Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory
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...
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| Main Authors: | , , |
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| Format: | text |
| Language: | English |
| Published: |
Institutional Knowledge at Singapore Management University
2013
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/soe_research/1533 https://ink.library.smu.edu.sg/context/soe_research/article/2532/viewcontent/city_optimal_072612_no_app.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| 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 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. |
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