两阶段免费增值商业模式中的定价优化与时序研究

Optimal Pricing and Releasing Order in a Two-stage Freemium Model

免费增值商业模式在信息产品和服务当中被广泛采用。针对企业首先推出免费产品再推出付费产品以充分利用两种产品推出的时间差来提升消费者学习效应、降低消费者使用成本的情形,本文首先建立两阶段模型,求解给定系统参数情况下的付费版产品最优定价问题并给出解析解,然后通过与企业应用单阶段免费增值模式时的利润进行比较,解析地得到企业选择两阶段模式可获得较高利润的条件,最后在数值计算基础上讨论了学习效应强度对企业利润的影响,和优化学习效应强度以拓展两阶段模式适用范围的问题。本文的研究成果为拟采用免费增值商业模式的企业提供了关于产品最优定价和模式选择的决策支持。

In business practices where firms adopt the freemium model,the free versions are often released prior to the premium versions to take the advantage of consumer learning.We develop a two-stage model to solve the optimal pricing problem for the firms.Given all other parameters fixed,the optimal price of the premium version is obtained analytically.Conditions to guarantee a higher profit for firms applying such two-stage model compared to the conventional single-stage model with simultaneous releasing are then constructed.Following numerical analysis we make a sensitivity analysis of the optimal profit against the strength of the learning effect,and it indicates that the aforementioned conditions could be partially relaxed after optimizing the strength.