A Mathematical Model for the Origin of Name Brands and Generics

Joseph D. Johnson; Adam M. Redlich; Daniel M. Abrams

doi:10.1137/20M1360888

A Mathematical Model for the Origin of Name Brands and Generics

Joseph D. Johnson, Adam M. Redlich, Daniel M. Abrams

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Firms in the U.S. spend over $200 billion each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a ``generic"" group) and one with significantly more advertising (a ``name-brand"" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.

Original language	English (US)
Pages (from-to)	625-639
Number of pages	15
Journal	SIAM Review
Volume	64
Issue number	3
DOIs	https://doi.org/10.1137/20M1360888
State	Published - 2022

Funding

This work was supported by the National Science Foundation through Research Training grant 1547394. We thank the Nielsen Corporation for their generosity in making their proprietary data available for scientific research. We also thank Vicky Chuqiao Yang for useful conversations. \ast Received by the editors August 19, 2020; accepted for publication (in revised form) September 20, 2021; published electronically August 4, 2022. https://doi.org/10.1137/20M1360888 Funding: This work was supported by the National Science Foundation through Research Training grant 1547394. \dagger Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 USA ([email protected], adamredlich2020@ u.northwestern.edu). \ddagger Department of Engineering Sciences and Applied Mathematics, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL 60208 USA ([email protected]).

Keywords

advertising
consumer behavior
differential games
dynamical systems
economic dynamics
nonlinear dynamics

ASJC Scopus subject areas

Theoretical Computer Science
Computational Mathematics
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1137/20M1360888

Cite this

@article{2ba9d803c20e407d90bf6ce9774589e2,

title = "A Mathematical Model for the Origin of Name Brands and Generics",

abstract = "Firms in the U.S. spend over $200 billion each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a ``generic{"}{"} group) and one with significantly more advertising (a ``name-brand{"}{"} group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.",

keywords = "advertising, consumer behavior, differential games, dynamical systems, economic dynamics, nonlinear dynamics",

author = "Johnson, {Joseph D.} and Redlich, {Adam M.} and Abrams, {Daniel M.}",

note = "Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",

year = "2022",

doi = "10.1137/20M1360888",

language = "English (US)",

volume = "64",

pages = "625--639",

journal = "SIAM Review",

issn = "0036-1445",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "3",

}

TY - JOUR

T1 - A Mathematical Model for the Origin of Name Brands and Generics

AU - Johnson, Joseph D.

AU - Redlich, Adam M.

AU - Abrams, Daniel M.

PY - 2022

Y1 - 2022

N2 - Firms in the U.S. spend over $200 billion each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a ``generic"" group) and one with significantly more advertising (a ``name-brand"" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.

AB - Firms in the U.S. spend over $200 billion each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a ``generic"" group) and one with significantly more advertising (a ``name-brand"" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.

KW - advertising

KW - consumer behavior

KW - differential games

KW - dynamical systems

KW - economic dynamics

KW - nonlinear dynamics

UR - http://www.scopus.com/inward/record.url?scp=85137618467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85137618467&partnerID=8YFLogxK

U2 - 10.1137/20M1360888

DO - 10.1137/20M1360888

M3 - Article

AN - SCOPUS:85137618467

SN - 0036-1445

VL - 64

SP - 625

EP - 639

JO - SIAM Review

JF - SIAM Review

IS - 3

ER -

A Mathematical Model for the Origin of Name Brands and Generics

Abstract

Funding

Keywords

ASJC Scopus subject areas

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this