The enrichment of a sector (individual, region or country) benefits others: the third welfare theorem?

The economic enrichment of a sector may make other sectors as a whole better or worse off. However, for the benchmark case of proportionate enrichment, other sectors tend to gain. This result is shown using offer curves, supply and demand analysis, Cobb-Douglas utility functions, and a more general case. Allowing the enriching sector to be monopolistic does not affect the result. Semi-economic enrichment through migration and population growth also makes others better off. Most enrichments also tend to be equalizing in their effects on others.