Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models

Alain Venditti (1)

1 AMSE - Aix-Marseille Sciences Economiques

We study the existence of endogenous competitive equilibrium cycles under small discounting in a two-sector discrete-time optimal growth model. We provide precise concavity conditions on the indirect utility function leading to the existence of period-two cycles with a critical value for the discount factor that can be arbitrarily close to one. Contrary to the continuous-time case where the existence of periodic-cycles is obtained if the degree of concavity is close to zero, we show that in a discrete-time setting the driving condition does not require a close to zero degree of concavity but a symmetry of the indirect utility function’s concavity properties with respect to its two arguments.

Mots clés: period-two cycles; small discounting; strong and weak concavity; two-sector optimal growth model

Domaines: Economies et finances

Alain Venditti. Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models. Studies in Nonlinear Dynamics and Econometrics, 2019, 23 (4), pp.20190021. ⟨10.1515/snde-2019-0021⟩. ⟨hal-02352979⟩