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Closed form solutions to a generalization of the Solow growth model


  • Erick José Limas Maldonado

    (Universidad Autónoma de Ciudad Juárez, México.)

  • Juan Gabriel Brida

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


The Solow growth model assumes that labor force grows exponentially. This is not a realistic assumption because, exponential growth implies that population increases to infinity as time tends to infinity. In this paper we propose replacing the exponential population growth with a simple and more realistic equation - the Von Bertalanffy model. This model utilizes three hypotheses about human population growth: (1) when population size is small, growth is exponential; (2) population is bounded; and (3) the rate of population growth decreases to zero as time tends toward infinity. After making this substitution, the generalized Solow model is then solved in closed form, demonstrating that the intrinsic rate of population growth does not influence the long-run equilibrium level of capital per worker. We also study the revised model's stability, comparing it with that of the classical model.

Suggested Citation

  • Erick José Limas Maldonado & Juan Gabriel Brida, 2005. "Closed form solutions to a generalization of the Solow growth model," GE, Growth, Math methods 0510003, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:0510003
    Note: Type of Document - pdf; pages: 8

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    1. repec:ebl:ecbull:v:10:y:2004:i:6:p:1-6 is not listed on IDEAS
    2. Andreas Irmen, 2004. "Malthus and Solow - a note on closed-form solutions," Economics Bulletin, AccessEcon, vol. 10(6), pages 1-6.
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    Cited by:

    1. Juan Sebastián Pereyra & Juan Gabriel Brida, 2008. "The Solow model in discrete time and decreasing population growth rate," Economics Bulletin, AccessEcon, vol. 3(41), pages 1-14.

    More about this item


    Solow growth model; population growth;

    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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