Pushkinskaya st. 43. office 10
Rostov-on-Don, Russia
344082
e-mail: info@hjournal.ru 
tel. +7(863) 269-88-14

cubsEN (2)

Economic-Mathematical Models for Studying of Mesolevel of Economy

Economic-Mathematical Models for Studying of Mesolevel of Economy

Journal of Institutional Studies, , Vol. 9 (no. 3),

The review of a number of the mathematical models applied to the description and analysis of mesolevel of economy is presented in article. The criteria for assigning models to a class of meso-level models that distinguish them from purely microeconomic or macroeconomic models are proposed. Examples of the use of mathematical models in the literature on mesoeconomics are given. The some classical models like input–output model of Leontief, or, for example, game theory, and rather new models using a mathematical apparatus of systems of nonlinear mappings or the differential equations, diverse simulation models, can be considered as models of mesolevel. Just as development of nonlinear physics has led to a possibility of the description of multi-scale self-organizing structures, the mesolarge-scale level of economy understood as set of the subsystems evolving, interacting among themselves, competing and cooperating generating the emergent phenomena like the increasing return, the hyperbolic growth or self-organized criticality can be appropriate to describe by means of models of econophysics and use of the principles of synergetrics. Also discussed are the prospects for the development of meso-level models and the problem of the conventionality of separating the levels of the economy, due, for example, to signs of scale invariance in some socio-economic systems.


Keywords: mesoeconomics; mesolevel of economy; game theory; econophysics; simulation modeling; production functions; scale invariance

References:
  • Akaev, A. (2000). Transition economy through the eyes of physics. Bishkek. Uchkun, 262 p. (In Russian).
  • Arrow, K. J. and Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica, 22 (3), 265–290.
  • Bak, P. (2013). How nature works: The science of self-organized criticality. Moscow, URSS, 276 p. (In Russian).
  • Beklaryan, L. A., Borisova, S. V. and Khachatryan N. K. (2012). A single-dynamic model of replacement assets. Main properties. Zh. Vychisl. Mat. Mat. Fiz., 52 (5), 801–817. (In Russian).
  • Boucekkine, R., de la Croix, D. and Licandro, O. (2006). Vintage Capital. Department of Economics, European University Institute, Eco no. 2006/08 (http://cadmus.iue.it/dspace/bitstream/1814/4346/1/ECO2006-8.pdf – Access Date: 10.07.2017).
  • Bronshpak, G. K. and Moskovkin, V. M. (2004). Economic Clusters: Elements of a Quantitative Theory, Network Structures, Typology. Business Inform, 11–12, 20–29. (In Russian).
  • Chekmareva, E. A. (2016). Review of Russian and foreign experience of agent-oriented modeling of complex socio-economic mesolevel systems. Economic and social changes: facts, trends, forecast, 2 (44), 225–246. (In Russian).
  • Chernavsky, D. S., Starkov, N. I. and Shcherbakov, A. V. (2002). On some problems of physical economics. Phys. Usp, 45, 977–997. (In Russian).
  • Chukanov, S. V. (1984). On one dynamic model of the economy with funds differentiated by the moments of creation. Models and methods in forecasting scientific and technical progress, 2, VNIISI, Moscow, pp. 46–61. (In Russian).
  • Cohen, A. J. and Harcourt, G. C. (2003). Whatever Happened to the Cambridge Capital Theory Controversies? Journal of Economic Perspectives, 17 (1), 199–214.
  • Dementev, V. E. (2015). Micro- and meso-bases of macroeconomic dynamics. Bulletin of the University (State University of Management), 8, 103–109. (In Russian).
  • Diamond, P. A. (1965). National Debt in Neoclassical Growth Model. American Economic Review, 55 (5), 1126–1150.
  • Elsner, W. (2015). The Theory of Institutional Change Revisited: The Institutional Dichotomy, Its Dynamic, and Its Policy Implications in a More Formal Analysis. Tenth International Symposium on Evolutionary Economics “The Evolution of Economic Theory: Economic Reproduction, Technologies, Institutions”. SPb, Aletheia, pp. 280–292. (In Russian).
  • Erofeenko, V. T. and Kozlovskaya, I. S. (2011). Partial differential equations and mathematical models in economics: a course of lectures. Moscow, URSS Editorial. 248 p. (In Russian).
  • Forrester, J. (1958). Industrial Dynamics: A Major Breakthrough for Decision Makers. Harvard Business Review, 36 (4), 37–66.
  • Frisch, R. (1933). Propagation Problems and Impulse Problems in Dynamic Economics. Economic essays in honor of Gustav Cassel, London, pp. 171–205.
  • Gale, D. (1956). A closed linear model of production. In Harold W. Kuhn and Albert W. Tucker, editors, Linear Inequalities and Related Systems. Annals of Mathematics Studies, 38 (18), 285–303.
  • Grebnev, M. I. (2015). The aggregate production function for the Russian economy (with progress in science and technology considered). Perm University Bulletin. Economy, 4 (27), 71–79. (In Russian).
  • Johansen, L. (1959). Substitutions versus Fixed Production Coefficients in the Theory of Economic Growth: A Synthesis. Econometrica, 27 (2), 157–175.
  • Kantorovich, L. V., Zhiyanov, V. I. and Khovansky, A. G. (1978). The analysis of dynamics of economic indicators on the basis of single-product dynamic models. Sb.tr. VNII sistemnyh issled., 9, 5–25. (In Russian).
  • Keynes, J. (1936). The General Theory of Employment, Interest and Money, London, Macmillan.
  • Kirdina, S. G. (2014). Institutional Matrices and Development in Russia. (3nd revised and supplemented edition). Moscow-St. Petersburg, Nestor-history, 468 p. (In Russian).
  • Kirdina, S. G. (2015). Methodological institutionalism and mesolevel of social analysis. Sotsiologicheskie Issledovaniia, 12, 51–59. (In Russian).
  • Kirilyuk, I. L. (2013). Models of Production Functions for the Russian Economy. Computer Research and Modeling, 5 (2), 293–312. (In Russian).
  • Kirilyuk, I. L. (2016). The discrete form of the equations in the theory of the shifting mode of reproduction with different variants of financial flows. Computer Research and Modeling, 8 (5), 803–815. (In Russian).
  • Kleiner, G. B. (2003). Mesoeconomic problems of the Russian economy. Economic bulletin of Rostov State University, 1 (2), 11–18. (In Russian).
  • Kolpak, E. P. Gorynya, E. V. (2015). Mathematical models of “care” from competition. Young scientist, 11 (91), 59–70. (In Russian).
  • Korotaev, A. V., Malkov, A. S. and Khalturina, D. A. (2007). Compact mathematical macromodel of technical-economic and demographic development of the world-system (1-1973). Justification. History and modernity, 1, 9–37. (In Russian).
  • Kuznetsov, Yu. A., Markova, S. E. and Michasova, O. V. (2014). Mathematical modeling of dynamics of competitive replacement of generations of innovative goods. Vestnik Nizhegorodskogo gosudarstvennogo universiteta im. N. I. Lobachevskogo, 2 (1), 170–179. (In Russian).
  • Leontief, W. (1936). Quantitative input and output relations in the economic systems of the United States. The Review of Economic Statistics, 18 (3), 105–125.
  • Maevsky, V. I. and Malkov, S. Yu. (2013). A New Approach to the Theory of Reproduction. Moscow, INFRA-M, 238 p. (In Russian).
  • Malkov, S. Yu. and Kirilyuk, I. L. (2013). Modeling the dynamics of competing communities: options for interaction. Information wars, 2 (26), 49–56. (In Russian).
  • Matveenko, V. D. (1981). Discrete model with the funds that differ in life cycle. Optimizacija, 26 (43), 90–102. (In Russian).
  • Mesoeconomics of development (2011) / Ed. G. B. Kleiner; Central Economic Mathematical Institute RAS. Moscow, Science, 805 p. (In Russian).
  • Mirowski, P. (1981). Is there a mathematical neoinstitutional economics? Journal of Economic Issues, 15, 593–613.
  • Nash, J. (1951). Non-cooperative games. Annals of Mathematics, 54 (2), 286–295.
  • Ng, Y.-K. (1986). Mesoeconomics: A Micro – Macro Analysis. New York, St. Martin’s Press.
  • Ng, Y.-K. (1992). Business Confidence and Depression Prevention: A Mesoeconomic Perspective. American Economic Review, 82 (2), 365–371.
  • Ng, Y.-K. and Wu, Y. (2004). Multiple Equilibria and Interfirm Macro-Externality: An Analysis of Sluggish Real Adjustment. Annals of Economics and Finance, 5 (1), 61–77.
  • Olenev, N. N. and Pospelov, I. G. (1989). Exploring of the Investment Policy of Firms in Market Economy. In: Mathematical Modelling: Methods of Description and Investigation of Complex Systems / Ed. A. A. Samarsky, N. N. Moiseev, A. A. Petrov / Moscow, Nauka, pp. 175–200. (In Russian).
  • Petrosyan, D. S. (2006). Mathematical models of institutional economics. Audit I finansivyj analiz, 4, 279–313. (In Russian).
  • Podlazov, A. V. (2002). Distribution of competitors, scale invariance of the state and models of linear growth. Izvestiya Vuzov. Applied nonlinear dynamics, 10 (1–2), 20–43. (In Russian).
  • Romanovsky, M. Yu. and Romanovsky, Yu. M. (2012). Introduction to Econophysics: Statistical and Dynamical Models. Moscow – Izhevsk, Regular and Chaotic Dynamics, 340 p. (In Russian).
  • Samuelson, P. A. (1958). An exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money. Journal of Political Economy, 66 (6), 467–482.
  • Shubik, M. (2012). Mathematical Institutional Economics. Cowles Foundation Discussion Papers 1882, Cowles Foundation for Research in Economics, Yale University.
  • Slovokhotov, Yu. L. (2010). Phase transitions associated with economy and demography. Computer Research and Modeling, 2 (2), 209–218. (In Russian).
  • Solow, R. (1960). Investment and technical progress. Arrow, Kenneth J.; Karlin, Samuel; Suppes, Patrick, Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium, Stanford mathematical studies in the social sciences, IV, Stanford,
  • California: Stanford University Press, pp. 89–104.
  • Taleb, N. N. (2009). The Black Swan: The Impact of the Highly Improbable. Moscow, Kolibri, 528 p. (In Russian).
  • Vasechkina, E. F. and Yarin, V. D. (2002). Dynamic modeling of ecological-economic system. Ecological safety of coastal and shelf zones and integrated use of shelf resources. Sevastopol’, «JeKOSI – Gidrofizika», pp. 163–174. (In Russian).
  • Von Neumann, J. (1937). Uber einekonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. Ergebnisseeines mathematischen Kolloquiums, no. 8, pp. 73–83, translated as, A Model of General Economic Equilibrium. Review of Economic Studies, 13 (33) (1945–46), 1–9.
  • Von Neumann, J. and Morgenstern, O. (1944). O. Theory of Games and Economic Behavior. Prinston University Рress. America. 625 p.
  • Walras, L. (1874). Éléments d’économie politique pure. Lausanne, Corbaz.
  • Yudanov, A. Yu. (2007). The geniuses of national business. The expert, 23 apr, no. 16. (In Russian).
  • Zhang, W.-B. (1999). Synergetic Economics. Time and Change in Nonlinear Economics. Moscow, Mir, 335 p. (In Russian).
Publisher: Ltd. "Humanitarian perspectives"
Founder: Ltd. "Humanitarian perspectives"
Online-ISSN: 2412-6039
ISSN: 2076-6297