A two-period pricing model with intertemporal and horizontal reference price effects

Consumers tend to compare the current price with historical prices of the same brand and selling prices of other brands, when they make purchase decisions. The intertemporal and horizontal reference price effect (RPE), formed by the historical price and the competitor's price, respectively, should be taken into account when developing optimal pricing strategies over several periods and in a competitive environment. This paper considers a two-period pricing problem with two competing sellers, incorporating both types of RPE. We first develop a duopoly game to study the impacts and interactions of RPE of different types. Then we study a practice of price commitment when one firm gives up dynamic pricing. We find different types of RPEs have distinct impacts. The intertemporal RPE (IRPE) leads to a Hi-Lo pricing strategy, while the horizontal RPE (HRPE) drives the selling prices of both periods downward. The IRPE is weakened by the HRPE, while the HRPE is weakened (intensified) in the first (second) period as the IRPE becomes stronger. Also we find price commitment is not beneficial. On the contrary, both firms may be worse off if one firm makes price commitment. Furthermore, if one firm decides to make price commitment he should announce the selling price well in advance.

Automated summary

The study reveals that the intertemporal reference price effect leads to a Hi-Lo pricing strategy, while the horizontal reference price effect drives selling prices down in both periods. The intertemporal reference price effect is weakened by the horizontal reference price effect, and as the intertemporal reference price effect strengthens, the horizontal reference price effect weakens in the first period and intensifies in the second. Additionally, price commitment may not always be beneficial and can result in losses for both firms.