A model for technology diffusion based on the “consumer – resource” equations

Mustafin A.
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The author presents a new macroeconomic model designed to analyze and forecast technology diffusion processes in markets characterized by bounded capacity. The study addresses the major limitations of classical phenomenological models, such as the Bass and Gompertz frameworks, which suffer from a rigidly fixed trajectory asymmetry and lack explicit microeconomic foundations. To overcome these constraints, we employ an interdisciplinary approach that transfers the ecological concept of limited resource rationing from the Arditi–Ginzburg–Contois model into operations management theory. This framework integrates the Karmarkar clearing function with the Leontief–Liebig production function to establish a rigorous dynamic balance. By applying this integration, the author analytically derives an alternative technological innovation diffusion law that expresses time as an explicit function of the cumulative market volume. To identify parameters from empirical data, the study develops a robust numerical grid inversion algorithm that utilizes vector linear interpolation within the MATLAB computing environment. This approach avoids iterative root-finding errors and ensures high computational stability for the non-linear least squares optimization procedure. We test the empirical validity of the developed diffusion law using two distinct historical macroeconomic cases: the quarterly cumulative sales of the Apple iPod and the annual subscription data for the mobile broadband market in Germany. The resulting statistical metrics demonstrate that the proposed model provides superior approximation quality and mathematical advantages on high-tech market data due to its highly flexible asymmetry parameter. The fundamental scientific novelty of this research lies in the theoretical justification of the macroeconomic S-curve through the internal balance equations of an open chemostat-type system operating under a competitive vacuum. The proposed mathematical apparatus offers a practical tool for corporate management and regulatory agencies to plan market capacity and accurately forecast peak technological substitution rates.

Keywords: technology diffusion, S-curve, Bass model, Gompertz model, Karmarkar clearing function, resource rationing, non-linear least squares, chemostat
Citation in English: Mustafin A. A model for technology diffusion based on the “consumer – resource” equations // Computer Research and Modeling, 2026, vol. 18, no. 4, pp. 1035-1052
Citation in English: Mustafin A. A model for technology diffusion based on the “consumer – resource” equations // Computer Research and Modeling, 2026, vol. 18, no. 4, pp. 1035-1052
DOI: 10.20537/2076-7633-2026-18-4-1035-1052
URL: http://crm-en.ics.org.ru/journal/article/3758/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Mustafin A.

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