Sunday, November 07, 2010

Universities, conservatism and Hotelling's Law

I'm not sure what to make of Simon Jenkins' recent article in the Guardian, in whch he accuses universities of being lazy, wasteful, addicted to public money, and resistant to any form of change or innovation. He is probably being more harsh than he really feels, in order to provoke a reaction in the comments contributed by readers, and any reader who takes his article at face value will find that the comments that follow are a useful antidote.

Let's take the article seriously for a moment, and consider whether there is any truth in the central charge that conservatism is the driving force behind academic life. Unreasonable resistance to change is so widespread that it would be amazing if universities were free of it. You only have to look at some of the reaction to Obama's health care reforms to verify this: the hysteria, fear and anger of the rhetoric against these highly incremental reforms is evidence of a psychological disability to cope with any form of change and innovation, one that affects tens of millions of Americans.

But there's another reason why universities might not make the changes that Jenkins urges, and that's Hotelling's Law. That is the observation that in a lot of competitive marketplaces, the rival providers (of goods or services) tend to position themselves very close to each other, rather than go for product differentiation. If one provider does decide to aim at a particular section of the market (say, lower-cost goods) then in order to do so, he just offers goods at a very slighter lower cost than his rivals: he does not consider his cost in isolation, but relative to the competition. (As an aside, I'm not sure that hotels obey Hotelling's law, but other things do, e.g. political parties.)

In an increasingly global marketplace for staff and students, universities are understandably reluctant to go to extremes in order to capture some segment of that market. Despite Jenkins' call for 2-year degrees and year-round teaching, even if there is indeed a big market for those things, universities should be reluctant to go there. British ones are already taking a fairly extreme position on short degree timescales (most countries have 4 or more years for first degrees). And they are, reluctantly, taking an extreme position on low levels of state support for their activities. They are already well into the danger zone and should go no further.


Phil Walker said...

Do Hotelling's assumptions apply to the case of universities, though?

I'm not convinced: prices will not be fixed and product quality is variable. A degree from Oxford Brookes or a degree from Oxford: most people who need to know the difference between the two. Moreover, Hotelling's Law is starkest in a situation where there are only two providers, not where there are over a hundred.

I think you may need to show a little more of your working to apply Hotelling plausibly here.

Leigh Caldwell said...

Interesting analysis. However, the effects of Hotelling's Law are much smaller in markets with more participants.

In the classic illustration of the ice-cream stalls on the beach (described on the wikipedia page you link to), the result only works when there are two stalls.

If there are three, the stable solution is for the third stall to set up some distance away, the distance being related to the capital cost of relocating a stall and the price of capital. If there are more, the distribution becomes more complex but it no longer makes sense for the suppliers all to cluster at the central point.

Thus, in highly competitive markets (and possibly those where there are high barriers to entry - I would need to work out the model in more detail) we are more likely to get differentiation.

As we have several hundred universities in the UK, I think we are likely to see some differentiation taking place. However, the cognitive costs of processing hundreds of different variants on the offerings will be a barrier to consumer adoption, and so there will probably be 'focal' points such as 1, 2 and 3-year degrees, and perhaps specific anchor price points such as the £3k and £6k levels. Thus a part of your point still stands.

Paul Goldberg said...

Thanks for those comments. Yes, I'm happy to acknowledge that my application of Hotelling is a bit simplistic as it stands. But there's a reasonable likelihood that "clusters" will emerge (the "focal points" you note above), in that some universities will want to continue to be the same general kind of institution as Harvard (albeit not so famous or well-funded), offering qualifications that would be recognised by a Harvard graduate as essentially similar to their own. Meanwhile others may decide to be essentially the same sort of thing as Buckingham University, speeding their students through 2-year degrees that are seen as more vocational.

The "Harvard-like" universities will be reluctant to depart too much from the traditional university framework, for fear of losing that image and brand recognition.

Anonymous said...

Dear Paul

I think the invocation of Hotelling's law (not to be confused with lemma) puts you own thin ice. First, it applies to non-price competition, i.e. prices are fixed and firms care only about market share. If one allows firms to choose price and location, then, in Hotelling's original set up, pure strategy equilibria disappear (perhaps his law should be called his error). Also, as noted by one of your commentators, with 3 or more firms, under non-price competition all firms locating at the same point is no longer an equilibrium.

Given the heated discussions about fees in the UK, it is still worth speculating about what the effect of removing restrictions on fees would produce. I do not side with those who think that doing so will lead to the destruction of western civilization as we know it. Indeed, if prodded, I'd be willing to argue it is, in 1066 and all that, style a good thing.

A puzzle is why HMG chose to institute the fee increase all at once rather than stages over time. This would have the same long term effect and not inspired the students to take to the streets.