Cross‐ownership and environmental R&D risk choices in a differentiated duopoly

Dongdong Li, Xiaochan Yan and Yue Zhang

International Journal of Economic Theory, 2025, vol. 21, issue 4, 473-493

Abstract: This paper develops a differentiated duopoly model to investigate the optimal environmental R&D (ER&D) risk choices of firms with cross‐ownership under an emission tax. The results show that when firms hold shares in each other, cross‐ownership incentivizes firms to undertake greater ER&D risks. The private incentive for ER&D risk is lower than the social incentive when the emission tax rate is low relative to the marginal environmental damage. However, a higher share of cross‐ownership can bring the private optimum closer to the social optimum under certain conditions. We also find that under unilateral shareholding, a firm partially owned by its rival assumes higher ER&D risk than the firm owning its shares, but both take on less risk than under cross‐ownership. Finally, we show that ER&D risk is higher under Bertrand competition than under Cournot competition.

Date: 2025
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