publication . Preprint . Article . 2009

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

Wen-Tai Hsu; Thomas J. Holmes; Frank Morgan;
Open Access
  • Published: 01 Jan 2009
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 ...
free text keywords: Dynamic programming, Mathematical economics, Bellman equation, Hierarchy, Social planner, Fixed point, Central place theory, Recursion, Mathematical optimization, Mathematics, Fixed cost
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