Resolving the paradox of fiat money

As the dimension of this simplex defined by the budget constraint Σ Ci = M increases, most points are near the budget constraint hyperplane ... and therefore the most likely point will be near the hyperplane.

In his recent post on neo-Fisherism, David Glasner links to an earlier post about the paradox of fiat money -- that money only has value because it is expected to have value:

But the problem for monetary theory is that without a real-value equivalent to assign to money, the value of money in our macroeconomic models became theoretically indeterminate. If the value of money is theoretically indeterminate, so, too, is the rate of inflation. The value of money and the rate of inflation are simply, as Fischer Black understood, whatever people in the aggregate expect them to be.

The problem then becomes the problem of the "greater sucker"; rational people would only accept money because they expect they will be able to find a greater sucker to accept it before its value vanishes. But since at some point e.g. the world will end and there won't be a greater sucker, the expected value should be zero today. Note that the idea of the future rushing into the present is a general problem of expectations, as I wrote about here.

After getting a question from Tom Brown about this, I started answering in comments. Now I think the information transfer framework gives us a way to invert that value argument -- that if you don't accept money, you are the greater sucker. The argument creates a stable system of fiat currencies.

The argument starts here; I'll quickly summarize the link. If we imagine a budget constraint that represents the total amount of money in the economy at a given time being used in transactions for various goods, services, investments, etc C₁, C₂, C₃, ... Cn, then using a maximum entropy argument with n >> 1 we find the most likely state of the economy saturates the budget constraint and minimizes non-ideal information transfer (see the picture at the top of this post for n = 3). And since:

k N/M ≥ dN/dM ≡ P

we can say minimized non-ideal information transfer maximizes prices for a given level of goods and services {Cn} because P is as close to k N/M as it can be. We would think of arrangements of trust (credit) or barter exchange as less ideal (very non-ideal) information transfer than using money or some money-like commodity.

This maximized monetary value critically depends on n >> 1 -- that as many goods and services are exchangeable for whatever is being used as money as possible. This means that whoever trades their goods and services for the most widely used money gets a higher price (more ideal information transfer) for those goods and services. If I don't accept money, then I'm getting a worse deal and I'm the greater sucker. That would stabilize an existing fiat currency system because if I refuse to take money, I'd contribute to the downfall of my own personal wealth. I'd also get a worse deal in that particular transaction.

I've explained this argument in terms of rational agents. However in the information transfer framework we'd think of this argument as money allowing agents to access larger portions of state space and hence achieve higher entropy. We would think of money as a dissipative structure, like convection cells in heated water or even life itself, arising in order to maximize entropy production to move the system towards equilibrium. Convection cells only cease to exist when the water reaches a uniform temperature. Analogously, money only loses its value when every scarce resource is equally allocated among everyone (the Star Trek economy) -- the economic equivalent of heat death.

Update +3 hours:

Although the money value argument admits a rational agent explanation, the truth is that there may not be any such explanation that is valid in terms of microeconomics -- that money is an emergent structure and its effects are entropic forces. The rational explanation may be like incentives or Calvo pricing: an attempt to 'microfound' a force (effect, or structure) that only exists at the macro level. Osmosis and diffusion have no microscopic mechanism (although you could invent one, an effective force [1]) and maybe the value of money has no micro explanation that is actually true.

Footnotes:

[1] An example of a (possible) entropic force that we tend to explain with an invented micro force is gravity. We think of it as mediated by gravitons that behave similarly to photons, but it might be closer to the stickiness of glue. It is important to note that because it is an entropic macro force doesn't mean it is impossible to model as a micro force.