Amidst the recent resurgence of inflation, this paper investigates the interplay of corporate profits and income distribution in shaping inflation and aggregate demand within the New Keynesian framework. We derive a novel analytical condition for profits to be procyclical and inflationary. Furthermore, we show that the cyclicality of profits is a key determinant of the propagation properties of these models under household heterogeneity, but there is a catch: for aggregate-demand fluctuations and inflation to be amplified by heterogeneity, profits have to be countercyclical—an implication that is at odds with the data. Adding physical capital investment to the model can resolve this conundrum, generating aggregate-demand amplification even under procyclical profits. However, the amplification works through an investment channel and not through profits, inconsistent with the narrative attributing elevated inflation to corporate greed.