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Growth and agglomeration in the heterogeneous space: A generalized AK approach

Author

Listed:
  • Boucekkine, R.
  • Fabbri, G.
  • Federico, S.
  • Gozzi, F.

Abstract

We provide 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. The technology is AK, K being broad capital. The social welfare function is Benthamite. In sharp contrast to the related literature, which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology and population. Both the transitional spatio-temporal dynamics and the asymptotic spatial distributions are computed in closed form. Concerning the latter, we find, among other results, that: (i) due to inequality aversion, the consumption per capital distribution is much atter than the distribution of capital per capita; (ii) endogeneous spillovers inherent in capital spatio-temporal dynamics occur as capital distribution is much less concentrated than the (pre-specified) technological distribution; (iii) the distance to the center (or to the core) is an essential determinant of the shapes of the asymptotic distributions, that is relative location matters.

Suggested Citation

  • Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2018. "Growth and agglomeration in the heterogeneous space: A generalized AK approach," Working Papers 2018-02, Grenoble Applied Economics Laboratory (GAEL).
  • Handle: RePEc:gbl:wpaper:2018-02
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    References listed on IDEAS

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    Citations

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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., 2020. "From firm to global-level pollution control: The case of transboundary pollution," Working Papers 2020-08, Grenoble Applied Economics Laboratory (GAEL).
    3. 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).
    4. Giorgio Fabbri & Francesco Russo, 2017. "HJB Equations in Infinite Dimension and Optimal Control of Stochastic Evolution Equations via Generalized Fukushima Decomposition," AMSE Working Papers 1704, Aix-Marseille School of Economics, France.
    5. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers hal-02548170, HAL.
    6. Carmen Camacho & Alexandre Cornet, 2020. "Soil pollution diffusion in a spatial agricultural economy," Working Papers halshs-02652191, HAL.
    7. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution," Working Papers hal-02314035, HAL.
    8. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "A Dynamic Theory Of Spatial Externalities," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2020017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    9. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," Working Papers halshs-02472772, HAL.
    10. 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".
    11. Giorgio Fabbri & Fausto Gozzi & Giovanni Zanco, 2020. "Verification Results for Age-Structured Models of Economic-Epidemics Dynamics," Papers 2008.07335, arXiv.org.
    12. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "From firm to global-level pollution control: The case of transboundary pollution," Working Papers 2020-08, Grenoble Applied Economics Laboratory (GAEL).
    13. Carmen Camacho & Alexandre Cornet, 2020. "Soil pollution diffusion in a spatial agricultural economy," PSE Working Papers halshs-02652191, HAL.
    14. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).

    More about this item

    Keywords

    GROWTH; AGGLOMERATION; HETEROGENEOUS AND CONTINUOUS SPACE; CAPITAL MOBILITY; INFINITE DIMENSIONAL OPTIMAL CONTROL PROBLEMS;

    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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