Design and Dynamic Pricing of Vertically Differentiated Inventories

46 Pages Posted: 2 Nov 2016 Last revised: 16 Apr 2018

Date Written: March 21, 2017


We study a model in which a monopoly firm designs the quality profile of its inventory 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 the problem of dynamically pricing heterogeneous-quality (vertically differentiated) inventories is equivalent to that of dynamically pricing homogeneous-quality 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 product drives up the prices on all remaining products, whether of higher or lower quality. We then consider product line design under a production technology that utilizes costly and potentially limited resources. We show that with unlimited (but costly) resources, the revenue maximizer under-supplies quality to all products compared to the social planner. With limited resources, we show that the revenue maximizer exhibits elitism: he over-allocates (under-allocates) resources on the production of high-quality (low-quality) products. However, as the volume of expected consumer arrivals increases to infinity, both the revenue maximizer and the welfare maximizer 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: or

Ioannis Stamatopoulos (Contact Author)

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

2110 Speedway B6000
Austin, TX 78705
United States

HOME PAGE: http://

Christos Tzamos

Massachusetts Institute of Technology (MIT) ( email )

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

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