IDEAS home Printed from https://ideas.repec.org/p/gla/glaewp/2007_27.html
   My bibliography  Save this paper

Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model

Author

Listed:
  • Raouf Boucekkine
  • C. Camacho
  • B. Zou

Abstract

We study a Ramsey problem in in¯nite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to loca- tions with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin con- ditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard (1923). We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly dfferent from those of the non-spatial linear Ramsey model due to the spatial dynamics induced by capital mobility.

Suggested Citation

  • Raouf Boucekkine & C. Camacho & B. Zou, 2007. "Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model," Working Papers 2007_27, Business School - Economics, University of Glasgow.
  • Handle: RePEc:gla:glaewp:2007_27
    as

    Download full text from publisher

    File URL: http://www.gla.ac.uk/media/media_43620_en.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476, January.
    2. Gaines, R. E., 1976. "Existence of solutions to Hamiltonian dynamical systems of optimal growth," Journal of Economic Theory, Elsevier, vol. 12(1), pages 114-130, February.
    3. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    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. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
    7. 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)

    More about this item

    Keywords

    Ramsey model; Economic geography; Parabolic partial differential equations; optimal control.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gla:glaewp:2007_27. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tedi Racheva). General contact details of provider: http://edirc.repec.org/data/dpglauk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.