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Firms in the U.S. spend over 200 billion dollars each year advertising theirproducts to consumers, around one percent of the country's gross domesticproduct. It is of great interest to understand how that aggregate expenditureaffects prices, market efficiency, and overall welfare. Here, we present amathematical model for the dynamics of competition through advertising and finda surprising prediction: when advertising is relatively cheap compared to themaximum benefit advertising offers, rational firms split into two groups, onewith significantly less advertising (a "generic" group) and one withsignificantly more advertising (a "name brand" group). Our model predicts thatthis segmentation will also be reflected in price distributions; we use largeconsumer data sets to test this prediction and find good qualitative agreement.

A Mathematical Model for the Origin of Name Brands and Generics