Aggregate price shocks generate unequal welfare losses both across and within income groups. Policymakers face a trade-off: price subsidies target those most affected but create inefficiencies, while transfers are less distortionary but harder to target. We develop and implement a framework to quantify this trade-off using rich panel data on households’ energy spending and incomes, alongside price and policy variation from the 2022–23 European Energy Crisis. Absent policy intervention, average household welfare losses would have equalled 6% of income, with some households facing much larger losses. The combination of an energy-price subsidy and universal transfers reduced both the mean and dispersion of losses, but incurred efficiency costs equal to 12% of the total relief package revenue costs. Optimal policy entails a strictly positive price subsidy; its level is lower when transfers can be targeted using income and past energy usage.











