A multidimensional, nonconvex model of optimal growth
Résumé
In this article, we consider a multidimensional economy where the standard
supermodularity property fails. We generalize the notion of net gain of
investment, introduced by Kamihigashi and Roy \cite{KR2007} and applied to
one-sector growth models, to the case of multiple capital stocks. We prove
the convergence to the set of steady states without relying on the
monotonicity of the optimal path. Our approach differs from the standard dynamic
programming based on convexity or supermodularity. We find that preferences
are key to shaping the economy in the long run.
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