The primary purpose of the paper is to provide characterizations of the conditions for welfare improvements in several situations that have received very little attention in the existing literature. The first aim is to exhibit the gains that can accrue to a country from the elimination of excess supplies as a result of a policy move from autarky to free trade. The second aim is to characterize the conditions under which the introduction of new goods into the economy will generate welfare gains. The third main area discussed is the extension of the authors’ methodology to a large open economy that can influence its terms of trade. The techniques used to illustrate the gains from eliminating excess supplies and from the introduction of new goods have a much wider applicability; they may be used to obtain and synthesize several welfare results from the literature.