Obstacles to Redistribution Through Markets and One Solution

Dworczak, Kominers, and Akbarpour (2021) study when certain market structures are optimal in the presence of heterogeneous preferences. A key assumption to apply the results is that the social planner knows the joint distribution of the value of the good and marginal value of money. We show that the features of the distribution needed to characterize optimal market structure cannot be identified from demand. While this is a negative result, we show that the distribution of good value and marginal utility of money is fully identified when there is an observed measure of quality that varies exogenously