Passive cross‐holdings, horizontal differentiation, and welfare

Abstract

AbstractWe 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.