How should monetary policy respond to sectoral shocks in a world where consumption baskets vary systematically across households? We present a multi-sector New-Keynesian model with generalized, non-homothetic preferences and inequality. The output gap is governed by a Marginal Consumer Price Index (MCPI), rather than the regular CPI. Policy trade-offs are shaped by a novel wedge in the New-Keynesian Phillips Curve (NKPC). Analytical results and quantitative simulations show that, following negative shocks to necessity sectors, the NKPC is shifted upward, increasing CPI inflation but decreasing the output gap. We find that the optimal policy response is relatively accommodative.