Monotone Comparative Statics for Equilibrium Problems

TL;DR

This paper introduces a unified framework for monotone comparative statics in equilibrium problems using new notions of substitutability, demonstrating broad applicability across demand systems, matching games, and supply correspondences.

Contribution

It develops the concepts of 'unified gross substitutes' and 'nonreversingness' to generalize monotone comparative static results across various economic models.

Findings

Supply correspondences satisfying the new properties have increasing solution sets.

The framework unifies several classical results in economic theory.

The set of equilibrium prices forms a sublattice under the proposed conditions.

Abstract

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result, unifying results such as the inverse isotonicity of M-matrices, Berry, Gandhi and Haile's identification of demand systems, monotone comparative statics, and results on the structure of the core of matching games without transfers (Gale and Shapley) and with transfers (Demange and Gale). More specifically, we introduce the notions of 'unified gross substitutes' and 'nonreversingness' and show that if Q is a supply correspondence defined on a set of prices P which is a sublattice of R^N, and Q satisfies these two properties, then the set of prices yielding supply vector q is increasing (in the strong set order) in q; and it is a sublattice of P.