Concave or S-Shaped Sales Response to Advertising: Does It Really Matter? A Mathematical Model Modifies Conventional Wisdom about Ad Budgeting

摘要

In many advertising situations, the optimal decision-how much to spend and where to allocate the advertising budget-is not sensitive to the exact functional form used in modeling the process under study. For decades, however, researchers have taken for granted the conventional theory that the major distinction is whether the "shape" of sales, as a function of advertising, is concave increasing, with diminishing returns-or S-shaped-convex to begin with, and after an inflection point, concave from then on. In fact, as the current study showed, the distinction between concave and S-shaped sales-response functions can be irrelevant. The optimal advertising decision may not vary depending on the type of function.