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Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

Author

Listed:
  • Serena Brianzoni

    (Università Politecnica delle Marche)

  • Cristiana Mammana

    (Università di Macerata)

  • Elisabetta Michetti

    (Università di Macerata)

Abstract

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas (2000) while assuming a nonconcave production function in the form given by Capasso et. al. (2010). We prove that complex features are exhibited related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions (see, for instance, Brianzoni et al. (2007) (2009) and (2011)).

Suggested Citation

  • 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.
    • Handle: RePEc:mcr:wpdief:wpaper00070
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    References listed on IDEAS

    as
    1. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    2. Claude Diebolt & Catherine Kyrtsou, 2005. "New Trends in Macroeconomics," Post-Print hal-00279607, HAL.
    3. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2009. "Nonlinear dynamics in a business-cycle model with logistic population growth," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 717-730.
    4. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    5. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2012. "Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 98-108.
    6. Luigi L. Pasinetti, 1962. "Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 267-279.
    7. 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.
    8. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    9. 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.
    10. Claude Diebolt & Catherine Kyrtsou (ed.), 2005. "New Trends in Macroeconomics," Springer Books, Springer, number 978-3-540-28556-4, September.
    11. Takashi Kamihigashi & Santanu Roy, 2006. "Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 325-340, October.
    12. 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.
    13. Giannis Karagiannis & Theodore Palivos & Chris Papageorgiou, 2005. "Variable Elasticity of Substitution and Economic Growth: Theory and Evidence," Springer Books, in: Claude Diebolt & Catherine Kyrtsou (ed.), New Trends in Macroeconomics, pages 21-37, Springer.
    14. Robert A. Becker, 2006. "Equilibrium Dynamics with Many Agents," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 13, pages 385-442, Springer.
    15. Winford H. Masanjala & Chris Papageorgiou, 2004. "The Solow model with CES technology: nonlinearities and parameter heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 171-201.
    16. Olivier de La Grandville & Rainer Klump, 2000. "Economic Growth and the Elasticity of Substitution: Two Theorems and Some Suggestions," American Economic Review, American Economic Association, vol. 90(1), pages 282-291, March.
    17. Paul A. Samuelson & Franco Modigliani, 1966. "The Pasinetti Paradox in Neoclassical and More General Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 33(4), pages 269-301.
    18. Mukul Majumdar & Tapan Mitra, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 143-151.
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    3. Grassetti, Francesca & Mammana, Cristiana & Michetti, Elisabetta, 2018. "Substitutability between production factors and growth. An analysis using VES production functions," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 53-62.
    4. Francesca Grassetti & Cristiana Mammana & Elisabetta Michetti, 2018. "Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 145-162, November.

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