As noted earlier, low usage is usually associated with declining average costs as fixed costs are spread over more users. For medium usage, the average costs are fairly flat and don’t change dramatically. With high usage, capacity constraints and congestion come into play and the average costs begin to increase.
Usage of infrastructure systems tends to vary considerably over time and over geography. As a result, costs also tend to vary considerably. As an example, Figure 6.3.1 illustrates a typical variation in traffic volumes by time of day, with the peak travel occurring the morning and the late afternoon. Roadway congestion is heaviest in these peak hours of travel. As another example, Figure 6.3.2 illustrates typical electricity demand by time of day for two different months. In this case, there is variation in demand over the course of a day, but it is not as extreme a fluctuation as for roadway traffic. Figure 6.3.2 also shows that electricity demand varies over the course of a year, with higher demand in the summer likely due to air conditioning use.
Infrastructure managers often must respond to these fluctuating demands. In many cases, maintenance activities are scheduled for low usage periods to avoid imposing costs. For example, building floors may be cleaned at night. As another example, power grid managers must respond to not only varying demand (as shown in Figure 6.3.2), but also varying supply as solar and wind generators respond to environmental conditions.
Another important variation in demand for many infrastructure systems occurs over time, from year to year or over the course of decades. For example, demand for water will typically increase with an increase in population. Demand for electricity will also typically increase with population, but may also depend upon the numbers of households being served, incomes and new technologies. New technologies may reduce demand (with more energy-efficient refrigerators for example) or increase demand (with battery electric vehicles or fancier entertainment systems).
To the extent that cost functions represent user costs, then the cost functions shown in Figure 6.2.1 can be coupled with demand functions to estimate equilibrium demand for service. Figure 6.3.3 illustrates a linear user cost and demand curve for a service. The 90
equilibrium demand occurs at the intersection of the two curves with usage \(q_e\) and user cost \(p_e\). Of course, demand is likely to be varying over time, so the equilibrium demand and user costs will similarly vary.