Existence of Monetary Equilibrium for Overlapping Generations Economies with Satiated Agents

This paper treats a general equilibrium existence problem on overlapping generations (OLG) economies with satiated agents and fiat money. The setting is important because it allows the analysis to incorporate Pareto optimality problems of the type where the value functions do not necessarily converge. For example, this is the case for optimal allocations such as a basic income under a budget deficit, which can only be realized with policies that require non-negative wealth transfers for all agents. Because of the existence of satiated agents, our argument can be identified with a dividend equilibrium (Aumann and Dreze 1986) or an equilibrium with slack (Mas-Colell 1992). For OLG settings, however, some conditions (like arguments for strictly positive endowments, resource relatedness and minimum wealth conditions with negative prices, and limit arguments for dividends) must be reconsidered. We note that by considering the OLG framework together with satiated agents, not only can the existence of a monetary equilibrium be assumed in advance, but the existence of a monetary equilibrium based on an arbitrary money supply is guaranteed. Taking into account that our setting includes production (without discount factor), the model here provides a basis for a wide range of difficult problems, including the player’s (equilibrium-dependent) survival problem, multi-sectoral capital accumulation, bequests, firm formation, and so on.