The computational content of Walras’ existence theorem

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In [Y. Tanaka, Undecidability of the Uzawa equivalence theorem and LLPO, Appl. Math. Comput. 201 (2008) 378–383] Yasuhito Tanaka showed that Walras’ existence theorem implies the nonconstructive lesser limited principle of omniscience ( LLPO); it follows that Walras’ existence theorem does not admit a constructive proof. We give a constructive proof of an approximate version of Walras’ existence theorem from which the full theorem can be recovered with an application of LLPO. We then push Uzawa’s equivalence theorem to the level of approximate solutions, before considering economies with at most one equilibrium.