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Existence of Equilibrium Prices: A Pedagogical Proof

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  • Simone Tonin

Abstract

Under the same assumptions made by Mas-Colell et al. (1995), I develop a short, simple, and complete proof of existence of equilibrium prices based on excess demand functions. The result is obtained by applying the Brouwer fixed point theorem to a trimmed simplex which does not contain prices equal to zero. The mathematical techniques are based on some results obtained in Neuefeind (1980) and Geanakoplos (2003).

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  • Simone Tonin, 2018. "Existence of Equilibrium Prices: A Pedagogical Proof," Papers 1808.03129, arXiv.org, revised Sep 2018.
    • Handle: RePEc:arx:papers:1808.03129
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    1. Quah, John K.-H., 2008. "The existence of equilibrium when excess demand obeys the weak axiom," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 337-343, February.
    2. Neuefeind, Wilhelm, 1980. "Notes on Existence of Equilibrium Proofs and the Boundary Behavior of Supply," Econometrica, Econometric Society, vol. 48(7), pages 1831-1837, November.
    3. Joseph Greenberg, 1977. "An Elementary Proof of the Existence of a Competitive Equilibrium with Weak Gross Substitutes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(3), pages 513-516.
    4. Reinhard John, 1999. "Abraham Wald's equilibrium existence proof reconsidered," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 417-428.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. John Geanakoplos, 2003. "Nash and Walras equilibrium via Brouwer," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 585-603, March.
    7. Ruscitti, Francesco, 2012. "On the boundary behavior of the excess demand function," Research in Economics, Elsevier, vol. 66(4), pages 371-374.
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