Tuesday, January 13, 2009

Increased Enrollment Does Not Mean Bigger Losses

by Andrew Gillen

People keep making a silly mistake when they jump from the accurate observation that because tuition does not cover the total cost of college, that colleges lose money on each student (see here, here, here, here, here, here, and here for examples) to the conclusion that if a college enrolls more students, they will lose even more (see here and here for examples).

This often flawed conclusion stems from confusion about total vs. marginal costs.

An example will illustrate my point.

Suppose that a school has fixed costs (FC) of 50, variable costs (VC) of 2 per student, charges tuition (T) of 5, has an enrollment (E) of 10 students, and a state appropriation (SA) of 20. This implies that they have total costs (TC) of 70 (TC = FC+VC*E = 50 + 2*10). They have 50 in tuition revenue (T*E = 5*10), and the 20 state appropriation for Total Revenue of 70.

Now along comes a recession, and the state government, which is facing budget deficits decides to cut the appropriation to 17 (SA’). What should the school do?

If you believe that public postsecondary education “is one of the few businesses where every new customer means bigger losses,” then you’ll also think that cutting customers will lower your losses. You’ll note that the tuition of 5 does not cover the average cost per student of 7 (ATC = TC/E = 70/10). You view this as a loss of 2 per student, and may conclude that you need to cut enrollment by 1.5 to make up for the cut in appropriations of 3. So, you cut enrollment to 8.5 (E’), and are surprised to discover that now your revenue doesn’t cover your costs (T*E’+SA’ = 5*8.5+17 = 59.5 < FC+VC*E’ = 50 + 2*8.5 = 67). The reason, of course, is that while cutting enrollment by 1.5 cut your costs by 3, it also cut your revenue by 7.5.

Alternatively, you could recall from your principles of economics class years ago, that the crucial thing to keep in mind is marginal costs and revenues. Noting that your tuition revenue of 5 is greater than your variable costs of 2, you increase enrollment to 11 (assume that the school is capacity constrained at 11). With enrollment of 11 (E’’), you have revenue of 72 (T*E’’+SA’ = 5*11+17) and costs of 72 (FC+VC*E’’ = 50+2*11).

Which scenario is better? Lower enrollment with deficits, or higher enrollment with a balanced budget?

The view that “every new customer means bigger losses” for higher ed is not true when the marginal cost of a student is less than the marginal revenue of that student (variable cost and tuition respectively in the example above).

The key question then is: What is the marginal cost of one more student?

Typically, a few more student will not require that you hire a new professor, create a financial aid department or registrar, build a new dorm or classroom - the school will already have these things. Thus, I have a very hard time believing that the marginal cost of a student is very high except when a school is at capacity along multiple dimensions.

While it no doubt varies by school, I would argue that the average tuition revenue per student of around $4,500 at public four year schools (first figure on page six of this report) is typically more than enough to cover marginal cost.

1 comment:

capeman said...

Ah, not such great understanding of university (or other) finances here.

Sure, one more student won't hurt. The problem is that you can't keep adding just one more student without reaching a point where your marginal costs ratchet up in a quantum leap.

Take biology, yes take it. One more student probably won't matter. But eventually, you need to open up a new section. A new section of biology lab. A new discussion section. At some point, heaven help us, a new lecture section of 100 or 300 or 700 students.

At some point -- a few thousand total enrollment, certainly 10,000 -- costs scale with size. Which means marginal costs are not so much different from average costs, and that marginal costs per student do not decrease with size. You might be able to go from 20,000 by squeezing another 500 or thousand in, but pretty soon, you run out of room (figuartively and literally), and you have to pay dearly for more.