Losses from cross-holdings in a duopoly with convex cost and strategic input price determination

Mukherjee, Arijit

Abstract

It is well-known that positive output externality on the outside firms is the reason for unprofitable passive cross-holding, which refers to a situation where a producer holds non-controlling shares in rival firms. Considering a final goods market with Cournot duopoly, where cross-holdings do not create positive output externality on the outside firms, we show that cross-holdings can be unprofitable under strategic input price determination by an input supplier if the final goods are produced with decreasing returns to scale technologies. Our results hold under symmetric and asymmetric cross-holdings. We show that cross-holdings can be unprofitable also under Bertrand duopoly in the final goods market. Thus, we provide a new reason for unprofitable passive cross-holdings. We also show the implications of a higher product differentiation on the profits and welfare.

• Journal Article Type: Article
• Acceptance Date: Dec 26, 2022
• Online Publication Date: Jan 24, 2023
• Publication Date: 2023-04
• Deposit Date: Jan 3, 2023
• Publicly Available Date: Jan 25, 2024
• Journal: Economic Theory Bulletin
• Electronic ISSN: 2196-1093
• Publisher: Springer Science and Business Media LLC
• Peer Reviewed: Peer Reviewed
• Volume: 11
• Pages: 81-91
• DOI: https://doi.org/10.1007/s40505-022-00241-3
• Keywords: Convex cost; Cross-holdings; Profit; Vertical structure
• Public URL: https://nottingham-repository.worktribe.com/output/15709179
• Publisher URL: https://link.springer.com/article/10.1007/s40505-022-00241-3