Abstract
In this chapter the focus is on general economic equilibrium problems, in particular, Walrasian price or pure exchange equilibria. This problem has been extensively studied in the economics literature dating to Walras (1874); see also Wald (1951), Debreu (1959), and Mas-Colell (1985). Specifically, in this chapter we apply the powerful theory of variational inequalities to both the qualitative analysis of general economic equilibria as well as to their computation.
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References
Border, K. C., Fixed Point Theorems with Application to Economics and Game Theory, Cambridge University Press, Cambridge, United Kingdom, 1985.
Cornwell, R., Introduction to the Use of General Equilibrium Analysis, North-Holland, Amsterdam, The Netherlands, 1984.
Dafermos, S., “Exchange price equilibria and variational inequalities,” Mathematical Programming 46 (1990) 391–402.
Debreu, G., The Theory of Value, John Wiley Sons, New York, 1959.
Eaves, B. C., “Where solving for stationary points by LCPs is mixing Newton iterates,” in Homotopy Methods and Global Convergence, pp. 63–78, B. C. Eaves, F. J. Gould, H. O. Peitgen, and M. J. Todd, editors, Plenum Press, New York, 1983.
Ginsburgh, V., and Waelbrock, J. L., Activity Analysis and General Equilibrium Modelling, Contributions to Economic Analysis 125, North-Holland, Amsterdam, The Netherlands, 1981.
Manne, A. S., “On the formulation and solution of economic equilibrium models,” Mathematical Programming Study 23 (1985) 1–22.
Manne, A. S., and Preckel, P. V., “A three-region intertemporal model of energy, international trade, and capital flows,” Mathematical Programming Study 23 (1985) 56–74.
Mas-Colell, A., The Theory of General Economic Equilibrium: A Differentiable Approach, Econometric Society Monographs 9, Cambridge University Press, Cambridge, United Kingdom, 1985.
Mathiesen, L., “An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model: an example,” Mathematical Programming 37 (1987) 1–18.
Rutherford, T, T.,“A modeling system for applied general equilibrium analysis,” Cowles Foundation Discussion Paper No. 836, Yale University, New Haven, Connecticut, 1987.
Scarf, H. (with T. Hansen), Computation of Economic Equilibria, Yale University Press, New Haven, Connecticut, 1973.
Shoven, J. B. B., “The application of fixed point methods to economics,” in Homotopy Methods and Global Convergence, pp. 249–262, B. C. Eaves, F. J. Gould, H. O. Peitgen, and M. J. Todd, editors, Plenum Press, New York, 1983.
Todd, M. J., The Computation of Fixed Points and Applications, Lecture Notes in Economics and Mathematical Systems 124, Springer-Verlag, Berlin, Germany, 1976.
Todd, M. J., “A note on computing equilibria in economics with activity models of production,” Journal of Mathematical Economics 6 (1979) 135–144.
Van der Laan, G., and Talman, A. J. J., “Simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds,” Mathematical Programming 38 (1987) 1–15.
Wald, A., “On some systems of equations in mathematical economics,” Econometrica 19 (1951) 368–403.
Walras, L., Elements d’Economique Politique Pure, Corbaz, Lausanne, Switzerland, 1874.
Whalley, J., “Fiscal harmonization in the EEC: some preliminary findings of fixed point calculations,” in Fixed Points: Algorithms and Applications, pp. 435–472, S. Karamardian and C. B. Garcia, editors, Academic Press, New York, 1977.
Zhao, L., “Variational inequalities in general equilibrium: analysis and computation,” Ph. D. Thesis, Division of Applied Mathematics, Brown University, Providence, Rhode Island, 1989, also appears as: LCDS 88–24, Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island, 1988.
Zhao, L., and Dafermos, S., “General economic equilibrium and variational inequalities,” Operations Research Letters 10 (1991) 369–376.
Zhao, L., and Nagurney, A., “A network formalism for pure exchange economic equilibria,” in Network Optimization Problems: Algorithms, Complexity, and Applications, pp. 363–386, D. Z. Du and P. M. Pardalos, editors, World Scientific Press, Singapore, 1993.
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Nagurney, A. (1999). Walrasian Price Equilibrium. In: Network Economics. Advances in Computational Economics, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3005-0_9
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DOI: https://doi.org/10.1007/978-1-4757-3005-0_9
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