Adopters as a Scarce Resource: A Chemostat-like Approach to Single-Technology Diffusion

Abstract

This paper models innovation diffusion trajectories within capacity-limited market niches. To overcome the structural limitations of classical phenomenological frameworks (Bass, Gompertz, and Mansfield models)—namely, rigidly fixed trajectory asymmetry and the lack of underlying microeconomic justification—the author proposes an interdisciplinary system-dynamics approach. The framework maps the ecological consumer–resource concept of resource rationing, specifically the Arditi–Ginzburg–Contois functional response, onto operations management theory by incorporating Karmarkar’s clearing function and the Leontief–Liebig production function. A mechanistic non-linear technological diffusion model is analytically derived as an implicit function of time. For parameter identification, a robust, grid-based numerical inversion procedure using fast vector interpolation is implemented. The model is empirically validated against classical benchmarks using two contrasting macroeconomic case studies: quarterly Apple iPod sales and the annual German cellular mobile internet market. The results demonstrate the high explanatory flexibility and competitive goodness of fit of the framework, yielding robust approximations due to a flexible structural asymmetry parameter that endogenously adapts to the initial market lag period. The scientific contribution lies in the fundamental justification of the macroeconomic S-curve through the underlying mass-balance equations of a non-linear consumer–resource system, providing a structurally stable tool for capacity planning.