The cost of an extra bottle of perfume

By Andrea Brady

Seth Godin, a marketer, author and one of my favorite bloggers, recently wrote an article about marginal cost.  In it, he asks, “How much does it cost Wikipedia to have one more person read an article? How much does it cost Chanel to produce one more bottle of perfume? How about one more digital copy of a Grateful Dead concert?”

Marginal, or incremental, cost is of great concern to school districts, too.  The standard measure of “how much it takes to educate a student” is the state’s calculation of expenditure per pupil.  However, this is not an accurate number for several reasons.

The way expenditure per pupil is calculated is to take total expenditures (in categories as defined by the state) and divide this by the total number of students served that past year.  If you understand what is in this number, it is a good way to compare districts and get a feel for a district’s efficiency.  And, I’m happy to say, Milford’s expenditure per pupil has been lower than not only other excellent districts, but also the state average, for quite a few years.  In addition, when you adjust the number to account for costs that shouldn’t be included because they aren’t truly expenses (see my article here), we look even better.

But the purpose of this article is not to talk about Milford’s efficiency in expenditure per pupil; instead, it’s to examine how much it costs us when a new student enters our doors, say on Day 3 of the school year.  Is it truly thousands of dollars (for most districts, tens of thousands) to serve that student?  Why or why not?

The concept of marginal cost can be a bit elusive:  when we think of producing another bottle of perfume, we think about the cost of the water; the fragrance; the bottle; the sprayer; the packaging.  But there are other costs associated with that bottle of perfume as well:  the plant; the manufacturing staff; the shipping; the accounting; and so on.

These fixed costs will be there whether an extra bottle of perfume is produced or not.  In fact, they will also be there if one fewer bottle of perfume is made.  They fall in the category of “overhead costs” that a company has to pay no matter what.

Sure, the company may not need as many manufacturing people; or as large a plant.  But once you have that staff and facility, until you need an even bigger plant, and another manufacturing person, that cost is “fixed.”

The same is true for school districts.  Every year, the district must pay to operate its buildings; for support services such as accounting, maintenance, etc; for management; and, of course, for teachers.

So, you have a classroom with 20 students in it.  You have already paid for the teacher; the books; the desks; the building.  You’re paying the utilities and the other support.  To figure the expenditure per pupil, you take all those costs and divide by (for this example), 20 students.   Let’s say the total cost was $200,000, which would make the expenditure per pupil $10,000.

But what if we put one more student in that classroom, bringing the total to 21?  Do any of those costs change?  What is added specifically for that student?  There may be more copying costs, some other supplies – but this is a very little amount.

Thus, the incremental cost for educating that 21st student is a very small number:  perhaps a few hundred dollars – let’s even make it as high as $1,000.  Yet, the fixed costs we were paying anyway – the $200,000 – stay the same.

Our new total expenditure is now $201,000.  When you divide by 21 students, our expenditure per pupil is now $9,571 – it goes down because the largest portion of the expense, which we were paying anyway, is now divided by a larger number.

This is what happens with Open Enrollment and why it is so valuable for a district like Milford.  With a neighborhood school concept, we often have “open seats” in certain classrooms across our six elementaries, as well as in the junior high and high school.  If we can fill those seats with students from other districts, we actually get more back from the state than we have to pay out.  This allows us to use resources we are already paying for – and that we’ll have to pay for, whether we have 20 students in that class or 21 – in a more efficient manner.

This year, we will bring in around $550,000 additional by accepting a few over 100 Open Enrollment students – yet the incremental cost to serve these students will be minimal.

That $550,000 does a lot for a district like ours.  For instance, it pays the salaries of more than a half-dozen teachers!

Some people would argue that class sizes are too high, and Open Enrollment students make them even higher.  But is that so?

First, remember these 100 or so students are spread across all grade levels.  If we look at an average over 12 grades, that’s only 9-10 per grade – for the elementaries, that’s an average of 1.5 per grade per BUILDING.  We are not talking large numbers of students in a district the size of Milford.

Second, we can – and do – refuse an Open Enrollment student if the class sizes are too high.  That allows us to make sure we are filling holes but not overloading our classes.

Third, does an extra student affect the quality of what a teacher provides?  The research says no.  Until you get to very small class sizes – like a dozen – research is inconclusive about the effect class size has on learning.  So adding one or even two students in a class that did not start out at capacity will not make any difference in what the students receive.

Based on all this, Open Enrollment is a win-win for both the Milford community and the families utilizing it.  We are actually able to provide more to our students because of this program, and utilize our resources more effectively.

Andrea Brady is a candidate in the November 5, 2013 school board election. Visit his website at kneppbradyforschoolboard.com.

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