A money is presumed to change in purchasing power in proportion to the demand for goods that it represents. In other words, with twice the amount of money each unit of the money will trade for half its previous amount of goods, as the increase in goods implies lower demand for them. This is a proportional relationship between monetary inflation and price inflation (or deflation). This money relation is an expression of the law of supply and demand.

• Rising supply market money, such as Gold and early Bitcoin, consumes the same value in goods as it creates in new units - including the opportunity cost of the capital invested in doing so. As such it produces no change in proportionality and therefore no price inflation.

• Monopoly money is not subject to competitive production, allowing its producer to obtain a monopoly premium in the pricing of new units. As such it increases the proportion of money to goods, resulting in price inflation.

• Fixed supply market money, such as late Bitcoin, creates no units. As such the proportion of money to goods decreases with economic growth, resulting in price deflation.

Proportionality refers to the goods "represented" by a money. If there was only one money, this would be a straightforward relation to all goods. However the relation must be addressed in the case of multiple monies. The goods represented by a money are those that it can be traded for. In other words, the relation implies demand for goods in the money.

Yet demand does not remain constant in the case of a decision to mine. New demand for goods is created by the fact of mining. The miner must consume "representation" goods in producing the money. The new money is entirely offset by the demand increase represented by the consumed goods and the opportunity cost (i.e. fewer new goods) of employing them in mining. Therefore proportionality is preserved in the case of multiple monies as well. Economic growth is not price-inflationary in a free market.

In expanding upon the Copernican quantity theory of money, Richard Cantillon formulated a theory now known as the Cantillon Effect. The theory is valid when applied to monopoly monies, but has no relevance to market money – a fact that seems to have escaped economists since Cantillon. The basis of the distortions explained by Cantillon is seigniorage, not money production. Market production of money, just as market production of all things, is not only neutral in real effects but also price neutral.

In Human Action, Ludwig von Mises, as his predecessors, attempts to demonstrate the validity of the Cantillon Effect to any money .

Changes in the supply of money must necessarily alter the disposition of vendible goods as owned by various individuals and firms. The quantity of money available in the whole market system cannot increase or decrease otherwise than by first increasing or decreasing the cash holdings of certain individual members.

Ludvig Von Mises: Human Action

This statement asserts that new money first effects existing money holdings. Yet this is not the case with market money. Its creation coincidentally reduces goods holdings as it increases money holdings. The increased demand for money is concurrently and proportionately offset by its increased supply. This reduction of goods cannot be ignored in evaluation of the money relation. The statement conflates market money with monopoly money, as the latter does not consume its value in goods through production. To the extent the goods are consumed in essentially the same location as money is produced, and at the same time, not even an uneven distribution of the money relation is implied. This error persists despite explicit recognition that mining consumes in goods the value that it produces in new money.

The fact that the owners of gold mines rely upon steady yearly proceeds from their gold production does not cancel the newly mined gold's impression upon prices. The owners of the mines take from the market, in exchange for the gold produced, the goods and services required for their mining [...]. If they had not produced this amount of gold, prices would not have been effected by it.

Taken literally the last sentence is a tautology (no creation implies no price effect from the creation). From the context it is clear Mises intends that, had the gold not been produced, prices would be unchanged. Yet without a change to the money supply, had the goods been consumed in other production, the implied economic growth would decrease prices; and if the goods had been consumed in leisure, the implied economic contraction would increase prices. In other words, the above conclusion is perfectly reversed. The money relation is preserved because of money production and would change due to lack thereof. This error then infects dependent theories.

As against this reasoning one must first of all observe that within a progressing economy in which population figures are increasing and the division of labor and its corollary, industrial specialization, are perfected, there prevails a tendency toward an increase in the demand for money. Additional people appear on the scene and want to establish cash holdings. The extent of economic self-sufficiency, i.e., of production for the household's own needs, shrinks and people become more dependent upon the market; this will, by and large, [p. 415] impel them to increase their holding of cash.

In other words, economic growth alone changes the money relation - a direct contradiction of the preceding statement.

Thus the price-raising tendency emanating from what is called the "normal" gold production encounters a price-cutting tendency emanating from the increased demand for cash holding. However, these two opposite tendencies do not neutralize each other. Both processes take their own course, both result in a disarrangement of existing social conditions, making some people richer, some people poorer. Both affect the prices of various goods at different dates and to a different degree. It is true that the rise in the prices of some commodities caused by one of these processes can finally be compensated by the fall caused by the other process. It may happen that at the end some or many prices come back to their previous height. But this final result is not the outcome of an absence of movements provoked by changes in the money relation. It is rather the outcome of the joint effect of the coincidence of two processes independent of each other.

This is a refutation of the idea of money creation as a "stimulus" to growth, which is correct. Yet it incorrectly assumes money demand and money creation are independent processes. They are explicitly dependent as expressed in the money relation and the law of supply and demand which it echoes. The effect of unrelated interactions is perfectly reversed in this argument, as it can only mask the money relation. Stimulus is a reversal of cause and effect, properly refuted, yet it is an error to both accept the money relation and reject it.

The underlying inflation error, like that of the regression theorem, may arise from an understandable desire to explain the adverse effects of monopoly money. Yet in the purely rational system of catallactics, any error in deduction produces inconsistency, which is evident in this case. Market money is subject to monetary inflation, yet produces no price inflation. Monopoly money is similarly subject to monetary inflation, but produces price inflation - solely due to the monopoly on production. Mises overgeneralizes that all monetary inflation is price inflationary.

Prices also rise in the same way if [...] the demand for money falls because of a general tendency toward a diminution of cash holdings. The money expended additionally by such a "dishoarding" brings about a tendency toward higher prices in the same way as that flowing from the gold mines [...]. Conversely, prices drop when the supply of money falls [when] the demand for money increases (e.g., through a tendency toward "hoarding," the keeping of greater cash balances).

All money is always owned by someone. Under the above assumption of no money creation, a greater "cash balance" for one person implies a lesser for another. Increased money hoarding implies only a decreased present demand for goods relative to anticipated future demand. Decreased hoarding implies only increased present demand for goods. It is not as if money has been sewn back into the earth. There is no cost of "dishoarding" (trading the money), so doing so is unlike money "flowing from the gold mines".

A generally increased level of hoarding gives the impression of greater wealth, but this is illusory. In order to be of value to people money must be traded for goods, at which point the illusion evaporates. Unlike with mining, the effect of dishoarding is uneven. The first to do so obtains the highest exchange value and the last the lowest. The speculative strategy of "pump and dump" is based on exploiting this unevenness. Wealth is transferred, not created.

Furthermore, increased hoarding implies higher time preference, which is the ratio of hoarded capital to loaned capital (capital ratio), reflected as the interest rate. This is increased time cost, not increased capital value. The same amount of goods exist (wealth) at the point where hoarding increases. Yet this increase proportionally reduces production, due to increased cost of capital. This creates a permanent and compounding reduction in wealth, as the time lost in production is never recovered even with subsequent dishoarding. If all money was hoarded for a decade (assuming no reversion to barter), people may dishoard only to find their money has lost significant value due to the dramatic reduction in the amount of goods.

Independent of economic growth (or contraction), a change in demand for a market money implies a proportional change in demand for, or supply of, goods traded for the money, as opposed to another money or barter. The supply of goods is the level to which the money is accepted in trade for them. A money exhibits monetary value only in its ability be directly or indirectly exchanged for things of use value, as directly implied by the money relation itself. The value of a money derives from people willing to accept it in trade (i.e. the economy). Given the fungibility of money, selling the money to another person implies no change to this acceptance.

To the extent it pertains to commodity money, this principle assumes that the amount of goods required to produce the money remains constant. The price of goods in the money is thereby held constant by the money relation. However, where the amount of goods required to produce a commodity money increases or decreases, decrease or increase of prices in the money is implied respectively. Therefore, independent of demand, the money relation is controlled by the rate of change in necessary production factors. Such changes are presumed to be unpredictable, as otherwise they are already incorporated into price. As such this constitutes speculative error.