PERIODIC SOLUTIONS AS FIRST-BEST PATHS IN THE AGGREGATIVE MODEL OF GROWTH

The present paper studies first-best solutions to the aggregative model of growth with externalities. Pareto-efficient accumulation paths are the result of policy measures that correct externalities. We show that there exist non-constant periodic solutions as a subclass of first-best paths. In particular, we prove the occurrence of a Hopf bifurcation for optimal paths of the deterministic aggregative model. The result may seem at odds with conventional wisdom according to which application of Bendixson's criterion implies the impossibility of orbiting in the planar system for optimal state and costate variables. We show that this argument need not hold when optimal policy changes investment behavior in a Pareto-efficient manner. Thus, conservative dynamics displaying perpetual fluctuations in both capital and supporting prices may be the result of optimal policy.