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Global attractor in Solow growth model with differential savings and endogenic labor force growth


  • Serena Brianzoni,

    (University of Macerata)

  • Cristiana Mammana,

    (University of Macerata)

  • Elisabetta Michetti,

    (University of Macerata)


In this paper we study the dynamics of a discrete triangular system T in capital per capita and population growth representing the neoclassical growth model with CES production function and differential savings, under the assumption that the labor force growth rate is endogenous and described by a generic iterative scheme having a unique positive globally stable equilibrium. The study herewith presented aims at confirming the existence of a compact global attractor for system T along the invariant line. Consequently asymptotic dynamics of growth models with constant population growth rate can be related to those with non-constant population growth if the steady state rate is globally stable. Furthermore we prove that the system exhibits cycles or even chaotic dynamics patterns if shareholders save more than workers, when the elasticity of substitution between production factors drops below one (so that capital income declines). The analytical results are supplemented by numerical simulations.

Suggested Citation

  • 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.
  • Handle: RePEc:mcr:wpdief:wpaper00035

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    References listed on IDEAS

    1. Stiglitz, Joseph E, 1969. "Distribution of Income and Wealth among Individuals," Econometrica, Econometric Society, vol. 37(3), pages 382-397, July.
    2. Brianzoni Serena & Mammana Cristiana & Michetti Elisabetta, 2007. "Complex Dynamics in the Neoclassical Growth Model with Differential Savings and Non-Constant Labor Force Growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-19, September.
    3. Becker, Robert A & Foias, Ciprian, 1994. "The Local Bifurcation of Ramsey Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 719-744, August.
    4. Swan, Trevor W, 2002. "Economic Growth," The Economic Record, The Economic Society of Australia, vol. 78(243), pages 375-380, December.
    5. Bohm, Volker & Kaas, Leo, 2000. "Differential savings, factor shares, and endogenous growth cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 965-980, June.
    6. 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.
    7. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
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    Cited by:

    1. David Cheban & Cristiana Mammana & Elisabetta Michetti, 2012. "Non-Autonomous Difference Equations: Global Attractor in a Business-Cycle Model with Endogenous Population Growth," Working Papers 69-2012, Macerata University, Department of Finance and Economic Sciences, revised Sep 2015.
    2. Michetti, Elisabetta, 2015. "Complex attractors and basins in a growth model with nonconcave production function and logistic population growth rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 215-232.
    3. Serena Brianzoni & Cristiana Mammana & Elisabetta Michetti, 2012. "Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function," Working Papers 70-2012, Macerata University, Department of Finance and Economic Sciences, revised Sep 2015.

    More about this item


    chaotic dynamics; Compact global attractor; Developing Countries; endogenic population growth.;

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