Transport Infrastructure Investment and Demand Uncertainty

Abstract

In transportation planning, there can be long lead times to adapt capacity. This article addresses two questions. First, in a one mode world (e.g., rail or road), what is the optimal capacity choice when faced with uncertain demand, long lead times, and congestion. Using a simple analytical model, it is shown that when demand is inelastic, it is socially optimal to invest more than if only the expected level of demand is taken into account. In this case, it may be beneficial to overinvest in capacity because congestion costs are an increasing function of relative use. This result holds with or without optimal tolling. The second question deals with 2 competing modes in which only one mode has long lead times for capacity, whereas the other has flexible capacity. This is typical for the competition between high-speed rail and air for the medium distance trips (500–1,000 km), or for the competition between inland waterways and trucks for freight. We find that overinvestment is less justified because the substitute mode can more easily absorb the high-demand outcomes.

Keywords:

• Demand Uncertainty
• Infrastructure Investments
• Congestion
• Road Tolling
• Optimal Capacity

The second author benefited from financial support of the FUNDING consortium (6th Framework Research Program of the EC [6.2]) on the Funding of the Trans European Networks. The authors thank Andre de Palma, Nathalie Picard, and Patrick Van Cayseele for their helpful comments on earlier versions of this article.

Notes

¹One could generalize the user-cost function by adding a constant term. This would not affect Proposition 1.

²We could generalize our results by introducing continuous probability distributions. See Arnott et al. (1996) for an illustration.

³We used a model formulation in which the demand level for a given price is uncertain. An alternative formulation would start from uncertain willingness to pay levels for a given demand. Would one obtain the same basic insights? The answer is “yes,” but one has to take care of the effect of the model calibration.

⁴The cost function for rail is highly simplified here. Compared with other modes such as air and road, it has important economies of scale in density. The simplest representation is a linear formulation with fixed costs.

⁵One could introduce monopolistic pricing by airlines, but this would divert our attention away from the central issue: the optimal level of capacity under uncertainty.

⁶The superscripts W and P corresponds to the welfare when rail serves the Whole market or just Part of the market.