This article overviews the development of the formal modelling framework for the urban spatial structure which started in 1960s and grew dramatically thereafter. Modelling in the 1970s focused on the endogenous formation of the central business district within a city. Then richer polycentric city models were developed in 1980s, where the number, location and spatial extent of the business districts are determined endogenously. The emergence of the new economic geography in 1990s provided a framework capable of explaining the spatial distribution of cities (rather than the business districts within a city) and their industrial structure in a general location-equilibrium model.

Tomoya Mori

English

Research Papers in Economics

 
 
 
 
 
 
 
KIER DISCUSSION PAPER SERIES 
KYOTO INSTITUTE 
OF 
ECONOMIC RESEARCH 
http://www.kier.kyoto-u.ac.jp/index.html 
KYOTO UNIVERSITY 
KYOTO, JAPAN 
Discussion Paper No. 611   
 
MONOCENTRIC VERSUS POLYCENTRIC MODELS IN URBAN ECONOMICS 
 
by 
Tomoya Mori 
 
January 2006   1
MONOCENTRIC VERSUS POLYCENTRIC MODELS IN URBAN ECONOMICS 
 
This article overviews the development of the formal modelling framework for 
the urban spatial structure which started in 1960s and grew dramatically thereafter. 
Modelling in the 1970s focused on the endogenous formation of the central 
business district within a city. Then richer polycentric city models were developed 
in 1980s, where the number, location and spatial extent of the business districts 
are determined endogenously. The emergence of the new economic geography in 
1990s provided a framework capable of explaining the spatial distribution of 
cities (rather than the business districts within a city) and their industrial structure 
in a general location-equilibrium model. 
 
The formal modelling of urban spatial structure originated in the monocentric city model 
by Alonso (1964). The model was extended to include production, transportation and 
housing by Mills (1967; 1972) and Muth (1969), and was eventually integrated into a 
unified framework by Fujita (1989). In these traditional models, the city is a priori 
assumed to be monocentric, that is, all production activities within a city are supposed to 
take place in a point representing the central business district (CBD), and all workers 
living in the surrounding area are supposed to commute to the CBD. The success of this 
model is primarily due to its compatibility with the competitive paradigm, since the 
existence of the CBD is a priori assumed. In order to explain the urban morphology, 
however, it is essential to endogenize the CBD formation. For this purpose, Fujita (1986) 
provided a very useful insight based on the spatial impossibility theorem of Starrett 
(1978): in order to have endogenous formation of economic agglomeration, the model 
must have at least one of the following three elements: (a) heterogeneous space, (b) non-
market externalities in production and/or consumption, and (c) imperfectly competitive 
markets.  
The approach based on (a) explains the formation of the CBD by comparative 
advantage among locations, while otherwise retaining the competitive paradigm. One of 
the earliest such attempts was made by Schweizer, Varaiya and Hartwick (1976).    2
Most models of type (b) are based on externalities from non-market interactions. 
The earliest attempt was made by Solow and Vickrey (1971). In the one-dimensional 
location space, they considered the optimal allocation of urban land between business 
areas and roads when each unit of business area is assumed to generate a given number of 
trips to every other unit. But the first model of residential land use of this type is by 
Beckmann (1976), where the utility of each individual directly depends on the average 
distance to all other individuals and the amount of her land consumption. This preference 
leads to a bell-shaped spatial population distribution as well as land rent curves, where 
the CBD is represented by a densely inhabited area around the central location.  
While Beckmann, Solow and Vickrey considered only a single type of agents 
(firms or consumers), Ogawa and Fujita (1980) and Imai (1982) developed two-sector 
monocentric models of a one-dimensional city. The dispersion force in this case is 
generated through land and labour markets. That is, the agglomeration of firms increases 
the commuting distance for their workers on average, which in turn pushes up the wage 
rate and land rent around the agglomeration, and this higher cost of labour and land 
discourages further agglomeration of firms. The most recent contribution along this line 
is by Lucas and Rossi-Hansberg (2002), who formally demonstrate the existence of an 
equilibrium and the endogenous formation of the CBD.  
In the endogenous monocentric models discussed so far, the optimal distribution 
of firms requires greater concentration near the centre than does the equilibrium 
distribution. The reason is the locational externality generated by individuals: while the 
location of each individual directly affects the travelling cost for others to make contact 
with this individual, it is not taken into account when each individual makes a location 
decision.  
Building on Ogawa and Fujita (1980), the first model of a polycentric city was 
developed by Fujita and Ogawa (1982). Their key assumption is that the benefit from 
interactions between two firms is a negative exponential function of the distance between 
them, unlike the linear dependence in previous models. When commuting costs are 
relatively high, this assumption leads to the formation of multiple business districts and 
the possibility of multiple equilibria.   3
  The first urban economic model based on (c) is by Fujita (1988). His model 
demonstrated that pure market interactions alone can explain the agglomeration of 
economic activities with the use of the Chamberlinian monopolistic competition model. 
The agglomeration force is generated from the interaction among preference for product 
variety, transport costs, and increasing returns at the level of individual producers. In this 
model, the city may be monocentric or polycentric. Also it is possible that business and 
residential districts are mixed. These works were critical for the emergence of the new 
economic geography (NEG) in the 1990s (Krugman, 1991a; 19 91b; Fujita, 1993).  
In the application of the NEG to urban economics initiated by Fujita and 
Krugman (1995), there are two key features. The first is the general equilibrium 
modelling of an entire spatial economy unlike all the models presented so far. The second 
is its focus on the spatial distribution of cities, while abstracting from the intra-city 
spatial structure. In particular, it is assumed that mobile firms and workers do not occupy 
land, so that an agglomeration of firms and population, that is, a city, forms at a point on 
the continuous location space. The second feature dramatically increases the tractability 
of the model. The agglomeration force in this model is essentially the same as in Fujita 
(1988), while the dispersion force is generated from the presence of immobile resources 
through transport costs between cities and non-city locations. The key to this approach is 
the recognition that the profitability of any given location for a firm can be represented 
by an index of market potential. The market potential at a given location reflects the 
trade-off among the proximity to consumers, the degree of competition, and the 
production cost at that location. In particular, the market potential of a given industry 
sharply decreases when it moves away from a city in which this industry is agglomerated, 
and then starts increasing again after a certain distance, exhibiting the presence of an 
agglomeration shadow. Differences in the degree of product differentiation and/or 
transport costs among industries lead to differences in the size of the agglomeration 
shadow, which in turn result in variations in the (roughly constant) spacing of 
agglomerations among industries (Fujita and Mori, 1997). In the presence of multiple 
industries, the inter-industry demand externalities lead to a formation of hierarchical city 
systems (Fujita, Krugman and Mori, 1999). This is reminiscent of Christaller (1933): the 
set of industries found in a smaller city is a subset of those found in a larger city.   4
Furthermore, the relative decrease in transport costs for urban sectors may eventually 
lead to the formation of a megalopolis consisting of large core cities that are connected 
by an industrial belt, that is, a continuum of small cities (Mori, 1997). NEG remains the 
only general location-equilibrium framework which can investigate the spatial 
distribution of cities and their industrial structure in a unified manner. 
There is also a large literature of spatial oligopoly (hence, type c) aiming to 
explain the spatial concentration of stores through statistical economies of scale. These 
models assume that consumers have imperfect information regarding the types (and the 
prices) of commodities sold by stores before they visit them. The greater the 
agglomeration of stores, the more likely it is that consumers will find their favourite 
commodities. The concentration of stores is explained by the market-size effect due to 
taste uncertainty and/or lower price expectation (see, for example, Konishi, 2005).  
Finally, in all the models introduced thus far, all agents are assumed to be 
atomistic. Hence, land and labour markets are perfectly competitive. In contrast, 
Henderson and Mitra (1996) offer a model of suburbanization in which new edge cities 
are formed by large land-developers in the suburbs of the old CBD, formalizing 
Garreau’s observation (1991) on the recent development of edge cities within large US 
metro areas. Given an existing CBD, the developer of a new edge city chooses the 
location and capacity of its business district strategically to maximize profits. The 
developer exercises monopsony power in the labour market in the edge city though her 
control over aggregate employment there. The proximity to the old CBD increases 
production efficiency through easier communication of firms between the CBD and the 
edge city, while it also increases residential land rents and wages of workers in the edge 
city.  This model thus incorporates elements (b) and (c). 
Tomoya Mori   
 
See also location theory; spatial economics; urban agglomeration; urban economics; 
urban growth; urbanization; urban production externalities  
   5
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A modeling of megalopolis formation: the maturing of city systems.

A monopolistic competition model of spatial agglomeration: a differentiated product approach.

An aggregative model of resource allocation in a metropolitan area.

CBD hypothesis and economies of agglomeration.

Central Places in Southern Germany.

Cities and Housing.

Concentration of competing retail stores.

Economics of Agglomeration: Cities, Industrial Location, and Regional Growth. Cambridge:

Edge City: Life on the New Frontier.

Equilibrium land use patterns in a non-monocentric city.

General equilibrium and location theory.

Geography and Trade.

Land use in a long narrow city.

Location and Land Use.

Market allocations of location choice in a model with free mobility.

Monopolistic competition and urban systems.

Multiple equilibria and structural transition of nonmonocentric urban configurations.

Monocentric Versus Polycentric Models in Urban Economics

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