Shared Production and the Persistence of Absolute Inequality

Knowledge sharing can benefit every participant while reproducing unequal productive positions. This paper develops a two-group model that separates access to shared resources from the efficiency of converting them into output. It derives exact conditions under which production shares move closer together while the absolute output gap continues to widen, including an explicit threshold for partial sharing and a proof of the subsequent trajectory. Equal-efficiency, depreciation, and normalized-resource cases distinguish continuing disadvantage from inherited inequality. Language barriers and AI-assisted communication illustrate why removing a current efficiency disadvantage need not erase an accumulated production gap. The paper provides analytical proofs and reproducible numerical examples; it does not estimate country-level language effects. The accompanying supplement contains Python verification scripts, figures, and the numerical trajectories.