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An Algebraic Proof of the Existence of a Competitive Equilibrium in Exchange Economies
Department of Economics, Faculty of Social Sciences, University of Macau, Macau, China
- 1 Department of Economics, Faculty of Social Sciences, University of Macau, Macau, China
Theoretical Economics Letters·Volume 04 (2014)·Pages 232–234·Published 3 April 2014·DOI10.4236/tel.2014.43031
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Abstract
The standard excess demand argument for existence of competitive equilibria in exchange economies invokes maximizing the market value of the aggregate excess demand function and thereby adjusting the prices toward equilibrium. By exploiting the Perron-Frobenius theorem on stochastic matrices, we offer an algebraic proof of the existence of a competitive equilibrium without resorting to such a device of excess demand.
KeywordsExchange EconomyExistence of Competitive EquilibriumPerron-Frobenius Theorem
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