A theory of optimal investment timing in railways

In a random utility model for mode choice in transportation we allow for stochastic shifts of preferences following the upgrade of an existing mode. We take the measurable part of the conditional indirect utility function on the upgraded mode to be scaled-up relative to that of a competing mode according to a geometric Brownian motion. Next the likelihood that one mode is preferred to the other is determined with binary logit and the marginal utility of income is constant. We identify the law of motion of both the likelihood that the upgraded mode will be chosen and the corresponding volume of the demand. We take the respective mode to be a railway, which is upgraded from traditional to high-speed railway (HSR). Our results reveal that the law of motion of the volume of the demand for HSR generalizes that used by public officials to estimate demand growth, and which are fully based on macroeconomic trends. The law of motion reduces to that adopted in practice if and only if the demand for both competing modes (HSR and highway or airway) is expected to change in the same proportion over time. A good approximation of the discounted expected consumer surplus exists and can be used for the analysis of the optimal investment timing on HSR. The latter depends on how optimistic are the forecasts about both the total demand and the diverted demand from the competing mode. On two specific projects, we simulate our results based on available data to show under which conditions public decisions were optimal.