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The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects

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  • Elizabeth Baldwin
  • Paul Klemperer
  • Alex Teytelboym
  • Omer Edhan Ravi Jagadeesan

Abstract

We show that, with indivisible goods,the existence of competitive equilibrium fundamentally depends on agents’substitution effects, not their income effects. Our Equilibrium ExistenceDuality allows us to transport results on the existence of competitiveequilibrium from settings with transferable utility to settings with incomeeffects. One consequence is that netsubstitutability—which is a strictlyweaker condition than gross substitutability—is sufficient for the existence ofcompetitive equilibrium. We also extend the “demand types†classification ofvaluations to settings with income effects and give necessary and sufficientconditions for a pattern of substitution effects to guarantee the existence ofcompetitive equilibrium.

Suggested Citation

  • Elizabeth Baldwin & Paul Klemperer & Alex Teytelboym & Omer Edhan Ravi Jagadeesan, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Economics Series Working Papers 912, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:912
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    References listed on IDEAS

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    Cited by:

    1. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    2. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    3. P. Jean‐Jacques Herings & Yu Zhou, 2022. "Competitive Equilibria In Matching Models With Financial Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 777-802, May.
    4. Ahmadzadeh, Amirreza & Kamali-Shahdadi, Behrang, 2023. "Matching Unskilled/Skilled Workers to Firms Facing Budget Constraints," TSE Working Papers 23-1446, Toulouse School of Economics (TSE).
    5. Edward E. Schlee & M. Ali Khan, 2022. "Money Metrics In Applied Welfare Analysis: A Saddlepoint Rehabilitation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 189-210, February.

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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