This has particular applications in public goods such as public urban transportation, where day demand (peak period) is usually much higher than night demand (off-peak period). By subtracting the marginal costs of operation from the original demands we find the marginal benefits of capacity, which must then be vertically aggregated and equated to the marginal cost of increasing capacity.
With the optimal capacity found, the optimal peak-load prices are found by adding the marginal costs of operation to the marginal benefit generated, in each period, by the optimal capacity.
It may happen, however, that the optimal capacity is not fully used during the off-peak period. In that case, the capacity expansion will be totally supported by the peak demanders.