Minimal Revenue Tolls: Price Stability for Networks With BPR Cost Function

Abstract

Marginal-Cost (MC) tolls are known to produce economic efficiency of network flows. Yet, MC pricing has not been widely adopted, because of various perceived unpopular aspects, such as complexity, collection costs, and inequities. Minimal Revenue (MinRev) pricing has been suggested as a means to achieve most of the economic improvements of MC pricing with fewer unpopular aspects. One claimed improvement of MinRev tolls is the ability to maintain fixed tolls while flows change. We show that single-power-law congestion costs are sufficient (but not always necessary) conditions for the stability (flow independence) of Minimal-Revenue (MinRev) tolls in transportation networks, so long as the links that are actually used do not change. This is particularly important because the usual Bureau of Public Roads (BPR) cost function recommended as a good representation of real road traffic, has this single power-law congestion cost. For cases of elastic demand, these MinRev tolls do not achieve the full economic efficiency of Marginal-Cost (MC) tolls. However, they may still prove desirable because of greater stability, greater simplicity, lower out-ofpocket costs, and greater perceived equity. Furthermore, in cases of major congestion problems, where all links are used, the MinRev tolls are totally stable, i.e. totally independent of flows; also, if demand is relatively insensitive to price, the flows are nearly equal to the optimal flows obtained by MC pricing. The discussion is based on the equilibrium assignment method, with tolls to encourage System Optimal (SO) flows rather than User Optimal (UO) flows. Results are obtained for general networks, and also illustrated with a very simple example.