Little, John D. C.
March 1986
Marketing Science;Spring86, Vol. 5 Issue 2, p107
Academic Journal
This article presents author's comments on a research paper written by researchers Vijay Mahajan and Eitan Muller who has analyzed a particular class of advertising policies under the assumption of an S-shaped response function. Researcher M.W. Sasieni characterizes optimal advertising policies for a broad class of dynamic response models. As Mahajan and Muller note, Sasieni has shown that an S shaped response function can, without loss of generality, be replaced by an entirely concave one, if we admit policies in which the advertising rate alternates rapidly between zero and a particular value. Sasieni (1975) has subsequently shown in a private communication that the same type of policy is optimal when the advertising budget is constrained. He does this by introducing a Lagrange multiplier for the budget constraint. The result is reasonably intuitive, since the Lagrange multiplier recreates an unconstrained problem. In the limited budget case, there is a reasonable possibility of chattering because the budget constraint may force the advertising rate into the range.


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