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The spatial Solow model

Author

Listed:
  • Carmen Camacho

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Zou Benteng

    (uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

Abstract

In this paper, we solve a Solow model in continuous time and space. We prove the existence of a solution to the problem and its convergence to a stationary solution. The simulations of various scenario in the last section of the paper illustrates the convergence issue.

Suggested Citation

  • Carmen Camacho & Zou Benteng, 2004. "The spatial Solow model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00683802, HAL.
    • Handle: RePEc:hal:cesptp:hal-00683802
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    Citations

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    Cited by:

    1. João Juchem Neto & Julio Claeyssen, 2015. "Capital-induced labor migration in a spatial Solow model," Journal of Economics, Springer, vol. 115(1), pages 25-47, May.
    2. Herb Kunze & Davide La Torre & Simone Marsiglio, 2019. "A Multicriteria Macroeconomic Model with Intertemporal Equity and Spatial Spillovers," Papers 1911.08247, arXiv.org.
    3. Herb Kunze & Davide Torre, 2022. "Solving inverse problems for steady-state equations using a multiple criteria model with collage distance, entropy, and sparsity," Annals of Operations Research, Springer, vol. 311(2), pages 1051-1065, April.
    4. 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.
    5. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    6. Gilberto González-Parra & Benito Chen-Charpentier & Abraham J. Arenas & Miguel Díaz-Rodríguez, 2022. "Mathematical Modeling of Physical Capital Diffusion Using a Spatial Solow Model: Application to Smuggling in Venezuela," Economies, MDPI, vol. 10(7), pages 1-16, July.
    7. Juchem Neto, J.P. & Claeyssen, J.C.R. & Pôrto Júnior, S.S., 2018. "Economic agglomerations and spatio-temporal cycles in a spatial growth model with capital transport cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 76-86.
    8. Emmanuelle Augeraud-Véron & Arnaud Ducrot, 2019. "Spatial externality and indeterminacy," Post-Print hal-02306568, HAL.
    9. Juchem Neto, Joao Plinio & Claeyssen, Julio Cesar Ruiz & Porto Junior, Sabino da Silva, 2014. "A spatial Solow model with transport cost," MPRA Paper 59766, University Library of Munich, Germany.
    10. 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.
    11. Sahar Amidi & Ali Fagheh Majidi & Bakhtiar Javaheri, 2020. "Growth spillover: a spatial dynamic panel data and spatial cross section data approaches in selected Asian countries," Future Business Journal, Springer, vol. 6(1), pages 1-14, December.
    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. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    14. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    15. Herb Kunze & Davide Torre & Simone Marsiglio, 2022. "Sustainability and spatial spillovers in a multicriteria macroeconomic model," Annals of Operations Research, Springer, vol. 311(2), pages 1067-1084, April.
    16. 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.
    17. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    18. Fanze Kong & Jiayi Sun & Shuangquan Xie, 2025. "Stability and slow dynamics of an interior spiky pattern in a one-dimensional spatial Solow model with capital-induced labor migration," Papers 2510.19204, arXiv.org.
    19. Gilberto Gonz'alez-Parra & Benito Chen-Charpentier & Abraham J. Arenas & Miguel Diaz-Rodriguez, 2015. "Mathematical modeling of physical capital using the spatial Solow model," Papers 1504.04388, arXiv.org.
    20. 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.

    More about this item

    Keywords

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    JEL classification:

    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics
    • O0 - Economic Development, Innovation, Technological Change, and Growth - - General

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