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


  • Polterovich, Victor
  • Henkin, Gennadi


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.

Suggested Citation

  • Polterovich, Victor & Henkin, Gennadi, 1989. "An Evolutionary Model with Interaction between Development and Adoption of New Technologies," MPRA Paper 22555, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:22555

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    Cited by:

    1. repec:nea:journl:y:2017:i:34:p:193-201 is not listed on IDEAS
    2. Polterovich, Victor, 2017. "Теория Эндогенного Экономического Роста И Уравнения Математической Физики
      [The theory of endogenous economic growth and equations of mathematical physics]
      ," MPRA Paper 78622, University Library of Munich, Germany.

    More about this item


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

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes


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