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Ecological barriers and convergence: a note on geometry in spatial growth models

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  • Giorgio Fabbri

    (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne)

Abstract

We introduce an AK spatial growth model with a general geographical structure. The dynamics of the economy is described by a partial differential equation on a Riemannian manifold. The morphology interacts with the spatial dynamics of the capital and is one determinant of the qualitative behavior of the economy. We characterize the conditions on the geographical structure that guarantee convergence of the detrended capital across locations in the long run, and those inducing spatial capital agglomeration.

Suggested Citation

  • Giorgio Fabbri, 2015. "Ecological barriers and convergence: a note on geometry in spatial growth models," Working Papers hal-01159253, HAL.
  • Handle: RePEc:hal:wpaper:hal-01159253
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01159253
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    4. 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.
    5. Danny Quah, 2002. "Spatial Agglomeration Dynamics," American Economic Review, American Economic Association, vol. 92(2), pages 247-252, May.
    6. 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.
    7. Gani Aldashev & Serik Aldashev & Timoteo Carletti, 2014. "On Convergence in the Spatial AK Growth Models," Papers 1401.4887, arXiv.org.
    8. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
    9. MOSSAY, Pascal, 2013. "A theory of rational spatial agglomerations," LIDAM Reprints CORE 2499, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Mossay, Pascal, 2013. "A theory of rational spatial agglomerations," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 385-394.
    11. Klaus Desmet & Esteban Rossi‐Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63, February.
    12. 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.
    13. Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany.
    14. 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.
    15. 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.
    16. Danny Quah, 2002. "Spatial Agglomeration Dynamics," CEP Discussion Papers dp0521, Centre for Economic Performance, LSE.
    17. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    18. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
    19. Quah, Danny, 2002. "Spatial agglomeration dynamics," LSE Research Online Documents on Economics 2042, London School of Economics and Political Science, LSE Library.
    20. 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.
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    Cited by:

    1. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.

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    More about this item

    Keywords

    Dynamical spatial model; growth; agglomeration; Riemannian manifolds; convergence; infinite di-mensional optimal control problems;
    All these keywords.

    JEL classification:

    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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