Price discrimination with divisible goods - Cont, Walter Alberto (2012)
This paper studies second-degree price discrimination (SPD) in cases involving products with divisible quantities and sold in many presentations (carbonated soft drink, beer, packaged bread, ready-to-eat cereals, laundry products, etc.). Differently from the standard case, consumers may have the option to choose more than one package when comparing different product presentations; therefore, standard SPD may not cover all self-selection constraints. We solve an extended SPD problem (ESPD) and characterize the solution for two types of preferences. As in SPD, the seller provides the efficient quantity to high-WTP consumers and introduces inefficiencies in packages designed for low-WTP consumers. But the distortion is less than that suggested by SPD, provided that the seller attends both consumer types. Closing the market for low-WTP consumers (when SPD suggests to keep it open) is also a possibility if the two distortions introduced in the ESPD -the standard trade off between inefficiency and consumer surplus, and the n-arbitration constraint for high-WTP consumers- are too costly to the seller. Given the possibility for high-WTP consumers to consume more than one unit of small packages, the seller offers deeper quantity discounts, provided that he finds profitable to sell both consumer types.