2025/04/30 by Gianandrea Lanzara, Lanzara, Gianandrea, Matteo Santacesaria +1
Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Global Urban Networks and Dynamics #Optimization and Control (math.OC) #Regional Economic and Spatial Analysis #Regional Economics and Spatial Analysis #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2504.21819
openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.