Optimal growth theory as it stands today does not work. Using strictly concave utility functions systematically inflicts on the economy distortions that are either historically unobserved or unacceptable by society. Moreover, we show that the traditional approach is incompatible with competitive equilibrium: Any economy initially in such equilibrium will always veer away into unwanted trajectories if its investment is planned using a concave utility function. We then propose a rule for the optimal savings-investment rate based on competitive equilibrium that simultaneously generates three intertemporal optima for society. The rule always leads to reasonable time paths for all central economic variables, even under very different hypotheses about the future evolution of population and technical progress.
