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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, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpge:0508006
    Note: Type of Document - pdf; pages: 11
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    References listed on IDEAS

    as
    1. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    2. Oliver, F R, 1969. "Another Generalisation of the Logistic Growth Function," Econometrica, Econometric Society, vol. 37(1), pages 144-147, January.
    3. 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(1), pages 104-110, February.
    4. repec:ebl:ecbull:v:10:y:2004:i:6:p:1-6 is not listed on IDEAS
    5. Costanza, Robert, 1995. "Economic growth, carrying capacity, and the environment," Ecological Economics, Elsevier, vol. 15(2), pages 89-90, November.
    6. 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. Marsiglio, Simone & La Torre, Davide, 2012. "Population dynamics and utilitarian criteria in the Lucas–Uzawa Model," Economic Modelling, Elsevier, vol. 29(4), pages 1197-1204.
    2. 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.
    3. Luis A. Quezada-Téllez & Guillermo Fernández-Anaya & Dominique Brun-Battistini & Benjamín Nuñez-Zavala & Jorge E. Macías-Díaz, 2021. "An Economic Model for OECD Economies with Truncated M -Derivatives: Exact Solutions and Simulations," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    4. Roman G. Smirnov & Kunpeng Wang, 2017. "In search of a new economic model determined by logistic growth," Papers 1711.02625, arXiv.org, revised Oct 2018.

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    More about this item

    Keywords

    Population growth; Solow's growth model; Richards equation.;
    All these keywords.

    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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