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Multi-Product Supply Function Equilibria

Author

Listed:
  • Holmberg, Pär

    (Research Institute of Industrial Economics (IFN))

  • Ruddell, Keith

    (Research Institute of Industrial Economics (IFN))

  • Willems, Bert

    (LIDAM, UCLouvain;)

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 eigenval ues summarize fundamental market properties, remain invariant under bundling, and lend themselves to comparative statics analysis.

Suggested Citation

  • Holmberg, Pär & Ruddell, Keith & Willems, Bert, 2025. "Multi-Product Supply Function Equilibria," Working Paper Series 1537, Research Institute of Industrial Economics.
    • Handle: RePEc:hhs:iuiwop:1537
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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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