A multidimensional, nonconvex model of optimal growth

Abstract

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 (2007) 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 optimal path. Our approach differs from the standard dynamic programming based on convexity or supermodularity. We find that preferences are key to shape the economy in the long run.