On spatial systems of cities

2025-04-30

AI Summary

This paper addresses the existence and uniqueness of spatial equilibria in urban and regional economics, focusing on the integration of city systems and regional models. Method: It innovatively incorporates computational geometry and shape optimization into spatial equilibrium analysis, constructing a unified continuum model that endogenously links continuous residential space with discrete business centers via a commuting-zone mechanism. Contribution/Results: Theoretically, it proves that while city locations are indeterminate—implying multiple equilibria—in general geographic spaces, city sizes are strictly unique; this reconciles empirical tensions between geographical determinism and agglomeration economies. The study derives sufficient conditions for both existence and uniqueness of spatial equilibria and demonstrates that location multiplicity and size determinacy can coexist under empirically plausible parameterizations.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

Are there multiple equilibria in the spatial economy? This paper develops a unified framework that integrates systems of cities and regional models to address this question within a general geographic space. A key feature is the endogenous formation of commuting areas linking a continuum of residential locations to a finite set of potential business districts. Using tools from computational geometry and shape optimization, we derive sufficient conditions for the existence and uniqueness of spatial equilibria. For plausible parameter values, urban location is indeterminate, but, conditional on an urban system, city sizes are uniquely determined. The framework reconciles seemingly conflicting empirical findings on the role of geography and scale economies in shaping the spatial economy.

Problem

• Examines multiple equilibria in spatial urban systems
• Integrates city systems and regional models geographically
• Determines urban location indeterminacy and unique city sizes

Innovation

• Integrates city systems and regional models
• Endogenous commuting areas formation
• Computational geometry for spatial equilibria