Joint pricing and advertising strategy with reference price effect

Consumers are susceptible to reference price effects when they make purchase decisions for a certain product. Meanwhile, the sales price and advertisement are the determinable factors that have impact on consumers' reference price which are also fundamental marketing strategies. Therefore, how to determine an appropriate sales price and advertising effort level to maximise firms' profits is an essential task. A joint pricing and advertising problem for a monopolistic firm with consideration of reference price effect is investigated, where consumer demand rate is price-sensitivity and depends on the gap between the sales price and the reference price in consumers' mind. An optimisation model is established to maximise the firm's total profit by making a joint pricing and advertising strategy. The static and dynamic joint strategies are obtained by applying Pontryagin's maximum principle. Results show that the dynamic strategies dominate the static ones. Furthermore, the dynamic pricing and dynamic advertising strategies are strategic complements. Additionally, the length of the sales period plays a key role in determining the superiority of the two dynamic strategies. Specifically, a relatively short sales period highlights the value of the dynamic advertising while a long sales period strengthens the function of the dynamic pricing.