Cities as Solitons: Analytic Solutions to Models of Agglomeration and Related Numerical Approaches

Abstract

Economic geography equilibria that represent spontaneous agglomeration in a featureless underlying geographic space have been solved only numerically, and the resulting spatial configurations were symmetric. This paper introduces a method of obtaining analytic solutions to similar models. In the case of continuum space, the multi-city equilibria are again symmetric. However, by working in discrete space it is possible to generate stable equilibria with multiple cities of various population levels and spatial extent, asymmetrically distributed across space. The properties of these equilibria may be understood in terms of deterministic chaos theory. The analytic approach makes it possible to find all equilibria, stable and unstable. There are two qualitative predictions that may be empirically tested: (1) the stability of an isolated city does not depend on its precise position, and (2) if two cities are too close to each other, the configuration becomes unstable and the space between the cities is filled with newcomers, turning the two cities into a megalopolis. In addition, the stable equilibria of the model are compared to population density in northern Chile. It is possible to find equilibria that match the real-world population density profile with correlation of 0.9 or more.

Keywords: Agglomeration, Economic Geography

JEL Classification: F10, R12, R30