Impeding the Juggernaut of Innovation Diffusion: A Production‐Constrained Model

Abstract

Models of innovation diffusion typically depict an inexorable momentum once the process begins to roll. Limited production capacity, however, can place a cap on this process, leading to waiting lines of potential customers, thus diminishing overall service quality and the speed of diffusion. Identifying the minimum production capacity needed for unimpeded and unimpaired diffusion can ensure that there are no customers waiting to adopt the product. We propose a production‐capacity‐constrained diffusion model that considers an exogenous industry production capacity and accounts for word‐of‐mouth effects from adopters as well as waiting customers. We derive analytical expressions for minimum capacity needed under multiple production scenarios. We present a dual‐objective non‐linear least squares procedure with large‐scale grid search for estimating the parameters. We apply our model to several new product innovation data sets, ranging from vacuum cleaners to sports utility vehicles in the United States to iPhones globally. Our estimates show that product shortages exist, ranging from mild to severe, in all of these product markets. We are able to corroborate some of our findings with independent external sources of evidence. We find that information on industry capacity can be recovered with as few as 5 years of sales data. Our model has practical implications for policy makers and can help equity analysts triangulate industry capacity better, particularly when such information is closely held.