Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory

Author

Wen-Tai HSU, Singapore Management UniversityFollow
Thomas J. HOLMES, University of Minnesota
Frank MORGAN, Williams College

Publication Type

Journal Article

Version

acceptedVersion

Publication Date

11-2014

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. 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

Discipline

Behavioral Economics | Economics | Economic Theory | Urban Studies and Planning

Research Areas

Applied Microeconomics

Publication

Journal of Economic Theory

Volume

154

First Page

245

Last Page

273

ISSN

0022-0531

Identifier

10.1016/j.jet.2014.09.018

Publisher

Elsevier

Citation

HSU, Wen-Tai; HOLMES, Thomas J.; and MORGAN, Frank. Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory. (2014). Journal of Economic Theory. 154, 245-273.
Available at: https://ink.library.smu.edu.sg/soe_research/1642

Copyright Owner and License

Authors

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Additional URL

https://doi.org/10.1016/j.jet.2014.09.018