Analysis of non-linear quantity discount for heterogeneous characteristics

From the supplier’s point of view, the paper examines the existence of a Pareto superior pricing schedule for one wholesaler with multiple retailers. In the case of multiple retailers, an order quantity pricing schedule should depend on the retailer’s underlying characteristics. But identification of each retailer’s characteristics may be impossible; rather, the wholesaler knows only the probability distribution of each retailer’s characteristics. Perfect price discrimination is impossible because a separate pricing schedule cannot be tailored for each retailer. Some degree of discrimination is possible only by using a non-linear pricing schedule. From this analysis based on the non-linear pricing, the paper concludes that there is no Pareto superior pricing schedule for the case of multiple retailers.