This paper reports a new theorem and proof for optimizing the advertising budget. The theorem is that the optimal rate of advertising is equal to gross profit multiplied by advertising elasticity. This does not involve a ratio of elasticities, and so is an advance on the Dorfman-Steiner theorem...

The negative binomial distribution (NBD) has been widely used in marketing for modeling purchase frequency counts, particularly in packaged goods contexts. A key managerially relevant use of this model is Conditional Trend Analysis (CTA)—a method of benchmarking future sales utilizing the NBD...