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Optimal city hierarchy: a dynamic programming approach to central place theory. (English) Zbl 1309.91110

Summary: 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 W. Christaller [Central places in southern Germany. Translation into English by C. W. Baskin. Englewood Cliffs, NJ: Prentice-Hall (1966)]. 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.

MSC:

91D20 Mathematical geography and demography
90C90 Applications of mathematical programming
90C39 Dynamic programming
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References:

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