Market Areas in General Equilibrium

TL;DR

This paper develops a spatial general equilibrium model with realistic geography, analyzing how market areas form and change in response to shocks, using computational geometry and shape optimization tools, with an empirical illustration.

Contribution

It introduces a novel spatial equilibrium framework with tessellated market areas, incorporating realistic geography and dynamic border responses to shocks.

Findings

Existence of a unique equilibrium is proven.

Market borders and city sets change with economic shocks.

The framework is applicable to empirical spatial economic analysis.

Abstract

This paper proposes a spatial model with a realistic geography where a continuous distribution of agents (e.g., farmers) engages in economic interactions with one location from a finite set (e.g., cities). The spatial structure of the equilibrium consists of a tessellation, i.e., a partition of space into a collection of mutually exclusive market areas. After proving the existence of a unique equilibrium, we characterize how the location of borders and, in the case with mobile labor, the set of inhabited cities change in response to economic shocks. To deal with a two-dimensional space, we draw on tools from computational geometry and from the theory of shape optimization. Finally, we provide an empirical application to illustrate the usefulness of the framework for applied work.