Road use charging and inter-modal user equilibrium: The Downs-Thompson paradox revisited

Abstract

This paper looks at the impact of charging for road use in cities where an intermodal equilibrium prevails, where increased transit use leads to efficiency gains, and where the roads are congested. Demand is assumed to be elastic and transit is assumed not to be directly affected by road congestion, as would be the case where transit uses a reserved track. It is shown that at a stable intermodal user equilibrium a version of the Downs-Thompson paradox applies if the efficiency gains arising from increased transit use are passed on to passengers as reduced generalised costs (reduced fares, increased service frequencies or both). The paradox arises because the imposition of a road user charge not only reduces road congestion but also reduces the generalised cost of travel at the intermodal user equilibrium, including the road user charge for those who choose to drive. The paper then goes on to consider what would be expected if, rather passing on the efficiency gains to transit users, the transit operator(s) as a whole maximise profits, and establishes that the paradox no longer arises. The implications of these findings for the regulation of transit fares are considered.