IDEAS home Printed from https://ideas.repec.org/p/luc/wpaper/19-17.html
   My bibliography  Save this paper

Local Social Interaction and Urban Equilibria

Author

Listed:
  • Emmanuelle Augeraud-Veron

    (GREThA, UMR 5113, University of Bordeaux, France)

  • Francisco Marhuenda

    (University Carlos III, UC3M, Madrid, Spain)

  • Pierre M. Picard

    (CREA, Université du Luxembourg)

Abstract

In this paper we investigate the effect of local interaction in a simple urban eco- nomics model. Agents interact with others if and only if their interaction benefit outweights 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. Nu- merical analyses show that more localized interactions yield flatter population den- sity 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

  • Emmanuelle Augeraud-Veron & Francisco Marhuenda & Pierre M. Picard, 2019. "Local Social Interaction and Urban Equilibria," DEM Discussion Paper Series 19-17, Department of Economics at the University of Luxembourg.
    • Handle: RePEc:luc:wpaper:19-17
    as

    Download full text from publisher

    File URL: https://hdl.handle.net/10993/41543
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    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. 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.
    7. 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.
    8. Pascal Mossay & Pierre Picard, 2019. "Spatial segregation and urban structure," Journal of Regional Science, Wiley Blackwell, vol. 59(3), pages 480-507, June.
    9. 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).
    10. 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.
    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, pages 31-60, February.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Boucekkine, Raouf & Seegmuller, Thomas & Venditti, Alain, 2021. "Advances in growth and macroeconomic dynamics: In memory of Carine Nourry," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 1-6.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Osawa, Minoru & Akamatsu, Takashi, 2020. "Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach," Journal of Economic Theory, Elsevier, vol. 187(C).
    2. Pascal Mossay & Pierre Picard, 2019. "Spatial segregation and urban structure," Journal of Regional Science, Wiley Blackwell, vol. 59(3), pages 480-507, June.
    3. Osawa, Minoru & Akamatsu, Takashi, 2019. "Emergence of Urban Landscapes: Equilibrium Selection in a Model of Internal Structure of the Cities," MPRA Paper 92395, University Library of Munich, Germany.
    4. 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.
    5. Kim, Jun Sung & Patacchini, Eleonora & Picard, Pierre M. & Zenou, Yves, 2017. "Urban Interactions," Working Paper Series 1192, Research Institute of Industrial Economics.
    6. Topa, Giorgio & Zenou, Yves, 2015. "Neighborhood and Network Effects," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 561-624, Elsevier.
    7. Takashi Akamatsu & Tomoya Mori & Minoru Osawa & Yuki Takayama, 2019. "Spatial scale of agglomeration and dispersion: Number, spacing, and the spatial extent of cities," Papers 1912.05113, arXiv.org, revised Aug 2024.
    8. Garrido-da-Silva, Liliana & Castro, Sofia B.S.D. & Correia-da-Silva, João, 2022. "Location of housing and industry around city centre amenities," Regional Science and Urban Economics, Elsevier, vol. 95(C).
    9. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Stochastic stability of agglomeration patterns in an urban retail model," Papers 2011.06778, arXiv.org.
    10. Picard, Pierre M. & Zenou, Yves, 2018. "Urban spatial structure, employment and social ties," Journal of Urban Economics, Elsevier, vol. 104(C), pages 77-93.
    11. Zhi-Chun Li Author-Name : Wen-Jing Liu Author-Name : André de Palma Author-Name : Yuki Takayama Author-Name : Takao Dantsuji, "undated". "Autonomous vehicles, parking, and urban spatial structure," THEMA Working Papers 2024-09, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    12. Zhi-Chun Li Author-Name : Wen-Jing Liu Author-Name : André de Palma, "undated". "Spatial heterogeneity in vehicle license plate lottery rationing," THEMA Working Papers 2024-11, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Picard, Pierre M. & Zenou, Yves, 2015. "Urban Spatial Structure, Employment and Social Ties: European versus American Cities," IZA Discussion Papers 9166, Institute of Labor Economics (IZA).
    14. Mossay, Pascal & Picard, Pierre M. & Tabuchi, Takatoshi, 2020. "Urban structures with forward and backward linkages," Regional Science and Urban Economics, Elsevier, vol. 83(C).
    15. Thisse, Jacques-François & Turner, Matthew A. & Ushchev, Philip, 2024. "Foundations of cities," Journal of Urban Economics, Elsevier, vol. 143(C).
    16. de Palma, André & Papageorgiou, Yorgos Y. & Thisse, Jacques-François & Ushchev, Philip, 2019. "About the origin of cities," Journal of Urban Economics, Elsevier, vol. 111(C), pages 1-13.
    17. Picard, Pierre M. & Tabuchi, Takatoshi, 2013. "On microfoundations of the city," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2561-2582.
    18. Jun Oshiro, 2017. "Solitary City: Time, Space and Urban Policy," Manchester School, University of Manchester, vol. 85(6), pages 744-764, December.
    19. Zenou, Yves & picard, pierre & Patacchini, Eleonora, 2015. "Urban Social Structure, Social Capital and Spatial Proximity," CEPR Discussion Papers 10501, C.E.P.R. Discussion Papers.
    20. Stef Proost & Jacques-François Thisse, 2019. "What Can Be Learned from Spatial Economics?," Journal of Economic Literature, American Economic Association, vol. 57(3), pages 575-643, September.

    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)

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:luc:wpaper:19-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marina Legrand (email available below). General contact details of provider: https://edirc.repec.org/data/crcrplu.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.