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

2025-11-01

AI Summary

This paper investigates the existence of competitive equilibria in large-scale economies featuring production, harmful commodities (non-free-disposal goods), price-dependent preferences, and global externalities (where each consumer’s utility depends on all firms’ outputs and all consumers’ consumption bundles). Addressing Hara’s (2005) counterexample—demonstrating nonexistence of equilibrium in atomless exchange economies due to harmful goods and inadequate externality modeling—the paper introduces economically natural assumptions and establishes, for the first time, equilibrium existence under simultaneous harmful commodities and strong global externalities. Methodologically, it pioneers a synthesis of nonstandard analysis and measure theory, constructing preference and externality representations via equivalence classes in integral function spaces—thereby circumventing standard approaches’ implicit reliance on free disposal and local externalities. The result provides a rigorous foundational equilibrium theory for real-world markets characterized by pronounced negative externalities and stringent resource constraints.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Establishes equilibrium existence with bads and externalities
• Addresses non-disposable deleterious commodities in competitive markets
• Overcomes Hara's counterexample using integrable consumption bounds

Innovation

• Uses nonstandard analysis for equilibrium proofs
• Handles comprehensive externalities via integrable functions
• Establishes integrable bounds on bads consumption