Tcer Working Paper Series Golden Rule Optimality in Stochastic Olg Economies

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. Eisei Ohtaki TCER and Faculty of Economics Keio University Mita 2-15-45, Minato-ku, Tokyo 108-8345, Japan [email protected] Golden Rule Optimality in Stochastic OLG Economies Eisei Ohtaki† † Faculty of Economics, Keio university, Mita 2-15-45, Minato-ku, Tokyo 108-8345, Japan email address: [email protected] First Draft: August 30, 2011 Current Draft: June 1, 2012 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. 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.