• Corpus ID: 250526154

Monotone Comparative Statics for Equilibrium Problems

@inproceedings{Galichon2022MonotoneCS,
  title={Monotone Comparative Statics for Equilibrium Problems},
  author={Alfred Galichon and Larry Samuelson and Lucas Vernet},
  year={2022}
}

• Alfred Galichon, L. Samuelson, Lucas Vernet
• Published 14 July 2022
• Economics

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 , 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 . †Economics Department, FAS, and Mathematics Department, Courant Institute, New York University; and Economics Department, Sciences Po. Email: [e-mail]. Galichon gratefully acknowledges funding from NSF grant DMS1716489 and ERC grant CoG-866274. [Department of Economics, Yale University. Email: [e-mail]. §Economics Department, Sciences Po, and Banque de France. Email: [e-mail]. ar X iv :2 20 7. 06 73 1v 1 [ ec on .T H ] 1 4 Ju l 2 02 2