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Re-formulation of the Solow economic growth model whit the Richards population growth law

Author

Listed:
  • Elvio Accinelli

    (Universidad Autonoma Metropolitana - Unidad Xochimilco)

  • Juan Gabriel Brida

    (School of Economics & Management - Free University of Bolzano)

Abstract

In standard economic growth theory it is usually assumed that labor force follows exponential growth. That is not a realistic assumption. In this paper we introduce a generalized logistic equation (Richards law) that describes more accurately population growth. Then we analyze the neoclassical Solow model with growth of population following the Richards law, and compares it with the classical model with exponential growth. We show that with the Richards law, the intrinsic rate of population growth plays no role in determining long run equilibrium per worker level of capital. We also present the closed-form solution of the model when the production function is Cobb-Douglas and we analyze the stability of the model, contrasting its long run equilibrium with the steady state of the traditional model.

Suggested Citation

  • Elvio Accinelli & Juan Gabriel Brida, 2005. "Re-formulation of the Solow economic growth model whit the Richards population growth law," GE, Growth, Math methods 0508006, EconWPA.
  • Handle: RePEc:wpa:wuwpge:0508006
    Note: Type of Document - pdf; pages: 11
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0508/0508006.pdf
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    References listed on IDEAS

    as
    1. Oliver, F R, 1969. "Another Generalisation of the Logistic Growth Function," Econometrica, Econometric Society, vol. 37(1), pages 144-147, January.
    2. Arrow, Kenneth & Bolin, Bert & Costanza, Robert & Dasgupta, Partha & Folke, Carl & Holling, C.S. & Jansson, Bengt-Owe & Levin, Simon & Mäler, Karl-Göran & Perrings, Charles & Pimentel, David, 1996. "Economic growth, carrying capacity, and the environment," Environment and Development Economics, Cambridge University Press, vol. 1(01), pages 104-110, February.
    3. repec:ebl:ecbull:v:10:y:2004:i:6:p:1-6 is not listed on IDEAS
    4. Andreas Irmen, 2004. "Malthus and Solow - a note on closed-form solutions," Economics Bulletin, AccessEcon, vol. 10(6), pages 1-6.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Serena Brianzoni, & Cristiana Mammana, & Elisabetta Michetti,, 2006. "Global attractor in Solow growth model with differential savings and endogenic labor force growth," Working Papers 35-2006, Macerata University, Department of Finance and Economic Sciences, revised Oct 2008.
    2. Roman G. Smirnov & Kunpeng Wang, 2017. "Towards a new paradigm for mathematical modelling of growth," Papers 1711.02625, arXiv.org, revised Jan 2018.

    More about this item

    Keywords

    Population growth; Solow's growth model; Richards equation.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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