Microeconomics of a taxi service in a ring-shaped city

To a client, taxi quality of service involves not only the riding time and comfort, but also the access time between the instants of booking (or readying oneself) and pickup. In turn, the access time depends on fleet size and the macroscopic patterns of service usage: demand volume and its spread in space, average ride time, transaction times. In this article, we investigate the formation of the access time and derive its economic consequences for a taxi service in an idealized city with ring shape and spatial homogeneity, hence circular symmetry. At the operational level, under given supply and demand conditions the access time stems from the number of busy vehicles, which obeys to a second-degree characteristic equation. This enables us to model fleet size as a function of target demand volume and access time. Taking then a broader perspective, demand is elastic to supply conditions including access time, ride time, transaction time and tariff fare. We model short-term traffic equilibrium and demonstrate the existence and uniqueness of an equilibrium state. Next, at the tactical level the service supplier sets up the fleet size and the tariff fare in order to satisfy an economic objective. We model medium-term supply-demand equilibrium under three regulation patterns of, respectively, (i) service monopoly and the maximization of production profit, (ii) system optimum and the maximization of social surplus, (iii) second best system optimum subject to a budgetary constraint. In each pattern, both the tariff fare and the access time are linked by analytical formulas to exogenous conditions about the territory, the demand and the cost function of service provision. Theoretical properties are obtained to compare the patterns under specific demand function with constant elasticity of volume to generalized cost: under constant elasticity of-2, the monopoly tariff and generalized cost are more than twice as large as their system optimum counterparts, and exact doubles of their second best optimum counterparts in the absence of fixed production costs. At the strategic level, the model can be applied to assess decisions on vehicle technology (motor type, driving technology) and on service location by the service supplier, as well as the regulation policies by public authorities.