Constructing Valuation Distributions from a Single Sales Observation

55 Pages Posted: 27 Mar 2016 Last revised: 12 Mar 2019

See all articles by Will Ma

Will Ma

Massachusetts Institute of Technology (MIT)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: June 14, 2016

Abstract

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

Ma, Will and Simchi-Levi, David, Constructing Valuation Distributions from a Single Sales Observation (June 14, 2016). Available at SSRN: https://ssrn.com/abstract=2754279 or http://dx.doi.org/10.2139/ssrn.2754279

Will Ma (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

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

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

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