Saturday, 7 November 2009

The value of money - someone else pondering the same question.

Following on from my earlier posts about the value (purchasing power) of money here and here. I have discovered that Ludvig von Mises, one of the founders of the "Austrian" school of economics had pondered the same question. i.e. what determines the purchases power of a purely fiat (not backed by gold or any other asset) currency. To answer this question Mises proposed his "regression theory". This theory relies upon the assumption that all currencies, even fiat ones, were at some earlier time, non fiat, i.e. they were backed by some commodity. Mises suggested (a rather clumsy theory in my opinion) that you can trace the value of a fiat currency through time back to the point where it was not fiat and therefore derive the purchasing power of a fiat currency in modern times. Mises also thought that if a new pure fiat currency as suddenly hoist upon a society then its value could not be determined for the following reason: Imagine day one of the new fiat currency - you are a shop keeper selling some product, say a television set - what on earth do you charge?... Lets say that in the days of the old currency a television set usually sold for about ten times the cost of a kettle. You could see what kettles were selling for and then charge ten times as much as that, but because its day one of the new currency the people selling the kettles also have no idea what to charge. This is an apparent impasse and Mises assumed the situation was insoluble.

This situation is rather like saying if X depends on Y and Y depends on X then you can never find out what X and Y are. For example if we say:

X = 2 times Y
Y = X / 2

Then this arrangement does not find a specific X and Y. There are infinitely many X's and Y's that fit. I guess this is why Mises thought that the problem was insoluble. But this is where he missed an opportunity to make a less clumsy version of his theory because the X and Y problem is not always insoluble. Consider the statements

X = sqrt(Y)
Y = sqrt(X)

I wrote a little computer program to demonstrate what happens when you start off with some arbitrarily chosen values for X and Y.

a = 12;
b = 7;

for (i = 1;i < 10;i++)
a = sqrt(b);
b = sqrt(a);
print ("a = %f b = %f\n",a,b);

The output when you run the program is as follows:

a = 2.6458 b = 1.6266
a = 1.2754 b = 1.1293
a = 1.0627 b = 1.0309
a = 1.0153 b = 1.0076
a = 1.0038 b = 1.0019
a = 1.0010 b = 1.0005
a = 1.0002 b = 1.0001
a = 1.0001 b = 1.0000
a = 1.0000 b = 1.0000

Now x=1 and Y = 1 is the correct (and only) solution!

What this demonstrates is that even if you start out with the wrong values, the correct values can quickly emerge all by themselves. So in the case of the TV seller and the Kettle seller, as long as someone can be persuaded to have a stab at an initial selling price and as long as the selling price is viewable to all around, then this can give other people a benchmark and people can make more informed guesses as to their prices.

I need to add a bit of detail here. When the TV seller sets his price to say 1000 units of the new currency the Kettle seller can not immediately conclude that he should be selling his kettles for exactly 100 units. It may be that the TV's price is too cheap, or perhaps too expensive. What the Kettle seller should do is wait a while and see what happens. If a big crowd of people instantly form outside the TV shop scrambling to buy every TV in sight then the kettle seller can deduce that perhaps the price was too low and he may try selling his kettles for 200 units. However if the TV's went unsold for months then the kettle seller can deduce that the price was too high and he may try selling his kettles for 50 units. Obviously everyone will be carefully watching everyone else. The key thing they are trying to arrange is for their typical time-to-sale to be about right. Too short and that may indicate that your price is too low, too long (incurring storage costs) and that tells you your prices are too high.

Deriving the purchasing power of a new fiat currency is thus not impossible.


  1. Aren't you making an assumptive leap? From providing an example that the X and Y problem can be solved, you're concluding that it's not impossible to derive the purchasing power of a fiat currency. Surely it's only not impossible if the relationship between X and Y is of the nature that allows an answer to drop out?

    I'm a big fan of this blog by the way, and love your posts. Keep up the awesome work :D

  2. David - first of all thanks for the support :-)

    With regard the assumptive leap: Maybe I do need to investigate the math in more detail. But my gut feeling - combined with the results of my computer simulations (see "The value of money. A computer simulation."), tells me that the answer does indeed drop out.