Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory

• Main Authors: HSU, Wen-Tai, HOLMES, Thomas J., MORGAN, Frank
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2013
• Subjects: Central place theory; City hierarchy; Dynamic programming; Fixed point; Principle of optimality; R12; R13; Behavioral Economics; Economics; Economic Theory; Urban Studies and Planning
• 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
• Institution: Singapore Management University

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.