A Marketing Promotion Model With Word of Mouth Effects

Cover A Marketing Promotion Model With Word of Mouth Effects
A Marketing Promotion Model With Word of Mouth Effects
Gary L Lilien
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Assume that response to detailing is a quadratic function of detailing effort, i. E. X^(d(t))= X^^d(t) + X^^d^Ct). This particular functional form has the following properties: (a) X^(o) = (b) Neither increasing nor decreasing returns to scale are specified a priori; however, if \ is <0 (as would be expected) 2 then X (d(t)) has an upper bound of -( X / 4X ) and detailing above the level of " ^i-, /^X results in decreasing response. So, a practical upper bound on detailing is established. Certainly, more complex forms of X could be generated; this simple quadratic form is rather flexible and leads to a simple estimation procedure. We assume that X, X and X are linear functions of their arguments, i. E. X2(C2(t-l)) = X2C"2(t-l), etc. 12. Note that we only observ^e K^(t) + K2(t) directly and not N(=C^(0)), C (t) or C^Ct). We can resolve this issue as follows: Let us assume that our time intervals have been chosen such that it is not unreasonable to assert that 2 E(w) Now. Using that value in place of C^Ct), choose a time t=T such that 03(1) =0 for t < T.

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