Dominant root characterization of Pareto optimality and the existence of optimal equilibria in stochastic overlapping generations models

We characterize Pareto optimality of interior stationary allocations in single-good overlapping generations models with stochastic aggregate shocks and heterogeneous but recurring generations. An interior stationary allocation is Pareto optimal if and only if it is an equilibrium allocation and the associated contingent claims price matrix has a dominant root less than or equal to unity. We then use this characterization to show that there always exists an optimal equilibrium with or without valued fiat money.