Existence and efficiency of equilibrium in infinite economies with finite aggregate wealth
The author considers an exchange economy with infinitely many consumers and with finite aggregate wealth. His goal is to obtain some generalization of known results of existence and efficiency of an equilibrium in such an economy which were created earlier by Aliprantis, Brown and Burkinshaw (1990) also by Wilson (1981) and others. The consumer set of the used economy model is countable and the commodity space is an abstract vector lattice \(E\). The commodity-price dual space \((E, E')\) is a symmetric Riesz dual system. Consumers' preferences are incomplete and intransitive in common. The main assumption of the paper is the existence of a finite set of agents who own a positive portion of the aggregate endowment. Another author's novelty is the notion of forward properness of consumer's preference relation. This notion is some weakness of the uniformly properness one that having used earlier by another authors. The main results are presented in eight statements. The most general of them (theorem 1) is the weakly Pareto optimality of a competitive equilibrium (the notion is introduced). The first welfare theorem is stated for complete, transitive and strictly convex preferences. Other results present conditions (from given above and others) under which the economy has an individually rational Pareto optimal allocation, a quasiequilibrium and when any weakly Pareto optimal commodity allocation can be supported by a price (second welfare theorem). At last, the economy with consumers' preferences presented by stochastic differential utility (introduced by Duffi and Epstein, 1992) is investigated.
scientific article; zbMATH DE number 1439923