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Monotone Comparative Statics for Equilibrium Problems

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Alfred Galichon & Larry Samuelson & Lucas Vernet, 2022. "Monotone Comparative Statics for Equilibrium Problems," SciencePo Working papers Main hal-03936102, HAL.
    • Handle: RePEc:hal:spmain:hal-03936102
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03936102
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    References listed on IDEAS

    as
    1. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    2. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    3. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    4. Howitt, Peter, 1980. "Gross Substitutability with Multi-Valued Excess Demand Functions," Econometrica, Econometric Society, vol. 48(6), pages 1567-1573, September.
    5. Georg Nöldeke & Larry Samuelson, 2018. "The Implementation Duality," Econometrica, Econometric Society, vol. 86(4), pages 1283-1324, July.
    6. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    7. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    8. repec:dau:papers:123456789/6486 is not listed on IDEAS
    9. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
    10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    11. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    12. Polterovich, V. M. & Spivak, V. A., 1983. "Gross substitutability of point-to-set correspondences," Journal of Mathematical Economics, Elsevier, vol. 11(2), pages 117-140, April.
    13. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    14. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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