Passive cross-holdings, horizontal differentiation, and welfare

We study how passive cross-holdings affect product differentiation and welfare in a Cournot duopoly. We show that increasing unilateral ownership stimulates total investments, and therefore improves social welfare. Such cross-holdings should not be controlled in view of social welfare. However, we identify an inverted-U (a negative) relationship between consumer surplus and ownership when the demand is small (large). Then a government might apply intervention thresholds for passive ownership if it uses consumer surplus as the appropriate standard for antitrust enforcement. We further consider symmetric bilateral cross-holdings and show that our results are in general robust, but increasing ownership will generate more serious competition harms than unilateral cross-holdings. Thus, special concerns need to be given to bilateral cross-holdings.