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Spatial Growth Theory: Optimality and Spatial Heterogeneity

Author

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  • Anastasios Xepapadeas
  • Athanasios Yannacopoulos
Abstract
Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth in which capital moves towards locations where the marginal productivity of capita is relatively higher. We extend Pontryagin's maximum principle to account for transition dynamics governed by a nonlinear partial differential equation emerging for spatial capital flows. The potential spatial heterogeneity of optimal growth as seen from the point of view of an optimizing social planner is examined. Our results suggest that for high utility discount rate the spatial capital flows induce the emergence of optimal spatial patterns while hor low utility discount a flat-earth steady state is socially optimal. Furthermore, when spatial heterogeneities exist due to total factor productivity differences across locations, we identify conditions under which the spatial capital flows could intensify or weaken spatial inequalities.

Suggested Citation

  • Anastasios Xepapadeas & Athanasios Yannacopoulos, 2020. "Spatial Growth Theory: Optimality and Spatial Heterogeneity," DEOS Working Papers 2033, Athens University of Economics and Business.
    • Handle: RePEc:aue:wpaper:2033
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    References listed on IDEAS

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    Cited by:

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    2. Calvia, Alessandro & Gozzi, Fausto & Leocata, Marta & Papayiannis, Georgios I. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2024. "An optimal control problem with state constraints in a spatio-temporal economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    3. Spyridon Tsangaris & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2022. "Spatial externalities, R&D spillovers, and endogenous technological change," DEOS Working Papers 2225, Athens University of Economics and Business.

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    More about this item

    Keywords

    Ramsey model; spatiotemporal dynamics; flat earth; pattern formation.;
    All these keywords.

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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