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Approximation of excess demand on the boundary and euilibrium price set

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Advances in Mathematical Economics

Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 9))

Abstract

When preferences may not be homothetic but satisfy other regularity conditions such as monotonicity, the market excess demand function is characterized by continuity and Walras’ law on almost entire region of the price simplex. In particular, Mas-Colell (1977) shows that for a continuous function f defined on the interior of the price simplex satisfying Walras’ law and the boundary condition, there exists an exchange economy ℰ whose excess demand function is approximately equal to f and the equilibrium price set of ℰ is exactly equal to the one of f. This paper shows that if f may be finite on the boundary of the price simplex, ℰ can be chosen so that the equilibrium price set of ℰ is approximately equal to the one of f. Theorem 3 in Wong (1997), showing the equivalence between Brouwer’s fixed-point theorem and Arrow-Debreu’s equilibrium existence theorem, follows from this result.

This research is financially supported by Waseda University 21COE-GLOPE and Grant-in-Aid for Scientific Research #15530125 from JSPS.

The author thanks Professors Kazuya Kamiya and Akira Yamazaki for their useful comments on an earlier version. He is also benefited from the comments and suggestions of two anonymous referees and a co-editor of the journal. Any remaining errors are independent.

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References

  1. Arrow, K.J., Hahn. F.H.: General Competitive Analysis. Holden Day, San Francisco 1971

    MATH  Google Scholar 

  2. Debreu, G.: Excess demand functions. J. Math. Econ. 1, 15–21 (1974)

    Article  MATH  Google Scholar 

  3. Eisenberg, B.: Aggregation of utility functions. Manage. Sci. 7, 337–350 (1961)

    Article  Google Scholar 

  4. Hildenbrand, W.: Core and Equilibria of a Large Economy. Princeton University Press, Princeton 1974

    MATH  Google Scholar 

  5. Mas-Colell, A.: On the equilibrium price set of an exchange economy. J. Math. Econ. 4, 117–126 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  6. Mas-Colell, A.: The Theory of General Economic Equilibrium, A Differentiable Approach. Cambridge University Press, Cambridge 1985

    Google Scholar 

  7. Shafer, W., Sonnenschein. H.: Market demand and excess demand functions, In: Handbook of Mathematical Economics, volume II (Arrow, K.J. et al. eds.). pp. 671–693 North Holland, New York, Amsterdam 1982

    Google Scholar 

  8. Shinotsuka T., Toda. M.: Equilibrium Existence and Fixed Point Theorems: Equivalence Theorems, unpublished (1994)

    Google Scholar 

  9. Sonnenschein, H.: Do Walras’ identity and continuity characterize the class of community excess demand functions? J. Econ. Theory 6, 345–354 (1972a)

    Article  MathSciNet  Google Scholar 

  10. Sonnenschein, H.: The utility hypothesis and market demand theory. Western Econ. J. 11, 404–410 (1972b)

    Google Scholar 

  11. Uzawa, H.: Walras’ existence and Brouwer’s fixed point theorem. Econ. Stud. Quart. 13, 59–62 (1962)

    Google Scholar 

  12. Wong, K.-C: Excess demand functions, equilibrium prices, and existence of equilibrium. Econ. Theory 10, 39–54 (1997)

    Article  MATH  Google Scholar 

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© 2006 Springer-Verlag

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Toda, M. (2006). Approximation of excess demand on the boundary and euilibrium price set. In: Kusuoka, S., Yamazaki, A. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 9. Springer, Tokyo. https://doi.org/10.1007/4-431-34342-3_6

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