Maćkowiak, Piotr
(2011):
*Some Equivalents of Brouwer's Fixed Point Theorem and the Existence of Economic Equilibrium.*
Published in: Quantitative Methods in Economics 2012, (M. Matłoka, ed.), Poznań University of Economics Press, ISBN: 978-83-7417-703-0
(2012): pp. 164-171.

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## Abstract

The primary goal of the paper is to deliver a simple proof of equivalence between Brouwer’s fixed point theorem and the existence of equilibrium in a simple exchange model with monotonic consumers. To achieve this end, we discuss some equivalent formulations of Brouwer’s theorem and prove additional ones, that are ’approximating’ in character or seem to be better suited for economic applications than the standard results.

Item Type: | MPRA Paper |
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Original Title: | Some Equivalents of Brouwer's Fixed Point Theorem and the Existence of Economic Equilibrium |

Language: | English |

Keywords: | existence of equilibrium, Brouwer’s fixed point, simple exchange model |

Subjects: | D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium |

Item ID: | 42461 |

Depositing User: | Piotr Maćkowiak |

Date Deposited: | 04 Jan 2013 12:24 |

Last Modified: | 29 Sep 2019 07:53 |

References: | Arrow, K., Hahn, F., 1971, General Competitive Analysis, Holden-Day,San Francisco. Brouwer, L., 1911-1912, Ueber Abbildung von Ma nnigfaltigkeiten, Mathematische Annalen, vol. 71, pp. 97-115. Jehle, G., Reny, P., 2001, Advanced Microeconomic Theory. International Edition., Addison-Wesley, Boston. Mas-Colell, A., 1977, On The Equlibrium Price Set of an Exchange Economy, Journal of Mathematical Economics, vol. 4, pp. 117-126. Tijs, S., Torre, A., Branzei, R., 2001, Approximate Fixed Point Theorems, Tilburg University, Center for Economic Research Discussion paper No. 2001-55. Toda, M., 2006, Approximation of Excess Demand on the Boundary and Equilibrium Price Set, Advances in Mathematical Economics, vol. 9, pp. 99-107. Uzawa, H., 1962, Walras’ Existence Theorem and Brouwer’s Fixed-Point Theorem, The Economic Studies Quarterly, vol. 13, pp. 59-62. Wong, K.-C., 1997, Excess Demand Functions, Equilibrium Prices, and Existence of Equilibrium, Economic Theory, vol. 10, pp. 39-54. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/42461 |