ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Dynamics of the Economic Evolution with the Capital Depreciation

Author(s):

Alexander Nikolajevich Kirillov

Federal Research Center "Karelian Research Center of the Russian Academy of Sciences"
185910, Petrozavodsk, Pushkinskaya ul., 11
Institute of Applied Mathematical Research
Dr. Sci. in Physics and Mathematics, Associate Professor

kirillov@krc.karelia.ru

Alexander Mihaylovich Sazonov

Federal Research Center "Karelian Research Center of the Russian Academy of Sciences"
185910, Petrozavodsk, Pushkinskaya ul., 11
Institute of Applied Mathematical Research
Postgraduate student

sazon-tb@mail.ru

Abstract:

The mathematical model of sector capital distribution dynamics over efficiency levels with the depreciation is proposed. The qualitative analysis of the model is presented. The globally stable set (attractor) is constructed. The equilibria of the proposed dynamical model are determined, in the case of two efficiency levels their global stability is proved. It is shown that the global stability of the equilibrium means that the depreciation process causes excess production. It is proved that in the case of three efficiency levels there exists a unique equilibrium. In the case without the capital migrating from the second level to the first one the global stability of the equilibrium is proved.

Keywords

References:

  1. Schumpeter J. The theory of economic development (English translation of Theorie der wirtschaftlichen Entwicklung, 1912). Oxford University Press, 1961
  2. Nemytskii V. V., Stepanov V. V. The qualitative theory of differential equations. Princeton University, 1960. 523 p
  3. Lefschetz S. Differential Equations: Geometric theory. Princeton University, 1967. 390 p
  4. Acemoglu D., Cao D. Innovation by entrants and incumbents. J. Economic Theory. 157 (2015), 255-294
  5. Christensen C, Raynor M. The innovator's solution. Harvard Business School Press, 2003. 320 p
  6. Dosi G., Napoletano M., Roventini A., Treibich T. Micro and Macro Policies in the Keynes+Schumpeter Evolutionary Models. J. Evolutionary Economics. 27: 1 (2017), 63-90
  7. Henkin G. M., Polterovich V. M. A Difference-Differential Analogue of the Burgers Equation: Stability of the Two-Wave Behavior. J. Nonlinear Science. 4: (1994), 497-517
  8. Iwai K. Schumpeterian dynamics. Part I: an evolutionary model of innovation and imitation. J. Economic Behavior and Organization. 5: 2 (1984), 159-190
  9. Iwai K. Schumpeterian dynamics. Part II: technological progress, firm growth and " economic selection". J. Economic Behavior and Organization. 5: 3-4 (1984), 321-351
  10. Kirillov A. N., Sazonov A. M. Global schumpeterian dynamics with structural variations. Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming & Computer Software (Bulletin SUSU MMCS). 12: 3 (2019), 17-27
  11. Klimek P., Hausmann R., Thurner S. Empirical confirmation of creative destruction from world trade data. CID Working Paper. 238 (2012), 1-13
  12. Henkin G. M., Shananin A. A. Mathematical Modeling of the Schumpeterian Dynamics of Innovation. Matemetical Modeling. 26: 8 (2014), 3-19
  13. Polterovich V. M., Henkin G. M. An evolutionary model with interaction of the processes of development and adoption of technologies. Economics and Mathematical Methods. 24 (1988), 1071-1083
  14. Gelman L. M., Levin M. I., Polterovich V. M., Spivak V. A. Modeling of the dynamics of firms distribution in accordance with efficiency levels (ferrous metal industry case). Economics and Mathematical Methods. 29: 3 (1993), 460-469

Full text (pdf)