# Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences

## TL;DR

This paper proves the existence of a competitive equilibrium in a complex production economy with infinitely many commodities and agents, using advanced mathematical tools in infinite dimensional spaces.

## Contribution

It introduces a novel approach employing saturated measure spaces and recent infinite dimensional analysis results to establish equilibrium existence.

## Key findings

- Existence of competitive equilibrium in infinite commodity spaces.
- Application of Lyapunov's convexity theorem in this context.
- Use of an exact Fatou's lemma for infinite dimensional spaces.

## Abstract

We prove the existence of a competitive equilibrium in a production economy with infinitely many commodities and a measure space of agents whose preferences are price dependent. We employ a saturated measure space for the set of agents and apply recent results for an infinite dimensional separable Banach space such as Lyapunov's convexity theorem and an exact Fatou's lemma to obtain the result.