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Multi-Product Supply Function Equilibria

Author

Listed:
  • Pär Holmberg

    (CAM - University of Cambridge [Cambridge, UK])

  • Keith Ruddell

    (IFN - Research Institute of Industrial Economics)

  • Bert Willems

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We characterize Nash equilibria in multi-product markets in which producers commit to vectors of supply functions contingent on all prices. The framework accommodates (dis)economies of scope in production, and goods may be substitutes or complements in demand. We show that equilibrium allocations of underlying goods and payoffs are invariant under bundling. With quadratic costs and linear demand, this invariance reduces the multi-product problem to an equivalent set of single-product markets that can be analyzed independently. We introduce Lerner and pass-through matrices to capture markups and welfare losses; their eigenvalues summarize fundamental market properties, remain invariant under bundling, and lend themselves to comparative statics analysis.

Suggested Citation

  • Pär Holmberg & Keith Ruddell & Bert Willems, 2025. "Multi-Product Supply Function Equilibria," Working Papers hal-05294356, HAL.
    • Handle: RePEc:hal:wpaper:hal-05294356
    Note: View the original document on HAL open archive server: https://hal.science/hal-05294356v1
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    Cited by:

    1. is not listed on IDEAS
    2. Matteo Bizzarri, 2025. "General equilibrium with competition in schedules and input-output networks: an existence result," CSEF Working Papers 765, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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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
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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