Cross Holding and Imperfect Product Markets
September 1999
Matthew J. Clayton and Bjorn N. Jorgensen
ABSTRACT
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.
Clayton: (212) 998-0309 mclayton@stern.nyu.edu
Jorgensen: bjorgensen@hbs.edu
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