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Optimal City Hierarchy: A Dynamic Programming Approach To Central Place Theory, Wen-Tai Hsu, Thomas J. Holmes, Frank Morgan
Optimal City Hierarchy: A Dynamic Programming Approach To Central Place Theory, Wen-Tai Hsu, Thomas J. Holmes, Frank Morgan
Research Collection School Of Economics
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 …