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The purpose of this paper is to offer the theory of a parametrical regulation of market economy development, and the results of the theory development and usage.

Theoretical results of the abstract have been obtained by way of applying the theory of ordinary differential equations, geometrical methods in variation tasks and the theory of dynamic systems. These results have been used for solving a number of practical tasks.

The market economy development parametrical regulation theory structure has been offered. The approach to parametrical regulation of a nonlinear dynamic system's development has been suggested. An assumption about the existence of solution to the task of calculus of variations on the choice of the optimum laws of parametrical regulation within the given finite set of algorithms has been set forward. An assumption about the conditions sufficient for the existence of an extremal's bifurcation point of the task of calculus of variations on the choice of the optimum laws of parametrical regulation within the given finite set of algorithms is presented, formulated and proved. Theory application samples have been provided.

Future papers would be focused on studies of rigidness of other mathematic models of economic systems.

The research findings could be applied to the choice and realization of an effective budget and tax as well as monetary and loan state policy.

The market economy development parametrical regulation theory has been offered for consideration for the first time.

The purpose of this paper is to present some results of the development of parametrical regulation theory elements for computable general equilibrium models (CGE models), taking into consideration their peculiarities.

Theoretical results have been obtained by means of applying geometrical methods for variational problems and methods of the theory of discrete dynamic systems. These results have been used for solving concrete practical problems.

The authors proved a statement on the existence of solution for variational calculus problem on the choice of the optimal laws of parametrical regulation within the given finite set of algorithms for discrete dynamic systems. A statement has been proved on sufficient conditions for the existence of an extremal's bifurcation point of variational calculus problem on the choice of the optimum laws of parametrical regulation within the given finite set of algorithms for discrete dynamic systems. Optimal laws of parametrical regulation (on the level of one and two parameters) of economic system evolution on the basis of the examined mathematical model have been defined. The bifurcation line was constructed for the given area of uncontrolled parameter values.

The research results can be applied for the choice and realization of an effective state budget and tax policy.

The paper elaborates the elements of parametrical regulation theory of economic system development on the basis of CGE models and shows the effectiveness of parametrical regulation theory application on the example of one CGE model.

The purpose of this paper is to demonstrate an effectiveness of applying a number of the new methods, proposed in the parametric control theory for testing macroeconomic models for the possibility of their practical application.

Approaches of system analysis on building and calibrating the mathematical models; provisions of the parametric control theory for both numerical testing of the calibrated models for the possibility of their practical application and solving the parametric control problems.

First, one global computable general equilibrium model (CGE model) is built and calibrated. Second, in solving the problem of testing this model for the possibility of its practical application the effectiveness of applying two developed numerical algorithms is demonstrated. These algorithms are for estimating stability indicators and estimating stability (in the sense of the theory of smooth mappings stability) of mappings defined by the model. Third, on the base of the tested CGE model there are given the solution results for a number of the parametric control problems aimed at economic growth and decrease of economic disparities of regions.

By the example of the developed CGE model, it is demonstrated an approach of the parametric control theory for testing macroeconomic models for the possibility of their practical application.