Optimal Congestion Pricing with Diverging Long-run and Short-run Scheduling Preferences

Recent empirical work has suggested that there is an important distinction between short-run versus long-run scheduling behaviour of commuters, reflected in differences in values of time and schedule delays, as well as in preferred arrival moments, for the short-run versus the long-run problem. Peer et al. (2015) for example find that the average value of time when consumers form their routines in the long-run problem may exceed by a factor 6 the short-run value that governs departure time choice given these routines. For values of schedule delay, in contrast, the short-run value exceeds the long-run value, by a factor 2. And, when forming routines, consumers in fact choose a most preferred arrival time that may deviate from the value they would choose in absence of congestion because a change in routines may mean that shorter delays will be encountered. This paper investigates whether this distinction between short-run and long-run scheduling decisions affect optimal pricing of a congestible facility. Using a stochastic dynamic model of flow congestion for describing short-run equilibria and integrating it with a dynamic model of routine formation, it is found that consistent application of short-run first-best optimal congestion pricing does not optimally decentralize the optimal formation of routines in the long-run problem. A separate instrument, next to road pricing, is therefore needed to optimize routine formation.