The Beta Distribution as a Model of Behavior in Consumer Goods Markets

Loyalty in branded consumer goods markets is a subject that has often been discussed in the marketing literature. Virtually no matter what definition of loyalty has been adopted, it has been found to exist. This paper examines loyalty from a different perspective--that of an aggregation of consumers' probabilities of purchasing a particular brand, called the loyalty distribution. Loyalty in this context implies that most consumers should either have high probabilities of purchasing the brand or high probabilities of purchasing one of the competitive brands; few consumers have equally likely probabilities of purchasing the brands in a market. Another way of stating the point is that the majority of consumers are loyal and tend to repeat purchase their favorite brand while few are nonloyal and tend to switch back and forth. The Beta distribution is examined as a model of the loyalty distribution. It is demonstrated that, if this distribution is a good model for the underlying process, it is possible to define, in terms of brand share and repeat, the conditions under which the loyalty distribution will assume each of its possible shapes. Since the U or J shape is consistent with loyalty in consumer goods markets, the requirements for this shape are emphasized. It is shown, in particular, that, in order to maintain one of these shapes, a brand must have a greater percent of its share accounted for by repeat purchasing the larger its share of market. A model of switching and repeat based on the Beta is explored and a number of examples of the characteristics of the model in different markets are worked out. Maximum switching is shown to occur in markets with equal share brands, i.e., maximum entropy markets. Total switching is shown to increase at a decreasing rate as the number of brands in the market increases. Finally, a number of areas for further research are suggested. The model developed has barely scratched the surface of its potential.