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Local indeterminacy in continuous-time models: the role of returns to scale

Author

Listed:
  • Jean-Philippe Garnier

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Kazuo Nishimura

    (Kyoto University)

  • Alain Venditti

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

The aim of this paper is to discuss the role of the returns to scale at the private and social levels on the local determinacy properties of the steady state in a continuous-time two-sector economy with sector-specific externalities. First we show that when labor is inelastic, for any configuration of the returns to scale, local indeterminacy is obtained if there is a capital intensity reversal between the private and the social levels. Second, we prove that when labor is infinitely elastic, saddle-point stability is obtained as soon as the investment good sector has constant social returns while local indeterminacy arises if the investment good sector has increasing social returns, provided the consumption good is labor intensive at the social level and the elasticity of intertemporal substitution in consumption admits intermediary values. Finally, we show that local indeterminacy requires a low elasticity of labor when the investment good has constant social returns, but requires either low enough or large enough elasticity of labor when the investment good has increasing social returns.

Suggested Citation

  • Jean-Philippe Garnier & Kazuo Nishimura & Alain Venditti, 2008. "Local indeterminacy in continuous-time models: the role of returns to scale," Working Papers halshs-00281382, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00281382
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00281382
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    Cited by:

    1. Been-Lon Chen & Mei Hsu & Yu-Shan Hsu, 2018. "Progressive taxation and macroeconomic stability in two-sector models with social constant returns," Journal of Economics, Springer, vol. 125(1), pages 51-68, September.
    2. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2016. "Sunspot fluctuations in two-sector models: New results with additively separable preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 67-83, March.
    3. Jean-Philippe Garnier, 2014. "Keeping-up with the Joneses, a new source of endogenous fluctuations," Working Papers hal-01006912, HAL.
    4. Carmelo Pierpaolo Parello, 2021. "Free labor mobility and indeterminacy in models of neoclassical growth," Journal of Economics, Springer, vol. 133(1), pages 27-46, June.
    5. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2013. "Indeterminacy and Sunspot Fluctuations in Two-Sector RBC models: Theory and Calibration," Working Papers halshs-00796703, HAL.
    6. Jang-Ting Guo & Sharon G. Harrison, 2015. "Indeterminacy with Progressive Taxation and Sector-Specific Externalities," Pacific Economic Review, Wiley Blackwell, vol. 20(2), pages 268-281, May.
    7. Nishimura, Kazuo & Venditti, Alain, 2010. "Indeterminacy and expectation-driven fluctuations with non-separable preferences," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 46-56, July.

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