TITLE:
An Algebraic Proof of the Existence of a Competitive Equilibrium in Exchange Economies
AUTHORS:
Guang-Zhen Sun
KEYWORDS:
Exchange Economy, Existence of Competitive Equilibrium, Perron-Frobenius Theorem
JOURNAL NAME:
Theoretical Economics Letters,
Vol.4 No.3,
April
17,
2014
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.