Annals of Operations Research

, Volume 44, Issue 2, pp 173–193 | Cite as

General economic equilibrium and variational inequalities: existence, uniqueness and sensitivity

  • Lan Zhao
Economic And Financial Equilibria


In this paper we use the theory of variational inequalities to study the general economic equilibrium problem with production. The variational inequality is defined on a bounded set. Existence, uniqueness and sensitivity of the equilibrium point (pair of price vector and activity vector) are discussed through studying this variational inequality.


Walras' law general economic equilibrium variational inequality sensitivity analysis 


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  1. [1]
    K.C. Border,Fixed Point Theorems with Applications to Economics and Game Theory (Cambridge University Press, New York, 1985).Google Scholar
  2. [2]
    S. Dafermos, Traffic equilibria and variational inequalities, Trans. Sci. 14 (1980) 42–54.Google Scholar
  3. [3]
    S. Dafermos, The general multimodal traffic equilibrium problem, Networks 12 (1982) 57–72.Google Scholar
  4. [4]
    S. Dafermos, An iterative scheme for variational inequalities, Math. Progr. 26 (1983) 40–47.Google Scholar
  5. [5]
    S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421–434.Google Scholar
  6. [6]
    S. Dafermos, Exchange price equilibria and variational inequalities, Math. Progr. 46 (1990) 391–402.Google Scholar
  7. [7]
    S. Dafermos and S. McKelvey, Partitionable variational inequalities with applications to network and economic equilibria, J. Optim. Theory Appl. 73 (1992) 243–268.Google Scholar
  8. [8]
    S. Dafermos and A. Nagurney, A network formulation of market equilibrium problems, and variational inequalities, Oper. Res. Lett. 3 (1984) 234–250.Google Scholar
  9. [9]
    S. Dafermos and A. Nagurney, Sensitivity analysis for the general spatial economic equilibrium problem, Oper. Res. 32 (1984) 1069–1086.Google Scholar
  10. [10]
    S. Dafermos and A. Nagurney, Oligopolistic and competitive behavior of spatially separated markets, Reg. Sci. Urban Econ. 17 (1987) 245–254.Google Scholar
  11. [11]
    B.C. Eaves, Where solving for stationary points by LCPs is mixing Newton iterates, in:Homotopy Methods and Global Convergence, eds. B.C. Eaves, F.L. Gould, H.O. Peitgen and M.J. Todd (Plenum, New York, 1983) pp. 63–78.Google Scholar
  12. [12]
    M. Florian and M. Los, A new look at static spatial price equilibrium models, Reg. Sci. Urban Econ. 12 (1982) 579–597.Google Scholar
  13. [13]
    D. Gabay and H. Moulin, On the uniqueness and stability of Nash equilibria in noncooperative games, in:Applied Stochastic Control of Econometrics and Management Science, eds. Bensoussan, Kleindorf and Tapiero (North-Holland, New York, 1980) pp. 271–293.Google Scholar
  14. [14]
    J.M. Grandmont, Temporary general equilibrium theory, Econometrica 45 (1977) 535–572.Google Scholar
  15. [15]
    S. Karamardian, The nonlinear complementarity problem with applications, Part 1, J. Optim. Theory Appl. 4 (1969) 87–98.Google Scholar
  16. [16]
    J. Kehoe, Regular production economies, J. Math. Econ. 10 (1982) 147–165.Google Scholar
  17. [17]
    J. Kehoe, A numerical investigation of multiplicity of equilibria, Math. Progr. Study 23 (1985) 240–258.Google Scholar
  18. [18]
    D. Kinderlehrer and G. Stampacchia,An Introduction to Variational Inequalities and Their Applications (Academic Press, New York, 1980).Google Scholar
  19. [19]
    J. Kyparisis, Sensitivity analysis framework for variational inequality, Math. Progr. 38 (1987) 103–213.Google Scholar
  20. [20]
    G. van der Laan and A.J.J. Talman, Adjustment processes for finding economic equilibria, in:The Computation and Modelling of Economic Equilibria, eds. Talman and van der Laan, Contributions to Economic Analysis 67 (North-Holland, New York, 1987) pp. 85–123.Google Scholar
  21. [21]
    C.E. Lemke, Bimatrix equilibrium points and mathematical programming, Manag. Sci. 11 (1965) 681–689.Google Scholar
  22. [22]
    A. Mas-Colell,The Theory of General Equilibrium: A Differential Approach, Econometric Society Publication no. 9 (Cambridge University Press, New York, 1985).Google Scholar
  23. [23]
    A.S. Mann, On the formulation and solution of economic equilibrium models, Math. Progr. Study 23 (1985) 1–22.Google Scholar
  24. [24]
    L. Mathiesen, An algorithm based on a sequence of linear complementarity problems applied to Walras' equilibrium model: An example, Math. Progr. 37 (1987) 1–18.Google Scholar
  25. [25]
    A. Nagurney and G. Aronson, A general dynamic spatial price equilibrium model with gains and losses, Networks 19 (1989) 751–769.Google Scholar
  26. [26]
    E. Scarf (with T. Hansen),Computation of Economic Equilibria (Yale University Press, New Haven, 1973).Google Scholar
  27. [27]
    J.C. Stone, Formulation and solution of economic equilibrium problems, Technical Report SOL 88-7, Dept. of Operations Research, Stanford University (1988).Google Scholar
  28. [28]
    R.L. Tobin, Sensitivity analysis for variational inequalities, J. Optim. Theory Appl. 48 (1986) 191–204.Google Scholar
  29. [29]
    M. Todd,The Computation of Fixed Points and Applications, Lecture Notes in Economics and Mathematical Systems 124 (Springer, New York, 1976).Google Scholar
  30. [30]
    L. Zhao, General economic equilibrium and variational inequality: theory and computation, Ph.D. thesis, Division of Applied Mathematics, Brown University, Providence, RI 02912 (1988).Google Scholar
  31. [31]
    L. Zhao and S. Dafermos, General economic equilibrium and variational inequalities, Oper. Res. Lett. 10 (1992) 369–376.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Lan Zhao
    • 1
  1. 1.Department of MathematicsSUNY/College at Old WestburyOld WestburyUSA

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