Teorema de punto fijo de Brouwer en topología y su aplicación en el análisis de la existencia de distribuciones de equilibrio de precios en una economía de intercambio puro

Abstract

The microeconomics branch of general equilibrium theory attempts to provide a comprehensive explanation of the behavior of production, consumption and pricing in an economy with one or more markets. To achieve equilibrium, consumer preferences must be continuous, cumulative, and integrated, so it often relies on fixed-point theory, such as Brouwer’s fixed-point theory, to prove the existence of equilibrium. The aim of this degree work was to study Brouwer’s fixed point theorem in topology and its usefulness in the analysis of the existence of equilibrium price distributions in a pure exchange economy. The research is of documentary design with descriptive character and non-interactive qualitative approach that generated the referential document of the subject. This document contains selected topics of Topology to demonstrate the theorem, to continue with the application in the area of economics. Here, we can realize that the theorem is used to prove the existence of equilibrium price distributions, in other words, there is an equilibrium. It is recommended to extend the study, because the demonstration guarantees the existence of an equilibrium, but it does not guarantee the way to find it.