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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.
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