I think it can be proved that fiat currency will necessarily collapse at some future point. This is stronger than the empirical statement that, "all fiat currencies have collapsed in the past, so we can reasonably believe fiat currencies will fail in the future." Let me explain.
I will start with the assumption that is in the nature of this physical universe that no exponential function can go on indefinitely. I will also assume that the issuing institution of a fiat currency necessarily engages in monetary expansion at some non-zero rate.
Each time an issuing institution expands the monetary base, the monetary unit is eventually devalued. To expand the monetary base at a constant rate, the issuing institution must issue a larger number of dollars at each successive expansion. Beginning with a monetary base of m0, we have:
m_1 = (1+k)*m_0 k>0
Where k is the factor of expansion. So, if m0 is $1 billion and k = 0.5, then m1 = $1.5 billion. Let us repeat this procedure:
m_2 = (1+k)*m_1
Here we have m2 = $2.25 billion. We can turn this into a general equation:
m_n+1 = (1+k)*m_n
It turns out that this recursive equation is equivalent to the exponential function:
m_n = m_0*(1+k)^n
For any value of k greater than 0, this function grows exponentially. Since, by our first assumption, no exponential function can continue indefinitely, it follows that any monetary system with a non-zero rate of expansion must collapse and, by our second assumption, any issuing institution will necessarily expand the monetary base at a non-zero rate, it follows that every fiat currency necessarily collapses.
Clayton -
P.S. Please don't get hung up on the maths, I am not "modelling" economic activity with the mathematics - a fiat monetary base is a well-defined number (because it is artificial) and so it is appropriate to apply mathematical formalism in the analysis of how it will behave given the stated assumptions.
Interesting stuff. To nullify the exponential growth, k would need to decrease with every iteration and approach zero as n goes to infinity.
I can see where you're coming from... but as the currency base expands over time, market prices adjust with it. Just imagine a growth of 10%, year on year. Market prices will adjust, people will have more money, and things will get more expensive. We are increasing the amount of fiat out there, but the value of the fiat is always adjusting to the conditions of the market.
If market prices are 1x, and we increase the monetary base by 10%, prices might rise to 1.1x. And if we take that new monetary base, and increase that by 10%, then prices might increase 10% from 1.1x and become 1.21x. The amount of dollars in circulation may be growing exponentially, year on year, but the market prices are also adjusting. So I don't know if this works as an explanation as to why fiat currencies fail, but it is obvious that with k set high enough, and iterations occurring fast enough, we would have hyperinflation.
Giant_Joe: Interesting stuff. To nullify the exponential growth, k would need to decrease with every iteration and approach zero as n goes to infinity. I can see where you're coming from... but as the currency base expands over time, market prices adjust with it. Just imagine a growth of 10%, year on year. Market prices will adjust, people will have more money, and things will get more expensive. We are increasing the amount of fiat out there, but the value of the fiat is always adjusting to the conditions of the market. If market prices are 1x, and we increase the monetary base by 10%, prices might rise to 1.1x. And if we take that new monetary base, and increase that by 10%, then prices might increase 10% from 1.1x and become 1.21x. The amount of dollars in circulation may be growing exponentially, year on year, but the market prices are also adjusting. So I don't know if this works as an explanation as to why fiat currencies fail, but it is obvious that with k set high enough, and iterations occurring fast enough, we would have hyperinflation.
Well, my point is that if k is non-zero (my original argument assumes that k is a constant, but with sufficient effort it could be extended to include k's which vary with time), the currency must collapse. If that collapse occurs as a re-pegging to a new definition of the "same" unit, it's still a collapse... saying 1 trillion old dollars = 1 NEW dollar is still a currency collapse. And, even if k is very, very small this will still happen since the curve is still an exponential... it will just take longer to get there. On a long enough time scale, hyperinflation is inevitable.
ClaytonB: Well, my point is that if k is non-zero (my original argument assumes that k is a constant, but with sufficient effort it could be extended to include k's which vary with time), the currency must collapse. If that collapse occurs as a re-pegging to a new definition of the "same" unit, it's still a collapse... saying 1 trillion old dollars = 1 NEW dollar is still a currency collapse. And, even if k is very, very small this will still happen since the curve is still an exponential... it will just take longer to get there. On a long enough time scale, hyperinflation is inevitable. Clayton -
Well yes. If we extrapolate the US dollar's inflation to the next hundred years, we can say that there is hyperinflation over the period of 1900 to 2100. It's just that over this period of time, we wouldn't see a crack-up boom if the rate were (roughly) steady.
Although fiat money will collapse, exponential growth won't be the cause. Subjective preferences of people will be the cause.
There is nothing to stop us from just printing the following bills:
10^18$ (one quintillion dollars) with a picture of Bush
10^21$ (one sextillion dollars) with a picture of Obama
10^24$ (one septillion dollars) with a picture of Bernanke
Or we can just print a brazillion dollar bill.
ClaytonB:I will start with the assumption that is in the nature of this physical universe that no exponential function can go on indefinitely.
Under a fiat system, currency units aren't physical objects; most of the currency will exist in the form of bookkeeping entries at banks anyway, and these can be increased effectively without bound.
ClaytonB:I will also assume that the issuing institution of a fiat currency necessarily engages in monetary expansion at some non-zero rate.
Is this necessarily true for all fiat currencies?
ClaytonB:If that collapse occurs as a re-pegging to a new definition of the "same" unit, it's still a collapse... saying 1 trillion old dollars = 1 NEW dollar is still a currency collapse.
Wouldn't this just be a new notational convention?
ClaytonB:And, even if k is very, very small this will still happen since the curve is still an exponential... it will just take longer to get there. On a long enough time scale, hyperinflation is inevitable.
Take longer to get where? The absolute quantity of money doesn't matter -- it's not as though there's some special number such that the currency will collapse when the money supply exceeds it. Imagine that every dollar in existence, no matter where or in what form, turned into $1.05 every year. This is exponential growth, but the money supply increase wouldn't by itself have any real effect on economic activity. The value of each currency unit will approach zero but never reach it unless there are other real effects on the economy (such as seigniorage or business cycles caused by the non-neutrality of money creation). The point is that exponential growth is not in itself the reason why a currency collapse happens.
nandor is correct.
All you did is verify exponential growth. This is no proof for the inevitable collapse of the currency since any supply of money is optimal.
If the numbers get too large for the common man, you can always do a reset by issuing new currency. For example, government can define 1 New dollar = 1 Billion old dollars.
DD5: If the numbers get too large for the common man, you can always do a reset by issuing new currency. For example, government can define 1 New dollar = 1 Billion old dollars.
I define this as a currency collapse. The point is that that event (or complete dissolution of the currency) is inevitable, no matter how low the growth rate of the money supply.
baxter: Although fiat money will collapse, exponential growth won't be the cause. Subjective preferences of people will be the cause. There is nothing to stop us from just printing the following bills: 10^18tiny_mce_markernbsp;(one quintillion dollars) with a picture of Bush 10^21$ (one sextillion dollars) with a picture of Obama 10^24$ (one septillion dollars) with a picture of Bernanke Or we can just print a brazillion dollar bill.
10^18tiny_mce_markernbsp;(one quintillion dollars) with a picture of Bush
Hmm, if you have a pure ledger fiat currency (cashless fiat currency), then I think you're right, since there is no physical representation of the currency besides the ledgers and, since the number of digits in a decimal number grows logarithmically with the magnitude it describes, an exponential growth in monetary base is only a linear growth in the size of ledger entries. But if there is any physical cash, then the system must collapse.
Clayton: I define this as a currency collapse.
I define this as a currency collapse.
Your definition violates the rule that any supply of money is optimal.
Currency collapse is when the money doesn't buy anything, there is no demand for it, and it becomes useless for economic calculations.
It's not when the quantitative supply just goes beyond a certain point.