Congestive mode-switching and economies of scale on a bus route

This paper introduces a type of circular causation called Congestive Mode-Switching (CMS) that may arise when an increase in congestion penalizes transit relative to driving. In turn, rising congestion persuades some transit riders to drive, which exacerbates congestion further, and so on. This circular causation can beget multiple equilibria with different levels of congestion and transit ridership. The paper explores this logic with a static model of a bus route. When the bus fleet size is fixed, CMS applies because congestion raises the bus cycle time and thus lowers bus frequency, resulting in higher wait times. When the fleet size depends on bus ridership, CMS is joined by economies of scale as a second source of circular causation. We derive the system’s equilibria using a static model in the vein of Walters (1961), which permits us to graphically characterize equilibria in useful ways. The comparative statics of a road improvement show how feedback alters first-order effects. A Downs-Thomson paradox is not possible, because a road improvement aids buses even more than cars. Continuous-time stability analysis shows that multiple equilibria may be stable.