Résumé
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.
Mots-clés
Supply function equilibrium; multi-product pricing; divisible-good auction; bundling; pass-through; welfare;
Codes JEL
- C62: Existence and Stability Conditions of Equilibrium
- C72: Noncooperative Games
- D43: Oligopoly and Other Forms of Market Imperfection
- D44: Auctions
- L94: Electric Utilities
Référence
Pär Holmberg, Keith Ruddell et Bert Willems, « Multi-Product Supply Function Equilibria », TSE Working Paper, n° 25-1669, septembre 2025.
Voir aussi
Publié dans
TSE Working Paper, n° 25-1669, septembre 2025