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On the dynamics of capital accumulation across space

Author

Listed:
  • Camacho, Carmen

    (Center for Mathematical Economics, Bielefeld University)

  • Zou, Benteng

    (Center for Mathematical Economics, Bielefeld University)

  • Briani, Maya

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. Then, we study the roles of initial capital and technology distributions over space in various scenarios.

Suggested Citation

  • Camacho, Carmen & Zou, Benteng & Briani, Maya, 2011. "On the dynamics of capital accumulation across space," Center for Mathematical Economics Working Papers 376, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:376
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    Cited by:

    1. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Post-Print halshs-00674020, HAL.
    2. 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.
    3. 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.
    4. Herb Kunze & Davide La Torre & Simone Marsiglio, 2019. "A Multicriteria Macroeconomic Model with Intertemporal Equity and Spatial Spillovers," Papers 1911.08247, arXiv.org.
    5. 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.
    6. 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.
    7. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    14. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    15. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    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. 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.
    18. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2024. "Epidemic outbreaks and the optimal lockdown area: a spatial normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 349-411, February.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Carmen Camacho, 2013. "Spatial migration," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801109, HAL.
    25. 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.

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