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Unified gross substitutes and inverse isotonicity for equilibrium problems

Author

Listed:
  • Galichon, Alfred

    (Department of Economics, NYU and Sciences Po)

  • Samuelson, Larry

    (Department of Economics, Yale University)

  • Vernet, Lucas

    (Banque de France)

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.

Suggested Citation

  • Galichon, Alfred & Samuelson, Larry & Vernet, Lucas, 0. "Unified gross substitutes and inverse isotonicity for equilibrium problems," Theoretical Economics, Econometric Society.
    • Handle: RePEc:the:publsh:5686
    as

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Substitutes; inverse isotonicity; m-function; correspondence; monotone comparativce statics; equilibrium flow;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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