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Parametrical regulation of economic growth on the basis of one-class mathematical models

Ashimov A. A., Iskakov N. A., Borovskiy Y. V., Sultanov B. T., Ashimov A. A.

Systems Science

2009

Vol. 35, no 1

57-63

The paper is devoted to the application of the theory of parametrical regulation offered by the authors to tasks of maintenance of economic growth with the account of influence of the state's consumer expenses share in gross domestic product on development of economy. In the article, a mathematical model of economic system of the country is given in view of specified influence. The factors of the mathematical model considered have been evaluated as a result of solving the task of parametrical identification on the statistical data of national economy of the Republic of Kazakhstan. The weak structural stability of the specified mathematical model in a compact of four-dimensional Euclidean space of the phase variables without parametrical regulation has been proved. The proof is based on results of C. Robinson's work about structural stability on manifolds with boundary. The methods of the parametrical regulation theory determine the optimum laws of parametrical regulation of processes of economic growth of the Republic of Kazakhstan. These optimum laws are as extremals of the appropriate of variational calculus task at their choice in environment of the given finite set of algorithms. The specified algorithms represent dependences of these or those parameters of mathematical model on some endogenous variables. The dependences of the laws found on the two unguided parameters, i.e., interest rates on deposits of bank system of the Republic of Kazakhstan and rates of taxes on dividends, are being investigated. These dependences are submitted as corresponding graphs of the criterion's (gross domestic product) optimal values on one and two economic parameters. The appropriate bifurcation points and sets of bifurcation points have been determined on the basis of the graphs obtained. Also, the weak structural stability of the mathematical model with parametrical regulation has been proved.

On bifurcation of extremals of one class of variational calculus tasks with multiparametrical perturbation

Ashimov A. A., Sagadiyev K. A., Borovskiy Y. V., Iskakov N. A., Ashimov A. A.

Systems Science

2007

Vol. 33, no 4

85-91

A bifurcation of the extremals of one variational calculus task on the choice of optimum laws for a parametrical regulation of a dynamic system in the given finite set of algorithms is under consideration. An assertion about conditions sufficient for the existence of the specified variational calculus task's solution is formulated and proved. A defintion of a bifurcation point under a multiparametrical perturbation of the given variational calculus task is provided. An assumption on the sufficient conditions for its existence is formulated and proved. A numerical algorithm of calculating a bifurcation value of a parameter is offered. The findings are illustrated by the example of calculated set of bifurcation points of the extremals of the variational calculus task on the choice of optimum laws for a parametrical regulation of the market economy mechanisms in the given finite set of algorithms on the basis of a mathematical model of the economic system of the country, which is suggested in order to investigate the influence of state expenditures upon its evolution. The research findings could be applied to the process of development and implementation of an effective state economic policy.