Monotone Comparative Statics for Equilibrium Problems

Alfred Galichon (), Larry Samuelson () and Lucas Vernet ()
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Alfred Galichon: NYU - New York University [New York] - NYU - NYU System, CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique
Larry Samuelson: Yale University [New Haven]
Lucas Vernet: Centre de recherche de la Banque de France - Banque de France, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique

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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 : P ⇒ 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 equilibrium prices Q −1 (q) associated with a vector of quantities q ∈ Q is increasing (in the strong set order) in q; and it is a sublattice of P .

Date: 2022-07-15
New Economics Papers: this item is included in nep-des and nep-gth
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