This article presents a dynamic pricing model of a retailer selling an inventory, accounting for consumer behavior. The authors propose an optimal control model, maximizing the intertemporal profit with consumers sensitive to the selling price and to a reference price. The optimal dynamic pricing policy is solved with Pontryagin's maximum principle with a structural (general) demand function. The authors obtain an original pricing rule, which explicitly accounts for the impact of price and inventory on future profits. The dynamics of price do not have to imitate the dynamics of the reference price. Instead, the dynamics of price are tied to opposing effects linked to this reference price. The authors also discuss managerial implications with regards to behavioral pricing policies.

Dynamic pricing is a common practice where sellers adjust prices for products or services based on current demand. Developed initially by the airline industry with yield management, dynamic pricing is now a wide-spread phenomenon. Recent technological evolutions concerning real-time access to demand-related data (big data), real-time data processing, pricing algorithm automatization (allowing for real-time computation of optimal prices), and new technologies to implement frequent price changes (smart labels) contribute to dynamic pricing diffusion in the retailing industry. A retailer is traditionally confronted with inventory management issues, for which price is a main control. New dynamic pricing models need to be developed that also address inventory management issues together with actual consumer behavior. This point motivates our research.

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Adam Smith,
Editorial Manager,
Research Journal of Economics