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

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

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.

Suggested Citation

  • Hsu, Wen-Tai & Holmes, Thomas J. & Morgan, Frank, 2014. "Optimal city hierarchy: A dynamic programming approach to central place theory," Journal of Economic Theory, Elsevier, vol. 154(C), pages 245-273.
    • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:245-273
    DOI: 10.1016/j.jet.2014.09.018
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    More about this item

    Keywords

    Central place theory; City hierarchy; Dynamic programming; Principle of optimality; Fixed point;
    All these keywords.

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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