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

Listed author(s):
  • 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.

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Paper provided by Macerata University, Department of Finance and Economic Sciences in its series Working Papers with number 35-2006.

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Length: 22
Date of creation: Oct 2006
Date of revision: Oct 2008
Publication status: Forthcoming in AMSE periodicals, Modelling Measurement and Control.
Handle: RePEc:mcr:wpdief:wpaper00035
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  1. Swan, Trevor W, 2002. "Economic Growth," The Economic Record, The Economic Society of Australia, vol. 78(243), pages 375-380, December.
  2. Stiglitz, Joseph E, 1969. "Distribution of Income and Wealth among Individuals," Econometrica, Econometric Society, vol. 37(3), pages 382-397, July.
  3. 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.
  4. 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.
  5. 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.
  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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