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.
Central place theory, City hierarchy, Dynamic programming, Fixed point, Principle of optimality, R12, R13
HSU, Wen-Tai; Holmes, Thomas J.; and Morgan, Frank.
Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory. (2013). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1533
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