Carpooling with heterogeneous users in the bottleneck model

When drivers opt for carpooling, road capacity will be freed up, and this will reduce congestion. Therefore, carpooling is interesting for policy makers as a possible solution to congestion. We investigate the effects of carpooling in a dynamic equilibrium model of congestion, which captures various dimensions of heterogeneity: heterogeneity in preference for carpooling, "ratio heterogeneity" between the values of time and the values of schedule delay, and "proportional heterogeneity" that scales all values equally. We investigate three policy scenarios: no-toll, first-best pricing, and subsidization of carpooling. The optimal second-best subsidy equals each type's heterogeneous marginal external benefit (MEB) of switching to carpooling. If such differentiation is impossible, the third-best subsidy is a weighted average of the MEBs, where the weights depend on the number of each type and their sensitivity to the subsidy. In our numerical example, we find that when increasing the degree of "ratio heterogeneity", the relative efficiency of the second-best subsidization first increases and then falls with the degree of heterogeneity and L type carpoolers benefit more than H type carpoolers. However, when increasing the degree of "proportional heterogeneity", H type users benefit more than L types for both solo drivers and carpoolers. Moreover, the relative efficiency of the second-best subsidization decreases throughout.