We revisit the causes, welfare consequences, and policy implications of the dispersion in households' labor market outcomes using a model with uninsurable risk, incomplete asset markets, and home production. Allowing households to be heterogeneous in both their disutility of home work and their home production efficiency, we find that home production amplifies welfare‐based differences, meaning that inequality in standards of living is larger than we thought. We infer significant home production efficiency differences across households because hours working at home do not covary with consumption and wages in the cross section of households. Heterogeneity in home production efficiency is essential for inequality, as home production would not amplify inequality if differences at home only reflected heterogeneity in disutility of work.

We fully solve a sorting problem with heterogeneous firms and multiple heterogeneous workers whose skills are imperfect substitutes. We show that optimal sorting, which we call mixed and countermonotonic, is comprised of two regions. In the first region, mediocre firms sort with mediocre workers and coworkers such that the output losses are equal across all these teams (mixing). In the second region, a high-skill worker sorts with low-skill coworkers and a high-productivity firm (countermonotonicity). We characterize the equilibrium wages and firm values. Quantitatively, our model can generate the dispersion of earnings within and across US firms.