Optimal Pricing with Loyalty

Market prices vary along the time dimension. In some cases prices change monotonously and, in others they fluctuate in a zigzag pattern. The latter is due to marketers having to face the extremely complex task of setting profit or sales maximizing product prices on the one hand, while maintaining consumer loyalty on the other. This paper suggests an analytical approach for optimally setting product prices with respect to the interdependency between different prices and products, as well as habit formation in terms of both location and brand loyalties. We demonstrate that cyclic pricing policies of harmonic form become optimal when the management of a store is prepared to compromise its net profit goal in order to maintain an image of an affordable store, for the sake of keeping both location and brand loyalties steady. Furthermore, we show that the lower the weight assigned to these loyalties, the greater the optimal frequency of the harmonic zigzags.