Design and Dynamic Pricing of Vertically Differentiated Inventories.

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 undersupplies quality to all products compared with the social planner. With limited resources, we show that the revenue maximizer exhibits elitism: he overallocates (underallocates) 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.