Existence of Equilibrium Prices: A Pedagogical Proof

TL;DR

This paper provides a concise and accessible proof of the existence of equilibrium prices in economic models, utilizing fixed point theorems and specific mathematical techniques.

Contribution

It offers a simplified, pedagogical proof of equilibrium existence based on excess demand functions, expanding on prior mathematical approaches.

Findings

Proof confirms equilibrium prices exist under given assumptions.

Uses Brouwer fixed point theorem on a trimmed simplex.

Builds on mathematical results from Neuefeind and Geanakoplos.

Abstract

Under the same assumptions made by Mas-Colell et al. (1995), I develop a short, simple, and complete proof of existence of equilibrium prices based on excess demand functions. The result is obtained by applying the Brouwer fixed point theorem to a trimmed simplex which does not contain prices equal to zero. The mathematical techniques are based on some results obtained in Neuefeind (1980) and Geanakoplos (2003).