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Endogenous cycles with small discounting in multisector optimal growth models: Continuous-time case

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Abstract

This paper discusses the role of the trade-off between the level of discounting and the curvature of preferences and technology in establishing the existence of endogenous cycles. Using the equivalence between the Euler-Lagrange equations and a modified Hamiltonian dynamic system, in a general continuous-time multisector optimal growth model, it is proved that, if the indirect utility function is weakly concave (i.e., concave-γ, with γ>0 arbitrarily close to 0), then the discount rate values compatible with endogenous fluctuations are arbitrarily low. We show by numerical simulations that our result explains and generalizes to the multisector case the recent contribution of Benhabib and Rustichini in this field.

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Authors and Affiliations

  1. Groupement de Recherche en Economie Quantitative d'Aix-Marseille, Université d'Aix-Marseille II, Marseille, France

    A. Venditti (Teaching Assistant)

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  1. A. Venditti
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Communicated by G. Leitmann

The author would like to thank P. Cartigny, J. M. Grandmont, P. Michel, and L. Montrucchio for helpful discussions which greatly improved the exposition of the paper. He is also indebted to G. Sorger for a fruitful discussion which clarified some recent contributions. The paper also benefited from comments received during a presentation at the Meeting of the Society for Economic Dynamics and Control, University of California, Los Angeles, California, 1994.

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Venditti, A. Endogenous cycles with small discounting in multisector optimal growth models: Continuous-time case. J Optim Theory Appl 88, 453–474 (1996). https://doi.org/10.1007/BF02192180

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