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On the dynamics of capital accumulation across space

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Author Info

  • Carmen Camacho

    ()
    (Economics Department, Université catholique du Louvain)

  • Benteng Zou

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Maya Briani

    ()
    (LUISS Guido Carli)

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.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-376.pdf
File Function: First version, 2005
Download Restriction: no

Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 376.

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Length: 23 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:bie:wpaper:376

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Postal: Postfach 10 01 31, 33501 Bielefeld
Phone: +49(0)521-106-4907
Web page: http://www.imw.uni-bielefeld.de/
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Related research

Keywords: economics; economic geography; parabolic differential equations; optimal control;

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Cited by:
  1. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Documents de travail du Centre d'Economie de la Sorbonne 12012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. repec:hal:journl:halshs-00674020 is not listed on IDEAS
  3. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," DEOS Working Papers 1402, Athens University of Economics and Business.
  4. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Agglomerations in Dynamic Economics," DEOS Working Papers 1403, Athens University of Economics and Business.
  5. 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.
  6. Giorgio FABBRI, 2014. "Ecological Barriers and Convergence: a Note on Geometry in Spatial Growth Models," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2014014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  7. Carmen Camacho, 2013. "Spatial migration," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801109, HAL.

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