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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