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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