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Existence And Uniqueness Of Equilibrium For A Spatial Model Of Social Interactions

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  • Adrien Blanchet
  • Pascal Mossay
  • 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.

Suggested Citation

  • Adrien Blanchet & Pascal Mossay & Filippo Santambrogio, 2016. "Existence And Uniqueness Of Equilibrium For A Spatial Model Of Social Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 31-60, February.
  • Handle: RePEc:wly:iecrev:v:57:y:2016:i::p:31-60
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    File URL: http://hdl.handle.net/10.1111/iere.12147
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    Cited by:

    1. Akamatsu, Takashi & Mori, Tomoya & Osawa, Minoru & Takayama, Yuki, 2017. "Spatial scale of agglomeration and dispersion: Theoretical foundations and empirical implications," MPRA Paper 80689, University Library of Munich, Germany.
    2. repec:eee:juecon:v:100:y:2017:i:c:p:65-79 is not listed on IDEAS
    3. Takayama, Yuki & Kuwahara, Masao, 2017. "Bottleneck congestion and residential location of heterogeneous commuters," Journal of Urban Economics, Elsevier, vol. 100(C), pages 65-79.
    4. Ioannides, Yannis M., 2015. "Neighborhoods to nations via social interactions," Economic Modelling, Elsevier, vol. 48(C), pages 5-15.
    5. Carmen Camacho & Agustín Pérez-Barahona, 2017. "The diffusion of economic activity across space: a new approach," PSE Working Papers halshs-01670532, HAL.
    6. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Working Papers hal-00967662, HAL.
    7. Akamatsu, Takashi & Fujishima, Shota & Takayama, Yuki, 2017. "Discrete-space agglomeration model with social interactions: Multiplicity, stability, and continuous limit of equilibria," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 22-37.
    8. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2013. "Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria," Papers 1307.1685, arXiv.org.
    9. Vincent Boitier, 2014. "Unemployment Dispersion and City Configurations: Beyond the Bid Rent Theory," Working Papers hal-00999559, HAL.
    10. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Papers 1403.7800, arXiv.org.

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