Profit maximization by a private toll road with cars and trucks

•Demonstrate that a private toll road takes either a car-strategy or a truck-strategy.•Identify the profit-maximizing frontier and the strategy-switching frontier.•Tuck-to-car VOT ratio, total traffic demand, and relative travel distance difference shape the strategy of a private toll road.

This paper examines the profit maximizing behavior of a private firm which operates a toll road competing against a free alternative in presence of cars and trucks. Trucks differ from cars in value of time (VOT), congestion externality, pavement damage, and link travel time function. We find that the firm takes either a car-strategy or a truck-strategy for profit maximization. For a traffic mix with relatively large car volume and small truck volume, the car-strategy results in no trucks using the toll road, while the truck-strategy results in all trucks using the toll road. We derive the equilibrium flow pattern under any combination of car-toll and truck-toll, based on which we identify a profit-maximizing frontier and a strategy-switching frontier in the car-toll and truck-toll two-dimensional space. By geometrically comparing the two frontiers, we establish general conditions under which each strategy will be taken, which suggest that the truck-to-car VOT ratio, the total traffic demand, and the difference in travel distance between the two roads are critical in shaping the firm's strategy.