Continuity in the gains from trade with similar consumers

The conditions under which one can prove directly that all consumers gain from the elimination of prohibitive tariffs are very stringent. Yet it is intuitively plausible that if these conditions were ‘almost’ met, the results would still obtain and all would gain. We establish this rigorously by use of a topology on economic agents, as developed by Kannai, Debreu and Hildenbrand. Specifically, we show that if, in a given economy, all agents gain in going from autarky to free trade, then in any economies composed of agents sufficiently similar to those in the given one, all will gain.