I develop an analytical framework for monetary policy in a multi-sector economy with a general input-output network. I derive the Phillips curve and welfare as a function of the underlying production primitives. Building on these results, I characterize (i) the correct definition of aggregate inflation and (ii) how the optimal policy trades off inflation in different sectors, based on the production structure. I construct two novel inflation indicators. The first yields a well-specified Phillips curve. Consistent with the theory, this index provides a better fit in Phillips curve regressions than conventional specifications with consumer prices. The second is an optimal policy target, which captures the tradeoff between stabilizing aggregate output and relative output across sectors. Calibrating the model to the U.S. economy I find that targeting consumer inflation generates a welfare loss of 0.8% of per-period GDP relative to the optimal policy, while targeting the output gap is close to optimal.