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Optimal cross-holdings and upstream R&D

Author

Listed:
  • Qing Hu

    (Kansai University)

  • Tomomichi Mizuno

    (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.

Suggested Citation

  • Qing Hu & Tomomichi Mizuno, 2026. "Optimal cross-holdings and upstream R&D," Discussion Papers 2611, Graduate School of Economics, Kobe University.
    • Handle: RePEc:koe:wpaper:2611
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    File URL: http://www.econ.kobe-u.ac.jp/RePEc/koe/wpaper/2026/2611.pdf
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    Keywords

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    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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