I have been doing a fair bit of reading in the history of money and monetary theory to try and understand money, particularly its origin and use. A thing reveals its nature through history, to understand the history of something is to much better understand it.
I was aware that modern macroeconomics is bedevilled by a lack of a common analytical language in talking about money. But the problem goes deeper than that; money is a multi-dimensional phenomenon.
I am not talking here about debates over monetary base (coins, notes and bank reserves with the central bank) and the various monetary aggregates (M1, M2, M3 etc). These debates are even less interesting than they appear, not least because expectations matter so much.
Nor even that when economists talk of the "demand for money" they mean the demand to hold money, not the willingness to spend money (which, in a monetary exchange economy, is the demand for goods and services; and money actually spent on goods and services is aggregate demand). Though one way of thinking of money held is as a proportion of money passing through, and shifts in the proportion of money held rather than spent can be very important in its macroeconomic effects. Especially if the money supply does not adjust accordingly, because then an increase in the demand to hold money can lead to a fall in transactions and hence (since one person's spending is another person's income) a fall in incomes, spiralling down into those transaction crashes/goods-and-services gluts we call recessions or depressions.
The problem in talking about money qua money, is that there are so many institutional possibilities with money. Let us just consider the situation were notes exist, so cost of production is not an effective constraint (and ignoring coins and the history of money before notes).
A "theory of money" has to consider to following dimensions:
(1) Is there a monopoly supplier of local notes or are there competitive suppliers?
(2) Are the notes convertible into gold, silver or some other commodities?
(3) If not convertible, are the notes backed in some other way?
(4) If not, is the supply of notes limited in some other way beyond cost of production?
If (2) is true, then the price level (P) is determined by the ratio of monetised backing (for example, gold if a gold standard is operating) to output (y), since notes can always be "swapped out" for gold, so the level of monetised gold (mG) sets the swap value of notes for output. (So P = mG/y.) So, if monetised gold rises faster than output, prices rise. If monetised gold rises slower than output, prices fall.
Note that if (2) applies, then the swap value of the notes (in terms of gold) is set, but their supply is not.[i] This setting of the swap value by a fixed price in gold leads to considerable price stability, as the gold/output ratio generally changes fairly slowly.[ii] Changes in the rate of turnover of notes (i.e. in the demand to hold money) can easily be accommodated by changes in the supply of notes.
This price stability tends to lead to low levels of fluctuations in the rate of turnover/proportion of notes held--in Sweden, for example, in its gold standard era from 1873 to 1914, there was a steady decline (pdf) in the rate of turnover of notes/proportion of notes held.
If (2) does not apply, then the above is not how things work. So convertible or not convertible becomes a vital issue for effective analysis.
If you have a monopoly supplier of notes that are not convertible nor backed nor otherwise supply limited--so (2), (3) and (4) do not apply--then you have hyperinflation, for the reasons explained nicely here (pdf) using the example of the German 1922-3 hyperinflation:
throughout the hyperinflation episode the Reichsbank’s president, Rudolf Havenstein, considered it his duty to supply the growing sums of money required to conduct real transactions at skyrocketing prices. Citing the real bills doctrine, he refused to believe that issuing money in favor of businessmen against genuine commercial bills could have an inflationary effect. He simply failed to understand that linking the money supply to a nominal variable that moves in step with prices is tantamount to creating an engine of inflation. That is, he succumbed to the fallacy of using one uncontrolled nominal variable (the money value of economic activity) to regulate another nominal variable (the money stock).
[Read the rest at Skepticlawyer or at Critical Thinking Applied.]