An Algebraic Proof of the Existence of a Competitive Equilibrium in Exchange Economies
Author(s)
Guang-Zhen Sun*
Affiliation(s)
Department of Economics, Faculty of Social Sciences, University of Macau, Macau, China.
Department of Economics, Faculty of Social Sciences, University of Macau, Macau, China.
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.
Cite this paper
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.
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.
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.
[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.