Large-Scale Bundle-Size Pricing: A Theoretical Analysis

Bundle-size pricing (BSP) is a multidimensional selling mechanism where the firm prices the size of the bundle rather than the different possible combinations of bundles. In BSP, the firm offers the customer a menu of different sizes and prices. The customer then chooses the size that maximizes her surplus and customizes her bundle given her chosen size. Although BSP is commonly used across several industries, little is known about the optimal BSP policy in terms of sizes and prices, along with the theoretical properties of its profit. In this paper, we provide a simple and tractable theoretical framework to analyze the large-scale BSP problem where a multiproduct firm is selling a large number of products. The BSP problem is in general hard as it involves optimizing over order statistics; however, we show that for large numbers of products, the BSP problem transforms from a hard multidimensional problem to a simple multiunit pricing problem with concave and increasing utilities. Our framework allows us to identify the main source of inefficiency of BSP: the heterogeneity of marginal costs across products. For this reason, we propose two new BSP policies, "clustered BSP" and "assorted BSP," which significantly reduce the inefficiency of regular BSP. We then utilize our framework to study richer models of BSP, such as when customers have budgets.