Why does money have value and circulate, though it does not have value in itself? I will answer this question in terms of the system theory.
1. Money as a communication medium
Money is a communication medium, as it reduces the double contingency consisting of a pair of indeterminacy, whether the barter partner possesses what I desire and whether he desires what I possess.
When each of n persons has one unique equivalent commodity that the possessor does not intend to consume by himself and wishes for only one commodity which the other has, the probability of success in exchange between arbitrary pair is no more than 1/(n-1)2. In other words, the system that solves the inconvenience of barter can reduce entropy by 2log(n-1).
The fact is commodities are not always equivalent. So, a coincidence of mutual desire is actually even rarer. If none of the pair possesses what the other desires, they must work to produce the desired commodity. However, it catches them in the prisoner’s dilemma.
Suppose an inhabitant in a mountain that wishes for fish promised an inhabitant on the coast that wishes for boar to catch a certain number of boars and by a certain day exchange it with the coast inhabitant for a certain number of fish that he promised to catch.
In this case, the mountain inhabitant will reason as follows: It is uncertain whether the partner will catch a promised number of fish by the promised day or not. If he breaks the promise, I do not have to catch additional boars that I do not intend to consume by myself. Even if he keeps the promise, as he cannot consume all the fish, I can steal leftover fish…
Of course, the coast inhabitant thinks the same strategy. As a result, since both inhabitants break the promise and produce the minimum for themselves, the Nash Equilibrium turns out self-sufficiency. But it is not the most desirable state. As the theory of comparative advantage indicates, the specialization and trade increases the benefit of all, even if some gain an absolute advantage over the others. How is the specialization and trade possible, then?
2. Why does money circulate?
Suppose the third rich of reputation appears before the two hesitating about specialization and trade, who accepts any kind of valuable commodity, gives in return an equivalent commodity valuable to anybody and will exchange any other equivalent commodity for it, if they want to get it. This third can solve the problem. The mountain inhabitant can exchange boars for fish with the coast inhabitant through the universal medium of money.
Why can money circulate as something valuable to anyone? Once it circulates, it is obvious that money is useful as an exchange medium, a value-measuring rule or value saving means. But is there any ground for specific goods being money? Precious metals such as gold and silver were once used as material of money, but, as nowadays base materials, paper or an electromagnetic wave took the place of it, you cannot regard material of money as the ground for the value of money.
Does money function as money because it is so established by law? No. Even if the law provides that specific goods shall be money, people do not necessarily use them as money. Moreover, private enterprise can issue its original money. Some company issue money, when they make a rule that they pay consumers points to fill out a questionnaire and exchange presents for it.
3. What guarantee the value of money?
Does money have no ground for its value, then? Does it circulate as money just because it has circulated as money? No. If money had self-sufficient value, why deficit financing or unstable political situations could devalue the currency?
I consider money to be securities for the issuer’s asset and estimated earnings. As current money is inconvertible bank note, a Government or a Central Bank does not convert money into some valuable commodities. But that is because the nation pays tax in cash. The Government can make the nation pay in kind like the Tokugawa shogunate. In that case, it is evident that the money issued by the Central Bank is security for national property and revenue.
Of course, the whole sum of currency value exceeds the scale of national property and revenue. You cannot explain it just by means of utility value of money. It rather indicates that the credit creation multiplies the value. Deficit financing devalues money in fear of security value and unstable political situations devalue money in fear of credit.
A margin between the cost of producing a coin and its statutory currency value is called seigniorage. It is the U.S. that gains the largest benefit from seigniorage today. FRB can issue dollars as the global key currency more than domestically necessary. People often denounce seigniorage as unfair profit but it is actually a fair reward for political or military labor to produce the commodity of credit. In fact, credit creates value because it reduces indeterminacy (entropy).
It is because politically and militarily Japan plays a minor role in maintaining an international order that yen does not circulate internationally like the US dollar, although Japan is economically strong. The issuer itself must be universal so that the currency can have universal value.