Advertisement

Journal of Mathematical Sciences

, Volume 133, Issue 4, pp 1524–1538 | Cite as

Rationality, Property Rights, and Thermodynamic Approach to Market Equilibrium

  • V. M. Sergeev
Article

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.

Keywords

Economic Growth Phase Space Main Idea Economic System Linear Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    A. Smith, An Inquiry to the Nature and Causes of the Wealth of Nations, London (1776).Google Scholar
  2. 2.
    F. A. Hayek, “The fatal conceit,” in: Collected Works of F. A. Hayek, Univ. of Chicago Press (1988).Google Scholar
  3. 3.
    H. Simon, “Rationality in psychology and economics,” in: The Behavioral Foundations of Economic Theory R. M. Hogarth and M. W. Reder (eds.), Journal of Business (Supplement), 59, 209–224 (1986).Google Scholar
  4. 4.
    D. North, Institutions, Institutional Changes and Economic Performance, Cambridge Univ. Press, Cambridge (1990).Google Scholar
  5. 5.
    R. Coase, “The nature of the firm,” Economica, 4, 386–405 (1937).Google Scholar
  6. 6.
    R. Coase, “The problem of social cost,” J. Law Economics, 3, 1–44 (1960).Google Scholar
  7. 7.
    O. E. Williamson, Markets and Hierarchies: Analysis and Antitrust Implications, Free Press, New York; McMillan, London (1975).Google Scholar
  8. 8.
    R. Axelrod, Evolution of Cooperation, Basic Books, New York (1984).Google Scholar
  9. 9.
    F. V. Fisher, Disequilibrium Foundations of Equilibrium Economics, Cambridge Univ. Press, Cambridge (1963).Google Scholar
  10. 10.
    A. Wald, “On some systems of equations of mathematical economics,” Econometrica, 19, 368–403 (1951).MATHMathSciNetGoogle Scholar
  11. 11.
    G. Debreu, Theory of Value. An Axiomatic Analysis of Economic Equilibrium, Wiley, New York (1959).Google Scholar
  12. 12.
    K. J. Arrow and G. Debreu, “Existence of an equilibrium for a competitive economy,” Econometrica, 22 265–290 (1954).MathSciNetGoogle Scholar
  13. 13.
    V. Sergeev, The Limits of Rationality [in Russian], Phasis, Moscow (1999).Google Scholar
  14. 14.
    E. Cartan, Lecons sur les Invariants Integraux, A. Hermann & Fils, Paris (1922).Google Scholar
  15. 15.
    P. K. Rashevsky, Geometrical Theory of Partial Differential Equations [in Russian], OGIZ, Moscow-Leningrad (1947).Google Scholar
  16. 16.
    R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior Differential Systems Springer-Verlag, New York (1991).Google Scholar
  17. 17.
    V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York (1992).Google Scholar
  18. 18.
    C. Caratheodory, “Untersuchugen uber die Grundlagen der Thermodynamik,” Math. Ann., 67, 355–386 (1909).MathSciNetGoogle Scholar
  19. 19.
    M. Born, “Kritische Betrachtungen zur TraditionallenDarstellung der Thermodynamik,” Physik Z., 22 (1920) 218–224, 249–254, 282–286.Google Scholar
  20. 20.
    A. M. Vershik, “Classical and nonclassical dynamics with constraints,” in: Global Analysis — Studies and Applications. I, Yu. G. Borisovich and Yu. E. Gliklikh (eds.), Springer-Verlag, Berlin-New York (1984), pp. 278–301.Google Scholar
  21. 21.
    L. D. Landau and E. M. Livschitz, Course of Theoretical Physics, Vol. 5: Statistical Physics, 2nd edition Pergamon Press, Oxford-Edinburgh-New York (1968).Google Scholar
  22. 22.
    A. G. Wilson, Entropy in Urban and Regional Modeling, Pion, London (1970).Google Scholar
  23. 23.
    L. I. Rosenoer, “Exchange and distribution of resourses (generalized thermodynamic approach),” Avtomat. Telemekh., No. 5 (1973), 115–131; No. 6 (1973), 65–79; No. 8 (1973), 103 (in Russian).Google Scholar
  24. 24.
    L. I. Rosenoer and A. M. Tsirlin, “Optimal control over thermodynamic processes,” Avtomat. Telemekh., No. 1 (1983), 70–79; No. 2 (1983), 88–101, No. 3 (1983), 50–64.Google Scholar
  25. 25.
    E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev., 106, No.6 (1957), 620–630; 108 No. 2 (1957), 171–190.MATHMathSciNetGoogle Scholar
  26. 26.
    E. T. Jaynes, “Prior information and ambiguity in inverse problems,” in: SIAM-AMS Proc., 14, Amer. Math. Soc., Providence (1984), pp. 151–166.Google Scholar
  27. 27.
    R. D. Levine and M. Tribus, “Foreword,” in: The Maximum Entropy Formalism (Conf., Mass. Inst. Tech. Cambridge, Mass., 1978), MIT Press (1979), pp. VII–IX.Google Scholar
  28. 28.
    A. Golan, G. Judge, and D. Miller, Maximum Entropy Econometrics: Robust Estimation with Limited Data Chichester, Wiley (1996).Google Scholar
  29. 29.
    S. Durlauf, “Nonergodic economic growth,” Rev. Econ. Studies, 60, 349–366 (1993).MATHGoogle Scholar
  30. 30.
    S. Durlauf, “A theory of persistent income inequality,” J. Econ. Growth, 1, 75–93 (1996).CrossRefMATHGoogle Scholar
  31. 31.
    P. A. M. Dirac, “The Hamiltonian form of field dynamics,” Canadian J. Physics, 2, No.1, 1–23 (1951).Google Scholar
  32. 32.
    L. D. Faddeev, “Feynman integral for singular Lagrangians,” Teoret. Mat. Fiz., 1, No.1, 3–18 (1969).MATHMathSciNetGoogle Scholar
  33. 33.
    V. P. Pavlov, “Dirac's bracket,” Teoret. Mat. Fiz., 92, No.3, 451–456 (1992).MATHMathSciNetGoogle Scholar
  34. 34.
    P. A. M. Dirac, Lectures on Quantum Mechanics, Yeshiva University, New York (1964).Google Scholar
  35. 35.
    M. J. Klein, “Negative absolute temperature,” Phys. Rev., 104, No.3, 589 (1956).CrossRefMATHGoogle Scholar
  36. 36.
    G. A. Akerloff, An Economic Theorist's Book of Tales: Essays that Entertain the Consequences of New Assumptions in Economic Theory, Cambridge Univ. Press, Cambridge (1984).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. M. Sergeev
    • 1
  1. 1.Moscow State Institute of International RelationsMoscowRussia

Personalised recommendations