Social Optimum in the Basic Bathtub Model

The authors thank Joshua Buli, Wen-Long Jin, Robin Lindsey, Raphaël Lamotte, and participants at a session of the International Transportation Economics Association 2018 Conference in Hong Kong (Session 31, Traffic Management: Dynamics and Mechanism Design) for very helpful comments on an earlier version of this paper. The authors also acknowledge Antoine Benoit (a colleague of Kilani in the Mathematics Department) who clarified the definition of integrable functions and measures. Responding to the constructive critical comments and suggestions of the four referees, the associate editor, and the editor resulted in a paper that is clearer, more precise, and more compact than the original version. Arnott would like to thank the Université de Lille for its hospitality during visits he made to work with Kilani.