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The paper offers further development and applications of the theory of a parametrical regulation of market economy evolution. This theory consists of the following sections: formation of a library of economic systems' mathematical models; of rigidness (structural stability) of mathematical models; development of parametrical regulation laws etc. The work contains new results of the considered one class models' rigidness research with and without parametrical regulation.

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Purpose -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. Design/methodology/approach -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. Findings -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. Research limitations/implications -Future papers would be focused on studies of rigidness of other mathematic models of economic systems. Practical implications -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. Originality/value -The market economy development parametrical regulation theory has been offered for consideration for the first time.

The development of economic processes, within the frameworks of legislatively (normatively) established "game rules" adjusting attitudes (mechanisms of interaction) between the agents (enterprises, resources suppliers, and consumers), is appreciably defined by values of such economic parameters, as various tax rates, government spending , credit rates, norm of reservation, exchange rate, etc. The specified parameters frequently vary depending on an economic conjuncture and ways of an estimation their effective values are often unknown.The approach how to define effective values of the specified economic parameters -laws of parametrical regulation in the form of extremals of the corresponding variational problems is offered in the report.The offered approach is illustrated by the example of a choice effective laws of parametrical regulation of consuming government spending, norm of reservation and exchange rate in sense of maximum average gross domestic products of one of the states, on the basis of mathematical model [1]: ″Interaction between economic systems of two states through foreign trade″. After matched transformations mathematical model [1] can be performed as a form of the following system of the differential and algebraic equations (here i=1, 2 -the number of the state, t -time ):