The game theory of perfect complements

Can you think of a use for an unpaired left shoe?

Off the top of my head, I cannot. A left shoe only has value to me if I have the corresponding right pair. In economics terms, this is because left and right shoes are perfect complements.

But I am in fact wrong. An unpaired left shoe does have value. It took a clever businessman in India to discover this, but an unpaired left shoe has value precisely because no one thinks it has value.

The application is clever, and I learned about it from a story by Fred Flaxman in the Stanford alum magazine:

In the 1950s, Americans still manufactured things, and Indians were eager to purchase some of them. But import duties greatly reduced the profit margins of importers. However, if items–say, a load of tennis shoes–arrived at Indian customs and were not claimed by anyone within 30 days, they would be auctioned off.

My friend’s father ordered a huge shipment of sneakers from a U.S. company with the stipulation that all the left-footed shoes be packaged separately from all the right-footed shoes. The left-footed shoes were to be shipped to Bombay, and 60 days later the right-footed shoes were to be shipped to Calcutta.

The shipment sent to Bombay went unclaimed, so after 30 days it was auctioned off. Because no one could think of a use for a huge shipment of left-footed sneakers, no one bid against my friend’s father and he picked up these shoes for next to nothing. The situation was repeated with the right-footed sneakers in Calcutta. My friend’s father paired the shoes and made the kind of money that sent his son to a fine American university.

The strategy is ingenious, and it reminds me that a savvy businessperson is someone that can see value where others see none.

(And just a bit of closing trivia. Someone told me there is a Hindi film set in the 90s about Reebok shoes with exactly the same plot line (plus a love story, of course) called Badmaash Company)



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  • Christopher Browne

    It’s unclear how this would be a “good deal” overall.

    I’m presuming that the guy who ordered the shoes had to pay the shoe maker for them, no?

    If he did, then the auction adds to the costs he had already paid; that they auctioned off cheap merely means a small premium to add to the likely-high price already paid.

    If he hadn’t, then, in effect, the game also includes a big defrauding of the manufacturer, which suggests this is something that only gets played once.

    Or am I missing some customs issue? Perhaps this situation saves customs fees, if the goods are, due to the low auction price, deemed to be “effectively worthless” for tax purposes?

  • Dave

    So wait, the story is that the friend got to go to Stanford on the profits of a fraud perpetrated on an American company? Nice…

  • Hari Seldon

    Maybe I’m being dense, but I don’t get it, isn’t this just a scam?

    Hari

  • http://kidbuilder.net TIm Inman

    The left shoes were only valuable as an instrument for fraud. I’d argue that really isn’t value at all, because fraud is theft, not profit.

  • http://Sympodial.com Barry Melton

    I think it’s poorly described, but it seems as though the auction value would be far less than the cost of the import duties otherwise. By not claiming the shoes as they arrive, the auction cost replaces the duty cost, and as half a pair of shoes is all but worthless without the other, the auction value would be next to nil.

    Since nobody else would be able to purchase these shoes without paying import duties as well, he could sell the shoes at a markup anywhere between the cost of the shoes + the cost of the auction and the cost of the shoes + the cost of duty fees, while making a profit and still being cheaper than anybody else could deliver them.

    I’ll agree that it seems sketchy, however, most business profits are made by simply buying in bulk and reselling individually (hell, drug trade anybody?), so it’s not that odd, I suppose; especially given the story’s lack of specifics.

  • peter

    It’s basically a fraud which allowed him to avoid the income tax. But if you want to call cheating “ingenious”, so be it.

  • anomdebus

    I agree with Christopher wrt to this apparent fraud.

    Also, he didn’t find a use for unpaired left shoes. He created an information asymmetry that the people in that market were not able to exploit.

    I was expecting something actually related to the question of use for only left shoes. Here’s a couple ideas:
    Right foot may be more accident prone due to it being the leading foot, leading to an asymmetry in single footed individuals.
    Left foot may be more accident prone due to it being less coordinated. Surplus of left shoes used solely for flinging at enemies, politicians, etc.
    Eugene Levy in ‘Best in Show’.

    Btw, Americans still manufacture plenty of things. (http://cafehayek.com/2010/08/maybe-we-should-prohibit-the-wheel-too.html)

  • Qualko

    It seemed pretty clear to me that the importer avoid having to pay the customs duties, and that the auction price was quite a bit lower than he would have paid if he had imported them normally.

    Nothing in the article implies that he defrauded the supplier.

  • http://www.peerside.com Paul

    I’m guessing the “clever businessman” wasn’t defrauding the manufacturer but dodging the import tariffs.

    Instead of the “expensive” tariffs he paid the unclaimed auction price – which he minimized by reducing the apparent value of the shoes.

    Assuming the import tariffs cost more than the auction price then he found a cheaper way to import product into India and increase his profit margins or undercut competition.

  • anomdebus

    Driving into work, I came to the conclusion that he most likely did not defraud the shoe company. The relationship with the shoe company was probably more than one set of transactions in order to build the sort of fortune suggested.
    The duties were most likely a large percentage of the declared value and he still probably paid a fair amount of the duties that would have been paid, else someone could have bought the shoes merely for the raw materials. There could be a wrinkle here if the shoes were leather in a country that did not have a market for miscellaneous leather goods, yet has a expatriate market for leather shoes.
    Also, since he would most likely have been doing this multiple times, other auction goers should have eventually been able to catch onto his game and either bid up the price of the shoes or report his activities to the authorities.
    Still, technically he would most likely could have been charged with some sort of crime for his evasion of duties payments.

  • Tony

    Yes, I would assume this was fraud committed against the Indian government, and the businessman avoided paying the import duties but still paid the manufacturer for the shoes.

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Thanks all for the comments. The scheme was to avoid oppressive import duties from the Indian gov’t. Although it was borderline fraud, I guess I liked it since I like free trade and this seemed like a sort of civil disobedience.

  • teadrinker

    i think it was clever. he didn’t break any law and if this loop hole was really bad, they could always auction the thing with a starting price tag equal to the import duty.

    maybe the lawmakers then planned to import half a car and use this method to avoid import duties themselves. haha. :)

  • Stubbs

    You need to factor into the cost the risk that someone might outbid him on the right-footed shoes in Calcutta 60 days later. Failing to account for risk has led to things like the recent financial crisis in the US.

  • Ricardo Hernandez

    Presh beat me to the comment, but oppressive import duties are a big reality in corrupt countries like my own, and learning ways around them is pretty much the only way to start/stay in business. So you have an idea, I once paid 60% of the billed price on a laptop battery that I had to import. Just one battery. Imagine trying to set up a business selling those. Obviously, I had to buy it abroad and ship it because no one in their right mind would stock laptop batteries if they had to pay so much in taxes. I believe this same approach was taken in Venezuela a few times before they wised up to it.

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