The Implications of Diffusion Models for Accelerating the Diffusion of Innovation

This paper explores the implications of a simple, yet robust model of innovation diffusion for developing insight into the problem of controlling the rate of new product diffusion. Some basic, theoretical results are developed using a simple model. Those results are shown to relate to optimal policies developed from a more complex model of innovation diffusion, developed for the Department of Energy's photovoltaic program. Introduction Much work has been done recently (see [8, 141 for reviews) on the development of mathematical models to describe the diffusion of new products and technologies. Many of these models are quite good at describing the time path of the innovations, after the fact. But, with few exceptions [6, 7, 121, these models have not focused on ways of accelerating or controlling the diffusion rate over time or over regions. This paper has two objectives. The first is to demonstrate that a widely referred to and used model of innovation diffusion has some interesting implications (some questionable) for accelerating the rate of new product diffusion. The second is to show that those insights are consistent with the type of results we obtain for a more detailed model, currently being developed to assess government development program options for solar generated electricity (photovoltaics) . The Timing of Demonstration Programs Bass [2] introduced a flexible diffusion model that has useful behavioral implications. We choose this model for analysis as it has been applied by Bass and others [5] to a number of product situations and has been shown to work quite well. We introduce the following notation: S ( t ) = number of firms having adopted an innovation by time t ( ~ ( 0 ) = 0) . S" = total number of firms considered eligible to adopt the innovation. p = coefficient of innovation; this equals the rate of product adoption when there have been no previous purchases. q = coefficient of imitation; the effect of previous purchases on the rate of adoption. GARY L. LILIEN is Associate Professor of Management Science at the Sloan School of Management at MIT. His field of special interest is industrial marketing and he has developed a course on the subject at Sloan. Prior to coming to MIT, he was employed in the Management Science Department at Mobil Oil. @ Elsevier North Holland, Inc., 1980 00401625/80/080339 13s02.25