An Algebraic Proof of the Existence of a Competitive Equilibrium in Exchange Economies

Guang-Zhen Sun

doi:10.4236/tel.2014.43031

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Theoretical Economics Letters > Vol.4 No.3, April 2014

An Algebraic Proof of the Existence of a Competitive Equilibrium in Exchange Economies ()

Guang-Zhen Sun

Department of Economics, Faculty of Social Sciences, University of Macau, Macau, China.

DOI: 10.4236/tel.2014.43031 PDF HTML XML 3,940 Downloads 4,952 Views

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.

Keywords

Exchange Economy, Existence of Competitive Equilibrium, Perron-Frobenius Theorem

Share and Cite:

Sun, G. (2014) An Algebraic Proof of the Existence of a Competitive Equilibrium in Exchange Economies. Theoretical Economics Letters, 4, 232-234. doi: 10.4236/tel.2014.43031.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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