Design and Dynamic Pricing of Vertically Differentiated Inventories
49 Pages Posted: 2 Nov 2016 Last revised: 2 Nov 2017
Date Written: March 21, 2017
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
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