A note on the existence of monetary equilibrium in a stochastic OLG model with a finite state space

The present paper provides a simple and complete proof of the existence of a stationary monetary equilibrium for a stochastic overlapping generations model with a finite state space. Differently from previous studies, we show that all the prices are positive without the Frobenius theorem.Stochastic overlapping generations model, Stationary monetary equilibrium, Existence, Fixed-point theorem, Frobenius theorem.

Optimality under Demographic Shocks

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TCER Working Paper Series GOLDEN RULE OPTIMALITY IN STOCHASTIC OLG ECONOMIES Golden Rule Optimality in Stochastic OLG Economies

Abstract This study examines conditional golden rule optimality (CGRO) in stochastic overlapping generations models to complement the existing results on conditional Pareto optimality (CPO). Although an example in which CPO implies CGRO is presented, it is shown that such a situation is avoidable under strictly convex preferences. Under such preferences, both CPO and CGRO are characterized by the conditions on the dominant root for the agents' common matrix of marginal rates of substitution. We demonstrate that CGRO requires the dominant root being exactly equal to one, whereas CPO allows it to be less than one. By adopting CGRO rather than CPO,we provide welfare theorems in the financial economy. Abstract: This study examines conditional golden rule optimality (CGRO) in stochastic overlapping generations models to complement the existing results on conditional Pareto optimality (CPO). Although an example in which CPO implies CGRO is presented, it is shown that such a situation is avoidable under strictly convex preferences. Under such preferences, both CPO and CGRO are characterized by the conditions on the dominant root for the agents' common matrix of marginal rates of substitution. We demonstrate that CGRO requires the dominant root being exactly equal to one, whereas CPO allows it to be less than one. By adopting CGRO rather than CPO, we provide welfare theorems in the financial economy

TCER Working Paper Series EXISTENCE AND UNIQUENESS OF STATIONARY MONETARY EQUILIBRIUM: A SIMPLE PROOF Existence and Uniqueness of Stationary Monetary Equilibrium: A Simple Proof

Abstract This article provides a direct and simple proof of the equivalency between the existence of stationary monetary equilibrium and the conditional Pareto suboptimality of the initial endowment in a stochastic overlapping generations model. Further, the uniqueness of the equilibrium is demonstrated. Abstract: This article provides a direct and simple proof of the equivalency between the existence of stationary monetary equilibrium and the conditional Pareto suboptimality of the initial endowment in a stochastic overlapping generations model. Further, the uniqueness of the equilibrium is demonstrated. Eise

Nominal Idiosyncratic Shocks and Optimal Monetary Policy

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