Multi-Product Supply Function Equilibria

Pär Holmberg, Keith Ruddell and Bert Willems

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

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: Supply Function Equilibrium; Multi-Product Pricing; Divisible-Good Auction; Bundling; Pass-Through; Welfare (search for similar items in EconPapers)
JEL-codes: C62 C72 D43 D44 L94 (search for similar items in EconPapers)
Date: 2025-09-24
New Economics Papers: this item is included in nep-com, nep-gth, nep-ind and nep-mic
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https://www.econ.cam.ac.uk/sites/default/files/pub ... pe-pdfs/cwpe2565.pdf

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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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:2565

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