Constructing Valuation Distributions from a Single Sales Observation
55 Pages Posted: 27 Mar 2016 Last revised: 12 Mar 2019
Date Written: June 14, 2016
Firms typically require multiple sales observations under different prices to learn about the price elasticities of their products. In this paper, we show that a firm which offers a bundle discount for buying multiple items can, in fact, infer price elasticities from just a single sales observation.
We introduce this "informational value" of bundling and analyze a parsimonious model from the bundling literature, where the firm's customers are unit-demand with additive and independent valuations. We show that it is indeed possible to reconstruct such a valuation distribution from a single sales observation, and develop an algorithm which iteratively solves the fitting problem given the sales observation. An important insight from our fitting algorithm is that the price elasticity of an item ends up being largely determined by the sales of the other items in its bundles.
Based on this insight, we rank the items of a large online retailer according to price elasticity, given just a single sales count of each item and bundle. We show that the items' realized price elasticities, as indicated by their sales spikes after a Black Friday markdown, are generally consistent with the elasticities indicated by their bundle sales before Black Friday.
Keywords: bundling, valuation learning, revenue management
Suggested Citation: Suggested Citation