Article

Existence and uniqueness of equilibrium for a spatial model of social interactions

Adrien Blanchet, Pascal Mossay, and Filippo Santambrogio

Abstract

We extend Beckmann's spatial model of social interactions to the case of a two-dimensional spatial economy with a large class of utility functions, accessing costs, and space-dependent amenities. We show that spatial equilibria derive from a potential functional. By proving the existence of a minimizer of the functional, we obtain that of spatial equilibrium. Under mild conditions on the primitives of the economy, the functional is shown to satisfy displacement convexity. Moreover, the strict displacement convexity of the functional ensures the uniqueness of equilibrium. Also, the spatial symmetry of equilibrium is derived from that of the primitives of the economy.

Keywords

social interaction; spatial equilibria; multiple cities; optimal transportation; displacement convexity;

Replaces

Adrien Blanchet, Pascal Mossay, and Filippo Santambrogio, Existence and uniqueness of equilibrium for a spatial model of social interactions, TSE Working Paper, n. 14-489, May 2014.

Reference

Adrien Blanchet, Pascal Mossay, and Filippo Santambrogio, Existence and uniqueness of equilibrium for a spatial model of social interactions, International Economic Review, vol. 57, n. 1, February 2016, pp. 31–60.

See also

Published in

International Economic Review, vol. 57, n. 1, February 2016, pp. 31–60