Existence and local indeterminacy of periodic equilibrium paths in infinite horizon models with external effects

It is expected that every periodic equilibrium path may exist even under st andard assumptions such as low discounting and the concavity of utility fun ctions in infinite horizon models with external effects. Nevertheless, unti l now no such example has been presented. In this note we will first constr uct a bounded growth model that has an external effect and every periodic e quilibrium path under any discount factor. Next we will study the condition s under which periodic equilibrium paths have a local indeterminacy.