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

摘要： 产品价格作为市场营销的关键因素,直接影响产品扩散,为了明确产品价格和产品扩散之间的内在机理,在Bass模型的基础上,考虑重复购买和价格因素,构建产品市场扩散非线性微分动力学模型。对模型进行微分方程求解,获取产品累积扩散量和产品市场稳定累积扩散量的解析式;考虑成本学习效应,以最大收益为目标,求解模型对应的HJB方程,得到重复购买下产品扩散最优定价的解析式。通过仿真分析模型主要变量和最优定价的演进过程产品表明:最优定价随时间推移不断降低,在产品生命周期末期趋于平稳,最优定价应采取撇脂策略;灵敏度分析进一步揭示了各主要参数与最优定价的内在联系,为企业制定新产品开发和营销战略提供了理论指导。

关键词: 产品扩散, 重复购买, 产品定价, 动态控制