The General Validity of the Law of Comparative Advantage

It is well known that the law of comparative advantage breaks down when applied to individual commodities or pairs of commodities in a many-commodity world. This paper shows that the law is nonetheless valid if restated in terms of averages across all commodities. Specifically, a theorem and several corollaries are derived which establish correlations between vectors of trade and vectors containing relative-autarky-price measures of comparative advantage. These results are proven in a general many-commodity model that allows for tariffs, transport costs, and other impediments to trade.