A dynamic pricing model with goodwill influenced by price-quality effect

In this paper, we consider an important phenomenon of price‐quality effect in goodwill formulation process, that high price indicates high quality thus has a positive impact on goodwill. Based on the familiar Nerlove‐Arrow model, we set up a dynamic model, in which the firm maximises its profit by setting optimal price and quality, with the consideration of price‐quality effect, i.e., high price could increase the sales through enhancing the goodwill if quality has reached a threshold level. Our result shows that 1) in the high quality strategy scenario, the quality is set at the quality threshold of the existence of price‐quality effect, and the optimal price is increasing in the degree of price‐quality effect and the quality threshold; 2) in low quality strategy scenario, the quality is set at zero, and the optimal price is decreasing in the quality threshold.