces surrounding Bangkok (Labour Studies and
Planning Division, 1990). Meanwhile, the financial sector and various producer
services account for about 10% of the total employment in Bangkok, which
represents the 75% of the total employment of this sector in Thailand. Although a
firm in Bangkok could achieve cost savings by moving to a periphery location, the
loss of accessibility to the producer services provided in Bangkok tends to make
such a relocation unprofitable. Consequently, the sprawl of urbanization tends to
occur only within a limited distance from Bangkok.
Next, on the theoretical side, the present model (based on the product variety in
intermediate goods) yields a set of outcomes richer than the F–K model (based on
the product variety in consumer goods). In particular, the present model yields two
types of monocentric configurations involving very different patterns of trade. In
one type of monocentric configuration, called an integrated city equilibrium, both
the manufacturing sector (producing a homogeneous consumer good) and the
intermediate sector (supplying a large variety of intermediate goods to the
manufacturing sector) are agglomerated together in a single city that exports the
manufactured goods to the agricultural hinterland. Such a city resembles primate
cities in developing countries. In the other type of monocentric configuration
called an I-specialized city equilibrium, the intermediate good sector is concen-
trated in a single city; as for the manufacturing sector, it is partially concentrated
in the city, while the rest is mixed with the agricultural sector in such a way that
each area produces the manufactured goods for its own needs. The city now
exports the intermediate goods only, a pattern which resembles that of several
cities in developed countries. Not surprisingly, the integrated city equilibrium
(respectively, I-specialized city) tends to arise when the transport costs of
intermediate goods are relatively high (respectively, relatively low).
We will also show that once the economy is in an integrated city equilibrium, it
is in a primacy trap such that the growth of the economy’s population alone can
never lead to the formation of new major cities. In order to escape from such a
primacy trap, it is necessary to sufficiently lower the transport cost of intermediate
goods so that the utilization of such goods becomes possible in remote areas. In
contrast, in the case of an I-specialized city equilibrium, the population growth of
the economy eventually leads to the formation of new cities.
Although our model can potentially yield many different patterns of spatial

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M. Fujita, N. Hamaguchi / Regional Science and Urban Economics 31 (2001) 79–109
equilibria (involving multiple cities), in this paper we focus on the two types of
monocentric configurations mentioned above. This limitation of scope turns out to
be helpful in illuminating the essential role of intermediate goods in shaping the
spatial structure of an economy.
The plan of the paper is as follows. In the next section, we present the model
and establish equilibrium conditions. In Section 3, we examine the integrated city
equilibrium, followed by Section 4 in which the I-specialized city equilibrium is
examined. Finally, Section 5 concludes the paper.
2. The model
We consider a boundless, one-dimensional location space of the economy, X,
along which lies land of homogeneous quality, with one unit of land per unit of
distance. The economy has two final-good sectors, the agricultural sector (A-
sector) and the manufacturing sector (M-sector), and a single intermediate-good
sector (I-sector). The A-sector produces a homogeneous agricultural good (A-
good) under constant returns using labor and land. The M-sector also produces a
homogeneous consumer-good, called M-good, under constant returns, using labor
and a continuum of intermediate goods (I-goods). The differentiated I-goods are
produced in the I-sector under an increasing returns technology, using labor only.
For the transportation of each good, we assume Samuelson’s ‘iceberg’ form of
transport technology. That is, if a unit of the A-good [the M-good, or any variety
of I-good] is shipped from a location x [X to another location y [X, only a
AMI
2t ux2yu
2t
ux2yu
2t ux2yu
fraction, e[e , or e ], of the original unit actually arrives, while
the rest melts away en route, where each t , t , and t is a positive constant.
Finally, the economy has a continuum of homogeneous workers with a given size,
N. Each worker is endowed with a unit of labor, and is free to work in any location
and sector.
Although each consumption and production takes place at a specific location,
first we describe each type of activity without explicitly referring to the location.
The consumers of the economy consist of N workers plus a class of landlords,
who for simplicity are assumed to live on their own land holdings so that land
rents are consumed where they are accrued. Every consumer shares the same
Cobb–Douglas utility tastes,
AMI
12aa
U 5(A)(M) (1)
where A and M, respectively, represent the consumption of the A-good and that of
the M-good and a is a constant (0,a,1) representing the expenditure share on
the M-good. Given an income Y and a pair of prices, p
for the M-good, the consumer’s utility maximization yields the following demand
functions:
AM
for the A-good and p

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M. Fujita, N. Hamaguchi / Regional Science and Urban Economics 31 (2001) 79–109 83
AM
A5(12a)Y/p ,
M 5aY/p ,(2)
which in turn yield the following indirect utility function:
a
12a
A 2(12a)
Y(p )
M 2a
U 5a (12a)(p ).(3)
Next, the A-good is produced under an input–output technology such that each
unit of A-good requires a unit of land and a
M-good is produced with a Cobb–Douglas production function,
A
units of labor. In contrast, the
M 12m m
M 5(L )
I ,0,m ,1(4)
M
where M is the amount of M-good produced, L
I represents a composite index of I-goods given by
I 5 E q(i) di
56
0
is the associated labor input, and
n
1/r
r
, 0,r ,1. (5)
Here, n represents the range of the I-good varieties supplied by the I-sector, q(i) is
the input of each available variety i [[0, n], and r is the substitution parameter. A
smaller r means that I-goods are more highly differentiated. The variable n is to
be determined endogenously in equilibrium.
Given a wage rate, w, and the price of each I-good, p (i) for each i [[0, n], the
unit production cost of the M-good associated with the production function (4) is
given by
I
M
2m2(12m)12mm
c 5m
(12m)
wG , (6)
while the requirement for each input associated with an output level M is given by
MM
L 5(12m)c M/w,(7)
MI
2s s21
q(i)5mc Mp (i)
G
for
i [[0, n],(8)
where s ;1/(12r), and G is the price index of I-goods defined by
G 5 E p (j)
56
0
n
21/(s21)
I
2(s21)
dj
.(9)
Notice that since s .1, an increase in n ceteris paribus reduces the price index G
in Eq. (9), which in turn reduces the unit production cost c
Turning to the production of I-goods, each I-good is produced under an
increasing-return technology, using labor only. All I-goods have the same
production technology such that the production of quantity q(i) of any variety i at
any given location requires labor input l(i), given by
M
in Eq. (6).
I
l(i)5F 1a q(i),(10)