Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 1537: Multi-Product Supply Function Equilibria

Pär Holmberg (), Keith Ruddell and Bert Willems
Additional contact information
Pär Holmberg: Research Institute of Industrial Economics (IFN), Postal: Research Institute of Industrial Economics, Box 55665, SE-102 15 Stockholm, Sweden
Keith Ruddell: Research Institute of Industrial Economics (IFN)
Bert Willems: LIDAM, UCLouvain;, Postal: Department of Economics, TILEC & CentER, Tilburg University, and Toulouse School of Economics.

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.

Keywords: Supply function equilibrium; Multi-product pricing; Divisible-good auction; Bundling; Pass-through; Welfare

JEL-codes: C62; C72; D43; D44; L94

Language: English

61 pages, September 24, 2025

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