What’s a fair price?
My readers may be interested to know that I am currently composing an acceptance letter to be on the board of Goldman Sachs.
Not that they’ve offered it, but Felix Salmon was kind enough to suggest me for the job yesterday and I feel like I should get a head start. Please give me suggestions for key phrases: how I’d do things differently or not, why I would be a breath of fresh air, how it’s been long enough having the hens guard the fox house, etc., that kind of thing.
But for now, I’d like to bring up the quasi-modeling, quasi-ethical topic (my favorite!) of setting a price. My friend Eugene sent me this nice piece he read yesterday on recommendation engines describing the algorithms used by Netflix and Amazon among others, which is strangely similar to my post yesterday coming out of Matt Gattis’s experience working at hunch. It was written by Computer Science professors Joseph A. Konstan and John Riedl from the University of Minnesota, and it does a nice job of describing the field, although there isn’t as much explicit math and formulae.
One thing they brought up in their article is the idea of a business charging certain people more money for items they expect them to buy based on their purchase history. So, if Fresh Direct did this to me, I’d have to pay more every week for Amish Country Farms 1% milk, since we go through about 8 cartons a week around here. They could basically charge me anything they want for that stuff, my 4-year-old is made of 95% milk and 5% nutella.
Except, no, they couldn’t do that. I’d just shop somewhere else for it, somewhere nobody knew my history. It would be a pain to go back to the grocery store but I’d do it anyway, because I’d feel cheated by that system. I’d feel unfairly singled out. For me it would be an ethical decision, and I’d vocally and publicly try to shame the company that did that to me.
It reminds me of arguments I used to have at D.E. Shaw with some of my friends and co-workers who were self-described libertarians. I don’t even remember how they’d start, but they’d end with my libertarian friend positing that rich people should be charged more for the same item. I have some sympathy with some libertarian viewpoints but this isn’t one of them.
First of all, I’d argue, people don’t walk around with a sign on their face saying how much money they have in the bank (of course this is become less and less true as information is collected online). Second of all, even if Warren Buffett himself walked into a hamburger joint, there’s no way they’re going to charge him $1000 for a burger. Not because he can’t afford it, and not even because he could go somewhere else for a cheaper burger (although he could), but because it’s not considered fair.
In some sense rich people do pay more for things, of course. They spend more money on clothes and food than poor people. But on the other hand, they’re also getting different clothes and different food. And even if they spend more money on the exact same item, a pound of butter, say, they’re paying rent for the nicer environment where they shop in their pricey neighborhood.
Now that I write this, I realize I don’t completely believe it. There are exceptions when it is considered totally fair to charge rich people more. My example is that I visited Accra, Ghana, and the taxi drivers consistently quoted me prices that were 2 or 3 times the price of the native Ghanaians, and neither of us thought it was unfair for them to do so. When my friend Jake was with me he’d argue them down to a number which was probably more like 1.5 times the usual price, out of principle, but when I was alone I didn’t do this, possibly because I was only there for 2 weeks. In this case, being a white person in Accra, I basically did have a sign on my face saying I had more money and could afford to spend more.
One last thought on price gouging: it happens all the time, I’m not saying it doesn’t, I am just trying to say it’s an ethical issue. If we are feeling price gouged, we are upset about it. If we see someone else get price gouged, we typically want to expose it as unfair, even if it’s happening to someone who can afford it.
mathbabe 
But all this price differentiation already happens. Stores give out huge number of coupons. People who have the time cut them out and get the discount. Usually highly paid managers don’t and pay full price.
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I guess what the article is pointing out is that there’s a fine line between socially acceptable methods of price differentiation and those that aren’t.
Discounting vs jacking up prices is really the same thing, modulo flipping the sign. But one is far more acceptable than the other.
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A related post:
http://magic-maths-money.blogspot.co.uk/2011/10/st-thomas-aquinas-comes-to-defence-of.html
with this follow up
http://magic-maths-money.blogspot.co.uk/2012/03/markets-morality-and-mathematics.html
There is an issue of “equality”, Cardano wrote that “The most fundamental principle of all in gambling is simply equal conditions, e.g., of opponents, of bystanders, of money, of situation, of the dice box, and of the die itself. To the extent to which you depart from that equality, if it is in your opponent’s favour, you are a fool, and if in your own, you are unjust.”
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Strangely, I was just reading the chapter about this in Akerlof and Shiller’s book _Animal Spirits_, which I bet you’d like. They make this same point, that concerns about fairness drive people’s economic decision-making, e.g. refusing to pay a high price for milk if you find out that poorer people pay lower prices. This doesn’t fit the classical utility-maximizing theory and A-S consider it a serious blow to that theory (and by extension certain precincts of libertarian thinking, as you observed.)
Of course rich people do pay higher prices for government services in the form of income tax (or at least people who are rich but not rich enough to have their income concentrated in capital gains.)
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Actually, one common practice (e.g. in chains like K*Mart, CVS, and so on) is to price-discriminate in the inverse. That is, because lower-income groups are less likely to have the means to travel to a place with better prices and possibly even less knowledge that this is happening, those stores raise prices on goods in their stores serving low-income neighborhoods relative to the average or those at higher-income locations. I’ve heard it called “ghetto gouging” … if that’s not too politically incorrect.
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I tend to be a somewhat inattentive and impulsive shopper — not always very good at comparison shopping — and it’s a fear of mine that, as internet tracking gets more sophisticated, companies will catch on and start charging me inflated prices. So far I try to fight back by clearing cookies all the time and not being signed in to any websites when I shop for an item. Still, I don’t like that this is shaping up to be an arms race between me and my online merchants — I don’t like my chances in the long run.
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In response to K. That reminds me, some traveling agencies here were already caught charging higher prices to people using apple stuff.
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At least the JMM organizers appear not to gouge. Yesterday morning I registered online for the Joint Mathematics Meetings in San Diego (Jan. 9-13). After checking an “MAA” box on one screen, a pricing drop-down menu on the next defaulted to the badge price of $235 for MAA members ($132 off the nonmember price).
I figured “okay, that’s fair – I never donate, so $235 sounds reasonable enough.” But when I opened the drop-down, I delightedly discovered a whole slew of other pricing options, including an “Unemployed” one for just $52! Since I’m currently on hiatus from trucking, I jumped on it.
They evidently use the honor system. The price for some categories is actually $0. None applied to me – but then, $52 is pretty close.
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When Microsoft offered a position to Allen Cox, he declined.
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Food for thought: How could it be determined if a given online retailer shows the same price to all site visitors?
Better yet, a little research shows that differential pricing is probably quite common, and probably not well researched or well understood. Here’s one interesting study:
http://www.annenbergpublicpolicycenter.org/downloads/information_and_society/turow_appc_report_web_final.pdf Other very basic searching turns up plenty of stories of groups of people seeing different prices at the same time on line.
A basic premise of a market economy is price transparency, expressed as the “law of one price.” This states that in an efficient economy, identical goods must have the same price to all buyers. (Here, “efficient” is not just used in the colloquial sense. In economics, “efficiency” is a state where nobody in an economy can be made better off without making someone else worse off – regarded as an optimal state). Further, the field of economics makes the claim that a market-based economy produces the best possible allocation of resources (subject to a bunch of caveats).
So then in addition to the very good question of fairness, one has to ask what we are transforming our economy and therefore our society into? If we don’t all see the same prices for the same goods, we move away from a market economy into uncharted territory. At which point economics itself tells us rather confidently that the gradient is downwards-sloping in all directions.
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“First of all, I’d argue, people don’t walk around with a sign on their face saying how much money they have in the bank (of course this is become less and less true as information is collected online).”
This is patently false. Rich people walk around in designer clothes that ordinary people don’t wear. In a narrower context, the bosses wear higher quality suits and shoes – and anyone who knows a bit about suits and shoes can see this. More importantly, rich people drive nicer cars. Ordinary folks don’t drive Mercedes/BMW/etc and everyone can see at a glance that the person driving one is rich.
As for not charging Warren Buffett a different price when he walks into the hamburger joint – the reality is that he and his ilk don’t walk into the hamburger joint – they go somewhere fancy and private (and more expensive) – or when they do they are ushered directly to the VIP room (for which they pay a handsome surcharge).
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I know a bunch of people who wear expensive, hand-me-down clothes given to them by rich relatives or friends. I know even more truly rich people who wear fuddy-duddy clothes- indeed it’s a sign of status in some places to wear crap clothes. So no, I don’t think you’re right here. Moreover, even if someone could be fingered as “well off” it doesn’t actually translate into a hard figure.
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Your assertion about Buffett contradicts the incontrovertible proof supplied by the HBO documentary “Too Big to Fail”. As one blog commenter put it, “Warren in the fast food joint with his granddaughters brought a tear to my eye and a gentle Buffett-like chuckle to my belly.”
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(My reply was to Bobito.)
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suggests this article by my shared colleague with both John Riedl and Joe Konstan, Kartik Hosanagar (University of Pennsylvania – Operations & Information Management Departmentl);
“Blockbuster Culture’s Next Rise or Fall: The Impact of Recommender Systems on Sales Diversity”
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=955984
His result dovetails nicely with John’s conclusions about the long-term effects of recommender systems!
Timothy Vogel
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