关键词: 产品扩散, 重复购买, 产品定价, 动态控制

Abstract: Product price was the key factor of marketing,which directly affected product diffusion process.To definite the internal relationship between product pricing and product diffusion,based on Bass model,the non-linear differential dynamic model for diffusion behavior of product was built  by considering the factors of repeated purchase and price.The analytical expressions for cumulative number of adopters and market scale were obtained by solving differential equations.With consideration of learning effect,the analytical expressions for optimal price was obtained by solving the corresponding HJB equation.The evolution process of model's main variables and optimal price were analyzed with simulation analysis.The simulation results showed that the optimal price would decrease over time and tend to be constant at the end of product life cycle,and skimming strategy was the optimal pricing strategy.The inter-relationships between various parameters and optimal price were revealed through sensitivity analysis,which could provide a theoretical basis for the development of new product and marketing strategies.

Key words: product diffusion, repeated purchase, product pricing, dynamic control