In a couple of tweets to me and J. P. Koning, William Luther pointed out, I think correctly, that the validity of the backward-induction argument in my previous post explaining why bitcoins, or any fiat currency not made acceptable for discharging tax obligations, cannot retain a positive value requires that there be a terminal date after which bitcoins or fiat currency will no longer be accepted in exchange be known with certainty.
But if the terminal date is unknown, the backward-induction argument doesn’t work, because everyone (or at least a sufficient number of people) may assume that there will always be someone else willing to accept their soon-to-be worthless holdings of fiat money in exchange for something valuable. Thus, without a certain terminal date, it is not logically necessary for the value of fiat money to fall to zero immediately, even though everyone realizes that, at some undetermined future time, its value will fall to zero.
In short, the point is that if enough people think that they will be able to unload their holdings of a fundamentally worthless asset on someone more foolish than they are, a pyramid scheme need not collapse quickly, but may operate successfully for a long time. Uncertainty about the terminal date gives people an incentive to gamble on when the moment of truth will arrive. As long as enough people are willing to take the gamble, the pyramid won’t collapse, even if those people know that it sooner or later it will collapse.
Robert Louis Stevenson described the theory quite nicely in a short story, “The Bottle Imp,” which has inspired a philosophic literature concerning the backward induction argument that is known as the “bottle imp paradox,” (further references in the linked wikipedia entry) and the related related “unexpected hanging paradox,” and the “greater fool theory.”
Although Luther’s point is well-taken, it’s not clear to me that, at least on an informal level, my argument about fiat money is without relevance. Even though a zero value for fiat money is logically necessary, a positive value is not assured. The value of fiat money is indeterminate, and the risk of a collapse of value or a hyperinflation is, would indeed be a constant risk for a pure fiat money if there were no other factors, e.g., acceptability for discharging tax liabilities, operating else to support a positive value. Even if a positive value were maintained for a time, a collapse of value could occur quite suddenly; there could well be a tipping point at which a critical mass of people expecting the value to fall to zero could overwhelm the optimism of those expecting the value to remain remain positive causing a convergence of self-fulfilling expectations of a zero value.
But this is where network effects come into the picture to play a stabilizing role. If network effects are very strong, which they certainly are for a medium of exchange in any advanced market economy, there is a powerful lock-in for most people, because almost all transactions taking place in the economy are carried out by way of a direct or indirect transfer of the medium of exchange. Recontracting in terms of an alternative medium of exchange is not only costly for each individual, but would require an unraveling of the existing infrastructure for carrying out these transactions with little chance of replacing it with a new medium-of-exchange-network infrastructure.
Once transactors have been locked in to the existing medium-of-exchange-network infrastructure, the costs of abandoning the existing medium of exchange may be prohibitive, thereby preventing a switch from the existing medium of exchange, even though people realize that there is a high probability that the medium of exchange will eventually lose its value, the costs to each individual of opting out of the medium-of-exchange network being prohibitive as would be the transactions costs of arriving at a voluntary collective shift to some new medium of exchange.
However, it is possible that small countries whose economies are highly integrated with the economies of neighboring countries, are in a better position to switch from to an alternative currency if the likelihood that the currently used medium of exchange will become worthless increases. So the chances of seeing a sudden collapse of an existing medium of exchange are greater in small open economies than in large, relatively self-contained, economies.
Based on the above reasoning suggests the following preliminary conjecture: the probability that a fiat currency that is not acceptable for discharging tax liabilities could retain a positive value would depend on two factors: a) the strength of network effects, and b) the proportion of users of the existing medium of exchange that have occasion to use an alternative medium of exchange in carrying out their routine transactions.