The classical gains-from-trade conjecture was finally given a thorough Arrow-Debreu proof in 1972. Since then, the proposition has been repeatedly challenged. Some of the challenges rest on grounds which in no respect violate Arrow-Debreu assumptions. Those challenges are therefore without foundation. The remaining challenges rest on the assertion that some of the Arrow-Debreu assumptions are unnatural and unnecessarily restrictive or on the imposition of artificial restrictions on the set of permissible compensatory transfers. We conclude that none of the challenges can be sustained. Copyright Verein für Socialpolitik and Blackwell Publishers Ltd 2002.
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