Give or take? Rewards vs. Charges for a Congested Bottleneck

This paper analyzes the possibilities to relieve congestion using rewards instead of taxes, as well as combinations of rewards and taxes. The model considers a Vickrey-ADL model of bottleneck congestion with endogenous scheduling. With inelastic demand, a fine (time-varying) reward is equivalent to a fine toll, and to a continuum of combinations of time-varying tolls and rewards (including fine feebates). When demand is price sensitive, a reward becomes less attractive from the efficiency viewpoint, because it attracts additional users to the congested bottleneck. As a result, both the second-best optimal rate of participation in the scheme, and the relative efficiency that can be achieved with it, decreases when demand becomes more elastic. Our analytical and simulation results for coarse schemes suggest that a coarse reward is less effective than a coarse feebate, which is itself less effective than a coarse toll. The most efficient coarse system is the step toll, which is also allowed to be positive in the shoulder period.