missing class, even as the actual money value of time for learning might be harder to estimate. These costs should be added to the extra money the student has to pay in fees.
The most common method for placing monetary values on resources is that of using their market prices. According to economic theory, when a market for a particular good or service is perfectly competitive, the equilibrium price established by that market will represent the value of that good (Mankiw, 2011, Chapter 7). The market price reflects the point at which the demands of purchasers and the supplies of providers lead to transactions that clear the market. This is known as market value. These participants are basing their willingness to buy or sell on their own opportunity costs, so the market price should directly reflect opportunity cost.
However, market prices are not a very accurate reflection of opportunity cost in distorted markets. There are many reasons why markets might be distorted. These include highly concentrated markets with less competition, information failures, and externalities. In education systems, monopoly features are common. For example, the cost of hiring a teacher is often based on district salary scales or statewide certification requirements on the demand side and based on collective bargaining contracts on the supply side. These supply and demand distortions may move teacher pay away from what might be considered as a competitive market price for teaching services (see Eberts, 2007; Jacob, 2007). However, teachers can select alternative occupations, and districts/schools must pay competitive wages or their teachers will leave for other districts or schools or for other employment. Generally, the distortion in teacher labor markets might be small such that the market wage is appropriate. Nevertheless, for each input, it is important to consider if there are distortions away from market prices, how large these distortions might be, and if they apply to the decisionmakers’ context.
For some resources, market prices may not be available. When attempts are made to ascertain the value of a resource that does not have a competitive market price, the estimated value is called a shadow price (see Boardman, Greenberg, Vining, & Weimer, 2011, Chapters 16–17). Shadow prices should be based directly on opportunity cost. For example, a school district may decide to lend an old facility to a new program. There is no financial transaction, because the building was purchased and paid for a long time ago. Moreover, no market exists for this type of facility; there is no direct market price, so we must impute a shadow price valuation although the facility may have some lease value to nonschool users. This resource must therefore be valued based on what is would cost to maintain the facility in its current state, or to demolish the facility, or to refurbish it for alternative use. Another more common example is volunteer time: By definition, volunteers are unpaid, so there is no direct market price. Volunteer time must therefore be based on the opportunity cost of the volunteers’ time.
Both market and shadow pricing approaches may be used for purposes of cost estimation. Both approaches are derived from the idea of opportunity cost, although we recognize that opportunity cost is a subtle concept that requires careful interpretation. Imagine a school with a gym that is typically unused in the summer. A nonprofit agency proposes a summer school basketball program for high school dropouts. Claiming that the gym is empty, the school might think that the opportunity cost is zero. However, a zero opportunity cost is rarely appropriate because the facility has other uses that represent an opportunity cost if not exploited. It is unlikely that there really is no other alternative use of the gym (e.g., for a different program or leasing for nonschool activities). Also, using the gym in the summer will likely necessitate maintenance costs later. Finally, the assumption of zero opportunity cost might be invoked in an ad hoc way for any resource (e.g., for example, the assumption that the cost of parental time contributions are zero because the parents would otherwise be relaxing at home). Potentially, the analyst could claim that a lot of resources had no alternative use and hence assert that the costs of the program are almost nothing. The conventional—and correct—assumption is that all resources have a positive opportunity cost, as all are needed to replicate the program regardless of financing.
3.2. Cost Per Unit
It is important to be clear about what we mean by costs of education (for a parallel exercise for costing out prevention programs, see Foster, Porter, Ayers, Kaplan, & Sandler, 2007). Strictly speaking, in economics the term cost refers to “cost per unit of output,” for example, cost per car manufactured, cost per 1,000 computers produced, or cost per medical consultation. With this definition, an enterprise that has a lower cost per unit of output is more cost-effective (efficient) than one with a higher cost. This definition corresponds directly to the terminology of a standard economics textbook: Total cost is the cost to produce a given quantity of output, average cost is the cost per individual unit of output, and marginal cost is the cost per additional unit of output. These definitions work well for production decisions.
For educational services, the term cost is slightly different. It refers to the value of all the resources needed to deliver the intervention to the intended population. The cost term is therefore cost per participant, per cohort, or per class. It is helpful to always think about adding the word per after cost to clarify what is meant. This definition is more apt because we typically do not know how effective the intervention is (strictly speaking, the intervention’s output). Number of students served—the cost per student—is unlikely to be a satisfactory measure of effectiveness. Lower cost per student is likely to be associated with lower quality and hence lower effectiveness. Indeed, effectiveness is what the analyst is often seeking to identify in relation to costs as an explicit cost-effectiveness (CE) analysis. Importantly, in the cost analysis framework, total cost is the cost for the entire population served by the program or education (e.g., a school of 1,000 students), average cost is the cost per unit of education provided (e.g., each student within the school), and marginal cost is the cost per extra unit provided (e.g., from the 999th to the 1,000th student). When referring to costs of education, it is typically cost of provision that is intended.
The terms costs and expenditures should be distinguished: They are not interchangeable. Expenditures typically refer only to dollar outlays by a specific group. For example, commentators often refer to increases in the “cost of college” when they actually mean the “price of college paid by enrollees” or “what students spent on college.” Tuition prices paid by students are not the cost of college. The cost includes all the resources used to provide college and, because of public subsidies and charitable support, student tuition fees do not pay for all these resources (Desrochers & Hurlburt, 2016). In cost analysis, we are explicitly interested in all resources, regardless of where the dollars come from or if any money was transacted. In fact, cost analysis explicitly distinguishes between costs and financing—that is, between resources used and who pays for them.
An important cost concept for educational evaluation is incremental cost. As discussed in Chapter 2, CE and benefit-cost (BC) analyses evaluate programs relative to baseline, counterfactual, or business-as-usual conditions. Incremental cost refers to the relative difference in costs (Gray, Clarke, Wolstenholme, & Wordsworth, 2011, p. 13). (Incremental cost is not the same as marginal cost because we do not know how output has expanded.) In many cases, an intervention might be a supplement or add-on to regular schooling or college programs; incremental costs are then the costs of the program. But there are other cases. One is where the intervention involves a redistribution of resources such that intervention students get extra lessons in writing but fewer lessons in math; incremental costs might be very low in this case or even negative (if writing classes cost less than math classes). Another case is where students receive progressively more intensive interventions. So, if the analyst estimates the cost of a mentoring program at $1,000 per student and an after-school program with a similar objective at $1,500 per student, the incremental cost of the after-school program is $500. Note that in each case, we assume that each student receives some regular schooling, so the cost is genuinely incremental over regular schooling. Later on, we compare incremental costs with effects to derive an incremental cost-effectiveness
