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Optimal Economic Growth Through Capital Accumulation in a Spatially Heterogeneous Environment

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Abstract

We design a general set-up for the study of a generic economy whose development process is entirely driven by the spatio-temporal dynamics of capital accumulation. It allows to take into account spatial heterogeneities in technological level and population distribution. We solve analytically, via dynamic programming in infinite dimensions, the optimal control problem associated to the model, finding explicitly the optimal feedback and the value function. The expression of the optimal dynamics of the system in terms of eigenfunctions of an appropriate Sturm-Liouville problem allows to simulate the behavior of the variables and, in particular, their optimal discounted long-run spatial distribution.

Suggested Citation

  • Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico, 2016. "Optimal Economic Growth Through Capital Accumulation in a Spatially Heterogeneous Environment," AMSE Working Papers 1641, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:1641
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    File URL: http://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2016_-_nr_41.pdf
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    Cited by:

    1. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).

    More about this item

    Keywords

    Dynamical spatial model; growth; agglomeration; infinite dimensional optimal control problems; Sturm-Liouville theory;
    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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