We combine classic occupational choice (Roy model) and frictionless matching (following Sattinger) to explain earnings by occupation and firm in a way that is consistent with double assignment. In our model, within-firm inequality is globally nonzero whenever there is asymmetry in the revenue function or the occupational skill distribution across occupations. Occupational earnings overlap each other, and, unlike in the Roy model, the distributions of potential earnings are endogenous. In line with recent empirical findings on earning decomposition, skill-biased technical change increases within-firm inequality mostly among high-wage firms and not among low-wage firms.