EMPIRICAL IMPLICATIONS OF MATHEMATICAL FUNCTIONS USED TO ANALYZE MARKET PENETRATION OF NEW PRODUCTS - CIGARETTES CASE-STUDY

Three types of S-shaped growth curves-the logistic, the lognormal, and the Gompertz-are widespread in the literature on analysis of market penetration of new products/processes. This article discusses the mathematical properties of these function in the light of their empirical implications, such as location of the point of maximum growth rate, the symmetry/asymmetry of the growth rates around that inflection point, and the ease of estimation (linear and nonlinear regressions). The empirical economic expectations cannot specify these phenomena a priori so that a less restrictive function should be preferred. Such a function is the Gompertz function. It is, therefore, applied to the study of market penetration of filtered and menthol cigarettes and shown that the empirical verification vindicates the theoretical postulates of that function. The empirical estimates are also closer to actual estimates of growth rates of adoption. © 1979.