Skip to main content
SpringerLink
Log in

Equilibrium Analysis in Kantorovich Spaces

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The paper presents a survey of new results in general equilibrium theory with linear vector lattice commodity space (Kantorovich space). The importance of order structures and the Riesz-Kantorovich formula is clarified. The main novelty of the paper is new characterizations of elements of the fuzzy core in an exchange economy. Then we apply these characterizations to prove a new theorem on the existence of quasi-equilibrium for a linear vector lattice economy. This theorem, based on the E-properness of preferences by Podczeck-Florenzano-Marakulin, develops the Florenzano-Marakulin approach and generalizes previous Tourky's results. Bibliography: 29 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. C. D. Aliprantis, “On the Mas-Colell-Richard equilibrium theorem,” J. Econom. Theory, 74, 414–424 (1997).

    MATH  MathSciNet  Google Scholar 

  2. C. D. Aliprantis and D. J. Brown, “Equilibria in markets with a Riesz space of commodities,” J. Math. Econom., 11, 189–207 (1983).

    Article  MathSciNet  Google Scholar 

  3. C. D. Aliprantis, D. J. Brown, and O. Burkinshaw, “Edgeworth equilibria,” Econometrica, 55, 1109–1137 (1987).

    MathSciNet  Google Scholar 

  4. C. D. Aliprantis, D. J. Brown, and O. Burkinshaw, Existence and Optimality of Competitive Equilibria, Springer-Verlag, Berlin-New York (1989).

    Google Scholar 

  5. C. D. Aliprantis, R. Tourky, and N. C. Yannelis, “The Riesz-Kantorovich formula and general equilibrium theory,” J. Math. Econom., 34, 55–76 (2000).

    Article  MathSciNet  Google Scholar 

  6. A. Araujo and P. K. Monteiro, “Equilibrium without uniform conditions,” J. Econom. Theory, 48, 416–427 (1989).

    Article  MathSciNet  Google Scholar 

  7. K. J. Arrow and G. Debreu, “Existence of equilibrium for a competitive economy,” Econometrica, 22, 265–290 (1954).

    MathSciNet  Google Scholar 

  8. T. Bewley, “Existence of equilibria in economies with infinitely many commodities,” J. Econom. Theory, 4, 514–540 (1972).

    Article  MathSciNet  Google Scholar 

  9. G. Debreu, “Existence of competitive equilibrium,” in: Handbook of Mathematical Economics, Vol. II, K. Arrow and M. D. Intriligator (eds.), North-Holland, Amsterdam (1982), pp. 697–744.

    Google Scholar 

  10. G. Debreu, Theory of Value, John Wiley, New York (1959).

    Google Scholar 

  11. M. Deghdak and M. Florenzano, “Decentralizing Edgeworth equilibria in economies with many commodities,” Econom. Theory, 14, 297–310 (1999).

    MathSciNet  Google Scholar 

  12. D. Duffie and W. R. Zame, “The consumption based capital asset pricing model,” Econometrica, 57, 1274–1298 (1989).

    MathSciNet  Google Scholar 

  13. M. Florenzano, “Edgeworth equilibria, fuzzy core and equilibria of a production economy without ordered preferences,” J. Math. Anal. Appl., 153, 18–36 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Florenzano and V. M. Marakulin, “Production equilibria in vector lattices,” Econom. Theory, 17, No.3, 577–598 (2001).

    MathSciNet  Google Scholar 

  15. L. Jones, “A competitive model of product differentiation,” Econometrica, 52, 507–530 (1984).

    MATH  Google Scholar 

  16. C. Huang and D. Kreps, Intertemporal preferences with a continuous time dimension, Sloan School Working Paper (1986).

  17. D. M. Kreps, “Arbitrage and equilibrium in economies with infinitely many commodities,” J. Math. Econom., 8, 15–35 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  18. V. M. Marakulin, “Equilibrium in infinite dimensional commodity spaces revisited,” Econom. Theory, 18, No.3, 621–633 (2001).

    MATH  MathSciNet  Google Scholar 

  19. A. Mas-Colell, “The price equilibrium existence problem in topological vector lattices,” Econometrica, 54, 1039–1053 (1986).

    MATH  MathSciNet  Google Scholar 

  20. A. Mas-Colell, “Valuation equilibrium and Pareto optimum revisited,” in: Contribution to Mathematical Economics, W. Hildenbrand and A. Mas-Colell (eds.), North-Holland, New York (1986).

    Google Scholar 

  21. A. Mas-Colell and S. F. Richard, “A new approach to the existence of equilibria in vector lattices,” J. Econom. Theory, 53, 1–11 (1991).

    MathSciNet  Google Scholar 

  22. A. Mas-Colell and W. Zame, “Equilibrium theory in infinite dimensional spaces,” in: Handbook of Mathematical Economics, Vol. IV, W. Hildenbrand and H. Sonnenschein (eds.), North-Holland, Amsterdam (1991), pp. 1835–1898.

    Google Scholar 

  23. L. McKenzie, “On equilibrium in Graham's model of world trade and other competitive systems,” Econometrica, 22, 147–161 (1954).

    MATH  Google Scholar 

  24. B. Peleg and M. E. Yaari, “Markets with countably many commodities,” Internat. Econom. Rev., 11, 369–377 (1970).

    Google Scholar 

  25. K. Podczeck, “Equilibria in vector lattices without ordered preferences or uniform properness,” J. Math. Econom., 25, 465–485 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  26. S. F. Richard, “Production equilibria in vector lattices,” J. Math. Econom., 18, 41–56 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  27. R. Tourky, “A new approach to the limit theorem on the core of an economy in vector lattices,” J. Econom. Theory, 78, 321–328 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  28. R. Tourky, “The limit theorem on the core of a production economy in vector lattices with unordered preferences,” Econom. Theory, 14, 219–226 (1999).

    MATH  MathSciNet  Google Scholar 

  29. N. C. Yannelis and W. R. Zame, “Equilibria in Banach lattices without ordered preferences,” J. Math. Econom., 15, 85–110 (1986).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. M. Marakulin

Authors
  1. V. M. Marakulin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 188–214.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marakulin, V.M. Equilibrium Analysis in Kantorovich Spaces. J Math Sci 133, 1477–1490 (2006). https://doi.org/10.1007/s10958-006-0063-4

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-006-0063-4

Keywords

Search

Navigation