Dynamic Pricing of Perishable Products by Variational Method Facing Rational Consumers

Abstract

By variational method, this paper studies a dynamic pricing problem of perishable products when facing rational consumers. The seller dynamically sets the price for the perishable products to maximize its total profit and the rational consumers choose their consumption pattern to maximize the expected surplus. We present a game theoretic model based on their rational expectations and develop a rational expectations (RE) equilibrium. The equilibrium solution of the game is then studied by variational method. In particular, when the consumption pattern linearly depending on the consumer surplus, we get the right dynamic price by solving the variational problem. The results that followed imply practical recommendations for the sellers when setting the price for the perishable products.