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Design and Dynamic Pricing of Vertically Differentiated Inventories

49 Pages Posted: 2 Nov 2016 Last revised: 2 Nov 2017

Date Written: March 21, 2017

Abstract

We develop a model in which a monopoly firm designs the quality profile of its inventory upfront and then dynamically updates its pricing menu for a finite selling horizon to maximize revenue. In a counterfactual scenario, a social planner goes through the same process to maximize total welfare. We show that in both scenarios, perhaps surprisingly, the problem of dynamically pricing vertically differentiated inventories is equivalent to that of dynamically pricing identical inventories, in the sense that a solution to one implies a solution to the other. Moreover, we prove a strong scarcity result, which suggests that the sale of a unit of inventory pushes the price up on all remaining products, whether of higher or lower quality. We then consider product line design under two different production technologies: convex production costs and allocation of a fixed amount of resources. We show that under convex production costs, the monopoly firm under-provides quality in all its products compared to the social planner. In the resource allocation setting, the monopolist over-concentrates resources on the production of high-quality products. However, as the length of the selling period increases to infinity, both the revenue maximizer and the welfare maximizer choose to allocate resources equally across products.

Keywords: Revenue Management, Welfare Analysis, Product Line Design, Resource Allocation

Suggested Citation

Stamatopoulos, Ioannis and Tzamos, Christos, Design and Dynamic Pricing of Vertically Differentiated Inventories (March 21, 2017). Available at SSRN: https://ssrn.com/abstract=2862490 or http://dx.doi.org/10.2139/ssrn.2862490

Ioannis Stamatopoulos (Contact Author)

University of Texas at Austin - McCombs School of Business ( email )

2110 Speedway B6000
Austin, TX 78705
United States

Christos Tzamos

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

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