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

Wen Tai Hsu, Thomas J. Holmes, Frank Morgan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)245-273
Number of pages29
JournalJournal of Economic Theory
StatePublished - Nov 1 2014


  • Central place theory
  • City hierarchy
  • Dynamic programming
  • Fixed point
  • Principle of optimality

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