Том 16, № 1Страницы 5 - 22

Mathematical Modelling Economy

V.G. Mokhov
В статье представлен обзор основных методов моделирования экономики, используемых в научных исследованиях за последние двадцать лет. Обзор не претендует на охват всех направлений, методов и моделей, используемых в научных исследованиях в области экономики. Это невозможно сделать в рамках одной статьи. Рассмотрено математическое моделирование только двух разделов экономической теории: макроэкономики и микроэкономики. При этом отсутствует литературный обзор методов и моделей исследования в разделе микроэкономики, которые имеются в инструментарии научного исследования, но уже описаны в разделе макроэкономики. Надеюсь, что данный обзор будет полезен ученым, занимающимся опосредованным изучением экономических явлений и процессов.
Полный текст
Ключевые слова
моделирование; модель; макроэкономика; микроэкономика; источники; обзор.
Литература
1. Koshkin G., Kitayeva A. Nonparametric Identification of Static and Dynamic Production Functions. International Journal of Applied Mathematics, 2011, vol. 41, no. 3, pp. 228-234.
2. Suvorov N.V., Akhunov R.R., Gubarev R.V., et al. Applying the Cobb-Douglas Production Function for Analysing the Region'S Industry. Economy of Region, 2020, vol. 16, no. 1, pp. 187-200.
3. Guilhoto J.M. Input-Output Analysis: Theory and Foundations. Munich Personal RePEc Archive, 2011, vol. 72, article ID: 32566, 22 p.
4. Akhabbar A. The Case Against Indirect Statistical Inference. History of Political Economy, 2021, vol. 53, pp. 259-292. DOI: 10.1215/00182702-9414874
5. Busato M.I., Reif A.C., Possas M.L. Uma Tentativa de integracao entre Keynes e Kalecki: investimento e dinamica. Brazilian Journal of Political Economy, 2019, vol. 39, no. 3, pp. 509-526. (in Portuguese) DOI: 10.1590/0101-35172019-2909
6. Bruun C. Rediscovering the Economics of Keynes in an Agent-Based Computational Setting. New Mathematics and Natural Computation, 2016. vol. 12, no. 2, pp. 77-96. DOI: 10.1142/S1793005716500071
7. Myagotina E.D., Tregub I.V. Application of the Samuelson-Hicks Model in the Conditions of Modern Economy Case of Bhutan. The World Economics, 2021, vol. 5, pp. 404-413. DOI: 10.33920/vne-04-2105-06
8. Ovchinnikov A.V. On the Behavior of Solutions of a Modified Samuelson-Hicks Model with Two Accelerators. Journal of Mathematical Sciences, 2016, vol. 216, no. 5, pp. 722-724. DOI: 10.1007/s10958-016-2934-7
9. Miernyk W.H. Leontief and Dynamic Regional Models. Wassily Leontief And Input-Output Economics, 2004, pp. 90-101. DOI: 10.1017/CBO9780511493522.007
10. Kurz H.D., Salvadori N. The Dynamic Leontief Model and the Theory of Endogenous Growth. Economic Systems Research, 2000, vol. 12, no. 2, pp. 255-265. DOI: 10.1080/09535310050005734
11. Heikkinen T. A Study of Degrowth Paths Based on the von Neumann Equilibrium Model. Journal of Cleaner Production, 2020, vol. 251, article ID: 119562, 11 p. DOI: 10.1016/j.jclepro.2019.119562
12. Detemple J., Rindisbacher M. Dynamic Asset Allocation: Portfolio Decomposition Formula and Applications. Review of Financial Studies, 2010, vol. 23, no. 1, pp. 25-100. DOI: 10.1093/rfs/hhp040
13. Jancarik A. Dynamic Models. European Conference on e-Learning, 2015, pp. 264-271. DOI: 10.4324/9781351032148-3
14. Piiroinen P.T., Raghavendra S. A Nonsmooth Extension of Samuelson's Multiplier-Accelerator Model. International Journal of Bifurcation and Chaos, 2019, vol. 29, no. 10, article ID: 1930027, 15 p. DOI: 10.1142/S0218127419300271
15. Dassios I.K., Zimbidis A.A., Kontzalis C.P. The Delay Effect in a Stochastic Multiplier-Accelerator Model. Journal of Economic Structures, 2014, vol. 3, no. 1, article ID: 7, 15 p. DOI: 10.1186/s40008-014-0007-y
16. Grigorenko N., Lukyanova L. Optimal Control and Positional Controllability in a One-Sector Economy. Games, 2021, vol. 12, no. 1, pp. 1-12. DOI: 10.3390/g12010011
17. Loschenbrand M. A Transmission Expansion Model for Dynamic Operation of Flexible Demand. International Journal of Electrical Power and Energy Systems, 2021, vol. 124, article ID: 106252, 14 p. DOI: 10.1016/j.ijepes.2020.106252
18. Buzsaki G., Draguhn A. Neuronal Olscillations in Cortical Networks. Science, 2004, vol. 304, pp. 1926-1929. DOI: 10.1126/science.1099745
19. Roy S., Rana D. Machine Learning in Nonlinear Dynamical Systems. Resonance, 2021, vol. 26, no. 7, pp. 953-970. DOI: 10.1007/s12045-021-1194-0
20. Mutanov G. Mathematical Methods and Models in Economic Planning, Management and Budgeting. Berlin, Springer, 2015.
21. Grassetti F., Guzowska M., Michetti E. A Dynamically Consistent Discretization Method for Goodwin Model. Chaos, Solitons and Fractals, 2020, vol. 130, article ID: 109420, 9 p. DOI: 10.1016/j.chaos.2019.109420
22. Eichmeir P., Nachbagauer K., Lauf T. et al. Time-Optimal Control of Dynamic Systems Regarding Final Constraints. Journal of Computational and Nonlinear Dynamics, 2021, vol. 16, no. 3, article ID: 031003, 12 p. DOI: 10.1115/1.4049334
23. Arutyunov A.V., Karamzin D.Y., Pereira F. Pontryagin's Maximum Principle for Constrained Impulsive Control Problems. Nonlinear Analysis, Theory, Methods and Applications, 2012, vol. 75, no. 3, pp. 1045-1057. DOI: 10.1016/j.na.2011.04.047
24. Brock W.A., Taylor M.S. The Green Solow model. Journal of Economic Growth, 2010, vol. 15, no. 2, pp. 127-153. DOI: 10.1007/s10887-010-9051-0
25. Dombi M. The Golden Rule of Material Stock Accumulation. Environmental Development, 2022, vol. 41, article ID: 100638, 11 p. DOI: 10.1016/j.envdev.2021.100638
26. Mahroji D., Indrawati M. Analisis sektor unggulan dan spesialisasi regional kota bandar lampung. Jurnal Ekobis: Ekonomi Bisnis and Manajemen, 2020, vol. 9, no. 1, pp. 1-8. (in Indonesian) DOI: 10.37932/j.e.v9i1.44
27. Wei-Bin Zhang. A Three-Sector Spatial Growth Model of a Small Open Economy with Capital Accumulation. Journal of Economic Integration, 2009, vol. 24, no. 2, pp. 248-274. DOI: 10.11130/jei.2009.24.2.248
28. Songtao Li, Ruoran Chen, Lijian Yang et al. Predictive Modeling of Consumer Color Preference: Using Retail Data and Merchandise Images. Journal of Forecasting, 2020, vol. 39, no. 8, pp. 1305-1323. DOI: 10.1002/for.2689
29. Jisana T.K. Consumer Behaviour Models: an Overview. Journal of Commerce and Management, 2014, vol. 1, no. 5, pp. 34-43.
30. Martynenko A.V., Vikharev S.V. A Firm Model with Strict Regulation and Management Influence on Profit. Mathematical Notes of NEFU, 2020, vol. 27, no. 2, pp. 39-53. DOI: 10.25587/SVFU.2020.56.60.003
31. Junlong Chen, Xiaomeng Wang, Jiali Liu. Corporate Social Responsibility and Capacity Sharing in a Duopoly Model. Applied Economics Letters, 2021, vol. 28, no. 6, pp. 512-517. DOI: 10.1080/13504851.2020.1761531
32. Baqaee D.R., Farhi E. The Microeconomic Foundations of Aggregate Production Functions. NBER Working Paper, 2019, article ID: 25293. Available at: http://www.nber.org/papers/w25293.pdf (accessed on 24.11.2022)
33. Deride J., Jofre A., Wets R.J. Solving Deterministic and Stochastic Equilibrium Problems via Augmented Walrasian. Computational Economics, 2019, vol. 53, no. 1, pp. 315-342. DOI: 10.1007/s10614-017-9733-1