The existence of equilibrium in a simple exchange model
AbstractThis paper gives a new proof of the existence of equilibrium in a simple model of an exchange economy. We first formulate and prove a simple combinatorial lemma and then we use it to prove the existence of equilibrium. The combinatorial lemma allows us to derive an algorithm for the computation of equilibria. Though the existence theorem is formulated for functions defined on open simplices it is equivalent to the Brouwer fixed point theorem.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 46764.
Date of creation: Jan 2013
Date of revision: Apr 2013
Simple exchange model; equilibrium existence; zero of a function; fixed point; computation of equilibria; simplicial methods;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
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- Mackowiak, Piotr, 2010.
"The existence of equilibrium without fixed-point arguments,"
Journal of Mathematical Economics,
Elsevier, vol. 46(6), pages 1194-1199, November.
- Maćkowiak, Piotr, 2010. "The existence of equilibrium without fixed-point arguments," MPRA Paper 42044, University Library of Munich, Germany, revised 04 Sep 2010.
- Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
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