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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Balanced Growth in the Structural Dynamic Economic Model SDEM-2

Discontinuity, Nonlinearity, and Complexity 3(3) (2014) 237--253 | DOI:10.5890/DNC.2014.09.003

Dmitry V. Kovalevsky

Nansen International Environmental and Remote Sensing Centre, 14th Line 7, office 49, Vasilievsky Island, 199034 St. Petersburg, Russia

Saint Petersburg State University, Ulyanovskaya 3, 198504 St. Perersburg, Russia

Nansen Environmental and Remote Sensing Center, Thormøhlens gate 47, N-5006 Bergen, Norway

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The Structural Dynamic Economic Model SDEM-2, a follow-up of the model SDEM developed earlier, is essentially an actor-based, systemdynamic model of a closed economy evolving under conditions of conflict of interests of two powerful aggregated actors: entrepreneurs and wageearners. We derive the model equations applicable to both the balanced and unbalanced growth paths, and then study the balanced growth (with neither idle physical capital nor unemployment). Wefirst consider an inflexible control strategy of entrepreneurs for deterministic and stochastic cases, and then turn to a more sophisticated nonlinear control strategy. We also solve a simple optimization problem by calculating the (time-independent) value of model control parameter maximizing the discounted dividend of entrepreneurs. In view of simplicity of model equations, exact analytical solutions can be obtained in many cases, other cases being studied semianalytically. Even the simplest versions of SDEM-2 are able to produce rather versatile trajectories of the economy, dependent on the values of model parameters and initial conditions.


The author is indebted to Klaus Hasselmann for helpful comments. This study was supported by the Russian Foundation for Basic Research (Projects No. 10-06-00369-a and 12-06-00381-a). An earlier version of this paper appeared as a conference paper (Ref. [16]) but was then substantially updated.


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