Del Teorema de Debreu y Algunas Consecuencias

Abstract

In this paper, theoretical concepts about utility theory and order or topological density are presented. Reconstructing the article "Ordered topological spaces and the theorems of Debreu and Peleg" presents the definitions of preference relation, utility function, density of order, topological density, among others; this is done in order to build and characterize new topological spaces that are assembled with the preferred relation to achieve represent any preference by means of a utility function. For this, two propositions given in the article are shown and examined, and equivalences are constructed between the different types of densities. Subsequently, based on the article "Ordered topological spaces and utility functions", the demonstrations of Debreu's two theorems that guarantee the existence of a utility function for a given preference are given. Finally, in chapter 5, three examples are presented for this theory: two of preferences with their respective utility function and the well-known example of Cobb-Douglas type symmetric preferences. Additional examples of each of these preferences are presented in a more realistic context.