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Local social interaction and urban equilibria

Author

Listed:
  • Augeraud Veron, E.
  • Marhuenda, F.
  • Picard, P.M.

Abstract

In this paper we investigate the effect of local interaction in a simple urban economics model. Agents interact with others if and only if their interaction benefit outweighs their travel cost and therefore meet others only within finite geographic windows. We show that two or more cites may co-exist at the equilibrium provided that they are sufficiently distant. For any interaction surplus function, there exists a unique spatial equilibrium on not too large city supports. The population density within a city is determined by a second order advance-delay differential equation, whose solutions are fully characterized for linear interaction surplus functions. Numerical analyses show that more localized interactions yield flatter population density and land rents over larger extents of the city support. They do not give support to the idea that multiple subcenters can be caused by small and finite geographic windows of interaction.

Suggested Citation

  • Augeraud Veron, E. & Marhuenda, F. & Picard, P.M., 2021. "Local social interaction and urban equilibria," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 72-83.
    • Handle: RePEc:eee:matsoc:v:112:y:2021:i:c:p:72-83
    DOI: 10.1016/j.mathsocsci.2021.03.006
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    1. Büchel, Konstantin & Ehrlich, Maximilian v., 2020. "Cities and the structure of social interactions: Evidence from mobile phone data," Journal of Urban Economics, Elsevier, vol. 119(C).
    2. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Stability and determinacy conditions for mixed-type functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 119-129.
    3. Mossay, P. & Picard, P.M., 2011. "On spatial equilibria in a social interaction model," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2455-2477.
    4. Gabriel M. Ahlfeldt & Stephen J. Redding & Daniel M. Sturm & Nikolaus Wolf, 2015. "The Economics of Density: Evidence From the Berlin Wall," Econometrica, Econometric Society, vol. 83, pages 2127-2189, November.
    5. Mossay, Pascal & Picard, Pierre M. & Tabuchi, Takatoshi, 2020. "Urban structures with forward and backward linkages," Regional Science and Urban Economics, Elsevier, vol. 83(C).
    6. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    7. Pascal Mossay & Pierre Picard, 2019. "Spatial segregation and urban structure," Journal of Regional Science, Wiley Blackwell, vol. 59(3), pages 480-507, June.
    8. Adrien BLANCHET & Pascal MOSSAY & Filippo SANTAMBROGIO, 2016. "Existence and uniqueness of equilibrium for a spatial model of social interactions," LIDAM Reprints CORE 2805, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Berliant, Marcus & Peng, Shin-Kun & Wang, Ping, 2002. "Production Externalities and Urban Configuration," Journal of Economic Theory, Elsevier, vol. 104(2), pages 275-303, June.
    10. Adrien BLANCHET & Pascal MOSSAY & Filippo SANTAMBROGIO, 2013. "Existence and Uniqueness of Equilibrium for a Spatial Model of Social Interactions," Discussion papers 13055, Research Institute of Economy, Trade and Industry (RIETI).
    11. 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(1), pages 31-60, February.
    12. Levy, Moshe & Goldenberg, Jacob, 2014. "The gravitational law of social interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 418-426.
    13. Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 181-186, January.
    14. Diana Mok & Barry Wellman & Juan Carrasco, 2010. "Does Distance Matter in the Age of the Internet?," Urban Studies, Urban Studies Journal Limited, vol. 47(13), pages 2747-2783, November.
    15. 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.
    16. Fujita, Masahisa & Ogawa, Hideaki, 1982. "Multiple equilibria and structural transition of non-monocentric urban configurations," Regional Science and Urban Economics, Elsevier, vol. 12(2), pages 161-196, May.
    17. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
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    More about this item

    Keywords

    Social interaction; Cities; Spatial equilibrium;
    All these keywords.

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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