Can stabilization policies be efficient?

This paper makes use of optimal control relaxed problems to prove the absence of optimal trajectory in continuous time models with social increasing returns to scale where indeterminacy occurs. Although an efficient optimal policy does not exist, some chattering stabilization policies can mimic trajectories whose criterion functional approximates the supremum of the relaxed problem. This configuration is closely related to indeterminacy: by contrast, when the steady state is determined, an optimal policy is likely to exist.