Firms face significant constraints in their ability to differentiate pay by worker productivity. We show how these internal equity constraints generate a quantity-quality trade-off in hiring: firms which offer higher wages attract higher skilled workers, but cannot profitably employ lower skilled workers. In equilibrium, this results in workplace segregation and pay dispersion even among ex-ante identical firms. Our framework provides a novel interpretation of the (empirically successful) log additive AKM wage model, and shows how log additivity can be reconciled with sorting of high-skilled workers to high-paying firms. It can also rationalize a hump-shaped relationship between firm size and firm pay, and provides new insights into aggregate-level, regional and sectoral variation in earnings inequality—which we explore using Israeli administrative data.