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Population dynamics in a spatial Solow model with a convex-concave production function

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Vincenzo Capasso

    (University of Milan, Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences (ADAMSS) and Department of Mathematics)

  • Ralf Engbers

    (Westfälische Wilhelms-Universität (WWU) Münster,, Institute for Computational and Applied Mathematics)

  • Davide La Torre

    (University of Milan, Department of Economics, Business and Statistics)

Abstract

In this paper the classical Solow model is extended, by considering spatial dependence of the physical capital and population dynamics, and by introducing a nonconcave production function. The physical capital and population evolution equations are governed by semilinear parabolic differential equations which describe their evolution over time and space. The convergence to a steady state according to different hypotheses on the production function is discussed. The analysis is focused on an S-shaped production function, which allows the existence of saddle points and poverty traps. The evolution of this system over time, and its convergence to the steady state is described mainly through numerical simulations.

Suggested Citation

  • Vincenzo Capasso & Ralf Engbers & Davide La Torre, 2012. "Population dynamics in a spatial Solow model with a convex-concave production function," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 61-68, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2342-0_8
    DOI: 10.1007/978-88-470-2342-0_8
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