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THE GEOFF HAVERS COLUMN

Supply and demand

I’ve just finished Freakonomics, which means there’s only one person to go before everyone on the entire planet has read the most mega-massive blockbusteringest bestseller ever to analyse supply and demand.

That person, as it happens, is Hua Gue, a ten-year-old Mongolian yak herder who lives in a yurt pitched (usually) just outside Ulan Bator. “It brings great shame on my family to be last person on entire planet to finish Freakonomics,” rues Hua. “But what with subsisting on a diet of only whatever yak’s milk I can squeeze out during a hard winter’s herding – and don’t forget it has to ferment a bit first – plus a few dong here and there as payment for being tied to the saddle of some berserk pony and forced to race across the steppes for the entertainment of Nissan-driving holiday-makers, I simply haven’t had the time. And I want to finish Middlemarch first.”

While we can easily understand Hua’s plight, I could probably save him some bother. Freakonomics is one of those books which one reads eagerly and with enjoyment only to find that – what, ten minutes, at most a day, later? – one has forgotten pretty much everything in it. It pitches its tent, or yurt, on the grounds that it makes economics sexy, which would be no mean feat, and this it does by explaining, for example, why drug dealers still live with their mums (sorry, forgotten), why baseball teams, or their managers, or the players’ agents... (sorry, forgotten) and – sexiest of all for the UK reader – why estate agents are happy to recommend you take a £10,000–£20,000 drop in your asking price to secure a sale, when they wouldn’t let a single faded penny piece slip from their grasp when selling their own property. According to Steven D. Levitt, the hotshot economist author, this is because your agent’s commission loss on the £10,000–£20,000 hit taken by you is negligible, whereas it’s worth every second of her time to avoid a similar loss herself. Whereas we all thought it was because estate agents – and hey, if you’re an estate agent reader, don’t take this personally; we love ya! – are scum-sucking bottom-feeders with the morals of a weasel and the soul of a cockroach. Apparently not.

Sell your seat this semester

What has this – entertaining and informative though it is, in its own right – to do with the world of auctions? Well, recently, a student on an economics course at the University of Chicago tried to sell her place online. It wasn’t just any old economics course, though. The class was taught by – guess who! – Hua Gue? – that’s a good guess, but no; Steven D. Levitt. “How much is your education worth to you?!?” the ad asked. “E-mail me with your best offer.” The ad was removed soon after it came to the attention of university officials. A Chicago spokeswoman said the university “does not endorse” students’ selling their seats in classes.

The University of Chicago would seem to be alone amongst American seats of learning in adopting this purist approach. The University of Pennsylvania’s Wharton business school, for example, actually encourages it. Wharton auctions spots to its MBA students, allowing them to bid for their classes. Rather than use real money, students are each given 5,000 points when they enrol and 1,000 more for every credit they earn. An average course may sell for a few hundred points, while the most-sought-after ones can top 10,000.

Several other business schools and at least one undergraduate institution (Colorado College) let students bid, but Wharton takes it one step further, allowing students to sell their courses (for points) to other students. It’s all done through a website. Buyers and sellers are anonymous, so buddies can’t make deals.

“It’s capitalism gone nuts, but it’s also absolute socialism because everyone is born with the same number of points,” says Justin Wolfers, an assistant professor of business and public policy.

This may all seem like fun, some sort of role-playing exercise intended to give the young darlings a taste of the real world to come, but in fact it is an attempt to deal with concepts of relative value and demand that are addressed in auction theory.

Let’s remember, first, that an American university degree is not structured like the Classical Tripos. As I understand it, graduation is dependent on the accumulation of courses passed, and these can be in anything from quantum physics to quilt-making. Now, the goal of an efficient enrolment system is to allocate limited seats to the students who need them most. As it stands, however, the intensity of one student’s ‘need’ relative to another’s is hard to quantify. A fourth-year may need a biology credit so he can graduate on time, or an athlete may need a maths lecture that does not conflict with her morning workout. It’s impossible to rank all these needs in a coherent order.

The standard system tries to deal with ‘need’ by giving enrolment priority to students with more units, athletic obligations and other qualities that affect the amount they ‘need’ classes. Such a system is obviously imperfect, and students whose needs don’t give them priority are, as it were, cheated.

An auction solves this problem by forcing students to translate their own nebulous notion of ‘need’ into something quantifiable – a willingness to pay. Because students can place a numerical value on a class, they’re better able to express their preferences. If one student bids 500 points and another bids 2,000, then it’s clear, in theory, who wants it more. That way, everyone can be sure courses are allocated equitably and efficiently to those who ‘need’ them most.

Perhaps unsurprisingly to those of us with experience of real auctions, where those who bid for what they want or need are matched in number by those who bid for the future resale value of a commodity, things are not so simple. Students regularly buy classes they don’t actually want to take in hopes of selling them, making a profit and using those points to buy classes they really do want. For some, this involves hours spent strategising and trading, studying data from previous terms and trying to outsmart their classmates. It’s common knowledge among students which classes sell for a premium and which can be picked up for a song. Star professors such as Levitt command higher prices. Supply also plays a part. If a class is restricted to ten students, its price will probably rise.

Sometimes, bidders outsmart themselves. Students will, for instance, bid on a Friday-afternoon section of a class, assuming that it will be cheaper than the Tuesday section because most students want to get away for the weekend. But that will drive the price up until it’s higher than the more desirable Tuesday section. Poor bidding decisions can mean getting stuck with a roster of less desirable classes.

The second-price auction

In order to exert some control over the fairness of the system, Wharton uses a second-price auction, in which the highest bidder wins but pays the amount of the second-highest bid. Economists like the second-price auction because they think it encourages more honest bidding, and yet it almost never occurs in practice – in one paper it is referred to as the “lovely but lonely” auction because the beauty of the system is not matched by its popularity.

To economists, the second-price auction is known as a ‘Vickrey auction’, after Canadian-born Nobel Prize-winning economist William of that ilk. It is a type of sealed-bid auction, where bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins, but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction, and gives bidders an incentive to bid their true value.

Vickrey’s original paper considered only auctions where a single, indivisible good is being sold. When multiple identical units (or a divisible good) are being sold in a single auction, the most obvious generalisation is to have all bidders pay the amount of the highest non-winning bid. This is known as a uniform-price auction. The uniform-price auction does not, however, result in bidders bidding their true valuations as they do in a second-price auction unless each bidder only has demand for a single unit. Over to Wikipedia:

“A generalization of the Vickrey auction that maintains the incentive to bid truthfully is known as the Vickrey-Clarke-Groves (VCG) mechanism. The idea in VCG is that each player in the auction pays the ‘opportunity cost’ that their presence introduces to all the other players. For example, suppose that we want to auction two apples, and we have three bidders. Bidder A wants one apple and bids £5 for that apple. Bidder B wants one apple and is willing to pay £2 for it. Bidder C wants two apples and is willing to pay £6 to have both of them, but is uninterested in buying only one without the other. First, we decide the outcome of the auction by maximizing bids: the apples go to bidder A and bidder B. Next, to decide payments, we consider the opportunity cost that each bidder imposed on the rest of the bidders. Currently, B has a utility of £2. If bidder A had not been present, C would have won, and had a utility of £6, so A pays £6 – £2 = £4. For the payment of bidder B: currently A has a utility of £5 and C has a utility of 0. If bidder B had been absent, C would have won and had a utility of £6, so B pays £6 – £5 = £1. The outcome is identical whether or not bidder C participates, so C does not need to pay anything.” Is that clear? (I can feel a little lie-down coming on – Ed.)

One real-world market in which Vickrey auctions have been used is stamp collecting. EBay’s system of proxy bidding is similar, though not identical, to a Vickrey auction. A slightly generalized variant of a Vickrey auction, named generalised second-price auction, which is different from the VCG mechanism, is known to be used in Google’s and Yahoo’s online advertisement programme.

Smart bidding

The consequences of choosing the right type of auction can reach further than the walls of Wharton’s business school. In 2000, Turkey auctioned two telecom licences one after another, with the stipulation that the selling price of the first licence would be the reserve price for the second licence – the minimum price they would accept for it. One company bid an enormous price for the first licence, assuming that no one would be willing to pay that much for the second licence, which did in fact go unsold. The company thus gained a monopoly, making its licence very valuable indeed.

Sometimes, bidders find cunning ways to encode messages in their bids. In 1999, Germany sold ten blocks of spectrum in an English auction with only two bidders: Mannesman and T-Mobile. The auction rules stated that bidders placing new bids always had to raise the current high bid by at least ten per cent. In the first round, Mannesman bid 18.18 million Deutschmarks per unit on blocks 1–5 and 20 million on blocks 6–10. T-Mobile noticed, as did many observers, that adding 10 per cent to 18.18 million brings it almost exactly to 20 million. T-Mobile read Mannesman’s bid to mean, “If you raise our bid on blocks 1–5 to 20 million and leave blocks 6–10 for us, we won’t get into a bidding war with you.” T-Mobile did just that, and the two companies happily divided the spoils.

The music man

Talking of spoils, and changing the subject somewhat, when I was a child I went to a school that had a record library. This ‘library’ consisted of a wooden cabinet in the library proper, containing about eight LPs, amongst which was Charlie Parker’s great Salt Peanuts, my first exposure to modern jazz and the start of a relationship which has endured longer and more fruitfully than that with, say, Euclid or the gross domestic product of the Netherlands. One day I was called to the library and given the job of sorting out a bequest that had just come to the school – a collection of about 4,000 classical LPs, most of them unplayed, many of them unwrapped from the shop and a significant number of them duplicates. Significant to me because, after a week’s sorting and cataloguing, I was allowed to take the duplicates home. I’d forgotten all this until the recent news story concerning a bequest to the Oxfam shop in Tavistock – of around 4,000 classical LPs, virtually unplayed, covering every genre from Mozart to Ligeti.

The huge collection came with an accompanying spreadsheet listing each LP by composer, orchestra, record label, conductor and catalogue number, which means no week’s skiving off Geog and Bilge for a small grammar-school boy. The records will go on sale in the shop before being put online.

Oxfam makes around £5 million from the sale of films (videos, DVDs) and music each year. The charity has recently received and sold a rare Rolling Stones demo single, a sheet of music signed by Vaughan Williams and a Handel musical score from 1786. Next month a score by André Campra will be sold by the charity at a Bonhams auction.

For musical cognoscenti, trawling through vintage vinyl collections can reap financial rewards. Experts say that the prevalence of digital music has increased the market value of rare vinyl. The most-sought-after, Paul McCartney’s copy of That’ll be the Day, a record by the Quarrymen, the band that later became the Beatles, is thought to be worth more than £100,000.

The Tavistock collection is valued at around £25,000, a modest estimate considering that the crucial pressing dates for the records have not been established, and that the collection includes super-rare ‘private recordings’ – white labels in a plain white sleeve that says “Private Recording. Not For Sale”, by the likes of Wilhelm Furtwängler.

When I heard this, I rang my mother, or what’s left of her, and asked if she could be bothered to rootle around in those old records, you know, the ones from school, and see if there were any funny-looking ones in white sleeves…

“Oh, those,” she croaked. “I gave those away only recently. To a charity,” she added, as if that made it all right. “They sell things, and use the funds to sponsor clever children from faraway places. So much more satisfying than the donkey sanctuary. Anyway, your record collection is paying for a clever child from Mongolia, I think it is, to study economics, of all things. Would you believe it?”

Geoff Havers

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