The Mathematical Economics Analysis On Second Degree Price Discrimination

A systematic mathematics analysis was presented on second-degree price discrimination. On the basis of quantitative analysis, we got some qualitative conclusions. Firstly, we studied the method and characteristics of second-degree price discrimination that was enforced by monopoly enterprise on the basis of documents available. The results are as the following: 1. We proved the existence of solve of pricing of fixed discount ratio. 2. We compared the two methods of dividing up demand interval equally and pricing of fixed discount ratio, which are both methods of second -degree price discrimination. The study shows that the two methods are equal on the whole in the degree of consumer's surplus gained. 3. We also analyzed quantitatively the second-degree price discrimination under a sort of typical nonlinear demand functions. Secondly, the methods and characteristics of second-degree price discrimination in oligarchic enterprises were studied by using game theory. There are three results: 1. We studied the reasonable divisional number of demands while second-degree price discrimination was enforced by two oligarchic enterprises. We studied and compared the static and dynamic games of two oligarchic enterprises on second -degree price discrimination under the condition of linear demand functions. 3. We also studied the same problems under the condition of nonlinear demand functions. At last, the characteristics of second-degree price discrimination in monopoly market and oligarchic market were compared, we got two results: 1. The comparison under linear demand functions; 2. The comparison under nonlinear demand functions. Through the above results, we got final conclusions: competition can increase social welfare, while monopoly can decrease it. Second-degree price discrimination does not change social welfare, it just transfer consumer's surplus to producer's surplus. In highly competitive markets, consumer's surplus is more and producer's profit is less; while in markets that have more monopoly, consumer's surplus is less and producer's profit is more.