Market-based pricing of university education and university rankings

How New Zealand's university education sector is funded has been in the news lately. From the NZ Herald last Thursday:

Tertiary students should be charged much more if the Government is unwilling to invest enough to keep universities competitive, the country's largest university says.

University of Auckland vice-chancellor Stuart McCutcheon believes there is a strong case for following Britain and Australia's lead and raising the cost of study.

Fee deregulation or a similar system would allow universities to set their own fees and would likely lead to increases well above the current annual maximum 4 per cent...

...The latest international rankings released today show New Zealand universities losing ground or stagnating...

...Professor McCutcheon said such league tables were the main way international students judged quality, and the downward trend put the funding of universities at risk.

International students - and the high fees they pay - have become increasingly important, with all institutions attempting to increase them after domestic numbers and attached funding were effectively capped.

The funding available to NZ universities on a per-student basis was comparatively very low, Professor McCutcheon said. If the Government would not increase it substantially, then another way needed to be found.

This is timely given that my ECON110 class has just covered the economics of education. There are a couple of things I want to focus on in this post: (1) how university education is funded and the implications of moving to a purely market-based pricing model; and (2) the impact this has on university rankings.

University education in New Zealand for domestic students is part-funded by the government (each institution is subsidised on the basis of the number of full-time equivalent (FTE) students), and part-funded by the students themselves (through tuition fees). Alongside this, the tuition fees that universities are allowed to charge domestic students are capped (as noted above, they're only allowed to increase by 4 percent per year) - this is a price control, albeit a control that moves over time. And to complicate things further, the amount of FTE subsidy that the government will provide is negotiated with each university each year. In other words, universities are essentially limited in the number of students that they are allowed to enrol - a quantity control.

What would happen if the restrictions (on price and quantity) were removed? In ECON110, we describe the optimal level of subsidy for tertiary education, which is described in the figure below. The optimal subsidy would be the subsidy that ensured that marginal social benefit is exactly equal to marginal social cost. Any more subsidy than that and the extra cost (to society) of the additional students would outweigh the extra benefit (to society), and society would be worse off. Any less subsidy that that and the extra benefit of one additional student would be greater than the additional cost, and you should provide more subsidy.

The tricky bit is that education provides positive consumption externalities (higher productivity, lower crime, better outcomes for children of the educated, etc.) so the marginal social benefit (MSB) is greater than the demand (D) for tertiary education. The effect of the subsidy (which is paid to the universities - to keep thing simple we will ignore demand-side subsidies such as student allowances, interest-free student loans, etc.) is to lower the effective cost of providing university education (we show this with the new curve S-subsidy, which is below the supply curve S). If the size of the subsidy is optimal, then it will ensure that the market provides Q0 university places - the quantity where marginal social benefit (MSB) is exactly equal to marginal social cost (MSC). This is ensured because the students pay the low price PC and demand Q0 places at university, and the universities receive PC from the students, which is topped up to PP by the subsidy, leading them to offer Q0 places for students.

Now consider the effect of price and quantity controls. It's not possible for both price and quantity controls to be simultaneously binding on the market. This is because, if the quantity control was binding the price would adjust - the price that universities were willing to accept for each student would fall to below the level of the price control. On the other hand, if the price control was binding, the quantity would adjust  If the price control is binding, it makes the quantity control less likely to also be binding - the quantity of university places that are made available to students would likely fall to below the level of the quantity control. The lack of a binding quantity control is probably the situation we currently observe in most degree programmes other than those that have strictly limited places such as medicine or law. [*]

Let's assume that the price control is binding, but the quantity control is not. This is suggested by Professor McCutcheon's comments. Also, we've recently had a period where the quantity control was binding (we had severely limited spaces a few years ago), and that isn't the case now the sorts of things we observed then (e.g. long waiting lists for all degree programmes) isn't happening now. So, if the price control (in terms of the price paid by students) is binding at PMAX, the quantity of places available at university would be QS. However, at this artificially low price, there is excess demand for places at university - the number of places demanded is QD, but there are only QS places available. Some students, who would like to study at the subsidised price, are excluded. And because the market is operating at less than Q0 (where MSB = MSC), there is a loss of welfare - society is worse off overall.

On the flip side, removing the price (and quantity) controls would allow the market to move to Q0, maximising welfare. More students would go to university, and although they would pay a higher (out-of-pocket) cost for doing so and the government would pay more in subsidies (because there are more students), society would be better off overall.

Where do international students fit into this though? International students aren't subject to the quantity controls, so they don't directly affect the number of places available at universities. However, they do increase the demand for universities' scare education resources. This should push the price of education upwards, but it can't because of the binding price control. This should manifest in additional excess demand - more turned away students. However, it's not clear to me that this (turning students away) is happening in large numbers. So, maybe the degree of excess demand is relatively small.

However, think about the related effects. If the universities aren't bringing in as much income as they would be under market pricing (an effect of the price controls), then they can't afford to employ as many staff (or as high quality staff). Fewer staff means fewer courses (or courses with a higher student-to-staff ratio), and offering fewer courses means fewer places for students. So, perhaps the excess demand is absorbed by offering a lower quality education to all students than would have been obtained with market pricing.

There is a further flow-on effect of this, which should by now be becoming obvious. Lower quality staff means lower quality research output, which flows through into lower international rankings. Higher student-to-staff ratios also lead to lower international rankings (this is one of the dimensions that is taken into account in the Times Higher Education (THE) rankings, for instance - it is their crude measure of 'teaching quality'). So, as Professor McCutcheon notes, there is probably a close link between the lack of market pricing of education and falling rankings of New Zealand universities.

Lower international rankings reduce the demand for a New Zealand-based education by international students. Which lowers the excess demand and probably raises the quality of education for students. So, perhaps there is some dynamic equilibrium between below-marking pricing, university rankings, and international student demand. That doesn't mean we shouldn't be aiming instead for a new equilibrium with market pricing, optimal subsidies, and higher university rankings.

*****

[*] Update: Of course, the quantity and price controls are able to be simultaneously binding. A profit-maximising university will price on the basis of the willingness-to-pay of students, not their willingness-to accept. So, if the quantity control is binding and the number of student places is restricted, students are willing to pay more for their study and this makes the price control more likely to be binding as well. This seems likely for degrees where places are strictly limited, like law or medicine, but less likely for commerce, management, or arts degrees.