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