Methodologically it holds: “Questions of origin are ‘how and why’ questions. They are comparatively unimportant theoretically and usually have only a specific historical interest. (Popper) So, monetary theory deals NOT with the historical origin of money in a nation-state‡ but with the analytical origin.
Suppose the business sector consists initially of one giant fully integrated firm. There is no Central Bank and no sovereign political entity. The firm fixes the wage rate W arbitrarily at 1 dollar per hour. We then have a unit of account but nothing that looks like money. In principle, it suffices that the firm’s accountant keeps track of wage payments and the purchases of each employee at the firm’s store. We then have a nominal but not yet a monetary economy.#1
In the next step, the firm pays the monthly wages with a standardized IOU and declares that this conveniently denominated title will be unconditionally accepted at the firm’s store. The employees accept that the IOUs discharge their wage claim against the firm. Here is the logical point where the fiat comes in.* Since the household sector’s budget is balanced by the initial condition C=Yw, whatever the firm issues, returns until the end of the period under consideration. The firm creates IOUs ex nihilo and destroys them again within a given time span. No IOUs are carried over to the next period and therefore the IOU is not suited as a store of value. The firm’s IOU is a pure transaction medium.
We now split the business sector into two identical halves. Firm A’s wage rate remains unchanged at 1 dollar but firm B pays a wage rate of 2 bancors per hour and issues its own IOUs for the payment of wages. Now the question arises whether store A could accept the IOUs of firm B and vice versa. Technically there is no problem fixing an exchange rate between the IOUs. The advantage for the households consists of no longer being restricted to buy their firm’s product in their firm’s store. This increase in the number of buying locations, though, is not so impressive because both firms produce identical output and sell at the same price in dollar or bancor. At the end of the period under consideration firm B presents firm A’s IOUs and gets its own IOUs in return. Under the given ideal conditions the mutual claims cancel out exactly.
One important element of a functioning IOU economy is the unconditional mutual acceptance of IOUs and the final clearing of balances between the different issuers of IOUs.
IOUs have a time dimension, a duration. Because the duration between creation and destruction is relatively short, IOUs are only suited as transaction medium but not as a store of value. This duration, though, is enough to explode General Equilibrium Theory: “… it is generally acknowledged that no kind of exchange intermediary or, in common parlance, ‘money’ can be introduced into conventional general equilibrium theory without violating its logical underpinnings …”. (Clower) Equilibrium theory cannot handle duration because it is formally predicated on simultaneity.
As the number of firms increases the number of exchange rates multiplies by n(n-1)/2 and the handling of privately issued IOUs becomes obviously more and more cumbersome even under the ideal condition that each firm’s store voluntarily accepts all other IOUs, that all households fully spend their incomes in the period under consideration, and, above all, that all participants honor their obligations. A host of practical problems arises when people start gaming the system, e.g. by counterfeiting or over-issuing IOUs.
The final step on the way to money proper consists of the introduction of the Central Bank and of the definition of the means of payment. Instead of issuing their own IOUs, the firms now become the debtors of the Central Bank in the form of overdrafts and get deposits in return. These deposits are then used for wage payments and subsequently for the households’ purchases of the consumption goods. Thus, the firms’ overdrafts are eventually reduced again to zero. There is NO constant quantity of money in the economic system. This idea is the fundamental blunder of the Quantity Theory.
The household sector’s transaction pattern is shown on Wikimedia AXEC98. Money is created out of nothing at the beginning of the period and vanishes again at the period's end. The business sector's pattern is the exact mirror image.
In marked contrast to private IOUs, Central Bank money (= deposits) has no built-in short-term duration. This means that Central Bank money morphs from a pure transaction medium into a store of value.
The fact that deposits can at any time take the form of banknotes and vice versa in no way affects the characteristics of money but means that the Central Bank loses sight of that part of transactions that are carried out with cash. This feature is a precondition for the use of money in the black economy.
In the elementary production-consumption economy, money starts as an IOU of the single firm. The transaction medium is created out of nothing for wage payments and is destroyed when the households spend their income by buying the firm’s output. In the case of multiple firms, this leads to many different IOUs. The multiplicity of private IOUs, which becomes exponentially impractical as the number of firms increases, is finally replaced by the Central Bank’s generalized public IOU which is money in the proper sense or currency to distinguish it from IOUs created by commercial banks.
The ultimate rationale for Central Bank money is the enormous productivity gain for the economy as a whole that comes from the replacement of private IOUs. Central Bank money is the most efficient transaction medium and it has the additional property of a store of value.
Because the Central Bank is an institution that has to be established by the legal authority of a nation-state, money is, as the MMTers/Chartalists do not get tired of emphasizing, ultimately a creation of ‘the state’. This does not mean, though, that the government is needed to endow the economy with money.#2 This is the basic function of the Central Bank.
#1 The elementary production-consumption economy is for a start defined by three macroeconomic axioms (Yw=WL, O=RL, C=PX), two conditions (X=O, C=Yw), and two definitions (Qm≡C−Yw, Sm≡Yw−C). This determines the price as P=W/R and the 'value of money' as W/P=R.
#2 See cross-references Refutation of MMT: all proofs and arguments you ever need.
Related 'Money and time' and 'Money: from silly stories to the true theory' and 'Basics of monetary theory: the two monies' and 'The value of money and the worthlessness of economics' and 'The right and the wrong way to bring money into the economy' and 'Criminals and the monetary order'. For details of the big picture see cross-references MMT.