Dynamic pricing of fashion-like multiproducts with customers' reference effect and limited memory

We study a fashion retailer's dynamic pricing problem in which consumers present reference effect and memory window. Based on the theory of Baucells et al. (2011), we propose a new reference-price updating mechanism in fashion and textile (FT) industry where consumers have a bounded memory window and anchor on the first and most recent price in any memory window. Moreover, we study the impacts of this mechanism on optimal pricing policy for a retailer selling multiple fashion-like products and analyze optimal price's steady state, monotonicity, and convergence. For two-product case, we find that, for otherwise identical products, the steady-state price of a core product is lower than that of a noncore product. We compute the retailer's loss of revenue if he incorrectly assumes the reference-price effect to be at the product level and prices the products individually. Further, as illustrated with numerical results, our model is a flexible way to make pricing strategy if the retailer can anticipate the length of consumers' memory window.