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The Theory of Endogenous Economic Growth and Equations of Mathematical Physics

Author

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  • Polterovich, V.

    (Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia)

Abstract

The paper contains an overview of recent studies that use equations of mathematical physics, their analogs and modifications for describing endogenous evolution of firms' distribution by efficiency levels. The master equation is proposed that includes, as special cases, differential-difference analogues of the Burgers, Boltzmann, and Kolmogorov-Petrovsky-Piskunov equations. The analogues were applied by a number of authors in the study of Schumpeterian dynamics. The connections between the models of Schumpeterian dynamics and stochastic differential equations are demonstrated. A scheme for constructing multifactorial models of endogenous growth is also proposed, based on a combination of different imitation rules for different performance indicators. Directions for further research are outlined.

Suggested Citation

  • Polterovich, V., 2017. "The Theory of Endogenous Economic Growth and Equations of Mathematical Physics," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 193-201.
    • Handle: RePEc:nea:journl:y:2017:i:34:p:193-201
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    References listed on IDEAS

    as
    1. , & Lorenz, Jan & ,, 2016. "Innovation vs. imitation and the evolution of productivity distributions," Theoretical Economics, Econometric Society, vol. 11(3), September.
    2. Henkin, Gennadi M. & Polterovich, Victor M., 1991. "Schumpeterian dynamics as a non-linear wave theory," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 551-590.
    3. Robert E. Lucas Jr. & Benjamin Moll, 2014. "Knowledge Growth and the Allocation of Time," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 1-51.
    4. Acemoglu, Daron & Cao, Dan, 2015. "Innovation by entrants and incumbents," Journal of Economic Theory, Elsevier, vol. 157(C), pages 255-294.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Schumpeterian dynamics; imitation; innovation; Burgers equation; Boltzmann equation; Kolmogorov-Petrovsky-Piskunov equation;
    All these keywords.

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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