We consider a setting in which two firms first choose equity positions in each others stock (cross holdings) and then compete in an imperfect product market. We demonstrate that cross holdings lead to higher firm profits and higher consumer surplus when the competitors’ products are complements. We find that cross holdings lead to lower firm profits and higher consumer surplus when the products are substitutes. This finding is in contrast to the existing literature which establishes that cross holdings leads to higher firm profits and to lower consumer surplus. The contrasting results emerge because we solve for optimal cross holdings, whereas the existing literature considers exogenous cross holdings. In addition, allowing optimal cross holdings improves economic welfare. Furthermore, we demonstrate that cross holdings deter entry when the products are substitutes and facilitate entry when the products are complements
