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Kachevsky D.

Dynamic patterns of macroeconomics

Keywords: macroeconomics, thermodynamics, cluster structure, budget

The article is aimed to give an adequate mathematical description of budgetary cluster structures of macroeconomic systems. The mathematical description of the previously known n- and -clusters has a number of drawbacks: there was a need to introduce an additional parameter 'n' – a hierarchical parameter, the form of the dependence of macroeconomic quantities which determined the type of cluster; besides, that description involved quite a cumbersome mathematical apparatus; despite the fact that the clusters covered a sufficiently long time interval (a few years), the number of macroeconomic production units was assumed to remain unchanged within that period, which limited the possibility of applying mathematical description. This paper offers a new mathematical description applicable to all types of budget cluster, which is also aimed to overcome the disadvantages mentioned above, as well as to create a mathematical description of another form of clusters, which has never been considered before. Such structures are called -clusters. A thermodynamic approach to macroeconomics, which is conforming to Bose – Einstein statistics, is used as a mathematical tool, as before. The author has made up an equation to estimate the state of the macroeconomic system. The hierarchical parameter is assigned its limit value n = 1. A single description is provided for all types of clusters, including the n- and -clusters. There is an interchange of -clusters corresponding to a drop in profitability and its growth that can be considered as «breath» of macroeconomics. Each cluster is characterized by specific dynamics of the main macroeconomic parameters. The article provides the description of such cluster structures relevant for the world's leading economies (the US, China, Germany, Japan). The unified description of all types of clusters creates new opportunities of prognosticating the dynamics of the main macroeconomic parameters, as well as an effective mechanism for economic management.


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About authors

Kachevsky Dmitry
candidate of physical and mathematical sciences, higher mathematics department associate professor, Chuvash State University, Russia, Cheboksary (; )

Article link

Kachevsky D. Dynamic patterns of macroeconomics [Electronic resource] // Oeconomia et Jus. – 2015. – №1. P. 24-40. – URL: