ABSTRACT This article undertakes a theoretical post-Keynesian analysis to explore the relationship between inflation, unemployment, and inequality. Firstly, we show the compatibility of the inequality-augmented Phillips curve, which first appeared in Rolim, Carvalho, and Lang (2023), with the post-Keynesian macroeconomic theory. The curve combines the Phillips curve, which relates unemployment and inflation and can be derived from the conflicting-claims inflation model, with the positive relation between unemployment and inequality due to the heterogeneous impact of unemployment on workers. The unemployment rate thus connects the inflation rate to income inequality in a three-dimensional relationship described by the inequality-augmented Phillips curve, which indicates a possible trade-off between low inflation and low inequality. Secondly, we consider the profits inflation case: when inflation is simultaneous with markup increases. Increases in the ex-ante markup rate shift the curve upwards, thus increasing the inflation rate and inequality. In this context, if monetary policy aims to control inflation by increasing unemployment, it will operate along the inequality-augmented Phillips curve and will further increase inequality.