The Social Welfare for the Separable Road Toll Function

This paper considers a congested bottleneck, where some travelers are given priority and other travelers can use the reserverd capacity when it is not used. In this paper, a quasiconcave function of the scheduling utility is considered, which is weaker than a strictly concave function used by Mogens Fosgerau (2011). Furthermore, this paper proves that the socially optimal fast lane scheme for the separable toll function obtains more than half the social welfare for the optimal continuously time varying toll, which generalizes the results in Mogens Fosgerau (2011).