Friday, July 23, 2010

The pigeonhole principle

Shorter Prof. Anderson: "Math is hard."

I am amused by the resistance of Austrian "economists" to the use of modern statistical tools, which they sneeringly refer to as "aggregates". Mathematics is a fundamental tool of science, and by rejecting modern mathematics they thereby prove that they are not members of a branch of science but, rather, members of a religion, complete with a holy canon of Mises, Hayek, and Rothbard each of whose words must be accepted as holy doctrine and never criticized regardless of how little data there is supporting those beliefs.

The fundamental mathematical principle that applies at the zero bounds is the PIGEONHOLE PRINCIPLE. That is, if there are fewer dollars in the economy than are necessary to pay all the employees and buy all the goods, then clearly some of the employees will go unpaid and some of the goods will go unsold. This has nothing to do with mythical appeals to holy canon of Saint Rothbard, but, rather, a fundamental mathematical quality of the universe. If you have five holes and four pegs, it simply is impossible to put pegs in all the holes.

To counter this, Holy Saint Mises and His followers then came up with the theory of "price elasticity". That is, okay, so we have four pegs and five holes, we'll just chop a little piece off of each peg and glue them together to make a fifth peg and fill all the holes that way! The problem is that in a *real* economy, as vs. the fictional economy in the Holy One's scriptures, it took a whole peg's worth of money to create the goods and services available for sale, and no business is going to sell goods for less than it cost to create them. In other words, price elasticity is a crock of BS. When you hit the zero bounds and go into deflation, what happens is that one of those holes is going to go unfilled -- i.e., somebody's going to lose his job, and some goods are going to go unsold.

What Keynesian economics says is that when you hit the zero bounds -- where we are right now -- the solution is simple: Make another peg from scratch to fill that fifth hole. Given that our particular pegs happen to be made of zeros and ones in the mainframe computers of banks, clearly we aren't going to run out of zeros and ones anytime soon. And this is the situation that Keynes was pondering, and which describes the "zero bounds" issue that Krugman was talking about.

Now, neither Keynes nor Krugman proposed making more pegs when there was already sufficient pegs to fill all the holes. When the economy is at full employment then clearly printing more money simply causes inflation (more pegs getting jammed into the holes) rather than an increase in sales and employment (a peg now available for a previously unfilled hole). But given real unemployment in the US is close to 20% if you count the people who've been "disappeared" from the statistics as "not in workforce", can anybody say that this is the situation? Clearly we have holes (goods available for sale) that lack pegs (money available in the economy that can be used to purchase them), otherwise those people (who, remember, are a commodity available on the open market like any other commodity) would be employed!

Note that I talk pegs and holes because if I started talking mathematical induction and proofs then Austrians would start shouting "Heresy! Aggregates!" because, well, math is hard. Needless to say, all this *can* be expressed mathematically in terms that comport with the physical laws of this universe, as vs. of some fictional universe that exists only in the fertile mind of the authors of the holy scriptures of Austrian "economics"...

- Badtux the Snarky Economics Penguin


  1. Surely the point of the non-mathematical theory is that it can't be disproved, making it the perfect policy tool of the neo-liberals.

    Or am I just stating the obvious?

    Also, don't you have a job (I don't)?

    Just to be clear, I'm not serious about that last part.

  2. Since we are bounded by zeros, I have to say that 0's are in an oversupply situation.

    It's 1's that we don't have enough of.

    Who know it could be so simple?


    P.S. Here's the hard part about math. The number 1, which has all the characteristics of a prime, is not a prime. Riddle me that, Penguin.

  3. Seems to me the problem is that there are only four holes -- which can be called "jobs" or "food" or any of the resources needed to survive -- and five or six, maybe eight pegs -- who I like to call "people." Some of those pegs aren't motivated to take up a hole, or they need help getting over to one. Austerityan economists would say "Sweep those pegs off the table. They're not productive. We don't need them." But here's the secret I'd be screaming at the end of the book: "Swept-off pegs is people!"


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