THE "MONETARY EXPRESSION OF LABOR"

IN THE CASE OF NON-COMMODITY MONEY

by Fred Moseley

fmoseley@mtholyoke.edu

It is well known that Marx assumed in Capital that money is a produced commodity, such as gold. However, the question remains open: was this assumption an essential part of Marx's theory or just a historical contingency, which Marx assumed because he was trying to explain the actual capitalist economy in the 19th century. Some critics have argued that money must be a commodity in Marx's theory as a theoretical necessity (e.g. Lavoie 1986), and argue that the fact that money is no longer a commodity in today's economy contradicts Marx's theory. Therefore, these critics conclude that Marx's theory of money is invalid, or is no longer applicable to modern capitalism with non-commodity money.

In considering this criticism, it is important to distinguish between the different functions of money (which is not always done), and especially between the functions of measure of value and means of circulation. It is clear that money as means of circulation does not have to be a commodity in Marx's theory, as Marx himself emphasized (Marx 1867, pp. 221-27, and Marx 1859, pp. 107-22). The only question is whether money must be a commodity in Marx's theory in its function as measure of value.

I argued in Moseley 2004a that money does not have to be a commodity in Marx's theory, even in its function of measure of value. The measure of value does not itself have to possess value. Pure paper money (not backed by gold in any way) can also function as measure of value. In order to function as the measure of value, a particular thing must be accepted by commodity- owners as the universal equivalent, i.e. as directly exchangeable with all other commodities. Until the 1930s, in the absence of any state-mandated alternative, commodity owners required that the universal equivalent (and hence the measure of value) had to be a commodity, or at least convertible into a commodity at legally defined rates. However, in the Great Depression it became impossible to maintain the convertibility of paper money into commodity money. Governments legalized the inevitable, and commodity-owners had no choice but to accept paper money by itself as the universal equivalent, and hence as the measure of value.1

However, this conclusion raises the important further question for Marx's theory: if social labor is represented by pure paper money, then what determines the quantity of money that represents an hour of social labor (since it can no longer be determined by the gold produced in an hour, as in the case of commodity money)? In other words, what determines the "monetary expression of labour-time" (MELT) in the case of pure paper money? Unfortunately, that question has not yet been adequately answered. As Duncan Foley (2004) expressed it, this important question has been "left hanging theoretically".

The aim of this paper is to suggest a way to determine the MELT in the case of pure paper money - a way that is consistent with Marx's general theory of money and is essentially the same as the Marx's determination of the MELT in the case of the inconvertible paper money of his time. In order to explain this method of determination of the MELT in the case of pure paper money, it is first necessary to review Marx's determination of the MELT in the case of commodity money, and then in the case of incovertible paper money of Marx's time.

1. Commodity money

In Marx's labor theory of value with commodity money, the prices of commodities are the exchange-values between all other commodities and the money commodity, and these prices are determined by the relative quantities of socially necessary labor time contained in all other commodities and the money commodity (e.g. gold). Algebraically:

(1)	Pi = (1 / Lg ) Li

where Pi is the price of each commodity, Li is the socially necessary labour-time contained in each commodity, and Lg is the labour-time contained in a unit of gold (i.e. the "value of money"). The inverse of Lg is the gold produced per hour, which determines the quantity of money new-value produced by one hour of socially necessary labour-time in all other industries. This quantity of money new-value produced per hour has been called the "monetary expression of labor time" or the "MELT":

(2)	MELT = 1 / Lg

Equation (1) can be rewritten as:

(3)	Pi = (MELT) Li

Thus we can see that the price of each commodity is proportional to the socially necessary labour- time contained in it, with the MELT the factor of proportionality.2

An important conclusion that follows from Marx's labor theory of prices has to do with the relation between the quantity of money in circulation and the total sum of prices of commodities. According to Marx's theory, the prices of commodities are determined as in the equations above, as functions of the quantities of socially necessary labour-time contained in commodities and gold. It follows that the sum of prices also depends on the sum of the quantities of socially necessary labour-time contained in all the commodities together (the Li's in the above equations), and is independent of the quantity of money in circulation (i.e. there is no M in the above equations for prices). Marx argued, to the contrary, that the realtion between the quantity of money and the sum of prices is the other way around: the quantity of money in circulation is determined by the sum of prices (P = Pi), along with the velocity of money, according to:

(4)	M* = P / V

Marx argued that the quantity of money in circulation would adjust to the sum of prices (i.e. to the "needs of circulation") by hoarding and dishoarding and/or by changes in the velocity of money.3

These quantitative conclusions are the basis of Marx's critique of the quantity theory of money of Hume and Ricardo, etc. Marx argued that the fundamental mistake of the quantity theory is that it considers money only as means of circulation, and ignores the other functions of money, especially the most fundamental function of measure of value, and also the function of store of value. We have seen above that, when money functions as the measure of value in order to determine prices, prices depend on the relative quantities of labour-time contained in commodities and money, and do not depend on the quantity of money in circulation. An autonomous change in the quantity of money does not result in a change of prices (assuming no change in the labour-times contained in commodities), but instead is offset by hoarding and dishoarding (as hoards, money functions as store of value) and/or by a change in the velocity of money.

2. Inconvertible paper money

Marx's theory of the relation between the quantity of money in circulation and the sum of prices summarized above assumes that money in circulation is either gold coins or tokens or paper money that is convertible into gold at legally defined rates. The case of inconvertible paper money is somewhat different. In this case, according to Marx, the MELT depends not only on Lg, but also on the ratio between the quantity of paper money forced into circulation (Mp) and the quantity of gold money that would be required if money were convertible into gold (M*, as determined by equation (4) above) (see Marx 1857, pp. 131-36; Marx 1858, pp. 119-22; and Marx 1867, pp. 221-26). Algebraically:

(5)	MELTp = (1 / Lg ) ( Mp / M* )

For example, if twice as much paper money were forced into circulation than is required for circulation on the basis of gold prices (i.e. Mp / M* = 2), then the MELT would double and hence the prices of all commodities would also double. Marx argued that in this case, the paper money does not represent labor-time directly, but only indirectly through gold. In the above example, twice as much money would represent the same quantity of gold money required for circulation, and this quantity of gold money would continue to represent the same quantity of socially necessary labour-time contained in commodities.

If the paper money exceeds its proper limit, i.e. the amount of gold coins of the same	denomination that could have been in circulation, then ... it will still represent within the	world of commodities only that quantity of gold which is fixed by its immanent laws. No	greater quantity is capable of being represented. If the quantity of paper money represents	twice the amount of gold available, then in practice $1 will be the money-name not of 1/4	of an ounce of gold, but of 1/8 of an ounce. The effect is the same as if an alternation had	taken place in the function of gold as the standard of prices. The values previously	expressed by the price of $1 would now be expressed by the price of $2. (Marx 1867; p.	225)

Therefore, in the case of inconvertible paper money, Marx's theory is similar to the quantity theory of money, in the sense that the quantity of money is an exogenous variable that determines prices (in part). However, Marx's theory is still significantly different from - and superior to - the quantity theory in the following respects: (1) according to Marx's theory, the quantity of money does not determine prices directly, but only indirectly through the MELT;

(2) Marx's theory also explains the necessity of money in a commodity economy, and the quantity theory does not; (3) Marx's theory explains not only the general price level (by the MELT), but also explains individual prices, as determined by the MELT and quantities of socially necessary labour-time, and the quantity theory does not; and, most importantly, (4) Marx's theory of money also provides the basis for a theory of surplus-value, and the quantity theory does not.

3. Pure paper money

I suggest that, in the case of today's pure paper money, with no reference to gold at all, the determination of the MELT is essentially the same as Marx's case of incovertible paper money just discussed (paper money denominated in gold, but temporarily not convertible into gold). As we have just seen, the MELT is determined in this latter case by equation (5):

(5)	MELTp = [ 1 / Lg ] [ Mp / M*]

M* in this equation is determined by equation (4):

(4)	M* = P / V

where P in this equation is the sum of gold-prices ( Pi ) that would obtain money were convertible into gold. These gold prices are in turn determined by equation (1):

(1)	Pi = Li / Lg

And the sum of these gold prices are:

(1')	P = [ 1 / Lg ] Li = [ 1 / Lg ] L

Therefore, if we substitute equation (1') into equation (4), and then substitute equation (4) into equation (5), we obtain the following interesting result:

MELTp = [ 1 / Lg ] [ Mp / M*]

= [ 1 / Lg ] [ Mp / (P / V)] = [ 1 / Lg ] [ Mp V / P ]

= [ 1 / Lg ] [ Mp V / ( L / Lg ) ] = [ 1 / Lg ] [ Mp V Lg / L ]

(6)	MELTp = Mp V / L

Thus we can see that, in the case of inconvertible paper money, the MELT does not ultimately depend on the value of gold (i.e. the labor time contained in gold, Lg). The MELT in this case is the product of two fractions, and Lg is in the denominator of one fraction and in the numerator of the other fraction, so that Lg cancels out in their product. Therefore, a change of Lg has no effect on the MELT. For example, if Lg were doubled, then (1/ Lg) would be cut in half, so that the net effect on their product (the MELT) would be zero.

I think that this conclusion provides the answer to the question posed at the beginning of this paper about the determination of the MELT in the case of pure paper money. In this case,

the determination of the MELT is quantitatively identical to Marx's case of inconvertible paper money. In both cases, the MELT is determined as in equation (6), by the ratio of the total quantity of paper money in circulation (adjusted for velocity) (MpV) to the total quantity of SNLT (L). The difference between the two cases is that, in the case of pure paper money, the MELT is determined by the quantity of paper money directly, not indirectly through gold, as in equation (5). But the magnitude of the MELT is the same in both cases: MpV / L.

The theoretical rationale for this determination of the MELT in the case of pure paper money, that is consistent with Marx's general theory of the necessity of money is the following:

It is a requirement of a commodity economy (i.e. a market economy) that one hour of SNLT must be represented by some quantity of money. The reason for this requirement is that labor in a commodity economy is not regulated directly and consciously according to a social plan, but is instead regulated indirectly and unconsciously through money-prices. In any type of society, the quantities of labor-time necessary to produce different goods must of necessity play a role in the allocation of social labor. However, since there is no direct regulation of social labor in a commodity economy, the only way the quantities of labor-time necessary to produce goods can play a role in the regulation of social labor is by being indirectly represented as the (average) price of commodities. That is why SNLT must be represented as quantities of money-prices in a commodity economy. (For discussions of Marx's derivation of the necessity of money from his labor theory of value, see Rosdolsky 1977, Chapters 5 and 6; Banaji 1979; Weeks 1981, Chapter 6; and Murray 1988, Chapter 14):

In the case of commodity money, one hour or SNLT is represented soley by the quantity of gold produced in one hour of SNLT (Lg), as in equation (3). In the case of inconvertible paper money analyzed by Marx, the quantity of money that represents one hour of SNLT depends on the quantity of gold produced in one hour and also on the ratio between the quantity of paper money forced into circulation (Mp) and the quantity of gold money that would be required if money were convertible into gold (M*), as in equation (5). Equation (5) reduces down to equation (6), so that the magnitude of the MELT in this case does not really depend on gold at all, but instead depends on the ratio of the total quantity of paper money in circulation (adjusted for velocity) (Mp V), to the total SNLT (L), as in equation (6). In the case of pure paper money, the quantity of money that represents one hour of SNLT is determined in exactly the same way as in the case of inconvertible paper money analyzed by Marx - by the ratio of the total quantity of paper money in circulation (adjusted for velocity) to the total SNLT (Mp V/L), as in equation (6).

In the case of pure paper money, there exists in the economy L, the total quantity of SNLT that must be represented by some quantity of paper money. On the other hand, there exists Mp V, the total quantity of paper money adjusted for velocity that is available to represent SNLT. Therefore, the amount of paper money that represents one hour of SNLT is determined by the ratio of these two aggregate quantities. In this way, paper money performs the necessary function of the measure of value: one hour of SNLT is represented by a definite quantity of paper money, which is determined by the ratio MpV / L.

4. Conclusion

In this paper, I have suggested a theory of the determination of the MELT in the case of pure paper money that is consistent with Marx's general theory of money, and is also quantitatively identical to Marx's theory of the determination of the MELT in the case of the inconvertible paper money of his time. Therefore, I conclude that the new monetary regime of pure paper money does not contradict Marx's theory, and that Marx's theory of money remains applicable to the modern monetary regime of pure paper money, as well as to the commodity money of Marx's day. Paper money functions as the measure of value, even though it is not a produced commodity.

This conclusion suggests that the debate over whether or not gold still plays a role in the function of measure of value in today's economy is less important for Marx's theory. Whether or not gold still plays such a monetary role, i.e. whether it is assumed that paper money represents SNLT directly by itself, or indirectly through gold, it does not make any difference to the quantitative determination of the MELT in Marx's theory. In both cases, the MELT is determined by the ratio Mp V / L, as in equation (6).

Campbell, Martha (1997). "Marx's Theory of Money: A Defense" in Moseley and Campbell

(eds 1997), New Investigations of Marx's Method (New Jersey: Humanities).

ENDNOTES

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