IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v42y2014icp143-174.html
   My bibliography  Save this article

Spatial externalities and agglomeration in a competitive industry

Author

Listed:
  • Brock, William A.
  • Xepapadeas, Anastasios
  • Yannacopoulos, Athanasios N.

Abstract

We introduce spatial spillovers as an externality in the production function of competitive firms operating within a finite spatial domain under adjustment costs. Spillovers may attenuate with distance and the overall externality could contain positive and negative components with the overall effect being positive. We show that when the spatial externality is not internalized by firms, spatial agglomerations may emerge endogenously in a competitive equilibrium. The result does not require increasing returns at the private or the social level, increasing marginal productivity of private capital with respect to the externality, or location advantages. In fact agglomerations may emerge with decreasing returns to scale, declining marginal productivity of private capital with respect to the externality, and no location advantage. The result depends on the interactions between the structures of production technology and spatial effects as shown in the paper. No agglomerations emerge at the social optimum when spillovers are internalized and diminishing returns both from the private and the social point of view prevail. Numerical experiments with Cobb–Douglas and CES technologies and an isoelastic demand confirm our theoretical predictions.

Suggested Citation

  • Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Spatial externalities and agglomeration in a competitive industry," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 143-174.
  • Handle: RePEc:eee:dyncon:v:42:y:2014:i:c:p:143-174
    DOI: 10.1016/j.jedc.2014.03.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188914000785
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2014.03.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-681, September.
    3. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    4. Benteng Zou & Carmen Camacho, 2004. "The spatial Solow model," Economics Bulletin, AccessEcon, vol. 18(2), pages 1-11.
    5. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    6. M. Kurz, 1971. "The General Instability of a Class of Competitive Growth Processes," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 17, pages 218-237, Palgrave Macmillan.
    7. Baldwin, Richard E. & Martin, Philippe, 2004. "Agglomeration and regional growth," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 60, pages 2671-2711, Elsevier.
    8. Robert E. Lucas, Jr., 2001. "Externalities and Cities," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(2), pages 245-274, April.
    9. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics," AMSE Working Papers 1334, Aix-Marseille School of Economics, France, revised 05 Jun 2013.
    10. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
    11. Breinlich, Holger & Ottaviano, Gianmarco I.P. & Temple, Jonathan R.W., 2014. "Regional Growth and Regional Decline," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 4, pages 683-779, Elsevier.
    12. Danny Quah, 2002. "Spatial Agglomeration Dynamics," American Economic Review, American Economic Association, vol. 92(2), pages 247-252, May.
    13. José Alexandre Scheinkman, 1978. "Stability of Separable Hamiltonians and Investment Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 559-570.
    14. Maryann Feldman, 1999. "The New Economics Of Innovation, Spillovers And Agglomeration: Areview Of Empirical Studies," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 8(1-2), pages 5-25.
    15. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-1119, July.
    16. Camacho, Carmen & Zou, Benteng & Briani, Maya, 2008. "On the dynamics of capital accumulation across space," European Journal of Operational Research, Elsevier, vol. 186(2), pages 451-465, April.
    17. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    18. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, vol. 38(3), pages 252-270, May.
    19. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    20. Brock, William A, 1974. "Money and Growth: The Case of Long Run Perfect Foresight," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(3), pages 750-777, October.
    21. Grossman, Gene M. & Helpman, Elhanan, 1991. "Trade, knowledge spillovers, and growth," European Economic Review, Elsevier, vol. 35(2-3), pages 517-526, April.
    22. Nocco, Antonella, 2005. "The rise and fall of regional inequalities with technological differences and knowledge spillovers," Regional Science and Urban Economics, Elsevier, vol. 35(5), pages 542-569, September.
    23. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
    24. repec:esx:essedp:729 is not listed on IDEAS
    25. Quah, Danny, 2002. "Spatial agglomeration dynamics," LSE Research Online Documents on Economics 2042, London School of Economics and Political Science, LSE Library.
    26. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the optimal control of some parabolic differential equations arising in economics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01498240, HAL.
    27. Danny Quah, 2002. "Spatial Agglomeration Dynamics," CEP Discussion Papers dp0521, Centre for Economic Performance, LSE.
    28. Stefano Breschi & Francesco Lissoni, 2001. "articles: Localised knowledge spillovers vs. innovative milieux: Knowledge "tacitness" reconsidered," Papers in Regional Science, Springer;Regional Science Association International, vol. 80(3), pages 255-273.
    29. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
    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. Mohsen Rahimi Piranfar & Hadi Khatibzadeh, 2021. "Long-Time Behavior of a Gradient System Governed by a Quasiconvex Function," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 169-191, January.
    2. Anastasios Xepapadeas & Athanasios Yannacopoulos, 2015. "Spatial Resource Management under Pollution Externalities," CEEES Paper Series CE3S-05/15, European University at St. Petersburg, Department of Economics.
    3. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    4. Weiliang Chen & Xinjian Huang & Yanhong Liu & Yan Song, 2019. "Does Industry Integration Improve the Competitiveness of China’s Electronic Information Industry?—Evidence from the Integration of the Electronic Information Industry and Financial Industry," Sustainability, MDPI, vol. 11(9), pages 1-18, May.
    5. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    6. Anastasios Xepapadeas & Athanasios Yannacopoulos & Andreas Ioannidis, 2014. "Spatial Growth: The Distribution of Capital across Locations when Saving Rates are Exogenous," DEOS Working Papers 1412, Athens University of Economics and Business.

    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. Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Optimal agglomerations in dynamic economics," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 1-15.
    2. Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany.
    3. W.A. Brock & A. Xepapadeas & A.N. Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," Annual Review of Resource Economics, Annual Reviews, vol. 6(1), pages 33-68, October.
    4. Giorgio FABBRI, 2014. "Ecological Barriers and Convergence: a Note on Geometry in Spatial Growth Models," LIDAM Discussion Papers IRES 2014014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, vol. 162(C), pages 114-136.
    6. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    7. Giorgio Fabbri, 2014. "Ecological Barriers and Convergence: A Note on Geometry in Spatial Growth Models," Documents de recherche 14-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    8. Emmanuelle Augeraud-Véron & Arnaud Ducrot, 2019. "Spatial externality and indeterminacy," Post-Print hal-02306568, HAL.
    9. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    10. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    11. Anastasios Xepapadeas, 2012. "Diffusion and Spatial Aspects," DEOS Working Papers 1232, Athens University of Economics and Business.
    12. Spyridon Tsangaris & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2022. "Spatial externalities, R&D spillovers, and endogenous technological change," DEOS Working Papers 2225, Athens University of Economics and Business.
    13. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    14. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    15. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    16. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    17. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    18. Klaus Desmet & Esteban Rossi-Hansberg, 2014. "Spatial Development," American Economic Review, American Economic Association, vol. 104(4), pages 1211-1243, April.
    19. Anastasios Xepapadeas, 2010. "Modeling complex systems," Agricultural Economics, International Association of Agricultural Economists, vol. 41(s1), pages 181-191, November.
    20. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.

    More about this item

    Keywords

    Competitive equilibrium; Social optimum; Spatial externality; Endogenous agglomerations;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • R3 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:eee:dyncon:v:42:y:2014:i:c:p:143-174. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.