Economic analysis of technological innovation, diffusion, and decline often proceeds according to sigmoid (S-shaped) models, either directly or as a component in more elaborate mathematical representations of the creative process. Three distinct aspects of American innovation policy — Aereo’s failed attempt to retransmit television broadcasts, agricultural biotechnology, and network neutrality — invite analysis according to one variant or another of the logistic function. Innovation and legal policies designed to foster it follow the leaps, metes, and bounds of sigmoid functions.
Part I introduces the logistic function as the simplest analytical expression of a sigmoid function. Its parameters provide very clear interpretations grounded in physical principles. Part II evaluates the Aereo controversy and agricultural biotechnology as instances of logistic substitution between competing products. The deployment of plant-incorporated pesticides and herbicide-resistant crops arguably follows the Hubbert curve, a related function that describes peak production of depletable resources and their eventual exhaustion. Part III proposes multiple ways of understanding network neutrality as a problem of multilayered innovation. The presence of two different types of nonlinear growth, in network operating costs and in expressive diversity online, suggests that the law should prescribe independent rather than bundled solutions to these conceptually distinct subjects.