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

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  • Polterovich, Victor
  • Henkin, Gennadi

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.

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File URL: http://mpra.ub.uni-muenchen.de/22555/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22555.

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Date of creation: 1989
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Publication status: Published in Matekon 1.26(1989): pp. 3-19
Handle: RePEc:pra:mprapa:22555

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Keywords: innovation; imitation; diffusion; logistic distribution; efficiency; wave solution; stability; Burgers equation;

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