We study a problem in which policymakers need to screen self-selected individuals by unobserved heterogeneity in social welfare gains from a policy intervention. In our framework, the marginal treatment effects and marginal treatment responses arise as key statistics to characterize social welfare. We apply this framework to a randomized field experiment on electricity plan choice. Consumers were offered welfare-improving dynamic pricing with randomly assigned take-up incentives. We find that price-elastic consumers—who generate larger welfare gains—are more likely to self-select. Our counterfactual simulations quantify the optimal take-up incentives that exploit observed and unobserved heterogeneity in selection and welfare gains.