Optimal product line design with reference price effects

A reference price is the price expectation of consumers for a product. When considering whether to buy a product, consumers usually compare its price with the reference price, which leads to psychological gain-loss utility affecting the consumers’ willingness to pay for the product. In this paper, we incorporate a reference price into the product line design problem and investigate the strategic implications of reference price effects for both the firm and consumers. We first study the optimal quality-price bundle design problem of a monopolistic firm and investigate the impact of reference price effects on the optimal quality and price decision when the number of products in the line is given. We show that as the importance of price comparison increases, the optimal range of qualities in the product line narrows. Specifically, the lowest quality in the product line is distorted upward, while the quality gap between adjacent products narrows. In particular, when consumers attach great importance to price comparison, the reference price effects may cause the firm to abandon discrimination among consumers and instead offer just a single product. We also investigate the optimal product variety setting problem considering a fixed setup cost incurred for each product in the choice set. Our numerical studies using synthetic and real-world data demonstrate that the demand model with reference price has better goodness of fit and prediction accuracy. The impact of neglecting reference price in the product line design problem is significant, potentially leading to substantial profit loss. Finally, we extend our work through general discussions of the model and through the dynamic pricing problem incorporating temporal reference price effects.