Existence of Equilibrium Prices: A Pedagogical Proof
Simone Tonin

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).
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Taxonomy
TopicsEconomic theories and models
