The marginal costs of education

The issue of tax credits for private schools is now being debated in the Legislature, with several new bills moving through the State House.

One key question in the debate is: what are the costs or educating a single child, and how do those costs change when that child (or several children) leave a public school? As part of this discussion, the Center was asked to help calculate the marginal costs of public education, as a way of estimating the potential financial impact of such legislation. Our conclusion is that the financial impact of the proposed tax credits would vary considerably depending on several factors, including the size of the school, desired student-teacher ratios, and the magnitude of the changes in public school enrollment that followed the implementation of the legislation in question.

Our full response follows.

Estimating the marginal costs of educating students – either the cost of providing an education to one additional student, or the savings of losing one student – is complicated by several factors. You must determine the ratio of fixed to marginal costs in public education, as well as account for issues of scale and time. Estimates of the cost of educating students vary considerably as a result of these factors.

In short, for the loss or addition of students to impact a school’s fixed costs, the change has to either occur on a large scale (i.e., many students leaving at once) or over a long period of time (a small amount of students leaving every year, for several years.)

According to 2009-2010 data from the New Hampshire Department of Education, the per-pupil amount of all expenditures -- operating, tuition, transportation, equipment, construction, interest and non-K-12 expenditures -- is $14,549.61.

Even though the average cost-per-student is often calculated by the DOE and others, the real question here is: What is the marginal cost per student?

While the average cost is about $14,000 per student, if one student leaves a school, the school certainly does not save that amount. This is because the majority of school costs are fixed in the short term. Transportation, building, equipment and interest costs will not change if one student, or even a handful of students, leaves the school. Table 1 below shows the costs used in this calculation.

Even the variable costs of education will not change much if one student leaves a school. For example, in our 2009 paper on the new school funding formula (“New Hampshire’s Latest School Funding Formula”) we calculate a cost-per-pupil for teachers of $2,570. That calculation assumes a student-teach ratio of 25 to 1. If one student leaves the school, it would be logical to assume that the average class size might decline, but that it is unlikely that the number of teachers in the school would change. In this case, one would expect that the number of students in the school would have to decline by more than two dozen before there would be any staff reduction, and therefore any savings.

Thus, in the short term, the marginal cost of education per student, especially for one student, is probably only a few hundred dollars. The school would have to see an enrollment decline by at least 20 students before it could consider eliminating a classroom and a teacher. And eliminating a teacher would not affect overall administrative costs, building costs, etc.

Finally, consider the element of time. If a large high school gained five new students a year, the cost of educating those additional students results in a relatively small annual increase, but could grow quite sizable over 10 years.

Thus, in the short term, the marginal costs of educating students is limited, as are the costs savings, as a result of fixed costs, unless you experience significant reductions in enrollment. What defines significant? That depends on a variety of factors, including the degree to which the existing capital infrastructure is under strain (building occupancy rates, transportation occupancy rates and the like), and tolerances for high student-teacher ratios.

The long-term implications are that virtually all costs are marginal. That is, when you expand the dimension of time, the share of costs categorized as marginal expands considerably. In fact, other studies, such as Grecu and Lindsay (2006) and Coulson (2009), found that approximately 80 percent of costs are marginal over time.

Comments

[John Tuthill]

" - the per-pupil amount of all expenditures -- operating, tuition, transportation, equipment, construction, interest and non-K-12 expenditures -- is $14,549.61." para. 5.

What are "non-K-12 expenditures?"

[Admin]

Thanks for picking that up. We have fixed that!

[John Tuthill]

Table 1 is referenced but does not seem to appear.