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The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects

Author

Listed:
  • Elizabeth Badlwin

    (Dept of Economics and Hertford College, University of Oxford)

  • Omer Edhan

    (Department of Economics, University of Manchester)

  • Ravi Jagadeesan

    (Harvard Business School and Department of Economics, Harvard University)

  • Paul Klemperer

    (Department of Economics and Nuffield College, University of Oxford)

  • Alexander Teytelboym

    (Department of Economics, Institute for New Economic Thinking, and St. Catherine’s College, University of Oxford)

Abstract
We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents’ substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability—which is a strictly weaker condition than gross substitutability—is sufficient for the existence of competitive equilibrium. We also extend the “demand types” classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium. JEL codes: C62, D11, D44

Suggested Citation

  • Elizabeth Badlwin & Omer Edhan & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Economics Papers 2020-W08, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:2008
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    References listed on IDEAS

    as
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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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    More about this item

    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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