Optimal city hierarchy: A dynamic programming approach to central place theory

• 成果类型: Article
• 署名作者: Hsu, Wen-Tai; Holmes, Thomas J.; Morgan, Frank
• 署名单位: Singapore Management University; University of Minnesota System; University of Minnesota Twin Cities; Federal Reserve System - USA; Federal Reserve Bank - Minneapolis; National Bureau of Economic Research; Williams College
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.09.018
• 发表日期: 2014
• 页码: 245-273
• 关键词: Central place theory; City hierarchy; dynamic programming; Principle of optimality; Fixed point

摘要

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. (c) 2014 Elsevier Inc. All rights reserved.