LAST ONE, I PROMISE

Well, I said our last exchange was the final one, but here we are again.   This one really is the last one.  I think I at least am finally clear where Andrew and Alan Freeman and I part company, and since it at the initial stage of basic premises, there is really nothing more to be said.

May 13, 2014

Dear Bob,

Thanks for another very quick reply.

I agree that I am focusing on the restriction you have imposed, that there is never a negative physical surplus (or negative net output) of any produced commodity, not even momentarily. And I agree that this is probably not “what separates us.” I am not focusing on the restriction in order to pinpoint or discuss what separates us. I am focusing on it in order to make clear that

(a)    the “death spiral” justification for the restriction is untenable: economies can and do physically reproduce themselves when the restriction does not hold true;

(b)   the physicalist analytical framework implies that there can be positive surplus X-value but negative profit, and vice-versa, if this restriction is not imposed; and

(c)    it follows from (b) that it has not been and cannot be proven, within the physicalist analytical framework, that exploitation of workers (positive surplus X-value) is the exclusive source of profit.

As far as I can see, your latest reply does not address any of these points. I hope we can reach agreement on them, so that we can then move on.

To explain what I think separates us, I will begin by rephrasing a passage near the end of your reply in a form that we—Alan Freeman and I, and perhaps Chris Byron as well—can accept:

Let me repeat.  I do not think that Marx contradicted himself.  Quite to the contrary, I think when we cast what we take to be his claims in the particular mathematical form that the physicalist analytical framework requires––that is, when per-unit prices and “values” of outputs are constrained to equal per-unit prices and “values” of inputs, and prices and “values” are determined wholly independently––we can demonstrate that many of them [not all, to be sure] are correct compatible with the implications of the physicalist models. The problem is, all of the same claims, without exception, are also true of compatible with the implications of the physicalist models when one replaces so-called “labor-values” with iron-values, corn-values, and so forth.

So it really does not matter to me whether you construct models with net negative output for some input, because whatever you prove thereby to be an implication of the physicalist models when the “values” are iron-values, corn-values, and so forth can be replicated for physicalist “labor-values” simply by adjusting the example and the notation appropriately.  Thus, the supposed contradictions between Marx’s conclusions and the implications of the physicalist models you generate can be generated as well, under the same assumptions, for physicalist “labor-values.”

When recast in this neutral manner—such that it does not presuppose that Marx has been interpreted correctly or that compatibility with the physicalist analytical framework is tantamount to truth––what this passage says is basically what we said in our co-authored reply of a few days ago:

The above argument has demonstrated that, if one wishes to argue that “capital rests on the exploitation of the working class,” it is not possible do so validly by means of Wolff’s version of the physicalist model. Freeman and Kliman’s previous demonstrations have shown that it is also not possible to do so validly by means of physicalist versions of “the labor theory of value.”

The original version of your passage seems to suggest that Marx’s conclusion that surplus labor is the exclusive source of profit is simply incorrect. It’s not correct when we use corn-values, etc., but neither is it correct when we use “labor-values.” My amended version suggests something quite different, precisely because it does not presuppose that Marx has been interpreted correctly or that compatibility with the physicalist analytical framework is tantamount to truth.

If these presuppositions are incorrect, then it is possible that a non-physicalist interpretation and formalization of Marx’s arguments replicates the conclusions of his that the physicalist models cannot replicate—“under the same assumptions.” And it is further possible that this non-physicalist interpretation and formalization interprets Marx correctly. It follows that it is possible that the arguments of Marx that have been declared logically invalid (since his conclusions, it is alleged, are not deducible from his premises) are in fact logically valid.

We contend, and we think we have demonstrated beyond reasonable doubt, that these things are not only possibly true but actually true as well. This is what we contend regarding all of the alleged internal inconsistencies in the quantitative dimension of Marx’s value theory, including the inconsistency that allegedly renders untenable his own, original version of his exploitation theory of profit. Thus, as we said in our co-authored reply,

if one wishes to argue that “capital rests on the exploitation of the working class,” … there is a valid way to make such an argument––Marx’s way.

But Marx’s argument is logically valid only if it is interpreted properly, not misinterpreted in the physicalist manner. On the basis of the non-physicalist interpretation of which we are proponents, the temporal single-system interpretation of Marx’s value theory (TSSI), it does indeed follow validly that surplus labor is the exclusive source of (real) profit.^[[1]] A decade of debate confirmed this result beyond reasonable doubt.^[[2]]

This isn’t the place to set out the details of the TSSI or to place to reproduce all the proofs and our defenses of them, which is why I’ve included the footnotes to the passage just quoted. What I can do here is illustrate a key difference between physicalist interpretations and the TSSI. The question I will address is, “Does it matter which specific value-forming substance we ‘choose’?” We agree that it doesn’t matter within the physicalist framework. I want to show that it does matter within a non-physicalist and temporalist (i.e., dynamic) framework.

Consider a corn model in which returns to scale are constant. Corn is produced by means of seed corn and labor. Let A be the quantity of seed corn that is planted at the start of the year, L be the quantity of labor performed during the year, and X be the quantity of corn output harvested at the end of the year. Also, let V_c(s) and V_c(e) be the per-unit values of corn at the start and end of the year, respectively, and let V_L be the value added by each unit of labor.

The general form of the value-determination equation is

V_c(s)A + V_LL = V_c(e)X

 In the physicalist framework, the per-unit value of the output is constrained to equal the per-unit values of the seed-corn input. Thus, V_c(s) = V_c(e) = V*, and the value-determination equation becomes 

V*A + V_LL = V*X

so that

V*/ V_L  = L/(X – A)

This is the case whether we choose corn, or whether we choose labor, as the value-forming substance.

In a temporalist framework, there is no constraint that V_c(s) must equal V_c(e). However, if corn is the value-forming substance, then V_c(s) = 1 and V_c(e) = 1, so the value-determination equation becomes

A + V_LL = X

So that

V_{L =} (X – A)/L

and thus

                            V_c(e) /V_L = L/(X – A)             (since V_c(e) = 1)

Thus, in a temporalist framework in which corn is the value-forming substance, the relative per-unit values of corn and labor are the same as those of the physicalist framework.

But what about a temporalist framework in which labor is the value-forming substance? In this case, V_L = 1, so the value-determination equation becomes

V_c(s)A + L = V_c(e)X

and thus

V_c(e) /V_L  =  _­(V_c(s)A + L)/X

Now, the right-hand side of this last equation does not generally equal L/(X – A). Hence, in a temporalist framework in which labor is the value-forming substance, the relative per-unit values of corn and labor are, in general, not equal to

(a)     the relative physicalist per-unit values; or 

(b)   the relative temporalist per-unit values when corn is the value-forming substance.

It follows from (a) that, if Marx did not constrain output values to equal input values, then the results of physicalist models cannot properly be assumed to be the actual implications of his theory.

It follows from (b) that the specific value-forming substance does matter within a non-physicalist and temporalist framework.

Best wishes,

Andrew

---

[1] See Kliman (2001), chap. 10 of Kliman (2007), and Kliman and Freeman (2006, 2008, 2009).

[2] See Kliman and Freeman (2008) and Freeman and Kliman (2009).

 

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Dear Andrew,

I am rushing to write this while preparing to leave for Seattle where, on Saturday, my wife's grandson will be bar mitzvah'd.  As I am sure you will understand, this event takes precedence over merely settling the fate of capitalism.

Let me pass over your re-writing of some of what I have written and come directly to the eight lines of equations in the second half of your message.  You introduce what you call the temporalist framework  by distinguishing between the value of a unit of corn at the start of the year [which I take it means as input] from the value of a unit of corn at the end of the year [which, again, I assume means as output.]  The key to your analysis is your insistence that corn and other commodities that are both inputs into and outputs of production may have values as inputs that differs from their values as outputs.

However, in your fourth equation, which you say represents the situation, in a temporalist framework, where corn is the "value-forming substance," there is only a term for labor [represented in the equation by the letter L], not a term for labor at the start of the year and another term for labor at the end of the year.  If there were such terms, then the temporalist framework representations of a labor-value and corn-value analysis would be identical.

But, you may object, there is no labor industry;  labor is not a produced commodity.  So the distinction between the value of labor at the start and at the end of the production process makes no sense.

And suddenly it dawned on me why we have been unable to come to an agreement.  To put it simply, you and the Sraffians agree that labor is, as economists like to say, exogenous to the system.  It is given, it is not produced.  I, on the other hand, think that the only way to capture Marx's brilliant insight into the real nature of capitalism is to treat labor as a produced commodity. 

Well, you may once more object, if labor is a produced commodity, why doesn't the labor-producing industry earn the economy-wide rate of profit?  But that is not an objection to my analysis.  It is the whole point of my analysis!  Let me explain.  As I read Capital, Marx sees capitalism as thoroughgoingly mystified, precisely in order to conceal from view the fact that it rests on exploitation.  One aspect of this mystification is capitalism's treatment of the worker. In the marketplace, that "very Eden of the rights of man," as Marx puts it with brilliant irony, the worker stands "as owner of the commodity 'labour-power' face to face with other owners of commodities, dealer against dealer."  But of course this is a delusion, a mystification, as Marx goes on to show us, for as soon as he steps into the factory he is no longer treated as the producer of commodities, but as a wage-slave, chained to the machine.

The point of my effort to model labor as a produced commodity which yet does not earn a profit when it is sold was to find some way of capturing, in the equations, the anomalous status of labor in a capitalist economy.  I freely acknowledge that  I may have failed, but that is what I was trying to do.

From my point of view, you and the Sraffians against whom you argue agree on the one premise that I reject -- you both assume that labor is exogenously given.  Thirty years ago and more, when I was working on these ideas, Sraffa and his followers were the only game in town, or so I thought [I was unaware of your work -- perhaps you had not then begun to publish it].  Consequently, I directed my arguments against their modern reformulation of Marx's critique of capitalism.  Now that we have had this interesting series of exchanges, I finally realize that you share with Sraffa the very assumption that I rejected.  Not surprisingly, therefore, I am no more able to come to an agreement with you than I was with them.

In light of this fundamental difference between us about the premises of our alternative analyses of capitalism, I do not think there is any further we can go, so I am going to call it a tie and leave the field of battle.  I wish you good fortune in your on-going struggle with the Sraffians.  Perhaps if you and I are more fortunate than we have any right to expect, there will be barricades where may meet and join forces.

All the best,

Bob