The unit root property and optimality with a continuum of states—Pure exchange

Abstract

We study general one good pure exchange stochastic overlapping generations economies with stationary Markovian uncertainty and a continuum of states for the Markov process. We show that a unit root property provides a complete characterization of the optimality properties of stationary equilibrium allocations when markets are sequentially complete and the welfare criterion is conditional Pareto optimality.

Do not Blame Bellman: It Is Koopmans' Fault

“…22 Importantly, even for linear operators, we are not aware of any Perron–Frobenius theorem suitable for our analysis, except under certain restrictive assumptions (e.g., in the recent economic literature, Chattopadhyay (2018, Section 3) and Christensen (2017, Section 2.3)). Therefore, the spectral radius might not be an eigenvalue of the operator.…”