Policymakers often distort goods markets to effect redistribution—for example, via price controls, differential taxation, or in-kind transfers. We investigate the optimality of such policies alongside the (optimally-designed) income tax. In our framework, agents differ in both their ability to generate income and their consumption preferences, and a planner maximizes a social welfare function subject to incentive and resource constraints. We uncover a generalization of the Atkinson-Stiglitz theorem by showing that goods markets should be undistorted if the heterogeneous consumption tastes (i) do not affect the marginal utility of disposable income, (ii) do not enter into the social welfare weights and (iii) are statistically independent of ability. We also show, however, that market interventions play a role in the optimal resolution of the equity-efficiency trade-off if any of the three assumptions is relaxed. In a special case of our model with linear utilities, binary ability, and continuous willingness to pay for a single good, we characterize the globally optimal mechanism and show that it may feature means-tested consumption subsidies, in-kind transfers, and differential commodity taxation.