A new theorem for optimizing the advertising budget

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 that has dominated this topic for the last 50 years. The elegant nature of the proof makes it especially suitable for managerial economics textbooks. The simple nature of the theorem means that it is easily adopted, by both large and small businesses, in place of heuristics such as industry advertising to sales ratios. From meta-analysis, the mean advertising elasticity is .11. Therefore, in the absence of any other information, companies should spend 11% of gross profit on advertising.