A Mathematical Model for the Origin of Name Brands and Generics

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)625-639
Number of pages15
JournalSIAM Review
Issue number3
StatePublished - 2022


  • advertising
  • consumer behavior
  • differential games
  • dynamical systems
  • economic dynamics
  • nonlinear dynamics

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


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