Non-existence of optimal programs for undiscounted growth models in continuous time

Giorgio Fabbri (1) , Silvia Faggian (2) , Giuseppe Freni (3)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 University of Ca’ Foscari [Venice, Italy]
3 Department of Business and Economics, Parthenope University of Naples

We report an example of a two-dimensional undiscounted convex optimal growth model in continuous time in which, although there is a unique “golden rule”, no overtaking optimal solutions exists in a full neighborhood of the steady state. The example proves, for optimal growth models, a conjecture advanced in 1976 by Brock and Haurie that the minimum dimension for non-existence of overtaking optimal programs in continuous time is 2.

Keywords: Optimal Growth; Overtaking; Continuous time models

Domains: Humanities and Social Sciences; Humanities and Social Sciences; Economics and Finance

Giorgio Fabbri, Silvia Faggian, Giuseppe Freni. Non-existence of optimal programs for undiscounted growth models in continuous time. Economics Letters, 2017, 152 (C), pp.57--61. ⟨10.1016/j.econlet.2016.12.022⟩. ⟨hal-01590006⟩