Household heterogeneity has been shown to be an important driver of aggregate demand. In this research, we demonstrate that it also impacts the supply side. We build a model in which heterogeneous households vary in their extent to which they supply production factors (labor and capital). Our model offers novel results about the consequences of inequality for the supply side, showing that (i) inequality distorts the factor allocation leading to higher marginal costs, and (ii) inequality becomes part of the Phillips curve. This is the "misallocation channel of inequality". The cyclicality of inequality crucially depends on how important capital is for production. Our findings have important implications for building models with household heterogeneity and for optimal monetary policy.