Dynamic Pricing Models With Consumers’ Reference Effects And Mental Accounting

Implementing dynamic pricing requires to accurately understand consumer behavior where mental accounting is closely related with price anomalies. However, there is no dynamic pricing model incorporating mental accounting. In this paper, we attempt to model mental accounting into the dynamic pricing model in three different ways, with considering the consumer’s reference dependent behavior. We establish and solve these new dynamic pricing models to get more realistic dynamic pricing strategies and other related management insights.Firstly, we build a dynamic pricing model with reference price’s updating and double-comparison process. Under the double-comparison process of mental accounting, consumer’s transaction utility and acquisition utility changes with the updating of reference price, and we build new demand functions in view of consumer’s utility. We obtain the model’s steady-state prices and find out that the steady-state prices interval becomes larger as the degree of loss aversion gets larger. In addition, we compare the models of different double-comparison processes.Secondly, we establish dynamic pricing models with consumer’s double-entry mental accounting and reference effects under different payment schemes. According to the double-entry mental accounting thory, we analyze how consumer’s psychological perception price and psychological perception value changes under different payment schemes, and we rebuilt new dynamic pricing models by intrducing coupling parameters. We solve the two-period model and obtain the relation expressions between different payment schemes’ optimal price paths and maximum profits. And in the infinite horizon dynamic pricing models, we find that both the steady-state prices of pre-pay payment and post-pay payment are greater than that of pay-per-use payment when the demand function is linear. Besides, we obtain the convergence property of the optimal price paths which indicates that when the initial reference price is higher (lower), the optimal pricing strategy is similar to skimming pricing strategy (penetration pricing strategy). Finally, via numerical analysis, we provide the advice about how to choose the best payment scheme for higher profits.Lastly, we build dynamic pricing models with consumer choosing payment scheme. The influences of mental accounting on the updating of reference price are different under different payment schemes, thus consumer’s corresponding total utilities are different too. In the deterministic model, consumer would select the payment scheme with maximum total utilities for sure. We find out that the firm can reach the theoretical maximum profit when consumers choose to pay in advance. And at the monment, the optimal price sequence is to set the maximum price in each period. And in the QRE probability selection model, we introduce consumer’s bounded rationality, and consumer would select the larger utilities scheme with greater probability. We find out when the degree of consumer’s bounded rationality is relatively low, we can get the following results. The firm’s profit improves with the increasing of each period’s price, and besides, when the recency effect is great, the maximum profit increases as the degree of consumer’s bounded rationality becomes higher.The paper incorporates behavioral economics concepts such as reference-dependence and mental accounting into dynamic pricing models, which makes up the shortage of assumption on customer’s behavior and enrichs and perfects the field of dynamic pricing. Besides, it provides a new perspective and useful research findings for the pricing strategies and related sales strategies of retailers, manufacturers and other market participants.