Abstract
Private provision of public roads through build-operate-transfer (BOT) approaches is increasing around the world. By considering both social welfare gain and profitability, the BOT problem is to determine the optimal BOT contract which can be viewed as a combination of three primary variables of concession period, road capacity and toll charge. This paper models the BOT problem as the isoperimetric problem in calculus of variations to maximize the social welfare with a profit constraint. The model explicitly incorporates the effect of road deterioration and maintenance over the years, which is assumed to depend on the traffic loads, road capacity and road natural deterioration. We find that an optimal pricing policy requires toll increase over calendar time to reduce traffic load due to time-increasing and load-increasing maintenance cost. If, however, the marginal user damage on road is independent of time, then the optimal toll charge is free from the effect of road natural deterioration and thus time-invariant. We also discuss how to reach an optimal contract through government regulations and investigate the effects of economic growth on the solution properties of the problem.
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