Abstract
The work develops and investigates a mathematical model for evolution of the technological structure of an economic system where different technologies compete for the common essential resources. The model is represented by a system of consumer–resource rate equations. Consumers are technologies formalized as populations of weakly differentiated firms producing a similar commodity with like average output. Firms are characterized by the Leontief–Liebig production function in stock-flow representation. Firms self-replicate with a rate proportional to production output of the respective technology and dissolve with a constant rate of decay. The resources are supplied to the system from outside and consumed by concerned technologies; the unutilized resource amounts are removed elsewhere. The inverse of a per firm break-even resource availability is proposed to serve as a measure for competitiveness towards a given resource. The necessary conditions for coexistence of different technologies are derived, according to which each contender must be a superior competitor for one specific resource and an inferior competitor for the others. The model yields a version of the principle of competitive exclusion: in a steady state, the number of competing technologies cannot exceed the number of limiting resources. Competitive outcomes (either dominance or coexistence) in the general system of multiple technologies feeding on multiple essential resources are shown to be predictable from knowledge of the resource-dependent consumption and growth rates of each technological population taken alone. The proposed model of exploitative competition with explicit resource dynamics enables more profound insight into the patterns of technological change as opposed to conventional mainstream models of innovation diffusion.
Highlights
The pioneering empirical works on technology adoption initiated by Ryan and Gross [1] and taken up by Griliches [2] induced a steady stream of studies aiming at describing the diffusion, i. e. spread, of technological innovations that has persisted to this day and remained highly topical
In economics terms, according to Stoneman [3], “Technological diffusion is the process by which innovations spread within and across economies.”
Combining the Schumpeter’s vision of production function as unique code for technology with ideas of the evolutionary economics we presume that fund factors of production facilitate the conversion of resources to product in much the same catalytic way as do enzymes in living cells when transforming substrates into different chemical compounds
Summary
The pioneering empirical works on technology adoption initiated by Ryan and Gross [1] and taken up by Griliches [2] induced a steady stream of studies aiming at describing the diffusion, i. e. spread, of technological innovations that has persisted to this day and remained highly topical. In economics terms, according to Stoneman [3], “Technological diffusion is the process by which innovations (be they new products, new processes or new management methods) spread within and across economies.”. Inasmuch as the present research is not directly concerned with the validation of diffusion models by the instruments of regression analysis, we refer the reader to comprehensive surveys [12, 16,17,18,19,20] for more information in that direction
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