# Questions about Marx's arithmetic in Capital Vol. II

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AnythingForProximity
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Sep 2 2019 04:27
Questions about Marx's arithmetic in Capital Vol. II

I recently finished reading Capital Vol. II in a non-English translation; I was also checking the text against the English edition available at marxists.org for passages that I found ambiguous. That mostly cleared everything up, but I still have two lingering questions about some of the numbers Marx used in his examples.

(1) In Chapter 4, Marx explains that capitalists (both individual capitalist producers and the capitalist class as a whole) throw a greater sum of values in the form of commodities into circulation than they withdraw from it; i.e., their supply of commodity value always necessarily exceeds their demand for commodity value. He then gives a numerical example (p. 198 in the Ben Fowkes translation / Penguin edition): c = £800, v = £200, rate of surplus value = 100%. I.e., with a capital of £1,000, the capitalist produces £1,200 worth of commodities. The idea is that both the capitalist and his workers buy from other capitalists, who (taken together) work "with the same capital and under otherwise similar conditions". Marx says: "his demand [covering strictly speaking only his constant capital, i.e. his demand for means of production] covers two thirds of their [other capitalists'] supply" – okay, his demand for £800 worth of means of production covers two thirds of their £1200 worth of supply, I can see that. But then he goes on to say: "his own total demand [i.e. including v, the articles of consumption bought by his workers] is only four fifths of his own supply, considered in value terms". But his own supply is £1,200; and (4/5)*£1,200 = £960, a number that I don't know where it could have possibly come from. Shouldn't that be £1,000, i.e., five sixths rather than four fifths?

(2) In the very last chapter ("Accumulation and Reproduction on an Expanded Scale"), my edition diverges from the English ones right at the end of the first example (p. 589 in Fowkes/Penguin). My edition gives 535 as the surplus value originally consumed by dept. II (original total = 1,035) and 958 as the surplus value consumed by it in the final year (final total = 1,690), yielding a ratio of 100:163. Both of the English editions (the Progress Publishers one at marxists.org and the Penguin one) give 600 originally (total = 1,100) and 745 in the final year (total = 1,477), arriving at a ratio of 100:134. The numbers given for the surplus value consumed by dept. I are the same everywhere (500 originally, 732 in the final year).

Now, if you follow all the calculations, it's not hard to find out that it's the "English" numbers which are correct. In particular, I have no idea how you can get 535 as the surplus value consumed by II at the start. Which leads me to a question: what's happening in my edition of the book? Are these Marx's original numbers, which were quietly replaced in the English editions to make the results numerically correct? Or is it the other way around, and my book had an overzealous editor who for some reason decided to "correct" the right numbers to the wrong ones?

I'm not pretending these are questions of great importance – I'm just curious, that's all.

zugzwang
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Sep 2 2019 19:35

I'm also wondering about (1), if anyone can shed some light there. If total demand were 800 and supply 1000 then 4/5 of 1000 (supply) would be 800 (total demand), but that doesn't make any sense... He repeats the same four fifths thing later on:

Marx wrote:
We now come to reproduction. Let us assume that the capitalist consumes the entire surplus-value m and reconverts only capital C of the original magnitude into productive capital. Then the demand of the capitalist is equal in value to his supply; but this does not refer to the movement of his capital. As a capitalist he exercises a demand for only four-fifths of his supply (in terms of value). He consumes one-fifth as a non-capitalist, not in his function as capitalist but for his private requirements or pleasures.

His calculation, expressed in percentages, is then as follows:

Demand as capitalist . . . . . . . . . . . 100, supply 120
Demand as man about town . . . . . . . 20, supply —
_________________________________________
Total demand . . . . . . . . . . . . . . . . 120, supply 120

4/5 of 120 doesn't give 100...

jura
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Sep 3 2019 20:22
AnythingForProximity wrote:
"his demand [covering strictly speaking only his constant capital, i.e. his demand for means of production] covers two thirds of their [other capitalists'] supply" – okay, his demand for £800 worth of means of production covers two thirds of their £1200 worth of supply, I can see that. But then he goes on to say: "his own total demand [i.e. including v, the articles of consumption bought by his workers] is only four fifths of his own supply, considered in value terms". But his own supply is £1,200; and (4/5)*£1,200 = £960, a number that I don't know where it could have possibly come from. Shouldn't that be £1,000, i.e., five sixths rather than four fifths?

I get how this can be confusing, but it's not a mistake. The trick is to think about a part of the surplus value as forming a part of total demand of the capitalist vis-a-vis other capitalists. Assuming that organic composition does not change, the 200 squeezed out in surplus value value will be divided in the same ratio as before, i.e. 160c and 40v. Now, adding 160c to the original 800c, we get 960c as that capitalist's total demand. And this is 4/5ths of his total supply (i.e. 4 : 5 = 960 : 1200).

Edit: I've looked at this again and it might be just a mistake. My "solution" reduces capitalist's total demand to just demand for the means of production. It works numerically but goes against the way in which Marx defines the capitalist's total demand before this passage.

AnythingForProximity wrote:
(2) In the very last chapter ("Accumulation and Reproduction on an Expanded Scale"), my edition diverges from the English ones right at the end of the first example (p. 589 in Fowkes/Penguin). My edition gives 535 as the surplus value originally consumed by dept. II (original total = 1,035) and 958 as the surplus value consumed by it in the final year (final total = 1,690), yielding a ratio of 100:163. Both of the English editions (the Progress Publishers one at marxists.org and the Penguin one) give 600 originally (total = 1,100) and 745 in the final year (total = 1,477), arriving at a ratio of 100:134. The numbers given for the surplus value consumed by dept. I are the same everywhere (500 originally, 732 in the final year).

I didn't run the calculations, but this was probably a mistake. The figures appearing in your translation are the ones used in the original 1885 German edition as reprinted in the MEGA. The figures from the English editions are the same as in the contemporary MEW24. The MEW editors simply left a note reproducing the original passage (from the 1st and 2nd edition, they say) with the same figures as in your translation, but corrected the figures in the body of the text.

Can you tell me what translation it is you're using? I guess it's pretty old or not based on any recent edition of MEW. For example, the Czech 1954 translation has the wrong figures as well. I'm pretty sure it was based on the then-contemporary MEW24, so the same mistake was there, too. However, the German MEW24 from 1963 already has the correct figures. So I'm guessing that the mistake was discovered sometime between 1954 and 1963 and duly corrected. None of the later editions in Slavic languages (all based on MEW) that I've looked at contain it.

jura
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Sep 3 2019 19:43

DP

jura
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Sep 3 2019 20:38

AnythingForProximity, you're definitely onto something . I've looked at the original manuscript as reprinted in MEGA II/11. Instead of 4/5ths, it says 5/6ths, in the case you quoted as well as in the one quoted by zugzwang (it's on pp. 681-682 if anyone wants to have a look). I then looked at the "Redaktionsmanuskript" (MEGA II/12), i.e. Engels' editorial manuscript that was the basis for the first edition (MEGA II/13). It says 4/5ths.

So for some reason, Engels "corrected" 5/6ths to say 4/5ths. Maybe Engels got confused in the first passage, correcting for added constant capital (as in my "solution"), i.e., treating total demand as total demand for constant capital. However, it doesn't really work in the passage quoted by zugzwang (since all of surplus-value is consumed), but he still corrected 5/6ths to say 4/5ths.

AnythingForProximity
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Sep 3 2019 21:18

Jura, thanks so much for your erudite replies!

jura wrote:
The trick is to think about a part of the surplus value as forming a part of total demand of the capitalist vis-a-vis other capitalists. Assuming that organic composition does not change, the 200 squeezed out in surplus value value will be divided in the same ratio as before, i.e. 160c and 40v. Now, adding 160c to the original 800c, we get 960c as that capitalist's total demand. And this is 4/5ths of his total supply (i.e. 4 : 5 = 960 : 1200).

Edit: I've looked at this again and it might be just a mistake. My "solution" reduces capitalist's total demand to just demand for the means of production. It works numerically but goes against the way in which Marx defines the capitalist's total demand before this passage.

This solution would make perfect sense, but one more reason why I think it's unlikely is that in order to break up the surplus value (and thus the capitalist's demand on other capitalists) into c and v, you'd have to assume that it was 100% capitalized – i.e. we would already be assuming reproduction on an expanded scale (on the maximally expanded scale, even), which doesn't seem likely this early on in the book.

Edit: oh, you just pointed that out as well.

jura wrote:
So for some reason, Engels "corrected" 5/6ths to say 4/5ths.

Heh, and Engels had the nerve to say that Marx was good at algebra but "did not get the knack of handling figures"...

jura wrote:
Can you tell me what translation it is you're using? I guess it's pretty old or not based on any recent edition of MEW.

I just sent you a message with the answer. Needless to say, your explanation is absolutely correct: the translation in question was indeed published before 1963!

zugzwang
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Sep 4 2019 08:19
Quote:
I get how this can be confusing, but it's not a mistake. The trick is to think about a part of the surplus value as forming a part of total demand of the capitalist vis-a-vis other capitalists. Assuming that organic composition does not change, the 200 squeezed out in surplus value value will be divided in the same ratio as before, i.e. 160c and 40v. Now, adding 160c to the original 800c, we get 960c as that capitalist's total demand. And this is 4/5ths of his total supply (i.e. 4 : 5 = 960 : 1200).

I'm not sure I follow that (probably just me). If the £200 gets accumulated on top of the £1000 wouldn't his total supply be £1440 then and not £1200?

C = £1200, 960c + 240v for a supply of C' = £1440, 960c + 240v + 240s

In any case, neat discovery about the 5/6 thing.

jura
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Sep 4 2019 10:13
zugzwang wrote:
I'm not sure I follow that (probably just me). If the £200 gets accumulated on top of the £1000 wouldn't his total supply be £1440 then and not £1200?

Yes, but only after the next iteration of production, right? I was thinking before that. Anyway, the manuscript shows my "solution" to be wrong.

zugzwang
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Sep 11 2019 13:57

Came across another error in the Penguin Edition, page 488 under the section "5. The Mediation of the Exchanges by Monetary Circulation", if anyone cares:

Quote:
Since the capitalists of both subdivisions spend their surplus-value 3/5
on products of IIa (necessary means of subsistence) and 2/5 on products
of IIb (luxuries), 2/5 of the surplus-value of (a), i.e. 240, is consumed
within subdivision IIa itself; similarly 2/5 of the surplus-value in (b)
(which was produced and is present in luxuries) is consumed within
subdivision IIb.

it should say "3/5 of the surplus-value of (a)" as it does here https://www.marxists.org/archive/marx/works/1885-c2/ch20_01.htm#5