A complete characterization of optimal growth paths in an aggregated model with a non-concave production function

We use the Principle of Optimality in addition to the Euler equation in order to provide a characterization of optimal one-sector growth for all ranges of interest rates when the technology is not convex. Our key result is that the sequence of capital stocks is necessarily monotonic. For certain interest rates we show that the optimal path converges to a steady state only if the initial capital stock is above a critical level, otherwise it converges to zero. Finally, we demonstrate that the set of points for which the value function is differentiable is precisely the set of initial capital stocks from which there is a unique optimal path.