Under bilateral competition, market-price is determined within a range whose upper limit is set by the valuations of the lowest bidder among the actual buyers and the highest offerer among the excluded would-be sellers, and whose lower limit is set by the valuations of the lowest offerer among the actual sellers and the highest bidder among the excluded would-be buyers.

The first value of money was clearly the value which the goods used as money possessed (thanks to their suitability for satisfying human wants in other ways) at the moment when they were first used as common media of exchange.

If the objective exchange-value of money must always be linked with a pre-existing market exchange-ratio between money and other economic goods (since otherwise individuals would not be in a position to estimate the value of the money), it follows that an object cannot be used as money unless, at the moment when its use as money begins, it already possesses an objective exchange-value based on some other use.

If the possessor of a units of money receives h additional units, then it is not at all true to say that he will value the total stock a + h exactly as highly as he had previously valued the stock a alone. Because he now has disposal over a larger stock, he will now value each unit less than he did before; but how much less will depend upon a whole series of individual circumstances, upon subjective valuations that will be different for each individual.

The doctrine of the importance of hoards for stabilizing the objective exchange-value of money has gradually lost its adherents with the passing of time. Nowadays its supporters are few.

Economic history shows us a continual increase in the demand for money. The characteristic feature of the development of the demand for money is its intensification; the growth of division of labour and consequently of exchange transactions, which have constantly become more and more indirect and dependent on the use of money, have helped to bring this about, as well as the increase of population and prosperity.

The aim was to regulate the value of money by increasing or diminishing the quantity of it. The effects of these measures appeared to provide an inductive proof of the correctness of this superficial version of the Quantity Theory, and incidentally concealed the weaknesses of its logic.

The central element in the economic problem of money is the objective exchange-value of money, popularly called its purchasing power.

In the case of money, subjective use-value and subjective exchange-value coincide. Both are derived from objective exchange-value, for money has no utility other than that arising from the possibility of obtaining other economic goods in exchange for it.