Dynamic Pricing with Consumer Habituation
DescriptionEmpirical evidence indicates that a consumer's willingness to pay for a product fluctuates with past consumption experience and willingness to pay typically has an inverted U-shape with the habitual level of consumption. This can be explained by the following two effects: inexperienced consumers' willingness to pay usually increases with consumption during episodes of "sensitiza-tion", while enduring consumption induces episodes of "habituation" and a consequent waning of willingness to pay. There is an extensive decision analysis and economics literature on posing dif-ferent utility models to account for each effect or both two effects. The existing literature indicates that ignoring consumer habituation by adopting a fixed pricing strategy can lead to a significant profit loss. However, how to exploit consumer habituation through dynamic pricing has received scant attention. This project aims to bridge the gap in the existing literature by investigating the optimal dynamic pricing strategy under a continuous time setting in the presence of consumer habituation. Our findings can potentially provide guidelines for sellers on how to carry out dynamic pricing in the presence of consumer habituation.Specifically, we consider the dynamic pricing problem to maximize the discounted expected profit under a discounted infinite horizon setting. Consumers make repeated purchasing decisions and their willingness to pay for the product in each time period is determined by past patterns of consumption according to the habituation dynamics in Wathieu (2004). Due to the technical chal-lenge imposed by the discrete time model, we consider the continuous time model by formulatingthe customers' habituation evolution as an ordinary differential equation. Then we shall formulate the dynamic pricing problem as a Hamilton-Jacobi-Bellman (HJB) equation.By exploiting the solution to the ordinary differential equations (ODE), we obtain some pre- liminary results regarding the relationship between the maximum profit function and the optimal pricing strategy. By solving the ordinary differential equations, we obtain the candidate forms of the maximum profit function, which encourages us to continue further analysis into the optimal pricing strategy. Numerically, we also find that dynamic pricing can reap significant profit gain against fixed pricing for the seller (see Table 1).We present our model and the preliminary results in this proposal along with the future plan to achieve our research goals. Current results have encouraged us to take up the challenge described.
|Effective start/end date||1/01/23 → …|