Equilibrium in dynamic models with an infinity of agents
In this paper, I investigate the existence of a competitive equilibrium in a dynamic model of pure exchange with a countable number of agents and a countable number of goods. The assumptions I employ are of the same level of generality as those generally used to establish the existence of equilibrium in classical competitive models. The commodity space is represented by the set of all non-negative sequences which contains the endowment of each agent. The preferences of each agent are assumed to satisfy a convexity requirement and to be continuous in the product topology.There is free disposal and the economy must satisfy a certain resource relatedness condition. Under these assumptions, I then establish the existence of a competitive equilibrium in two special cases: (1) when the endowment of each agent is positive for only a finite number of goods; (2) when the aggregate endowment of some finite subset of agents is greater than some fixed fraction of the economy-wide endowment in each period. In all other cases, the most that I can establish is the existence of a special kind of equilibrium with transfer payments. Specifically, I show that a set of market clearing prices will exist if we permit those agents endowed with a positive quantity of an infinite number of goods to augment the value of their endowment by a finite non-negative amount. The existence of a competitive equilibrium when there is only a finite set of agents has already been demonstrated by Bewley [3].’ Recently Balasko and Shell [ 1 ] and Balasko et al., [2] have established the same result for pure exchange economies composed of an infinite number of finite-lived agents. Although the assumptions which I adopt in this paper are not quite as general in every respect as the assumptions used by either of these authors, it is possible to modify my assumptions so that the theorem demonstrated here implies both Bewley’s theorem (for discrete-good, pure-