Unified gross substitutes and inverse isotonicity for equilibrium problems

Alfred Galichon (), Larry Samuelson () and Lucas Vernet ()
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Alfred Galichon: Department of Economics, NYU and Sciences Po
Larry Samuelson: Department of Economics, Yale University
Lucas Vernet: Banque de France

Theoretical Economics, Forthcoming

Abstract: We introduce a notion of substitutability for correspondences and establish a monotone comparative static result. More precisely, we introduce the notions of unified gross substitutes and nonreversingness and show that if Q : P ⇒ Q is a supply correspondence defined on a set of prices P which is a sublattice of RN , and Q satisfies these two properties, then the set of equilibrium prices Q−1(q) associated with a vector of quantities q ∈ Q is a sublattice of P and is increasing (in the strong set order) in q. We establish connections between our notion of substitutes and existing notions, and examine applications such as the structure of inverse demand, profit maximization, the structure of competitive equilibria, matching games, hedonic pricing, and routing problems.

Keywords: Substitutes; inverse isotonicity; m-function; correspondence; monotone comparativce statics; equilibrium flow (search for similar items in EconPapers)
JEL-codes: C6 D5 (search for similar items in EconPapers)
Date: 2024-11-25
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