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

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Author Info
BOUCEKKINE, Raouf
CAMACHO, Carmen
ZOU, Benteng

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Abstract

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations 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 conditions. 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 different from those of the non-spatial linear Ramsey model due to the spatial dynamics induced by capital mobility.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006072.

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Date of creation: 01 Sep 2006
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Handle: RePEc:cor:louvco:2006072

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Related research
Keywords: Ramsey model; economic geography; parabolic equations; optimal control;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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  1. 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. [Downloadable!] (restricted)
  2. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July. [Downloadable!] (restricted)
  3. Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers 2004/14, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon.. [Downloadable!]
  4. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April. [Downloadable!] (restricted)
  5. 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.
  6. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June. [Downloadable!] (restricted)
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  7. 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). [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers 2004/14, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon.. [Downloadable!]
  2. Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  3. Klaus Desmet & Esteban Rossi-Hansberg, 2009. "Spatial Development," NBER Working Papers 15349, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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