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The Mathematics of Urban MorphologyCentral Place Theory and the Power Law for Cities

The Mathematics of Urban Morphology: Central Place Theory and the Power Law for Cities [This chapter provides a review of the link between central place theory and the power laws for cities. A theory of city size distribution is proposed via a central place hierarchy a la Christaller (1933) either as an equilibrium results or an optimal allocation. Under a central place hierarchy, it is shown that a power law for cities emerges if the underlying heterogeneity in economies of scale across good is regularly varying. Furthermore, we show that an optimal allocation of cities conforms with a central place hierarchy if the underlying heterogeneity in economies of scale across good is a power function.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Mathematics of Urban MorphologyCentral Place Theory and the Power Law for Cities

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-12380-2
Pages
55 –75
DOI
10.1007/978-3-030-12381-9_3
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter provides a review of the link between central place theory and the power laws for cities. A theory of city size distribution is proposed via a central place hierarchy a la Christaller (1933) either as an equilibrium results or an optimal allocation. Under a central place hierarchy, it is shown that a power law for cities emerges if the underlying heterogeneity in economies of scale across good is regularly varying. Furthermore, we show that an optimal allocation of cities conforms with a central place hierarchy if the underlying heterogeneity in economies of scale across good is a power function.]

Published: Mar 24, 2019

Keywords: Central place theory; Zipf’s law; City sizes; Dynamic programming; Optimal city hierarchy

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