Transitive Equilibrium of a Finite Dimensional Competitive Economy

Abstract

The Walrasian model of general equilibrium of prices, production and exchange is today formulated in the concept of equilibrium of a so-called private ownership economy. In the classical model, only a finite number of commodities are exchanged, produced or consumed. Taking prices as given, finitely many consumers (who are endowed with initial holdings of the different commodities and who collect given shares of the profits from production), consume the commodities available on the market by optimizing their preferences among all possible consumption plans which satisfy their resulting budget constraint. Finitely many producers, who also take prices as given, maximize their profit on their individual set of possible production plans. They produce the commodities which satisfy consumers’ demand in competition with the initial resources not used by production. Market clearing determines equilibrium prices and the quantities actually consumed and produced at a state of equilibrium.