Size of nested cities

• Author: Fan‐chin Kung
• DOI: http://doi.org/10.1111/ijet.12239
• Published date: 01 March 2020
• Date: 01 March 2020

Int J Econ Theory. 2020;16:51–61. wileyonlinelibrary.com/journal/ijet © 2019 IAET

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51

Received: 24 February 2019

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Accepted: 23 July 2019

DOI: 10.1111/ijet.12239

ORIGINAL ARTICLE

Size of nested cities

Fan‐chin Kung

Department of Economics, East Carolina

University, Greenville, North Carolina

Correspondence

Fan‐chin Kung, Department of

Economics, Tenth Street, Greenville,

NC 27858.

Email: kungf@ecu.edu

Abstract

Models of cities based on conventional spatial market

theory are unable to replicate a realistic size distribution.

The stochastic process approach to size distribution, which

assumes proportionate growth, does not provide an

economic foundation for spatial trades. There is an

apparent irreconcilability. We propose that since there is

a continuum of equilibria in models of spatial markets with

endogenous location, proportionate growth can work as

equilibrium selection. We present computations for an

urban configuration that has not been presented in the

literature before. A small city locates inside a larger city's

agricultural supply zone. This generates a larger variation

in city size that may include a realistic size distribution.

KEYWORDS

city formation, distribution of city size, urban system

JEL CLASSIFICATION

F12; R12; R14

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INTRODUCTION

Models of endogenous city formation are subject to a large degree of indeterminacy, as has

been pointed out in the literature. This type of indeterminacy is due to agents being

indifferent to parallel spatial shifts of all agents. Many models simply endow cities with fixed

locations. For example, Fujita and Krugman (1995) introduce the consumption of land and

normalize location to the origin. Persistent indeterminacy is formally established by Berliant

and Kung (2006) in standard city economies with both manufacturing and agricultural

sectors. Indeterminacy in such models is not trivial since equilibria are not simple spatial

shifts from one another. Moreover, the dimension of indeterminacy rises with the number of

city locations.

Zipf's law impliesrobust empirical regularity of cities' size distribution; the sizes of larger cities

(small settlements are truncated) follow a Pareto distribution.Empirical findings can be found in,