The Mathematical Study On Second Degree Price Discrimination

The theory of price discrimination has been generally concerned in recent years. There are many articles in which it has been deeply researched. There are two ways to study the theory. One is to study the problem of maximizing monopoly revenue under the linear function and derived the necessary and sufficient condition that it should divide the demand section equally and fix the price piecewise. The other way is to study the problem of how to price with the fixed discount rate in order to make the gross income maximal under the linear demand, and have proved that the optimal fixed discount rate which makes the income maximal exists, and what more, have solved the optimal fixed discount rates in case of two and three sectional pricing.Based on the important results obtained from the presently applied two methods of second degree price discrimination-pricing of equal divisional demand section and fixed discount rate pricing, this dissertation makes a systematic and more practical mathematics study, including further and more deeply research on the determination of sectional number of demand section, the solution of fixed discount rate, Bayesian equilibrium of second degree price discrimination under the context of competition, the problem of dividing demand intervals of second degree price discrimination under the stochastic demand-the aggregate demand describes as a Poisson process. From the above mentioned researches, some important conclusions have made. First, we put forward the concept of divisional number of demand section, point out that the maximum for divisional number of demand section is from 2^nd section to 3^rd section, and explain the phenomenon that the level of segments is less in actually economic life by using the thought of marketing and strict mathematic reasoning. Secondly, we study monopolist's second degree price discrimination under the condition of fixed discount rate. The results are as the following: 1. We proved the existence of solve of pricing of fixed discount ratio under the nonlinear demand. 2. We gave the concrete result of fixed discount rate under two sorts of familiar typical nonlinear demand functions. Thirdly, when we discuss the shape and the existence condition of the equilibrium of second degree price discrimination, we use the dynamic games model full of information to make the problem more practical. Finally, we study respectively the condition of second degree price discrimination of monopoly enterprise and oligarchic enterprises under the stochastic demand-the aggregate demand described as a Poisson process. The results are as the following: 1. the best division points of demand interval in the case of two stage pricing and three stage pricing are respectively given. 2. the problem of dividing demand intervals of second degree price discrimination of two sectional pricing is studied, which is generalized as a complete static information model. Then the result of Nash equilibrium is given.