On the Phelps-Koopmans Theorem

We examine whether the Phelps-Koopmans theorem is valid in models with nonconvex production technologies. We show by example that a nonstationary path that converges to a capital stock above the smallest golden rule may indeed be efficient. This finding has the important implication that "capital overaccumulation" need not always imply inefficiency. We provide general conditions on the production function under which all paths that have a limit in excess of the smallest golden rule must be efficient, which proves a version of the theorem in the nonconvex case. Finally, we show by example that a nonconvergent path with limiting capital stocks bounded above (and away from) the smallest golden rule can be efficient, even if the model admits a unique golden rule. Thus the Phelps-Koopmans theorem in its general form fails to be valid.