Cost recovery from congestion tolls with random capacity and demand

According to the Cost Recovery Theorem the revenues from congestion tolls pay for optimal capacity of a facility if user costs are homogeneous of degree zero in usage and capacity, and if capacity is perfectly divisible and supplied with a unit cost elasticity. This paper examines the robustness of the Theorem to demand and capacity uncertainty in the context of highway travel. Three main results are derived. (1) The Theorem holds in expected values when users are perfectly informed about the state and the toll is set optimally as a function of the state. (2) The Theorem also holds in expected values when users are imperfectly informed about the state, the toll is set optimally given the information that users have, and the price elasticity of demand is the same in all states. (3) The Theorem does not hold if the toll is set using less information than users have. Whether an expected surplus or deficit results depends on the sign of the correlation across states between the Pigouvian toll and the ratio of the price elasticity of demand to the price. Examples show that the correlation can be positive or negative depending on the functional form of the demand and cost curves and the way the curves shift between states.