Cross Holding and Imperfect Product Markets

We consider a two stage game where two firms first take positions in each other's equity (cross holding) and next compete in an imperfect product market. When the firms' products are substitutes, the optimal cross holding involves a short position in the competitor's equity, resulting in an equilibrium with larger quantities produced, lower firm and industry profits, and higher consumer surplus than an equilibrium where short-selling is prohibited. This provides a new rationale for short selling that does not rely on capital market imperfections, such as taxes or private information. In contrast, when two firms' products are complements, a long position in the competitor's equity is optimal, yielding higher quantities and lower prices which results in higher consumer welfare, and higher firm and industry profits.