Comparative Advantage with and Without Gains from Trade

In 1980 Deardorff, Dixit and Norman generalized the law of comparative advantage to show that the value of net imports at autarky prices (or "DDN index") is nonnegative, so that net imports are correlated with autarky prices. The DDN index can be decomposed into the sum of (i) the equivalent variation of gains from trade and (ii) the difference in GNP at autarky prices between autarky and trade. Several examples are given of classical and neoclassical economies where (i) or (ii) can be zero. Hence gains from trade are sufficient but not necessary for the existence of comparative advantage