Optimal city hierarchy: A dynamic programming approach to central place theory

Wen-Tai Hsu, Thomas J. Holmes and Frank Morgan

Journal of Economic Theory, 2014, vol. 154, issue C, 245-273

Abstract: Central place theory is a key building block of economic geography and an empirically plausible description of city systems. This paper provides a rationale for central place theory via a dynamic programming formulation of the social planner's problem of city hierarchy. We show that there must be one and only one immediate smaller city between two neighboring larger-sized cities in any optimal solution. If the fixed cost of setting up a city is a power function, then the immediate smaller city will be located in the middle, confirming the locational pattern suggested by Christaller [4]. We also show that the solution can be approximated by iterating the mapping defined by the dynamic programming problem. The main characterization results apply to a general hierarchical problem with recursive divisions.

Keywords: Central place theory; City hierarchy; Dynamic programming; Principle of optimality; Fixed point (search for similar items in EconPapers)
JEL-codes: C61 R12 R13 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:154:y:2014:i:c:p:245-273

DOI: 10.1016/j.jet.2014.09.018

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