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Growth and Agglomeration in the Heterogeneous Space: A Generalized AK Approach

Author

Listed:
  • Raouf Boucekkine

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales, IMéRA - Institute for Advanced Studies - Aix-Marseille University)

  • Giorgio Fabbri

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Salvatore Federico

    (Università degli Studi di Siena, Dipartimento di Economia Politica e Statistica)

  • Fausto Gozzi

    (Dipartimento di Economia e Finanza [Roma] - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

Abstract

We provide with an optimal growth spatio-temporal setting with capital accumulation and diffusion across space in order to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. We choose the simplest production function generating growth endogenously, the AK technology but in sharp contrast to the related literature which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology (through the productivity parameter A) and population. Beside the mathematical tour de force, we ultimately show that agglomeration may show up in our optimal growth with linear technology, its exact shape depending on the interaction of two main effects, a population dilution effect versus a technology space discrepancy effect.

Suggested Citation

  • Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2017. "Growth and Agglomeration in the Heterogeneous Space: A Generalized AK Approach," Working Papers halshs-01399995, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01399995
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01399995v2
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    References listed on IDEAS

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    Cited by:

    1. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    2. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2018. "Geographic environmental Kuznets curves: The optimal growth linear-quadratic case," Working Papers 2018-10, Grenoble Applied Economics Laboratory (GAEL).
    3. Giorgio Fabbri & Francesco Russo, 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2017003, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. Silvia Faggian & Fausto Gozzo & Peter M. Kort, 2019. "Optimal investment with vintage capital: equilibrium distributions," Working Papers 2019: 12, Department of Economics, University of Venice "Ca' Foscari".

    More about this item

    Keywords

    infinite dimensional optimal control problems; heterogeneous and continuous space; capital mobility; growth; agglomeration;

    JEL classification:

    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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