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.[phone]                

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Debreu, G. (1983) Four Aspects of the Mathematical Theory of Economic Equilibrium. In: Mathematical Economics: Twenty Papers of Gerard Debreu, Cambridge University Press, New York, 217-231.
[2]	Mas-Colell, A., Whinston, M.D. and Green, J. (1995) Microeconomic Theory. Oxford University Press, Oxford.
[3]	Jehle, G.A. and Reny, P.J. (2000) Advanced Microeconomic Theory. 2nd Edition, Addison Wesley, Boston.
[4]	Aldrovandi, R. (2001) Special Matrices of Mathematical Physics. World Scientific, Singapore.