The existence of optimal consumption policies in optimal economic growth models with nonconvex technologies

An existence theorem for a class of continuous time infinite horizon optimal growth models is developed. The underlying technology set is not assumed to be convex, instead the “slices” of the technology set corresponding to a fixed capital stock vector are assumed convex and compact in the consumption and net investment variables. This allows consideration of the case of increasing returns to scale. Existence of an optimal capital stock and consumption policy is proved directly without consideration of the underlying Hamiltonian dynamical system that arises from applying Pontryagin's maximum principle.