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.
NON-EXISTENCE OF OPTIMAL PROGRAMS FOR UNDISCOUNTED GROWTH MODELS IN CONTINUOUS TIME
FAGGIAN, Silvia;
2017
Abstract
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.
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