We call any physical token of money a ‘coin’ here. It is a bearer instrument; physical custody of a coin is normally taken as sufficient proof of ownership. It must be fairly difficult to manufacture money, at least for most people. There are two distinct values associated with a coin. There is the cost of manufacturing it, M, and its worth in trade, W. Normally M < W but that need not always be the case.
Trade usually creates surplus value which is the net increase in wealth created by the trade. (Marx denied that wealth was created by trade but modern economics sees trade as increasing wealth. Marx attributed some fixed value to any useful object, much as an object has some fixed mass. Modern economics sees the market as establishing an object’s fluctuating value.) When a coin is used in trade it contributes to the wealth created thereby. A coin can be used many times in many different trades and thereby contribute much more wealth than its cost of manufacture.
A coin may be cheaper to manufacture by some than by others. The machinery used by mints is expensive, but attains an economy of scale that exceeds what the would-be small scale manufacturer can achieve. Any large scale manufacturer is likely to be found and opposed by physical force, unless it is broadly “approved”. This is a complex situation that I defer. Cloud(Some forms of digital money are easier to produce by some than by others because it requires a secret which can be effectively guarded. The ‘virtual’ coins produced thereby can be recognized by many but still not manufactured without the secret.)
Who is to be allowed to manufacture money? This is a difficult bootstrap problem but lets try to imagine an early stage where some enterprise, CB, is widely trusted to do so. CB must be trusted not to produce excessive amounts of its own brand of money so that people will be willing to take such money as a store of wealth—something that is worth putting under the mattress in lieu of gold or some other durable compact thing of more manifestly stable valuable. When CB does produce more money — x coins, whether or not in accordance with it charter, it would seem to gain thereby value = x(V−M). Is this value to flow to the individuals who compose the enterprise? This would certainly provide incentive to behave themselves (by carrying out the bank charter) in order to preserve the enterprise and their part in it. Alas it also provides a strong incentive to ‘print the money and run’. This depends on the subjective discount rate of the individuals and thus indirectly to the conventional view of bankers as necessarily conservative individuals.
Modern technology seems to be shifting towards making things, such as coins, easier to duplicate so as to avoid detection of such counterfeits. There are also tendencies in the other direction but I think the net effect is to make counterfeiting easier. At the same time network technology seems to provide a new form of on-line money that would seem to be safe from counterfeiting. The same issues of trusting the central bank remain, almost unaltered.