An Evolutionary Model with Interaction between Development and Adoption of New Technologies

Polterovich, Victor and Henkin, Gennadi (1989): An Evolutionary Model with Interaction between Development and Adoption of New Technologies. Published in: Matekon , Vol. 26, No. 1 (1989): pp. 3-19.

Abstract

We propose a difference-differential equation that reflects interactions between innovation and imitation processes to describe the evolution of the distribution curve of firms by efficiency levels. An explicit solution of this equation is obtained for arbitrary finite initial conditions. It is shown that this equation admits one-parametric family of logistic waves, and that arbitrary solution exponentially converges to one of the waves. This result explains two stylized empirical facts: the "logistic" shape of diffusion curves and the stable form of production capacities distribution by efficiency levels. Possible generalizations, modifications and applications are discussed.

• Item Type: MPRA Paper
• Language: English
• Keywords: innovation; imitation; diffusion; logistic distribution; efficiency; wave solution; stability; Burgers equation
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences ; Diffusion Processes

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