Planimetry of Economic States

Planimetry of Economic States

S. Melnyk (Kharkov National University of Radio Electronic, Kharkov, Ukraine), I. Tuluzov (Kharkov Regional Center for Investment, Kharkov, Ukraine) and A. Melnyk (Kharkov Regional Center for Investment, Kharkov, Ukraine)
DOI: 10.4018/IJPMAT.2015070102
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The new information physical method of constructing the space of economic states is proposed. Unlike the existing theories of consumption, its properties are completely determined axiomatically by the operation of measurement and do not require phenomenological assumptions. The authors consider a transaction of exchange of valuables between two proprietors as such operation. The result of measurement is a dimensional number equal to the proportion of exchange. The constructed space appears to be Euclidean vector space with ordinary operators of composition of vectors, their scalar product, etc. The task of determining the parameters of equilibrium of a complex economic system can be formulated as a task of statics in the constructed space and can be solved by one of the physical methods.
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2. Multidimensionality Of The Space Of Economic States

We have previously proposed the physical methodology of constructing unidimensional models of economic systems (Tuluzov & Мelnyk, 2010). The unidimensional space of states occurs as a consequence of the idealized assumption on the fact that in the process of exchange of a valuables A for B, B for C and C for A the following ratio is valid:

(1) where the symbol IJPMAT.2015070102.m02 determines the result of measurement – the quantitative proportion of exchange of valuables A for valuables B. This assumption can be conditionally interpreted as a statement – “everything is measured only in money”. Actually, if a fixed value in conventional units (money) is set for each valuable item, then it determines the proportions of its exchange for any other valuables. In this case, the ratio (1) is obvious. At the same time, in real economy it can be violated. Moreover, violation of this ratio actually represents the stimulus of every transaction! Each participant of the transaction assumes that his actions will be eventually profitable. At the same time, it becomes possible only in case of transition to the multidimensional space of states, in which each of the proprietors relies upon his own scale of values in the process of decision-making. In this case, in order that the transaction takes place, the two inequalities must be satisfied:
(2) where IJPMAT.2015070102.m04 and IJPMAT.2015070102.m05 are the units of the scale of values of the proprietors А and В, respectively. It follows from these inequalities that the values A and B cannot be considered as scalars and that the proportions of exchange of two valuable items in a certain transaction can depend on the preferences of the participants of the transaction. Let us note that the main task of the present paper is not so much a formal generalization of the unidimensional space of economic states into a multidimensional state, but rather finding economic analogs of simple mechanical models and notions. The developed instruments of modeling will further allow analyzing the dynamics of complex real economic systems.

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