Thursday, March 01, 2007

The Marginal Cost of Teaching

This post began as a comment on Tom’s post below on the (small) virtues of a large teaching load, but it grew long enough to justify a post of its own. Tom makes the intriguing claim that he “enjoy[s] a downward sloping marginal cost curve” for teaching. Downward-sloping MC curves are pretty rare in the world, so I immediately began to speculate on the possible explanations.

As a first approximation, I would think the MC is flat. Teaching a class involves a fairly high fixed cost of preparation plus lecturing, which is invariant to the number of students; and also an added cost per student, mostly in the form of grading. The latter is the marginal cost. If each student’s exam/paper takes about as much time (in expected value) as any other, then MC should be horizontal.

Tom might be thinking that the fixed costs of teaching (prep and lecture) get spread over a larger number of students as the class size increases. This is true, but it means you have a downward-sloping average cost, not marginal cost.

Another possibility is that grading gets faster as you go along: with each exam you grade, it becomes a little easier to grade the next because you’ve seen the more common errors, you don’t have to recall what the original questions were, etc. This happens with me up to a point – certainly the first few exams go much more slowly than the rest – but the MC still flattens out at some point. But Tom’s grading technology may differ from mine!

Another possibility is that I’m looking at the wrong margin; I’m thinking of the MC of added students, whereas Tom meant the MC of added classes. If you’re teaching more than one section of the same class, some preparation costs are fixed (I write the same lecture notes for all sections) while others are variable (I have to deliver the same lectures more times). But even here, it seems like the MC should be horizontal after the first section.

And all of the above analysis focuses on the time cost instead of the true opportunity cost, which is the value of the lost time in alternative uses. Let’s suppose it would have been spent on research. Assume research is subject to diminishing returns; to simplify drastically, suppose that five days of research will yield 40, 20, 10, 5, and 3 pages of output. If teaching takes away one of those days, the cost is 3 pages; if more teaching (either from extra classes or extra students) takes away a second day, the cost is 5 pages; if yet more teaching takes away a third day, the cost is 10 pages; etc. Thus, once we take account of opportunity cost, in combination with diminishing returns to research, it’s apparent that teaching exhibits the traditional upward-sloping MC curve.

[UPDATE: Tom later amended his post to replace "marginal" with "average."]


Tom W. Bell said...

Well put, Glen! I should probably go back and change "marginal" to "average." Maybe I will.

But, still, I do think there are decreasing marginal grading costs up to exam 30 or so. Similarly, I would say that there are decreasing or flat marginal teaching costs up to a pretty high number of students. At the least, I don't have to work any harder to teach the 62nd student than I do the 61st.

Finally, I was expressly excluding opportunity costs--I was focusing on the positive side of teaching an overload, recall, having already dissected the negative side.

Anonymous said...

Downward-sloping MC curves are pretty rare in the world

I'd be curious to hear some examples if you got any quick ones off the top of your head.