Pattern formation by advection-diffusion in new economic geography

TL;DR

This paper models spatial population patterns in economic geography using an advection-diffusion framework, revealing how diffusion stabilizes or destabilizes homogeneous states and leads to urban clustering.

Contribution

It introduces a tractable core-periphery model with an advection-diffusion equation to analyze pattern formation in economic geography.

Findings

Diffusion stabilizes homogeneous solutions at low transport costs.

Lower transport costs can inhibit agglomeration under certain conditions.

Numerical simulations show emergence of multiple urban areas when instability occurs.

Abstract

This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility function and an advection-diffusion equation that expresses population migration. It is found that diffusion stabilizes a homogeneous stationary solution when transport costs are sufficiently low, and it also inhibits the monotonic facilitation of agglomeration caused by lower transport costs in some cases. When the homogeneous stationary solution is unstable, numerical simulations show spatial patterns with multiple urban areas. Insights into the relation between agglomeration and control parameters (transport costs and preference for variety of consumers) gained from the large-time behavior of solutions confirm the validity of the analysis of linearized equations.