EXPRESS: Pricing under Consumer Habituation: The Optimality of a Familiarity-Based Threshold Policy

Empirical evidence indicates that consumers experience a relative loss of excitement over time and miss their habits when refraining from consumption under repeated purchases. Despite the practices of first-time trials and welcome-back offers, how to exploit this habituation behavior through customized dynamic pricing is overlooked in the existing literature. In this paper, we analyze the long-run optimal customized dynamic pricing strategy in the presence of consumer habituation for time/frequency-based consumption. The consumer’s willingness to pay is determined by past consumption via the habitual level of consumption. We formulate the seller’s continuous-time profit maximization problem over an infinite horizon as an optimal control problem and derive the closed-form value function and optimal pricing strategy. We identify a key condition on the willingness-to-pay function that captures both the magnitude of the habituation effect and the saturated willingness to pay, which plays a central role in determining the seller’s optimal pricing policy. When consumers retain interest even at high levels of habitual consumption, always selling by pricing at their current willingness to pay is optimal. In contrast, if consumers lose interest when saturated, the optimal policy becomes a cutoff strategy, where the seller offers the product only when consumption remains below a critical threshold and prices out consumers beyond it.We further examine the resulting pricing and consumption dynamics and characterize an equilibrium habitual level of consumption at which randomized promotions can be optimal. Furthermore, our key findings qualitatively hold under random consumer valuation, but with richer patterns. Our work provides a tractable, closed-form characterization of the optimal dynamic pricing policy under consumer habituation, offering a more nuanced understanding of the strategic implications of an inverted U-shaped willingness-to-pay.