Existence of Equilibria in Large Competitive Markets with Bads, Production and Comprehensive Externalities

TL;DR

This paper proves the existence of equilibrium in large markets with bads, production, and externalities, overcoming previous counterexamples by establishing bounds through nonstandard analysis techniques.

Contribution

It introduces a novel existence proof for equilibria in economies with bads and externalities, using nonstandard analysis and new methods for handling externalities.

Findings

Existence of equilibrium established under complex market conditions.

Bounded consumption of bads ensured by economic considerations.

Novel methodological tools for externalities are developed.

Abstract

This paper establishes the existence of equilibrium in an economy with production and a continuum of consumers, each of whose incomplete and price-dependent preferences are defined on commodities they may consider deleterious, bads which cannot be freely disposed of, and each of whom takes into account the productions of all firms and the consumptions of all other consumers. This result has proved elusive since Hara (2005) presented an example of an atomless measure-theoretic exchange economy with bads (but no externalities) that has no equilibrium. The result circumvents Hara's example by showing that, in the presence of bads and externalities, natural economic considerations imply an integrable bound on the consumption of bads. The proofs make an essential use of nonstandard analysis, and the novel techniques we offer to handle comprehensive externalities expressed as an equivalence class of integrable functions may be of independent methodological interest.