A Mathematical Model for New Product Diffusion: The Influence of Innovators and Imitators

Abstract

A simple mathematical model describing the diffusion of a new, infrequently purchased product is proposed. Many previous papers have reported that the differing behaviour of "innovators" and "imitators" is fundamental to the diffusion process. However, previous models have failed to represent this differing behaviour effectively. The model presented considers a new and, importantly, simple way of viewing the diffusion process for consumer durables based on a simplified representation of "innovative" and "imitative" response of adopters to certain types of product information. The resulting model can accommodate bimodal first purchase sales curves, which are found to occur quite frequently, in addition to the more traditional unimodal curves. The resulting shape of the diffusion curve, which is the early product life cycle (PLC), can be explained in terms of key dynamic parameters of the model. Data for six consumer durables are analysed to test the model's performance.

Keywords: Paul Steffens, product innovation, consumer behaviour, durable products, mathamatical model