Multi-Product Supply Function Equilibria

Pär Holmberg, Keith Ruddell and Bert Willems
Additional contact information
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

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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.

Keywords: Multi-product pricing; Divisible-good auction; Bundling; Pass-through; Welfare; Supply function equilibrium (search for similar items in EconPapers)
Date: 2025-10-02
Note: View the original document on HAL open archive server: https://hal.science/hal-05294356v1
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Related works:
Working Paper: Multi-Product Supply Function Equilibria (2025)
Working Paper: Multi-product supply function equilibria (2025)
Working Paper: Multi-Product Supply Function Equilibria (2025)
Working Paper: Multi-Product Supply Function Equilibria (2025)
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