Optimal cross-holdings and upstream R&D

Qing Hu () and Tomomichi Mizuno ()
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Qing Hu: Kansai University
Tomomichi Mizuno: Kobe University

No 2611, Discussion Papers from Graduate School of Economics, Kobe University

Abstract: While cross-holdings are widely observed, their degree varies across industries. We show that upstream R&D is one possible reason. In a vertically related market with two downstream firms and an upstream firm engaging in cost-reducing R&D, the cross-holding rate is determined through Nash bargaining. The equilibrium rate maximizes downstream joint profit and is always below the merger level. An interior optimum exists only when upstream R&D is sufficiently inefficient, and the rate decreases with R&D efficiency and market size. In the linear-quadratic case, any degree of cross-holdings can arise. Since total surplus falls with cross-holdings, the private optimum is socially excessive, justifying antitrust intervention.

Keywords: Cross-holdingsï¼›; vertical; structureï¼›; R&Dï¼›; optimal; choice (search for similar items in EconPapers)
JEL-codes: D43 L13 O32 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2026-07
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