Existence and uniqueness of Arrow-Debreu equilibria with consumptions in $\mathbf{L}^0_+$

TL;DR

This paper establishes necessary and sufficient conditions for the existence and uniqueness of Arrow-Debreu equilibria in an economy where agents' consumptions are modeled as non-negative measurable functions, extending previous results to a broader setting.

Contribution

It extends the theory of Arrow-Debreu equilibria to economies with consumption sets in ^0_+, providing necessary and sufficient conditions for existence and uniqueness.

Findings

Conditions for existence are necessary and sufficient.

Extended Arrow-Debreu equilibrium results to ^0_+ setting.

Confirmed uniqueness under specified conditions.

Abstract

We consider an economy where agents' consumption sets are given by the cone $\mathbf{L}^0_+$ of non-negative measurable functions and whose preferences are defined by additive utilities satisfying the Inada conditions. We extend to this setting the results in \citet{Dana:93} on the existence and uniqueness of Arrow-Debreu equilibria. In the case of existence, our conditions are necessary and sufficient.