When macroeconomic tools fail to respond to wealth inequality optimally, regulators can still seek to mitigate inequality within individual markets. A social planner with distributional preferences might distort allocative efficiency to achieve a more desirable split of surplus, for example, by setting higher prices when sellers are poor--effectively, using the market as a redistributive tool.
In this paper, we seek to understand how to design goods markets optimally in the presence of inequality. Using a mechanism design approach, we uncover the constrained Pareto frontier by identifying the optimal trade-off between allocative efficiency and redistribution in a setting where the second welfare theorem fails because of private information and participation constraints. We find that competitive equilibrium allocation is not always optimal. Instead, when there is substantial 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 within-side inequality, meanwhile, it may be optimal to impose price controls even though doing so induces rationing.