Mixed duopoly and the indirect effect in linear supply function competition

The 1980s market reforms in Europe led to far-reaching privatization. However, empirical data show that some countries experienced deterioration in market performance, such as in consumer prices and welfare, during a certain period. Although theorists have focused on the change in the stock holding rate and the degree of product differentiation between privatization, few paid attention to the change in competition mode or intensity. To grasp how the structural change of privatization can affect market performance, we investigate the infinitesimal change in competition intensity by parameterizing it, apart from using the traditional method of making a simple comparison between Cournot and Bertrand equilibria. Thus, we parameterize the intensity of competition, and consider a mixed duopoly market with product differentiation accompanying partial privatization using a linear supply function approach. We observe a non-monotonic change in prices, profits, and social welfare in the plane of the degree of product differentiation and privatization, when competition becomes aggressive. Intuitively, when the semi-public firm promotes privatization, the market is an ordinary private duopoly and the competition becomes weak, while the competition can be aggressive with nationalization, since the semi-public firm tries to lower its price to improve consumer surplus. Further, the thresholds’ roughly common property—the right-upwardness—depends on the degree of the cross-price effect. Analytically, these counterintuitive phenomena are caused by the indirect effect inherent in linear supply function competition.