Parallel Inverse Aggregate Demand Curves in Discrete Choice Models

33 Pages Posted: 29 Jun 2020 Last revised: 20 Jun 2022

See all articles by Kory Kroft

Kory Kroft

University of Toronto

René Leal Vizcaíno

Northwestern University, Department of Economics; Banco de Mexico

Matthew Notowidigdo

University of Chicago - Booth School of Business

Ting Wang

Northwestern University - Department of Economics

Date Written: June 2020

Abstract

This paper highlights a previously-unnoticed property of commonly-used discrete choice models, which is that they feature parallel demand curves. Specifically, we show that in random utility models, inverse aggregate demand curves shift in parallel with respect to variety if and only if the random utility shocks follow the Gumbel distribution. Using results from Extreme Value Theory, we provide conditions for other distributions to generate parallel demands asymptotically, as the number of varieties increase. We establish these results in the benchmark case of symmetric products, illustrate them using numerical simulations and show that they hold in extended versions of the model with correlated tastes and asymmetric products. Lastly, we provide a “proof of concept” of parallel demands as an economic tool by showing how to use parallel demands to identify the change in consumer surplus from an exogenous change in product variety.

Suggested Citation

Kroft, Kory and Leal Vizcaíno, René and Notowidigdo, Matthew and Wang, Ting, Parallel Inverse Aggregate Demand Curves in Discrete Choice Models (June 2020). NBER Working Paper No. w27437, Available at SSRN: https://ssrn.com/abstract=3637738

Kory Kroft (Contact Author)

University of Toronto ( email )

Toronto, Ontario M5S 3G8
Canada

René Leal Vizcaíno

Northwestern University, Department of Economics ( email )

Evanston, IL
United States

Banco de Mexico ( email )

Ave Cinco e Mayo 1
Col. Centro
Mexico City, Mexico DF 06059
Mexico

Matthew Notowidigdo

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Ting Wang

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States

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