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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 - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Giorgio Fabbri

    (GAEL - Laboratoire d'Economie Appliquée de Grenoble - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - INRA - Institut National de la Recherche Agronomique - CNRS - Centre National de la Recherche Scientifique - UGA [2016-2019] - Université Grenoble Alpes [2016-2019])

  • Salvatore Federico

    (UNISI - Università degli Studi di Siena = University of Siena)

  • Fausto Gozzi

    (Dipartimento di Scienze Economiche e Aziendali - 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, 2019. "Growth and Agglomeration in the Heterogeneous Space: A Generalized AK Approach," Post-Print hal-01825777, HAL.
    • Handle: RePEc:hal:journl:hal-01825777
    DOI: 10.1093/jeg/lby041
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01825777
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    More about this item

    Keywords

    cap- ital mobility; agglomeration; heterogeneous and continuous space; infinite dimensional optimal control problems; Growth;
    All these keywords.

    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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