The Second-Degree Price Discrimination of m Firms with n Demand Intervals Pricing Based on Cournot Model

Abstract

Under the condition of linear demand function, the distribution law of equilibrium segment points of firms enforcing second-degree price discrimination to maximize respective revenues is analyzed in the case of m firms with n intervals pricing by using complete information static game theory. This is a promotion for two firms pricing with n segment intervals and m firms pricing with two segment intervals. The results show that: when m firms divide demand to enforce second-degree price discrimination, the necessary condition of revenue maximization is to divide demand into some intervals and let the length of each interval become geometric series, whose common ratio is 1 / m. The unified formula of equilibrium production, equilibrium price and market equilibrium total revenue of all four kinds of markets under the condition of second-degree price discrimination are presented in the most general sense, further more, the nature of which are analyzed in detail.