Теория эндогенного экономического роста и уравнения математической физики.

Polterovich, Victor (2017): Теория эндогенного экономического роста и уравнения математической физики.

Abstract

It is given an overview of recent studies that use equations of mathematical physics, their analogs and modifications for describing endogenous evolution of technologies. A master equation is proposed that includes, as special cases, a number of known models of Schumpeterian dynamics. 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.

• Item Type: MPRA Paper
• English Title: The theory of endogenous economic growth and equations of mathematical physics
• Language: Russian
• Keywords: Schumpeterian dynamics, imitation, innovation, Burgers equation, Boltzmann equation, Kolmogorov-Petrovsky-Piskunov equation
• Subjects: A - General Economics and Teaching > A1 - General Economics > A12 - Relation of Economics to Other Disciplines; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; 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; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models

References

Александрова А.Ю. (2015). Исследование скорости бегущей волны в одной модификации модели Полтеровича–Хенкина. Труды МФТИ. Том 7, № 4, 11-16.

Берндссон Б., С. В. Кисляков, Р. Г. Новиков, В. М. Полтерович и др.(2017). Геннадий Маркович Хенкин (1942-2016). Успехи математических наук, №2.

Гельман Л.М., Левин М.И., Полтерович В.М., Спивак В.А.(1993). Моделирование динамики распределения предприятий отрасли по уровням эффективности (на примере черной металлургии). Экономика и математические методы. Том 29, вып. 3, 460-469.

Полтерович В. М., Г. М. Хенкин (1988). Эволюционная модель взаимодействия процессов создания и заимствования технологий. Экономика и математические методы, т.24, №6, с.1071-1083.

Хенкин Г.М., А.А. Шананин (2014). Математическое моделирование шумпетеровской инновационной динамики. Математическое моделирование, т. 26, № 8, 3-19.

Acemoglu Daron, Dan Cao (2015). Innovation by entrants and incumbents. Journal of Economic Theory, 157. 255–294.

Aleksandrova A.Y. (2015). Running wave speed analysis in one Polterovich–Henkin model modification. Proceedings of MIPT. Vol. 7, No. 4, 11-16 (in Russian).

Berndsson B., S. V. Kislyakov, R. G. Novikov, V. M. Polterovich, et al. (2017). Gennadi Markovich Henkin (1942-2016). Uspekhi Matematicheskikh Nauk, №2 (in Russian).

Gelman L. M., Levin M. I., Polterovich V. M., Spivak V. A. (1993). Modeling of the Dynamics of Firms Distribution in Accordance with Efficiency Levels (Ferrous Metal Industry Case). Economics and Mathematical Methods, Vol. 29, No. 3, 460-469 (in Russian).

Henkin G. M. (2012). Burgers type equations, Gelfand’s problem and Schumpeterian dynamics. Journal of Fixed Point Theory and Applications, June, Volume 11, Issue 2,  199–223.

Henkin G. M., V. M. Polterovich (1991). Schumpeterian Dynamics as a Non-linear Wave Theory. Journal of Mathematical Economics, Vol. 20, No. 6,  551-590.

Henkin G. M., A. A. Shananin (2014). Mathematical modeling of the schumpeterian dynamics of innovation. Matemetical Modeling, Vol. 26, No. 8, 3-19 (in Russian).

Hongler Max-Olivier, Olivier Gallay, Fariba Hashemi. Impact of Imitation on the Dynamics of Long Wave Growth. July 27, 2016. 28 pp.

König Michael D., Jan Lorenz, Fabrizio Zilibotti (2016). Innovation vs. imitation and the evolution of productivity distributions. Theoretical Economics 11, 1053–1102.

Lucas Jr. Robert E., Benjamin Moll. Knowledge Growth and the Allocation of Time. Journal of Political Economy, 2014, vol. 122, No. 1. 52 pp.

Luttmer Ezra G.J. Eventually, Noise and Imitation Implies Balanced Growth. Federal Reserve Bank of Minneapolis Working Paper 699August 2012. 29 pp.

Polterovich V., G. Henkin (1988). An Evolutionary Model with Interaction between Development and Adoption of New Technologies. Economics and Mathematical Methods, Vol. 24, N6, 1071-1083 (in Russian).