Oligopoly price discrimination, competitive pressure and total output

The effect of monopoly third-degree price discrimination on total output is intrinsically related to both the shape of demands and inverse demands in strong markets compared to the shape of direct and inverse demands in weak markets. This paper extends the traditional analysis of the output effect under monopoly (third-degree) price discrimination to a multimarket oligopoly. We show that under oligopoly price discrimination, differences in competitive pressure, measured by the number of firms, across markets can be more important than the relative demand curvature when determining the effect on total output.

We show that under symmetric Cournot oligopoly (all firms selling in all markets) similar results to those under monopoly are obtained: in order for total output to increase with price discrimination the demand of the strong market (high price market) should be more concave than the demand of the weak market (the low price one). When competitive pressure (measured by the number of firms) varies across markets, the effect of price discrimination on total output crucially depends on which market, the strong or the weak, is more competitive. Importantly, some new unexpected results are obtained, even with linear demand. First, we show that price discrimination in favor of the more competitive market is quite generally output reducing, therefore leading to a welfare deterioration. This result maintains unambiguously under linear demand or when the strong market exhibits convex demand and the weak market concave demand. Second, when the competitive pressure is higher in the strong market we obtain the important result that, independent of the shape of demands, and inverse demands price discrimination can increase total output. In particular, we show that even with linear demand price discrimination increases total output. We also consider an oligopoly model of price discrimination considering price competition and show that our main result maintains under linear demand.