The Effect of Tuition Subsidies On College Tuition

Alex Tabarrok [links to analysis by Virgina Postrel] that provides a very accurate analysis of who benefits from a tuition subsidy to college students - mostly the faculty and administrators of colleges and universities. I'm going to take it one step further.

Two reasons for subsidizing college education: one is fairness and the other is the external benefits someone with a college degree supposedly provides society. We want everyone to have a fair chance at financial success, including potentially capable students from lower income families. We therefore subsidize talented lower income individuals. And we also want to realize the presumed external benefits that result from someone attending college who might not otherwise have attended without a subsidy. 

But we can hopefully agree that it's most likely not beneficial to taxpayers to subsidize someone who will not realize the added benefits from a college degree, both personally and socially, in excess of the cost of the subsidy. In other words, we do not want to subsidize someone $100 if we expect the private and social benefits from that education won't exceed $100. Why subsidize someone to attend college whose desires and/or talents won't permit her to actualize the benefits of a college education in excess of the subsidy?

So now we can see the effect of subsidizing college education a little more thoroughly; it's not all internalized by all universities and their professors. The most selective schools and their affiliated faculty and administrators benefit handsomely, but that's not necessarily the case for less selective schools.

Look at the graphs below. To the left is the supply and demand for education at a very selective school, say a UNC Chapel Hill. Notice that the supply curve is relatively inelastic. UNC-CH, like most highly selective shools, is capacity constrained; an increase in demand cannot immediately be met by expanding enrollment. Therefore, a subsidy that increases applications results in an increase in tuition, which increases the marginal revenue product of the faculty and administrators of that college.

To the right is the supply and demand for a less selective college, say a Fayetteville State University. The supply curve for Fayetteville State is more elastic given that it is not capacity constrained. Even though the school does not accept 100% of its applicants (it still has standards), it is not necessarily operating at full capacity. An increase in demand for admission to FSU due to a tuition subsidy can largely be met by increasing enrollment. Though there are still restrictions that limit its expansion to something less than the total increase in new applicants, but it can still expand enrollment more than can UNC-CH. Therefore, a subsidy does not have the same effect on tuition and salaries at a less selective school that it does on a more selective school. (BTW - here is tuition data for 2009-2010 on schools in the UNC system.) In this case, enrollment expands.

Now, consider the type of student we believe will realize positive returns, both to herself and to society, from a subsidy. Where are they likely to attend? And consider the student who is less likely to realize positive returns, both to herself and to society, from a subsidy. Where are they likely to attend? The student with the most potential is likely to apply to and get into a UNC-CH, which means they benefit little from the subsidy. The less capable potential student likely goes to a Fayetteville State University. In other words, the colleges and their affiliate faculty and administrators likely internalize most of the financial benefits of a subsidy to students we expect will actually benefit from it, both themselves and society, while students not likely to realize benefits above and beyond the subsidy are likely to internalize more of those benefits of a subsidy. The faculty and administrators of the less selective colleges are not likely to benefit from a subsidy as much as their peers at the more selective colleges and universities. 

UPDATE: Virginia Postrel provides a comment (below) that first, the analysis was from her Bloomberg article and not Tabarrok (my apologies for the mistake), and second, that the demand curve for the less selective school should be more elastic than the demand curve for the more selective school. I totally agree. I was mostly trying to show that a subsidy is not always internalized by a college or university and its affiliated faculty and administration, not the impact on actual tuition paid by students at the different schools. Had I drawn a more elastic demand curve for the less selective school, and I drew the difference in tuition before and after the subsidy, it would show that what students actually pay out of pocket in both types of schools would not decline that much after a subsidy.  

Comments

[Mrrunangun]

So should we have a graph of SAT score against poverty score and scale subsidies according to the matrix? Then work off your debt year by year practicing your profession among the needy, in the military, or some other socially constructive if less remunerative venue?

[y81]

But Paul Krugman says that "no economic analysis" posits upward sloping supply curves. And he's a Nobel prize winner. So this analysis must be wrong.

More generally, it's clear that economists just make up whatever they want to suit their political predilections. There's no objective reality or agreed body of knowledge, like there would be in a real academic discipline.

[Virginia Postrel]

With all due respect to Alex, and I appreciate his link, the analysis is not his. It's a clearly labeled excerpt from my column here: http://www.bloomberg.com/news/2011-12-09/u-s-universities-feast-on-federal-student-aid-virginia-postrel.html

The demand curves in your second case should also be more elastic than those in the first case.

[Michael]

What evidence do we have that the marginal benefit to the individual and society of college attendance is lower at Fayetteville than Chapel Hill?

Sure, Chapel Hill students are going to do fancier things when they grow up, but it seems that the policy rationale should be based not on the total effectiveness of a college's grads but on the amount to which a degree at the college matters. Your assumption that UNC will make a larger marginal difference doesn't seem certain at all.

This doesn't mean that subsidies are entirely beneficial, but at least it might mean that more of the benefits are going where they're supposed to.

[Mark]

Michael,

There is no evidence that, ceteris paribus, students coming out of top-tier schools do better in labor markets than students coming out of other schools. In fact, research shows no correlation after controlling for many other factors. http://www.nber.org/digest/dec99/w7322.html

But that is not the point I was making. My point is that the student most likely to improve her human capital by obtaining a college degree is more likely to attend a more selective school, while students who do not have the prior academic record, scores, and attitude to improve their human capital attend less selective schools.

There are plenty of outstanding students who will benefit greatly from a college degree attending the Fayetteville State Universities of the world; there is just a far greater concentration of them at the Chapel Hills of the world. On the other end of the spectrum, there are certainly students attending the Chapel Hills of the world who will not do much better in the labor market relative to having not gone on to college, but a far greater concentration of that type of student attends the Fayetteville State Universities of the world.

[Michael]

Thanks for the quick, thoughtful response, for the link to the NBER report and the email heads-up, Mark.

But either I still don't understand your argument, or you don't understand mine. Here's how I see the two:

Let x equal a future FSU student's human capital before entering college; let F equal the additional capital contributed (on average, etc.) by an FSU degree; let y equal a future UNC student's human capital before entering college; let N equal the additional capital contributed by a UNC degree.

Finally, let's say that for an FSU grad, x' = x + F. For a UNC grad, y' = y + N.

You write: "Consider the type of student we believe will realize positive returns, both to herself and to society, from a subsidy. ... The student most likely to improve her human capital by obtaining a college degree is more likely to attend a more selective school."

You seem to be saying we should assess a college's social benefit by comparing x' to y', or possibly x to y.

I'm saying that if we're trying to subsidize valuable educational products, we should compare N to F. That (regardless of the initial values of x or y) seems like a better measure of educational quality.

[Michael]

Or to put things another way: Given the choice I'd rather turn a bunch of 4 students into 6's than turn a bunch of 7 students into 8's.

I've got no evidence that FSU does this. But what if they do?