The Generalized Network Problem

Many transport and other service problems come down to simple network choices: what mode and/or route to take, if some of the routes and modes are congested and their use can be priced or not priced by different operators. The operators can have different objective functions: public or private monopoly, private duopoly, etc.. This standard problem has been studied in many variants, mostly using the assumption of perfect substitutability between alternatives, so that in the deterministic Wardrop equilibrium, all routes that are used have the same generalized cost. This paper examines in more detail the role of the perfect substitutability assumption. Users of a network consume transport services, which are differentiated in two ways. There are objective differences in quality (length of route, congestion level) perceived by all users and there are individual idiosyncratic preferences for transport services. The resulting stochastic equilibrium is analysed on a simple parallel network for four types of ownership regimes: private ownership, coordinated public ownership, mixed public-private and public Stackelberg leadership. We find that, firstly, when total demand is fixed and there is congestion, then by controlling one route a government can achieve the First Best allocation, although the second route is privately operated or unpriced. This result holds whatever the level of substitutability and whatever the levels of congestion. Secondly, whenever imperfect substitutability is present, private supply of one of the two routes becomes relatively less efficient because the private supplier has an additional source of market power to exploit. If the better of the two routes is privately supplied it is always insufficiently used. However, if only one route can be privately operated, then this should always be the intrinsically better route