New products and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. People may realize different benefits and costs from the innovation, or have different beliefs about its benefits and costs, hear about it at different times, or delay in acting on their information. This paper analyzes the dynamics arising from different sources of heterogeneity in a completely general setting without placing parametric restrictions on the distribution of the relevant characteristics. The structure of the dynamics, especially the pattern of acceleration, depends importantly on which type of heterogeneity is driving the process. These differences are sufficiently marked that they provide a potential tool for discriminating empirically among diffusion mechanisms. The results have potential application to marketing, technological change, fads, and epidemics.
The diffusion of new products and practices usually takes time, and the proportion of people who have adopted at each point in time frequently, though not invariably, traces out an S-shaped curve. There is an extensive theoretical and empirical literature on this phenomenon and the mechanisms that might give rise to it. Different lines of explanation have been pursued in the various disciplines — marketing, sociology, and economics – where innovation diffusion has been most intensively studied. A crucial feature of some of these explanations is that heterogeneity among the agents is the reason they adopt at different times. Nevertheless, most of the extant models incorporate heterogeneity in a very restricted fashion, say by considering two homogeneous populations of agents, or by assuming that the heterogeneity is described by a particular family of distributions.