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Spatial dynamics and convergence: the spatial AK model

Author

Listed:
  • Raouf BOUCEKKINE

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Department of Economics and Core, Univerity of Glasgow, Department of Economics)

  • Carmen CAMACHO

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES) and FNRS)

  • Giorgio FABBRI

    (Dipartimento di Studi Economici S.Vinci, Universita di Napoli Parthenope,Naples and UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

Abstract

We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Despite constant returns to capital, we prove that transition dynamics will set in. In particular, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.

Suggested Citation

  • Raouf BOUCEKKINE & Carmen CAMACHO & Giorgio FABBRI, 2010. "Spatial dynamics and convergence: the spatial AK model," LIDAM Discussion Papers IRES 2010009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2010009
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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(1), pages 20-45, February.
    2. Klaus Desmet & Esteban Rossi‐Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63, February.
    3. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    4. Chatterjee, Satyajit, 1994. "Transitional dynamics and the distribution of wealth in a neoclassical growth model," Journal of Public Economics, Elsevier, vol. 54(1), pages 97-119, May.
    5. Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany.
    6. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    7. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    8. Silvia Faggian, 2008. "Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital," Working Papers 181, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Economic Growth; Inequality; Spatial Dynamics; Convergence;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies

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