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On the dynamics of capital accumulation across space

Author

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  • 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
    as

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    References listed on IDEAS

    as
    1. 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(01), pages 20-45, February.
    2. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    3. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
    4. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
    5. Pascal Mossay, 2003. "Increasing Returns And Heterogeneity In A Spatial Economy," Working Papers. Serie AD 2003-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers Department of Economics 2004/14, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. repec:hal:journl:halshs-00674020 is not listed on IDEAS
    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. 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.
    5. Giorgio Fabbri, 2015. "Ecological barriers and convergence: a note on geometry in spatial growth models," Working Papers hal-01159253, HAL.
    6. Carmen Camacho, 2013. "Spatial migration," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801109, HAL.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    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. 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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