I finished Capital V. 1....Huzza!

Hi Khawaga,

As I think I'm the only libertarian Marxist in the reading group, it's good to know there are libcomrades out there willing to discuss issues re Capital, vol 2.

In our first session -- on chapters 1 & 2 -- one of the issues that came up touched on Marx's discussion of the transport industry. At first I was a bit confused when Marx opened his discussion of this topic by saying that this was an example of an economically important branch of industry in which "the product of the production process is not a new objective product, a commodity." (p. 135, Peng. ed.).

Then I became more confused when he claimed this was an industry in which "people and commodities travel together with the means of transport, and this journeying, the spatial movement of the means of transport, is precisely the production process..." (p. 136) Here, I thought he was conflating the production process and the consumption of the service consumed. However, then I realised that all he was doing was saying the in this case production and consumption occur simultaneously, as distinct from what happens with goods, which are only consumed after they are produced.

This seems to lead into his distinguishing what might be called end-point consumption of the services produced by the transport industry, and their consumption for further production, i.e., productive consumption -- which is an important aspect of his main theme in this chapter, viz., the circuit of capital.

So am I correct in the above reading, and in thinking that when Marx initially says that "the product of the production process is not a new objective product, a commodity" (p. 135), he is not denying that the services provided by the transport industry are commodities, and that he's only opening his discussion of this topic by merely marking a preliminary distinction between goods and services as a lead-in to how at least some services provided by the transport industry are in fact commodities which can be productively consumed?

Perhaps I've already answered my own question by thinking it through in the process of writing what I've just written, but it would be good to get others' opinions as it seems to have wider implications...

Thanks.

Hey,

I don't think it has wider implications, though the connection to service industries is of course valid in terms of individual consumption. The point Marx is making with transportation is that opposed to other forms of circulation activities (such as accounting, warehousing etc.), it is an actual production process that creates a new use-value (the change of location), is productive of value and thereby creates surplus value and increase the value of the commodity that is transported. Other circulation activities are not productive and are merely a cost to the capitalist and therefore deducts from the surplus value the capitalist can realize. So, while you can connect this argument to services, Marx is not making a distinction between goods and services, but a point about costs of circulation. And the commodity of change of location is not productively consumed; it is the commodity that is created while it is individually consumed (i.e. used up). What is productively consumed in the transportation industry are labour power, train tracks/roads, vehicles, fuel etc. The change of location commodity does not go into the production process of the commodity that is produced (although in the Grundrisse, he might make that point. His account of transportation in his notes seems to contradict vol. 2), which is why he argues it is a “continuation of a production process within the circulation process and for the circulation process” (Vol.2: 229).

It is helpful to consider the difference between the typical circuit of capital M-C(LP+MP)...P...C' - M' and the transport industry, which is M-C(LP+MP)...P...M'. That the commodity form is not formally assumed could be beneficial to capital (faster to go through circulation), but also negative (lots of sunken costs that requires to fill capacity).

I hope some of this helps.

Yes Khawaga, I think some of that helps, especially the reference to the quote on vol. 2, p. 229. The reading group I'm in hasn't yet reached the chapter containing that quote. (With Marx as with Hegel, I suppose it often helps to be made aware of what's ahead in the text in order to understand the part I'm reading now.)

I also appreciate your reference to the Grundrisse, where you say that Marx's "account of transportation in his notes seems to contradict vol. 2'. That's something I'll look into.

I suppose my more general concern with how Marx treats service industries comes from thinking how one could give a Marxist account of service industries today given their expansion under modern capitalism as part of the tendency towards the commodification of everything.

Yeah, there are some substantive differences from vol. 2. Part of it is that transportation doesn't appear to be a separate branch of production, that the commodity is not really a commodity until it is on the market (meaning that transportation is part of production only, but in Vol. 2 it is part of circulation as the real circulation underlying the formal circulation of capital). There's more, but I would have to look in my notes to remember.

Well, the post-operaismo folks have done quite a lot on that, though you'd have to wade through all the immaterial labour stuff.

Thanks for those comments Khawaga. Our Cap v2 reading group is discussing ch 3 and 4 at our next meeting. I haven't starting reading them yet, but it would help to know what I should be on the lookout for.

Anyway, I'm finding v2 hard work. It's all theory -- altho interesting theory -- and virtually no empirical or historical evidence so far! It's so unlike v1, which I found riveting. And they say v2 gets worse later on!

Even tho I'm used to reading heavy theoretical stuff, I'd never be able to read v2 outside of a group!

Yoda, nicely done. Congrats. About animals, you might be interested in this article -
http://libcom.org/library/beasts-burden-antagonism-practical-history

888, a theory of animal exploitation is not a theory of machinery exploitation, because animals aren't machines. And, "you could do X objectionable thing with a theory that tried to accomplish Y goal" is kind of a goofy form for counter-arguments, generally.

But from the point of view of Marx's value theory, which can be read as a form of vitalism, machines and animals are for all intents and purposes the same (that is, if animals can be used to produce relative surplus value), or at best animals are reduced to means of production.

I just bought Capital volumes 2 and 3, so I would be up for doing a reading group on volume 2.

Do one of you guys want to start a new thread called Capital volume 2 chapters 1 and 2 reading group or something, and copy and paste your comments so far? Otherwise I will do it when I get a chance. N.b. my copies haven't arrived yet so it will probably take me a week or two for them to arrive and for me to read the first couple of chapters

Funnily enough, Steven, so have I. 'Great minds' think alike, eh?

Mine should be here by Saturday or Monday.

But I've bought them as part of my studies concerning 'modes of production' and historical theory... and most certainly not for all that economic shit! I've got enough problems with volume 1, in that area.

Perhaps I'll leave the 'great mind' accolade to you...

LBird,Volume 2 is basically "pure" economic theory, so you won't get much out of it if you're interested in historical theory, though it is connected to modes of production but not in as a straightforward way as you might want it. Justing a warning...

Yup. And depending on how the categories are interpreted, the same goes for enslaved people (the conceptual equivalent of machinery). That reduction seems like a mistake to me, in both cases. I don't mean primarily morally or politically, either, I mean primarily at the level of truth and explanatory power. Animals, like slaves, are not machines. A theoretical perspective that is indifferent to that difference isn't necessarily a problem, depends on the details, but it seems to me a matter worth thinking a little about in terms of actual social dynamics. That is, we know animals and slaves aren't machines. The theoretical presentation of abstract capitalism/capitalism in general treats them as equivalent in certain circumstances. It seems to me that the theory does so more as a matter of stipulation than based on evidence. It may be that the equivalence is a sensible one but we don't really know whether or not they're genuinely equivalent in social practice in actually existing historical capitalism. (There's a fair bit of historical scholarship that suggests the equivalence here with regard to slaves is mistaken, at least for the 19th century, and we can't really understand that era unless we set aside the slaves-machines equivalence, because slaves were in that era variable capital rather than constant capital, though the theory might lead us to believe the opposite.)

I should also say, for whatever it's worth, I doubt there are political stakes to this and I don't see that this has any effect on the accuracy of the LTV for human labor.

edit:
Please let me know if the v2 group is a go, I've been trying to read that for ages but I suck at reading things on my own. I'm kinda struggling between parenting and work but I'd definitely try to participate if that group happens.

Thanks for the 'warning', but I'm already aware of the 'dangers'...

Within my reading of a number of Marxist theorists, the issue of how we identify a mode of production (with especial reference to the 'tax/rent', ie. 'tributary/feudal', debate) seems to constantly refer back to sections of Volume 3, so I decided I needed that for discussing historical theory and to allow me to read for myself the wider context of the Marx quotes which are given. From there, it seemed to be a short step to get 2 aswell, both for the sake of completeness (OCD coming out here), and because I just know some bastard theorist somewhere will refer to the economic shit, too!

Do you have any examples of people who would equate slaves (within a system of generalised commodity production) with constant rather than variable capital? I've not come across that interpretation before.

As you guys probably already know from my recent posts, I'm in a face-to-face Capital v2 reading group which has just commenced -- so I'm definitely interested in discussing it.

Whoops, fixed capital not constant capital. My fault. This article: "Slaves as Fixed Capital: Slave Labor and Southern Economic Development" by Gallman and Anderson. I've also had this argument with folk in discussions before. The crux of the argument I've had as I remember it was whether or not slaves produce surplus value, that's part of the equation with machinery. It can be a bit complicated because slaves were both laborers and a form of property -- slave prices in the US south quadrupled between 1810ish and 1860 and slaves became a well-regarded form of collateral for getting loans, so it really is plausible that one component of slaveholder wealth was more of a speculative/financier variety, but that's only *one* component of that wealth. There's a fantastic and highly readable book on some of this, if you're interested in slavery history, Gavin Wright, Slavery and American Economic Development.

In Marx's terms - fixed capital can only ever be constant capital

I can see how logically, an attempt could be made using marxian approachs to do such a thing (putting aside the fact that from marx's assumptions/perspective/idealised viewpoint of capital in Capital - a slave owning capitalist would be a contradiction in terms)

It would go somewhat like this:-

- a key thing about variable capital/labour power is that it can be sold & purchased as a commodity, separate from its natural owner.

- with a slave, the inherent labour power, along with the owner of it itself, is sold & purchased as one.

- from that point onwards, the ongoing labour of the slave is appropriated not economically through the dull compulsion of the market, as with variable capital/labour power, but through extra-economic physical/legal coercion.

- the slave (not just their labour-power) therefore becomes a commodity in its own right that can be re-sold etc..and is the same as any other type of fixed productive capital.

- also in line with other types of fixed capital - the maintenance & upkeep & repair of the fixed capital/slave falls to the capitalist owner to provide for directly, and not indirectly through the wage labour market as with variable capital/wage labour.

- so in this regard the slave is just another component part of the means of production.

However the key thing that all of this misses out is that surplus labour/value can still be appropriated. If a slave is actually bought as a commodity (and making volume 1 assumptions about the price/value that commodities exchange at) - then the value of the slave should be equal to that which was required to (re)produce it - which in turn allows for that commodity to add more value in the production process than that which it iself contains (in exactly the same way as with variable capital/ commodified labour power). So from that perspective, a slave is clearly variable capital, although a strange type of fixed variable capital (something which in marxian categories is a contradiction in terms). If however slaves were sold at the value which they were likely to add to the capitalist who buys them, then from that perspective they would be constant capital as they would purely be transfering their value to the finished product in the production process, not adding any additional value. However to get to this definition, you need to move away from standard definitions of what constitutes the value of a commodity and effectively define surplus value (and with it capitalism) out of existence as labour is then paid for at the (capitalised) rate in which it contributes value, rather than what it took to (re)produce it.

Marx, however, does say something close to slaves being constant capital in chapter 26 of volume 1:-

Free labourers, in the double sense that neither they themselves form part and parcel of the means of production, as in the case of slaves, bondsmen, &c., nor do the means of production belong to them, as in the case of peasant-proprietors; they are, therefore, free from, unencumbered by, any means of production of their own.

Although not explicitly saying constant capital, but typically the means of production in marx's terms specificaly refers to fixed constant & circulating constant capital - and excludes variable capital (whether circulating or 'fixed')

Well put.

About the compulsion of the market, I think that's an important point. Capital I is about an idealized capitalism for the most part, and as I read it the point is to show that a perfected capitalism would still be highly imperfect, to put it mildly. In the more historical moments Marx recognizes that among the actually existing working class at times there are legally disqualified workers who don't fit the bill as "free laborers" -- women and children. If we make too much of legal disqualification aspect (I think that's part of overestimating the silent compulsion of the market) then those people would also have to not be workers and would be engaged in something that's not capitalism. That seems silly to me, and it seems much more straightforward to say that actually existing capitalism is fully compatible with a range of labor practices of which free waged labor is only one.

Also want to add, there were slaves paid wages, rented out by their owners and sometimes working alongside free waged laborers, so in historical capitalism enslaved and waged have not always been opposites. In some cases slave owners would let their slaves keep a portion of the wages paid as an incentive for getting the slaves to do work. I know of at least one prominent African American abolitionist who eventually saved up and purchased his freedom this way, John Parker is the name I think though I'd have to check. Worked as some kind of metalsmith. (Incidentally, the growth of the insurance industry and the willingness of insurers to issue policies covering slaves probably played an important role in allowing this to happen, which in turn made slave-based production more lucrative and slave society in the US more flexible. Personally, that challenged some views I had about finance capital, I had tended to see it as simply reactive/lagging behind productive capital.)

About this --

I've re-read the last longish sentence a couple times and am still having trouble. Partly because I'm tired, but would you mind expanding on that?
On the first bit, about slaves being sold at the value they were likely to add, I have two thoughts on this that I'd like your opinion on, Oisleep. One, we'd have to look at if this happened. It's possible, but I'd want to see an explanation about why there was a rise in slavery that was compatible with this. Slaves producing surplus value is a simple explanation for a drive to expand slave production. Two, let's say we grant that slaves were sold at a price tied to expectations of the price of the final product. Clearly mistakes in estimation are possible. In any case where the seller made a mistake and underestimated final value of slave product, then that would be a condition where surplus value was produced: the slaves in those cases would be purchased for a value below the value of the products they made.
Right?

So on that idea of estimation of slave prices, I think there are only three general scenarios possible: the estimates made are, on average, correct. In that case, the next question would be explaining the expansion of slavery. Or, the estimates are, on average incorrect in that slaves were priced too low than actual value of products made, resulting in surplus value. That seems to explain the drive to expand, but the drive to sell slaves is a bit unclear. Or, the estimates made are generally too high, so slaves were overpriced. That would, I think, entail that slave buyers who expanded should be losing money, and so the expansion of slavery would really be puzzling.

It basically means, that the only way you could legitimately categorise slaves as constant capital would be if there was no inherent capacity to extract surplus labour/value from them. This can only come about if we throw out marx's definition of the value of a commodity (i.e. the labour that it took to produce it) and instead define the value of a commodity as the capitalised amount of future value that this commodity will provide to the capitalist in the production process, i.e. the slaves value would have to be based on the capitalised amount of future value they would create, not the labour/value that was required to (re)produce a slave. This however moves completely away from a labour theory of value - so I guess what' i'm saying is that if you ditch the labour theory of value you could argue that slaves were constant capital - (if such a thing would have any meaning left after having done so - as on that basis what we currently class as variable capital would also become constant capital - meaning that value could never be appropriated from any kind of labour, and capitalism therefore wouldn't exist, but it does)

As to your points about estimation of the price of slave (and whether this is estimated correctly or incorrectly), this isn't really relevant at this level of abstraction of the discussion. Whether you approach the value of a slave (as a commodity) from the labour theory of value perspective or from a non-labour theory of value (i.e. capitalised value produced perspective), you'd still have the issue as to whether the market correctly priced that particular commodity - so it's irrelevant, imo, to the more conceptual discussion around slaves/constant/variable capital

Also even if we assume that surplus value can be extracted from slaves - it doesn't mean that it could ever be generalised/made widespread within the context of expanded reproduction capitalism, as that level of surplus value extraction would eventually come up against the problem of realisation

Probably not answered your point clearly - just passing through, so apologies if I don't get back on any responses you have on it

No worries, that's helpful.
About surplus value and expanded reproduction, isn't it controversial whether or no this is possible with waged labor as well? About slavery, I find that Gavin Wright book that I mentioned convincing on the argument that 19th century slavery was a form of capitalism, just a form with significantly different institutions. It's possible that there were internal dynamics making it inferior to waged labor but history doesn't furnish laboratory conditions for testing hypotheses. Slavery in the US was ended by military force, not economic power, so it's really hard to tell which was a more effective version of capitalism.

No worries, that's helpful.
About surplus value and expanded reproduction, isn't it controversial whether or no this is possible with waged labor as well? About slavery, I find that Gavin Wright book that I mentioned convincing on the argument that 19th century slavery was a form of capitalism, just a form with significantly different institutions. It's possible that there were internal dynamics making it inferior to waged labor but history doesn't furnish laboratory conditions for testing hypotheses. Slavery in the US was ended by military force, not economic power, so it's really hard to tell which was a more effective version of capitalism.

.

What did I say, Khawaga? I've just found John Haldon, discussing the meaning of 'Mode of Production, referring to Capital, Volume 2, p. 120 (Penguin edn.).

But, scanning the rest of the book, I'd say that your advice was generally spot on...

Hey Khawaga and all you Capital v2 readers out there.

In our Capital v2 reading group, we've just discussed chapters 5 and 6. There was some debate over the distinction Marx makes there between labour which is productive of value, and labour which is necessary for value to be realised but is not itself productive.

One viewpoint expressed in the group was that Marx is analysing and discussing the relationships between the circuits of capital and the circuits of circulation, in the larger context of distinguishing between and relating the spheres of production and circulation. Thus, from this perspective, productive labour is seen as belonging to the sphere of production, and unproductive but necessary labour to the sphere of circulation; so it is against the background of the larger distinction between production and circulation that the more specific distinction between the two types of labour was so important for Marx to make at this particular stage of his presentation in Capital.

The other view expressed in the group was that labour necessary for the realisation of value, although not directly engaged in producing material goods, should, contrary to Marx, be considered as productive labour, ie, that Marx was wrong on this point.

A third view expressed by an autonomist-oriented friend was that even if the distinction is valid, its significance has been fetishised by more orthodox Marxists.

People seemed to get quite worked up over this issue. What's the best way to interpret this part of Marx's theory? And why is it so important politically?

Hi Paul! I don't think the distinction has any political significance in relation to everyday struggles, but I do believe it is very important for the consistency of Marx's explanation of surplus-value (and its distribution from industrial capital to other spheres in the form of commercial profit, interest, rent etc.) and hence of capitalist reproduction. As such, I would see it as a theoretical abstraction, not a sociological/empirical category in the sense that every worker (or, more generally, every individual member of society) could or should be neatly pigeonholed into one or the other category (which is sometimes – unfairly, in my view – ascribed by autonomist-influenced people to "orthodox" marxists who wish to keep this distinction).

You may want to try searching around the libcom forums for arguments and explanations relating to the distinction. It has been debated over and over again, without a clear conclusion (at least in my view), but some of the debates were quite interesting. The positions expressed in your group pretty much reflect the various sides of the debates here on libcom. I would see my own position as close to the one first you mention, although the productive/unproductive labor distinction is not related only to the production/circulation distinction. Marx discusses the other aspects of it in the Theories of Surplus-Value (Vol. 1), as well as elsewhere.

With regards to the productive/unproductive distinction I would do as Jura suggested. Look up old threads on libcom. It's a recurring problematic. Often it is discussed in terms of domestic work (i.e. reproductive work) rather than circulation work, although that comes up from time to time.

One key thing to do is also to really understand what Marx means with productive and unproductive labour. For this I suggest visiting certain passages from Vol. 1, Grundrisse, Immediate results of production (the appendix to Vol. 1) and the theories of surplus value. Can't provide page #s now because I simply don't have time to look up this stuff in my notes.

Yes, the topic's been batted back and forth a lot here.

Call me a brutish functionalist but I see Capital as useful either as a political economic portrait of capitalist social relations or as a (at least indirectly) predictive a tool [Edit: or some combination but I know what useful quality you could add]. I can't see the logical consistency mentioned by Jura as serving either of these purposes. (I more or less continue this rant at http://libcom.org/forums/theory/strategic-sectors-working-class-usefulness-marxs-capital-10082011 )

And the same debate can be found here along with other discussions: http://libcom.org/forums/theory/how-does-advertising-affect-value-18072011

Older and maybe not as interesting: http://libcom.org/forums/thought/productive-versus-unproductive-workers.

The question of productive labor in Marx's Capital has certainly forced me to grapple with the question of Marxism as a historical force.

It seems to me now one would have to distinguish "Two Marxs" (not necessarily young versus old). To put it in terms of simplistic caricatures, one Marx outlined capitalism and communism as qualitatively incomparable systems based on incomparable social relations - to get from capitalism to communism requires thus a rather fundamental rupture. The other Marx outlined the distinction between capitalism and communism quantitatively. There is a neutral domain of distribution that can be used to decide whether you have capitalist distribution or communist distribution. Capital, the text, in this quantitative perspective is an ethical argument that capitalist class contributes nothing positive, nothing productive, to the production process. It is an answer to the "Holy Trinity" and similar such arguments (which indeed appear in more and more bedraggled forms under capitalism, see Ayn Rand etc). I suspect that Marx viewed that a "dialectical" unification of the two perspectives was possible but I believe that history has mainly demonstrated that such

And I'm saying all this is a non-expert in Capital-the-text. On the interpretation side, still staying a non-expert, it seems hard to believe Marx did not see Capital as having a strong political component. Perhaps indeed the category "productive labor" is useful now purely for consistency, I don't see how could interpret Capital historically and not see "productive labor" as not having a political implication. But hey, if someone wants to tell how, go ahead.

Sure, an inconsistent "political economic portrait of capitalist social relations" or an inconsistent "predictive tool" will be extremely useful .

I'm all for discreet, logical consistency. It is just that I can't see you arguing for that. It seems more like you're arguing for something else, something akin to an argument which answers counter-arguments.

IE, when I traces the long, earlier argument Jura and I already have had, starting here and continuing here, I find that Jura begins with [without it]" the whole theory of value falls apart" and ends with "the door is wide open to vulgar theories..". I would object that even if the removal of the productive/unproductive distinction does "open" this "door", this is not a logical inconsistency. It would be (according to the argument) a "weakening of the argument" but that is a different beast in the world of logic and rhetoric.

Perhaps, the formulation you would want to make would be that discarding the productive/unproductive distinction would make the theory so ambiguous as to be meaningless?

I apologize if this post seems like it is attacking your choice of words rather your inherent argument. I would a see logical consistency and answering counter-arguments as two distinct activities whose place bares discussion. If the distinction in your writing is just an artifact of your choice words, it is still useful for us to clarify what we're talking about.

OMG! What have I stirred up? I already knew people get worked up over these issues -- I said as much in my previous post.

I don't have a stake in this dispute; I'm just seeking some outside guidance on how to interpret Capital v2 as I read through it for the first time with my reading group.

Get real, guys! Please, less heat, more light!

Now I'm confused!

RedHughs, in the first post, you say:

Which seems to imply that you thought that a theory with predictive capabilities or a description of social relations need not be logically consistent. Now you've apparently taken a U-turn and say logical consistency is fine but... exactly what? To me, if something makes a theory "so ambiguous as to be meaningless", it is basically the same as making it logically inconsistent (contradictory): inconsistent premises validly entail any conclusion.

Anyway, here's an attempt to argue for the importance of the distinction:

Marx concecptualizes commercial profit as the difference between the retail price (at which the merchant sells the commodity to consumers) and the wholesale price (at which the merchant buys from the industrial capitalist). Presupposing a general rate of profit R, the wholesale price is deteremined as

WP = Kp + R(Cp),1

where Kp is the cost of production (constant + variable capital), R is the general rate of profit, and Cp is the sum of industrial capital.

The retail price is determined, presuppsing that circulation costs are zero, as

RP = WP + R(Cc),

where R is, again, the general rate of profit, and Cc is the sum of commercial capital.

Commercial profit then equals RP - WP.

What Marx's conceptualization of commercial profit basically says is: Commercial capital engaged purely in activities in the sphere of circulation does not create any surplus value. Instead, a part of the total surplus value (created by total industrial capital) is distributed to commercial capital and appears as the difference between the wholesale and the retail price.

Marx analyzes interest and rent in a very similar fashion: they are parts of the total surplus-value (produced by total industrial capital) acquired by financial capital and resource-/landowners. In other words, they are parts of the total unpaid labor expended by workers employed by industrial capital.

This whole conceptualization rests on the fundamental distinction between activities that (within a specific context) are productive of surplus-value and those that are not. If this distinction collapses, Marx's analyses of commercial capital, interest, rent, in other words, the analyses of sources of income – the critique of the "Trinity Formula" – go with it.

In other words, if you argue for getting rid of the distinction, then fine, but I expect you to provide a new theory of commercial capital, interest and rent, because the existing one becomes inconsistent.

I'm all for criticizing or correcting Marx, but I think one always has to think about how a seemingly simple change in the theory affects its other parts. Otherwise, the theory turns into rhetoric. Like in the hands of the autonomists: "All labour produces value for capital and we all struggle against value", as the title of an article by David Harvie goes, makes for a great battle cry, but as a theoretical statement it renders the critique of political economy completely useless and untenable.

• 1. Taken from Fred Moseley's "Marx's Theory of the Distribution of Surplus-Value", published in Moseley, F. & Campbell, M. (eds.) New Investigations of Marx's Method, 1997.

@jura:

That you very much for the detailed reply. I was indeed a bit sloppy. In my first comment, I should have said something like "what Jura labeled 'logical contradictions'". In any case, a term something "a position so ambiguous that it makes the theory meaningless" would be an objection that I could understand and which seems to me to make your objection understandable.

Anyway, now I will try to answer your argument...

Overall: I can't see a relation between the quantities presented and final conclusion... Unproductive labor and the activities of commercial capitalists are distinct things. A capitalist is not a cashier or a bookkeeper or a security guard.

If a commercial capitalist happened to employ some amount of "unproductive labor", say, a bookkeeper or cashier, then that is an expense and they have to pay for it. Moreover, it would go into their overall basket of expenses and so come out of their starting expenses, their initial capital outlay. They would expect to make a profit on this outlay and this unproductive expenditure would play the same formal role as the industrial capitalist's investment in labor.

Either the capitalists treat all their outlays as requiring profits and thus treats productive and unproductive labor pretty much exactly the same or the capitalists fail to maintain a uniform rate of profit.

In more detail

Let me first give a non-equation argument before diving into equations: Suppose a commercial capitalist serves two markets. In one market, the consumers are dishonest and the commercial capitalist must hire security guards to the protect the goods while they are sold. In the other market, the consumers are honest but live on a large hill and the commercial capitalist must drivers to transport the goods up the hill. The wages of the drivers and the security guards are the same, the resulting prices in each location are the same. In our formalism, the security guards are "unproductive" and the drivers are "productive". But all the prices involved are the same and resulting goods distributed are even the same. So any equation is going to look the same.

Let us assume we have a basic capitalist system with a fixed period of investment and a fixed rate of profit R, we have a process which consists of M-C...C'-M. Here. every capitalist buys commodities, engages in production, commerce or whatever, then sells the commodities and gets money to cover their initial outlay plus a given profit.

Assuming all our capitalist succeed, the price of the commodities they wind up with is (1 + R)(V +C). Here, V is the variable capital, labor they invest in and C is the constant capital they invest. I believe all this is more or less as outlined in the earlier chapters of Capital III, before any discussion of financial capital begins.

The thing is, if merchant capitalist is simply a capitalist who simply holds commodities without changing them at all, for whatever reason, then the value of the commodities he holds in this model is going to be (1+R)C. There's no problem as long Cp and Cc are adjusted accordingly. And if they aren't, the resulting system is simply out of balance.

All this is once-again drifting towards the "transformation problem" - and take note guys, I was not the first one who started with equations-for-arguments here.

A small amount of Google seemed to indicate that Fred Mosley, the author Jura cites above is an academic who works the Bortkiewicz-Sweezy approach but with certain modifications (see here) ... For all I know, I those modifications might indeed be used to preserve some distinction between financial capital and other capitals as well as between productive and unproductive labor. But this is all still within said accounting of Bortkiewicz-Sweezy, an interpretation which doesn't inherently accept this productive/unproductive distinction as seen in the writing of David Laibman.

And yes, all this is crazy complicated and abstract and references all this stuff. Well, I try to keep things on the level of "what does this actually matter to revolutionaries?" but hey, maybe I fail or maybe I'm just following the direction of the argument.