Policymakers frequently use price regulations as a response to inequality in the markets they control. In this paper, we examine the optimal structure of such policies from the perspective of mechanism design. We study a buyer‐seller market in which agents have private information about both their valuations for an indivisible object and their marginal utilities for money. The planner seeks a mechanism that maximizes agents' total utilities, subject to incentive and market‐clearing constraints. We uncover the constrained Pareto frontier by identifying the optimal trade‐off between allocative efficiency and redistribution. We find that competitive‐equilibrium allocation is not always optimal. Instead, when there is inequality across sides of the market, the optimal design uses a tax‐like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump‐sum payments. When there is significant same‐side inequality that can be uncovered by market behavior, it may be optimal to impose price controls even though doing so induces rationing.