This is a short dictionary entry. Central place theory is a descriptive theory of market area in a spatial context. Its definition, history, and relation to modern microeconomic theory are provided.Market Area, City Hierarchy, Hexagonal Structure, Spatial General Equilibrium Theory, Transport Cost, Increasing Returns to Scale

Marcus Berliant

English

Research Papers in Economics

Central place theory is a descriptive theory of market area in a spatial
context. Its de￿nition, history, and relation to modern microeconomic theory
are provided. JEL Classi￿cation: R12. Keywords: Market Area, City Hi-
erarchy, Hexagonal Structure, Spatial General Equilibrium Theory, Transport
Cost, Increasing Returns to Scale
Central Place Theory
Central place theory is a collection of loosely related, informal, descriptive
models of city size, city location, and market area based on the trade-o⁄ be-
tween increasing returns to scale in production and the cost of transport of
goods from ￿rm to home. Land markets are often absent. At its core, central
place theory is an empirically motivated description of production in Southern
Germany. It is a remarkable empirical regularity in search of a formal theory;
a better name would be ￿central place regularity.￿
The beginnings of the theory are attributed to Christaller (1933) who ￿rst
made detailed observations of urban hierarchies and then attempted to model
them. The basic ideas put forward are that consumer population is distributed
uniformly, while ￿rms locate in cities. Cities form a hierarchy, in that cities
higher in the hierarchy produce all the goods that cities one level lower in the
hierarchy produce, and one more. The ratio of market areas of a commodity
produced only at a given level of the hierarchy (and above) to the market area
of a commodity produced at the next lower level of the hierarchy (and above) is
assumed to be constant, independent of the level in the hierarchy considered.
Thus, the cities in a given area form a hierarchy where the size of a city￿ s
market area and the variety of commodities it o⁄ers are perfectly correlated.
In graphical terms, the result is a collection of hierarchically ordered cities with
the market areas of cities not at the same level of the hierarchy overlapping, but
market areas of cities at the same level disjoint. Commodities characterized
by low transport cost but high returns to scale are provided by few cities high
in the hierarchy. Commodities characterized by high transport cost but low
returns to scale are provided by most cities.
L￿sch (1944) expanded on this theory. He postulated a homogeneous agri-
cultural plane with farmers. Some turn to beer production, and face linear,
downward sloping demand curves with choke prices. For a given price at the
brewery, total delivered price increases with distance from the plant due to
transport cost. In the plane with a uniform distribution of inebriated con-
sumers or farmers, demand for a ￿rm￿ s beer is given by the volume of a cone
centered at the brewery with height given by the brewery￿ s mill price and the
1slope of its sides determined by the demand curve and the cost of beer trans-
port. With a marginal cost curve, equilibrium can be found. Unfortunately,
the collection of bases of cones, namely disks, do not partition the plane. So
hexagons are used, forming a Teutonic triangulation of hierarchical hexagons.
In this theory, the central places are the breweries.1
One can view the theory as producing a complex of overlapping, ordered
layers of hexagonal partitions of the plane corresponding to the market areas of
cities in a hierarchy. Agriculture is the basis for and genesis of this structure.
The theory has developed beyond these basic descriptive models; see Mc-
Cann (2001, chapter 2.7) for a nice summary and cites. Hartwick (2004) is
the culmination of a line of research more in accord with optimizing behavior,
pricing, and trade theory that also relates the models to the rank-size rule.
The reader should be cautious in interpreting this entire literature because
equilibrium and e¢ ciency are often confused, while the models tend to be
mechanistic in nature as opposed to allowing agents to optimize in equilibrium.
To the general economist, the theory will appear to be informal and imprecise.
Paul Krugman (1995, pp. 38-41) criticizes central place theory, or ￿Ger-
manic geometry,￿ for its lack of formal foundations, particularly regarding
market structure and ￿rm behavior.2
Even if one is willing to overlook these defects, there is one further impor-
tant ￿ aw. Central place theory generally runs afoul of Starrett￿ s Spatial Im-
possibility Theorem; see Starrett (1978), Fujita (1986), and Fujita and Thisse
(2002, chapter 2.3) for discussion. In essence, the Impossibility Theorem says
that in a closed economy with perfect and complete markets at all locations,
location independent utility and production functions, and no relocation cost,
there is no competitive equilibrium where commodities are transported. Thus,
if the assumptions are satis￿ed, either there is no equilibrium, or in equilibrium
agents and commodities are distributed uniformly and locations are autarkic.
Central place theory apparently makes these assumptions, though due to its
imprecision, perhaps it doesn￿ t. Naturally, although the literature considers
consumer migration at times, the assumption of a uniform distribution of con-
sumers could render the theorem inapplicable. I conjecture that it simply
makes the existence of an (autarkic) equilibrium more likely. But this is prob-
ably not worth pursuing, as location models that ￿x consumer locations in a
uniform distribution can only generate cities without people.
1St. Louis is a prime example.
2He is also credited with the ￿rst alliteration in this literature.
2So where does this leave us? The modern theory of agglomeration, and
thus the modern theory of central places, begins with the Impossibility The-
orem. Its contrapositive tells us that to generate models with non-trivial
agglomeration at equilibrium, at least one of the hypotheses must be violated.
Even then, equilibrium might not exist, or in equilibrium cities could collapse
to a point or have agents spread uniformly. Models of non-trivial cities involve
a very delicate balancing act between forces pulling agents together and forces
pushing them apart. The New Economic Geography has provided one of sev-
eral possible types of models capable of producing cities and even hierarchies of
cities. Fujita and Mori (1997) and Fujita, Krugman and Mori (1999) generate
a form of central place theory in a general equilibrium framework by employing
imperfect competition and increasing returns at the ￿rm level. Unfortunately,
this type of model has many defects, as detailed in Berliant (2005), including
a reliance on speci￿c functional forms and indeterminacy: one equilibrium is
selected from a continuum.
Central place theory is not grounded in the analytical tools of modern
economics, so it does not have ￿rm foundations. Thus, it is di¢ cult to build
on central place theory, either theoretically or empirically.
In my view, the future of central place theory is as a stylized fact to be
explained by our models, much like the rank-size rule.
Marcus Berliant
References
[1] Berliant, M. 2005. Well isn￿ t that spatial?! Handbook of Regional and
Urban Economics: A view from economic theory. Forthcoming in the
Journal of Economic Geography.
[2] Christaller, W. 1933. Die Zentralen Orte in S￿ddeutschland. Jena: Fis-
cher. Translated by C.W. Baskin. 1966. Central Places in Southern Ger-
many. Englewood Cli⁄s: Prentice-Hall.
[3] Fujita, M. 1986. Urban land use theory, in Location Theory. Edited by J.
Lesourne and H. Sonnenschein. New York: Harwood Academic Publishers.
[4] Fujita, M., Krugman, P. and Mori, T. 1999. On the evolution of hierar-
chical urban systems. European Economic Review 43, 209-251.
3[5] Fujita, M. and Mori, T. 1997. Structural stability and evolution of urban
systems. Regional Science and Urban Economics 27, 399-442.
[6] Fujita, M. and Thisse, J.-F. 2002. Economics of Agglomeration. Cam-
bridge: Cambridge University Press.
[7] Hartwick, J.M. 2004. Trade in a Hierarchical System of Cities. Mimeo.
[8] Krugman, P. 1995. Development, Geography, and Economic Theory. Cam-
bridge: MIT Press.
[9] L￿sch, A. 1944. Die Raumliche Ordnung der Wirtschaft. Jena: Fischer.
Translated by W.H. Woglom. 1954. The Economics of Location. New
Haven: Yale University Press.
[10] McCann, P. 2001. Urban and Regional Economics. Oxford: Oxford Uni-
versity Press.
[11] Starrett, D. 1978. Market allocations of location choice in a model with
free mobility. Journal of Economic Theory 17, 21-37.
4

Central Place Theory

http://128.118.178.162/eps/urb/papers/0505/0505001.pdf

Central Place Theory

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics