Abstract
We suggest a new approach to the description of complex economic systems. The main idea is to represent the phase space of the system by means of linear constraints on the differentials of the defining parameters of the system, i.e., by means of a system of Pfaff equations. Further investigation of the dynamical trajectories could be reduced to the studies of the geometry of integral surfaces of the system. This approach assumes a nonconventional definition of the notion of economic equilibrium in terms of nonholonomic systems, more precisely, in terms of statistical thermodynamics. In particular, our approach to economics explains the causes for unemployment and reveals mathematical reasons due to which “shock therapy” in the economies of East European countries and the Soviet Union in the 1990s did not lead to the result promised to the peoples of these countries, in particular, why money fled out of these, poor, countries to richer ones, and why during the same period China and Vietnam experienced an unusual economic growth. Our approach makes manifest the reasons why honesty in market relations has a price and qualitatively evaluates it; we also indicate the limits of rationality of the behavior of market agents (buyers and sellers). Bibliography: 36 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 275–302.
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Sergeev, V.M. Rationality, Property Rights, and Thermodynamic Approach to Market Equilibrium. J Math Sci 133, 1524–1538 (2006). https://doi.org/10.1007/s10958-006-0067-0
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DOI: https://doi.org/10.1007/s10958-006-0067-0