**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

and

Y = X / 2

and

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)

and

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.

The output when you run the program is as follows:

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.and

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.

XY_demonstration()

{

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!

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.

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?

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

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

ReplyDeleteWith 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.