According to the Mohring-Harwitz (1962) Cost Recovery Theorem (henceforth Theorem), revenues from optimal congestion tolls for a facility just cover the costs of optimal capacity if three conditions hold: (a) user costs are homogeneous of degree zero in usage and capacity, (b) capacity is perfectly divisible, and (c) capacity is supplied at a unit cost elasticity. Lindsey (2009) shows that the Theorem holds with random demand and capacity if tolls can be set optimally conditional on the state that is realized. Lindsey’s model deals with short-run recurring shocks such as road accidents. Given statistically independent events, the Law of Large Numbers applies and costs will be almost exactly recovered in practice. However, long-run and enduring fluctuations in demand and capacity can also be important that affect cost recovery over the lifetime of a facility. Arnott and Kraus (1998) show that the Theorem holds in such non-stationary environments without uncertainty.

This paper extends Arnott and Kraus (1998) and Lindsey (2009) by studying cost recovery in non-stationary environments with uncertainty. We show that the Theorem holds as follows: Expected present-value lifetime toll revenues just suffice to pay expected construction costs if: condition (a) above holds at any calendar date and in any state, conditions (b) and (c) hold for design capacity, realized capacity at any calendar date and in any state is proportional to design capacity, and tolls are set optimally conditional on the state. We then investigate the range of plausible surpluses and deficits for toll roads when demand follows Geometric Brownian motion.