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

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

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Official URL: http://tse-fr.eu/pub/28212

Abstract

We extend Beckmann’s spatial model of social interactions to the case of a two-dimensional spatial economy involving 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 minimiser of the functional, we obtain that of a spatial equilibrium. Under mild conditions on the primitives of the economy, the functional is shown to satisfy displacement convexity, a concept used in the theory of optimal transportation. This provides a variational characterisation of spatial equilibria. Moreover, the strict displacement convexity of the functional ensures the uniqueness of spatial equilibrium. Also, the spatial symmetry of equilibrium is derived from that of the spatial primitives of the economy. Several examples illustrate the scope of our results. In particular, the emergence of multiple of equilibria in the circular economy is interpreted as a lack of convexity of the problem.

Item Type: Monograph (Working Paper)
Language: English
Date: May 2014
Uncontrolled Keywords: social interaction, spatial equilibria, multiple cities, optimal transportation, displacement convexity
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse Capitole
Site: UT1
Date Deposited: 09 Jul 2014 17:44
Last Modified: 07 Mar 2018 13:22
OAI ID: oai:tse-fr.eu:28212
URI: http://publications.ut-capitole.fr/id/eprint/15918

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