[OPE-L] The lump of surplus value fallacy and the Moseley paradox

From: Jurriaan Bendien (adsl675281@TISCALI.NL)
Date: Fri Jan 11 2008 - 15:02:08 EST


In the Marxist literature I think there exists something like a "lump of surplus value fallacy". This is probably atributable to several factors: the analogy of surplus value with agrarian surplus, Marx's methodological assumption that the magnitude of surplus value available for distribution is fixed prior to exchange, and the application of accounting concepts to interpret Marx's analysis of the motion of capital. 

The fallacy is, that there is a fixed lump of surplus value, a bit like an economic "cake", from which different owners of capital take their cut. It is an appealing metaphor, which students can easily understand, but for a research statistician aiming to obtain empirical measures of economic surplus value either in money-units, labour hours, or stocks of outputs, this view of things is substantially misleading. 

Ironically, the same authors who argue that the wages of unproductive workers are a "deduction from surplus value" (which is actually literally an expression Marx uses in his manuscript) include those wages as a portion of surplus value, in their social account of gross product (e.g. Shaikh & Tonak, Moseley). 

From a mathematical point of view, this does not make much sense, since - at least as far as I know - a deduction cannot be an addition at the same time; that's a mathematical error. In the privacy of my own home I can turn a "-" into a "+" but I would not call that mathematical reasoning, more artistic interpretation. It's sounds "dialectical" of course (a negation of a negation) but it ain't good math. Subtraction is not addition.

For an economist, it does not make much sense either, among other things because it suggests that e.g. 

- productive workers who produce surplus value effectively fund the wages of unproductive workers who only redistribute it.
- some worker's wages are really profits, or surplus value.
- all unproductive workers' wages are paid out of surplus value produced by productive workers in the same accounting period. 

Lastly, for a Marxist firebrand it does not make sense at all. Why? It's because of the class struggle, you know. It would mean that unproductive workers effectively exploit productive workers, and that means, they really have no common interest but opposed interests. The unproductive workers live off the productive workers, not just because the latter produce the material goods they need, but because those material goods represent surplus labour of the productive workers. That cannot be correct, because Marx said the workers have common interests, and must work together to destroy capital. Sociologically this is of course hardly credible either, because the production of vendible commodities cannot occur anyway, without all sorts of supportive services.

What I call the "Moseley paradox" (which I think ultimately results from the lump of surplus-value fallacy) is, that every increase in paid unproductive labour boosts surplus-value, resulting in a rising rate of profit. 

I can prove this econometrically with just a simplified, easy-to-follow model of the increase in unproductive labour, where G=gross output, C=constant capital, V=variable capital, U=unproductive workers wages, P=generic profit, S=surplus value and R=the rate of profit. In this model, it is assumed that the only thing that changes in successive years is that U increases. As Marx recommends, we have to study things first in the simplest and purest cases.

Year 1:  G = 50C+10V+10U+10P. Since S = P+U, therefore S=20, and if R=S/(C+V) then R=33%
Year 2   G = 50C+10V+20U+10P. Since S = P+U, therefore S=30, and if R=S/(C+V) then R=50%

As you can see from the flawless mathematical reasoning, if the only variable that changes is that paid unproductive labour increases, surplus value increases, and the rate of profit increases. If, as a variation, there is a negative relationship between U and V such that if U increases, V decreases in the same proportion, then this boosts the rate of profit even more. I can prove that as well, as follows:

Year 1:  G = 50C+10V+10U+10P. Since S = P+U, therefore S=20, and if R=S/(C+V) then R=33%
Year 2   G = 40C+10V+20U+10P. Since S = P+U, therefore S=30, and if R=S/(C+V) then R=60%

As you can see, the result is that 60% is higher than 50%.

By implication, if the rate of profit falls because C+V rises more than S does, this cannot be because of an increase in paid unproductive labour, but in spite of an increase in unproductive labour. That is, if paid unproductive labour had not increased also, the rate of profit would have fallen even more. Thus, unproductive labour sustains the rate of profit, rather than reducing it. I can prove this as well, as follows:

Year 1:  G = 50C+10V+10U+10P. Since S = P+U, therefore S=20, and if R=S/(C+V) then R=33%
Year 2   G = 60C+20V+20U+10P. Since S = P+U, therefore S=30, and if R=S/(C+V) then R=37%
Year 3   G = 60C+20V+5U+10P. Since S = P+U, therefore S=15, and if R=S/(C+V) then R=18.7%

Of course, you could reply that I am not thinking dialectically enough. At one level of abstraction, a minus is a minus. But at a higher level of abstraction, a minus is a plus. I think there is something to be said for that idea in certain situations, it is just that I am not convinced yet that it is good economic science. But I will give you the benefit of the doubt. If for example you surf to NIPA table 6.21D, you will be able to see for yourself that during the years 2001-2004, undistributed profits in the US manufacturing sector were a negative figure, to a maximum of negative $71 billion, even although manufacturing profits stayed positive and by 2004 exceeded the level of 2000. So yeah, strange things can happen in economics, and where you'd expect a minus, you might find a plus, or vice versa.

Finally, of course you could object that I had it all wrong anyway, because the true Marxist formula is K=C+V+S and the U has nothing to do with that. Specifically, it is not true that S=P+U because Marx said S exists ontologically prior to P at a higher level of abstraction, and because Marx said that total surplus value equals total profits. So, the correct formula would be S=P, and therefore really the term P is redundant. It is just about S and only about S, the term P can only be introduced at a more concrete level of abstraction. But that still leaves the problem of "what are you going to do with the U ?". The U has to fit somewhere.

Hell if it was that easy to get into the Cambridge Review of Economics, I'd be home and hosed :-)


I just can't fit
Yes, I believe it's time for us to quit
When we meet again
Introduced as friends
Please don't let on that you knew me when
I was hungry and it was your world.

- Bob Dylan, "Just like a Woman""

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