Looking for an Example of Price-Elasticity of Demand?

The application results for UK universities in the wake of a tripling of tuition fees are in and they show a drop in applications.  The limit on tuition fees in September 2012 is projected to rise to up to 9,000 pounds per year up from about 3,350 pounds for an increase of about 169 percent.  University applications in the UK have dropped from 506,388 in 2011 to 462,507 -  a drop of 8.7 percent. 

This would suggest that the overall price elasticity of demand for university applications in the UK is quite inelastic at -0.051.  If course, the elasticity probably varies across programs of study as well as regionally and across universities.  In Scotland, where there are no fees, applications still dropped about 1.5 percent.  England, on the other hand saw the highest drop at 9.9 percent.  As well, there are sub-regional variations. Oxfordshire - home of Oxford University - saw a drop of 15 percent in applications - about twice the UK average. However, applications to Oxford University itself only fell by 0.6 percent.  The drop in applications also varied by disciplines with non-european languages down 21.5 percent, communications studies down 14.6 percent, business and administration down 5.7 percent, physicial sciences down 0.6 percent and subjects allied with medicine up 2.1 percent.  Have not been able to track down if economics applications are down though social sciences in general are down.  A couple of other points.  First, given the more severe impact of the recession in the UK, it is not possible to disentangle its effect from the tuition rise though Scotland did not see a fee increase and is still down in applications.  Second, a drop in applications need not necessarily translate into a drop in enrollment in the UK system as a whole as not all applicants get a place.  Still, interesting stuff.

(This post was written by Livio Di Matteo.)

Comments

[Britmouse]

It is probably worthwhile considering demographic changes, as the government spin did: http://nds.coi.gov.uk/content/Detail.aspx?ReleaseID=423050&NewsAreaID=2

It is also hard to judge whether or not prospective students really feel the burden of the higher fees in the new system, because of the changes to the loan system. For many the monthly repayments will be lower, but spread over a longer time, compared to graduates from previous years.

The 13% drop in mature applicants is significant because they no longer get loans, but there was also a rise in non-EU applicants who do pay up front.

[Andrew F]

Doesn't this low price elasticity of demand bode well for the policy? If governments are not increasing enrollment significantly per dollar spent on subsidizing tuition, it is probably not an effective use of scarce resources. I quite like the new loan system created to fill the void, though do I understand correctly that mature students do not qualify?

[Nick Rowe]

Just suppose that the supply curve of university seats is perfectly inelastic. Universities compete on price and quality of students. If the price rises, we get the same number of students admitted, but a lower quality of student at the margin. Now suppose that prospective students know this. Weaker students, who would not previously have applied, because they knew they would not get admitted, now decide to apply. So we would get a biased estimate of the price-elasticity of demand, holding quality constant, if we look at the data where quality varies with price.

It should be possible eventually for someone to do an estimate of the price elasticity adjusted for quality, since I think there is data on A-level results. (Of course, A-levels don't mean anything nowadays, since they have watered down all the courses and exams, not to mention that scandal when the examiners told some teachers what would be on the exam that year. A-levels really meant something when I took them -- and got rather cruddy grades.)

Even so, the drop in applicants is smaller than I would have expected. In fact, I would have expected something like that size of drop simply from students who had decided to study abroad, in Canada, or wherever.

[Bob Smith]

"So we would get a biased estimate of the price-elasticity of demand, holding quality constant, if we look at the data where quality varies with price."

Agree with the point, but the bias works both ways. If a post-secondary education is less valuable to low-quality students (because the returns to post-secondary education are lower for them), the effect of the price increase may be to discourage those students from appying, driving up the average quality of applicants. In that case, proper pricing may result in a better match between students and education, and a more efficient use of social resources (which is the usual pricing story we tell about reducing subsidies in other markets). I'd expect that this effect would dominate, but I'm happy to be proven wrong.

I'd be curious to see if higher tuition fees results in lower rates of "December graduates" (i.e., drop-outs). Given the higher price of education, you might expect students to do more due diligence about matching their education with their aspirations/abilities before applying to university.

[Nick Rowe]

Bob: Hmmm. I had to think about your response. I *think* you are wrong (not 100% sure).

Let's see: you apply if and only if:

Probability of admission x [(Present Value of education) - (Present Value of fees)] is greater than (cost of application).

A true price elasticity of demand would hold the probability of admission constant at one, and vary the price. But what we observe in # of applicants is where the probability of admission increases with price.

It's a bit like estimating a demand elasticity by exogenously increasing the price ceiling, and watching quantity sold, leaving the supply and demand curves constant. We don't know if we are moving up along the demand curve or the supply curve.

A better analogy might be watching how the length of the queue responds to changing a price ceiling. Some people won't be in the queue, even if they want to buy apples, because they see that the queue is too long. When you raise the price, some people leave the front of the queue, but others join the queue at the back once they see that the queue is now shorter.

[Nick Rowe]

Hmmm. You could also think of an application as buying an option. You don't have to accept an offer of a place. Maybe they will cut the fees back down again.

[Y. Msaid]

"This would suggest that the overall price elasticity of demand for university applications in the UK is quite inelastic at -0.051."

I don't think that's the right margin. You need to include opportunity costs (forgone earnings). If you do, the price increase is much less than 169% and elasticity much higher.

[Bob Smith]

Nick,

To take your queue example, you're assuming that the people joining the "shorter" queue are willing to pay the new higher price, while the people at the front aren't. But if the present value of education is linked to student quality, then it isn't clear why "low" quality students would want to join the queue at the higher price, not matter how short it is.

Put it this way, you've skipped a step. You're starting from the premise that, given that people want to get admitted to university, higher fees increase the probability of being admitted. But the question you have to ask yourself is, do people want to be admitted at the higher prices? Modifying your equation, you only want to get admitted if:

(Prevent Value of education) > (Present Value of fees) + (cost of application)

Note, it doesn't depend on the probability of admission. If (present value of education) is increasing in student quality (i.e., (Present Value of education - High) > (Present Value of education - Low), an increase in fees will have a biggest impact on low quality students. Given that they apply, yes, the probability of admission is higher, but what good is the higher likelihood of getting admitted, if the value of the education is worth less than what they're paying for it.

Now, I'm abstracting from reality a little bit here, because we can imagine "low" quality students applying for university because their parents told them they had to and money is no object (although they, presumably, would have applied anyways), and similarly one can imagine "high" quality students not applying because of sticker shock (although, if the government provides proper financing arrangements, that effect might be mitigated), so I can't rule out the countervailing impact you discuss, but my instinct is that's its a second order impact. Re-writing your equation, people will apply if:

(Present Value of education) - (Present Value of fees)] > (cost of application)/(Probability of admission)

Two points emerge, first, given that Present Value of education is increasing in equality, the value of the first part of that equation is more likely to be negative for low quality students than for high quality students, so assuming that (cost of application) is not less than zero, the probability of admission is irrelevant (note, this is just a reformulation of my initial equation). Second, unless the increase in the probability of admission is very significant (which the application numbers don't suggest) or (cost of application) is significant relative to the change in fees (which I'd be surprised to hear, given the magnitude of the fee increase), you'd expect the change in the leftside of the equation to dominate any effect on the right side of the equation.

[Y. Msaid]

Clarification: I meant elasticity is much higher than 0.051 (not 169...)

Moreover, the tuition increase could be endogenous to the fact that the outside option (market earnings) has lost value in recent years both because of growth related issues and individual-social preferences. This also increases the "true" elasticity.

[Bob Smith]

Sorry, the first setnece of the last paragraph was less literate than I intended. I meant to write:

[G]iven that (Present Value of education) is increasing in equality, the value of the first part of that equation is more likely to be negative for low quality students than for high quality students, in which case, assuming that (cost of application) is not less than zero, the probability of admission is irrelevant (note, this is just a reformulation of my initial equation).

[Britmouse]

"If a post-secondary education is less valuable to low-quality students (because the returns to post-secondary education are lower for them), the effect of the price increase may be to discourage those students from appying"

I'd say this should not happen with the UK system if students are rational and calculate the PV of their loans correctly. The loans are structured as a time-limited graduate tax; repayments are contingent on income, 9% of earnings above £21K.

For any given future flow of earnings, a student should not care about changes in fees above a certain threshold. If you expect to earn £25K (indexed) for the rest of your life, the PV of loan cost will not change above around £5K/year in fees.

Try wiggling the sliders here if this is not clear:

http://www.moneysavingexpert.com/students/student-finance-calculator

[Bob Smith]

Britmouse,

Great link. You're right that the design of the student aid system will affect the outcome, although again it isn't clear whether it will have a bigger impact on the effect Nick is describing or the effect I'm describing (i.e., if the effect of the student aid system is to reduce the real cost of the tuition increases, you're right that my effect would be reduced, but equally, then you'd wonder why "high" quality students are deciding not to attend university, which is what Nick is predicting). Morever, while they're "time limited", 30 years is a long time. I don't have a sense of UK compensation schemes, so I can't tell whether the 21k repayment threshold is likely to have a material impact on perceived university price for a good chunk of people (that would be roughly equivalent to the average starting stalary for Canadian university graduates, but of course the average salary for Canadian university graduates is well above that threshold.)

On the other hand, if UK students are as clueless about what they'll be earning after they graduate as Canadian students are ("6 figure salaries for everyone!"), the reality of the student funding scheme may not make much of a difference.

[K]

Livio: Assuming, as you do, that prices (rather than caps) went from 3350 to 9000 then elasticity is log(462/506)/log(9000/3350) = -9.2%. Since prices probably didn't rise that much, elasticity is higher. Still small, but not as small as you suggest.

Britmouse: "repayments are contingent on income, 9% of earnings above £21K."

Great stuff! Now make part of the Universities revenues contingent on that same income, then we might get a real improvement in the relevance of programmes. Universities ought to be required to publish their expectations of the future revenues of their graduates. The higher the projected revenues, the greater the fraction of their revenues should come from future earnings of graduates. That ought to keep them honest about their projections which would then serve as extremely useful information for applicants.

[Britmouse]

Bob, I agree they are probably clueless. But I'd suggest this should make demand perfectly inelastic, because the PV(repayment cost) will be *mostly* determined by future income, and only slightly by fees. That's what I'd tell my kids, anyway: optimise for future income, and ignore the price label - or use the price label as a signal for quality.

K: I'm betting the burden on general taxation will be too high with the new system, so they will want to find ways to push back, income sharing seems like a really excellent idea. Natural evolution: instead of the transfer from taxpayers to Uni to fund the running costs of courses, the Universities can securitise the cash flows from future graduate income, and sell those securities to fund their running costs. Neo-liberal perfection?

[K]

Britmouse: "Neo-liberal perfection?"

I think so. The only risk is the usual agency problems that result from selling (insuring) your human capital. But so long as students are only selling a relatively small fraction of their future income I think the incentives are well aligned. And I really like the idea of making universities accountable for their wares. Universities might put all that brainpower to work thinking up ways to generate big future revenues. Then scarce public resources can be directed towards programs that contribute significant social goods, if we so choose.

[Britmouse]

K: "I really like the idea of making universities accountable for their wares"

Yup! That would be a real revolution in tertiary education. It'd probably kill off a bunch of UK universities as well.

Back closer to topic, this data from the Guardian was interesting:

Reality check: have the middle classes been squeezed out of university?

That could support Nick's point, applicants from better off families are probably more willing/able to study abroad.