Dynamic policies with reference price effects and reference quality effects

Reference-dependent consumer preferences have been a central focus in economics, marketing, and operations management. However, existing literature predominantly concentrates on the effects of a single reference point. This study expands the framework to include both reference price and reference quality, motivated by anecdotal evidence demonstrating their interactive roles in consumer purchase decisions. This study develops a double reference-dependent demand model that clarifies how these two factors influence a monopolist's optimal control policies within a continuous, finite-time optimization framework. The results indicate that penetration-pricing strategies are optimal when initial consumer reference levels are low, while skimming strategies are preferable when reference levels are high. A high-price and high-quality policy is optimal under conditions of small reference price effects, large reference quality effects, or high-quality investment efficiency. In contrast, a low-price and low-quality policy is ideal in scenarios with large reference price effects, small reference quality effects, or low-quality investment efficiency. Additionally, a high-price and low-quality policy proves optimal when customers exhibit poor memory or when the firm's discount rate is low. Conversely, a low-price and high-quality policy is optimal when customers have good memory or when the firm's discount rate is high.