Correct me if you can - optimal non-linear taxation of internalities

A growing literature has shown that behavioral biases influence consumer choices. Such socalled internalities are ubiquitous in many settings, including energy efficiency investments and the consumption of sin goods, such as cigarettes and sugar. In this paper, we use a mechanism design approach to characterize the optimal non-linear tax (or subsidy) for correcting behaviorally biased consumers. We demonstrate that market choices are informative about consumers' bias, which can be exploited for benevolent price discrimination via a non-linear tax schedule. We derive that such "internality revelation" depends on two sufficient statistics: the correlation between valuations and biases, as well as the signal-to-noise ratio of the bias. Furthermore, we find that there must be a minimum alignment of preferences among the designer and the consumer to ensure internality tax implementability. We contrast our results with the insights from standard non-linear income taxation and discuss that the optimal corrective tax schedule is typically convex. In addition, we apply our findings to the light bulb market and determine the optimal non-linear subsidy for energy efficiency.