The math of inflation is extremely simple. There are 2 kinds, natural inflation, and pathological inflation.
Natural inflation is due to the scarcity of gold. The quantity of gold in the world does not grow exponentially, but rather grows LINEARLY.
Thus, if G is the amount of gold in the world today and it increases at, say 2% per year, then one can say that in 100 years the amount of gold will be 2G. Output, on the other hand, does grow exponentially, so that if Q is the output today, with a growth rate of 3%, then in 100 years the output will be 20Q. If P = 1 is today’s price level, and is equal to Q/G, then the price level in 100 years will be 20Q/2G = 10 . This is a perfectly normal consequence of the scarcity of gold.
Pathological inflation, on the other hand, is due to excess credit, where the money growth rate, m’/m, exceeds the real growth rate Q’/Q so that if m’/m – Q’/Q = c, then c is the excess credit growth rate. A corollary from the Quantity Theory of Money is that p’/p – V’/V = c also, which means that excess credit affects inflation and money velocity as well. When p’/p is suppressed, as in the US between 1879 and 1935 by setting a dollar equal to 1/20.60 of an ounce of gold, then p’/p = 0,and V’/V = -c. a huge credit strangulation occurs, because normal price and wage inflation is necessary for money to circulate. The effect was a collapse in money velocity shown by http://research.stlouisfed.org…
After the gold standard was abandoned in 1971, the price of gold rose exponentially in order to try and catch up with world output. The rise in the gold price carried the CPI along with it, and inflation was quite high between 1971 and 1983 as can be seen by https://research.stlouisfed.or….
This inflation, however, was not pathological, since money velocity was rising along with it. One can almost pinpoint to the day and hour on the curve when gold manipulation began: it was when Volcker was told to lower the Fed Funds rate in 1983. Immediately the money velocity began dropping and the CPI changed from exponential growth to linear growth in 1983. Pathological inflation only occurs when V is very low and can no longer absorb the excess credit by shrinking. Then, hyperinflation occurs quite suddenly with huge social upheavals.
Mises once said famously that math is not necessary to understanding economics. The Austrians, as a consequence, have fallen into the error of believing that all inflation is pathological, which it isn’t, as I have just demonstrated. I live in hope that someday an Austrian prophet will arise who can do the (simple) math.