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

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

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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.

Item Type: Article
Language: English
Date: February 2016
Refereed: Yes
Uncontrolled Keywords: Social interaction, spatial equilibria, multiple cities, optimal transportation, displacement convexity
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 18 Mar 2016 10:51
Last Modified: 08 Oct 2019 23:01
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