Mathematical Model of the Adjustment of the Optimal Price of the Substituting Commodity

In this paper, from the two economic concepts of the price elasticity of demand and the cross elasticity of demand, under the assumption that the operator's management goal is to obtain the profit maximization, the author established the mathematical model of the adjustment of the optimal price of the substituting commodity. The pricing and the adjustment of the prices of goods is an important content of the theoretical research in the marketing. In the fast-changing market, the price of goods must be ready for a corresponding adjustment. To make reasonable adjustments to the existing prices of the commodity, many factors need to be considered, such as the expected prices of the consumers, the original levels of the prices, the trend of the price changing, the periods of the demand, the patterns of the competition, and the life cycle of the products and other various complicated factors, among which the elasticity of demand is a very important quantitative indicator needing to be considered in the adjustment of the prices. Especially for the interconnected commodity, the changes in the prices will affect each other, and therefore, we should not only consider the price elasticity of demand of itself, but also the elasticity of demand of the related goods, namely the cross elasticity of demand. The related products include the substitutes and the complement. In the following, taking the substitutes for example, starting from the concepts of the above two elasticity of demand, under the assumption that the operator's management goal is to obtain the profit maximization, the author derived the scheme of the adjustment of the optimal prices, and conducted the calculation combined with the examples.