This note provides a nontechnical summary of a research paper (Bullard and DiCecio [2021, Classical policy benchmarks for economies with substantial inequality, Federal Reserve Bank of St. Louis, unpublished manuscript]) that I presented as the NIESR 2021 Dow Lecture on 9 February 2021. In the paper, we construct a simple benchmark macroeconomic model with substantial heterogeneity among households, enough to generate empirically plausible Gini coefficients for the distributions of consumption, income and financial wealth. The model includes aggregate shocks as well as both permanent and temporary idiosyncratic uncertainties. Four policymakers—implementing monetary, fiscal, labour market and education policies—act in concert to achieve a first-best allocation of resources. We argue that the roles of these policymaker types are ‘classic’ and match up well with observed policymaker roles in OECD countries. We regard this simple economy as a benchmark for the study of other aspects of the interaction between policy and inequality.