Dynamic inefficiency in an overlapping generations economy with production

Reichlin [Equilibrium cycles in an overlapping generations economy with production, J. Econ. Theory 40 (1986) 89-102] has shown in an OLG model with productive capital that whenever the steady state is locally indeterminate and undergoes a Hopf bifurcation, it is Pareto-optimal. While these results were established under the assumption of Leontief technology, the author has partially extended them to show that the Hopf bifurcation is robust with respect to the introduction of capital-labor substitution. In this note, we prove that the Pareto-optimality of the steady state does not extend to technologies with capital-labor substitution. When the steady state is a sink or undergoes a Hopf bifurcation, it is characterized by over-accumulation with respect to the Golden Rule-the interest rate is negative-hence not Pareto-optimal. Most importantly, it follows that stabilization policies targeting the steady state leave room for welfare losses associated with productive inefficiency, apart from the very special case of Leontief technology.