Social welfare and cross-ownership in a vertical industry: When the mode of competition matters for Anti-trust policy

tThe paper is motivated by the empirical observations of passive non-controlling partial ownership amongcompeting firms in vertical markets with imperfect competition. The model encompasses a two-stagegame. For given input prices, two downstream firms compete à la Bertrand in differentiated products. Eachfirm faces a firm-specific input supplier. The two input suppliers set publicly observable and linear inputprices non-cooperatively in the first stage. All technologies have constant returns to scale. The effects ofa one-sided increase in the non-controlling profit participation share of one firm in the other rival firm(i.e. cross-ownership) on social welfare are analysed. The main result is that under Bertrand, in contrastwith the common wisdom (which, for instance, holds under Cournot), an increase in cross-ownershipcan increase total surplus. The reason is that despite the cross-ownership share makes the downstreamquantity choice more “collusive”, hence more socially inefficient, it also reduces input prices, and whenthe competition is in strategic complements and products are not too differentiated the “input price”effect outweighs the “collusive” effect in determining the social welfare outcome. This result suggeststhat antitrust policy in a vertical industry should also consider the mode of competition in the finalproduct market in the case in which “more” collusion is achieved in the downstream sector through anincrease in the one-sided non-controlling profit participation share.