Rationality, property rights and thermodynamic approach to the market equilibrium

V. M. Sergeev

Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part XI, Tome 312 (2004), pp. 275-302

Résumé

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 geometry of integral surfaces of the system. This approach assumes a non-conventional 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 economics of East European countries and Soviet Union in 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 the 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 indicated the limits of rationality of behavior of market's agents (buyers and sellers).