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Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving

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  • Brianzoni, Serena
  • Mammana, Cristiana
  • Michetti, Elisabetta

Abstract

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas [4] while assuming VES production function in the form given by Revankar [24]. It is shown that the model can exhibit unbounded endogenous growth despite the absence of exogenous technical change and the presence of non-reproducible factors if the elasticity of substitution is greater than one. We then consider parameters range related to non-trivial dynamics (i.e. the elasticity of substitution in less than one and shareholders save more than workers) and we focus on local and global bifurcations causing the transition to more and more complex asymptotic dynamics. In particular, as our map is non-differentiable in a subset of the states space, we show that border collision bifurcations occur. Several numerical simulations support the analysis.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:1:p:98-108
    DOI: 10.1016/j.chaos.2011.10.004
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    2. 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.
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    1. 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.
    2. 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.
    3. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    4. Nguyen Ngoc Thach, 2020. "Macroeconomic Growth in Vietnam Transitioned to Market: An Unrestricted VES Framework," Economies, MDPI, vol. 8(3), pages 1-15, July.

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