An Empirical Model of Quantity Discounts with Large Choice Sets; Ao Wang (University of Warwick)

Abstract

We present methods to estimate demand for bundles and investigate quantity discounts with large choice sets. We introduce a Generalized Nested Logit model with as many overlapping nests as products which can be estimated by a constrained 2SLS. For implementation, we propose an optimization- and derivative-free algorithm that can be parallelized over both bundles and markets, virtually eliminating any challenge of dimensionality related to large choice sets. We use our model to explore the welfare implications of the observed quantity discounts in the US market for carbonated soft drinks by simulating a counterfactual with linear pricing. This leads to a 23.7% reduction in the prices of small quantities (up to one liter) and a 20.5% increase in the prices of larger quantities, making purchases of smaller quantities relatively more attractive. Total quantity purchased in the market decreases by 17.9% and industry profit shrinks by 9%. Despite the steep reduction in quantity purchased, consumer surplus remains on average approximately unchanged, suggesting—somehow provocatively—that linear pricing may be an effective alternative policy to sugar taxes.