May 11, 2014Dear Professor Wolff,
Thank you for another quick reply (to my reply to your reply to the co-authored reply to your initial blog post).
Last night, I finally guessed that you had a semi-positive vector of physical surpluses (or net outputs) in mind, so that when you specified that the surplus of X didn't have to be positive, you didn't mean that it could be negative. You meant only that it could be either positive or zero. That eliminates the apparent self-contradiction in your premises; I was wrong about that.
But this restriction of yours, which prevents there from being a deficit (negative surplus) of anything, doesn't help you to prove what I think you want to prove, that exploitation of workers (positive surplus X-value) is the exclusive source of profit. In fact, the restriction makes it impossible to prove that, as I said.
You can at best claim to have proved that if there is exploitation of workers and there is never a negative surplus of anything, then positive surplus X-value and positive profit will happen to coexist. But what you need to prove is that they coexist because there is positive surplus X-value, and to try to prove that, you would need to remove the additional restriction. And then you'd find that you still couldn't prove what I think you want to prove, because (as we've shown) profit can then be negative even though surplus X-value is positive.
This was the point of my concluding comment about sheep and arsenic, of course. You appreciated the comment, but as far as I can see, you haven't yet addressed the crucial logical point at issue. I say it's the crucial logical issue because the validity of your main conclusion is at stake. So permit me to ask you directly: do you accept that one has not proven that positive surplus X-value is either a necessary condition or a sufficient condition for positive profit if the only thing that one has actually proven to be necessary and sufficient is positive surplus X-value in conjunction with the restriction that there's never a negative physical surplus of any produced commodity? If you don't accept this, why not?
I trust that you understand that this is a point about logical validity of arguments, not a point about realism of premises.
My apple-broccoli example is definitely about capitalism. It refers explicitly to wage-labor and capital ("Workers are paid at the end of the day. ... The capitalists, who own the land ...."). Of course, real-world capitalist production requires non-labor inputs. I excluded them in order to make the example easy to follow and the computations simple. But it's easy to include them, and I will be happy to provide an example that does so, if you wish.
However, if you insist on rejecting any counterexample unless it's one in which there is never a negative physical surplus of any produced commodity, not even for a moment, there is obviously no point in working up a version of my apple-broccoli demonstration that includes non-labor inputs. It will still be the case that there is a negative physical surplus of something on every day (or hour, or minute, etc.) even though there is a positive physical surplus of everything over each two-day (or -hour, or -minute, etc.) period.
But the apple-broccoli demonstration does more than show that physicalist profit can be negative even though physicalist surplus X-value is positive and all physical surpluses are positive over every two-day (or -hour, or -minute, etc.) period. It also removes your justification for the restriction that there is never, ever, a negative physical surplus of any produced commodity.
In your blog post of yesterday, you justified this restriction on the grounds that, if there is a negative physical surplus of anything (even in one period), then the economy is incapable of reproducing itself physically. It's in a "death spiral." The apple-broccoli demonstration removes this justification because it shows that the economy can indeed reproduce itself physically, even if there is always a negative physical surplus of one of the two goods.
As far as I can see, you haven't yet addressed this aspect of the demonstration. So permit me to ask you directly: do you accept that it removes the stated justification for the restriction you wish to impose? If not, why not? (If necessary, I can provide a similar, but more cumbersome, example that includes non-labor inputs.)
Let me emphasize that here, too, realism of premises is not the issue. The issue is simply whether the existence of some negative physical surplus implies that the economy is in a death spiral.
Best wishes,Andrew Kliman
Thank you again for your message, and my apologies for the Google problems, which are far above my level of competence to do anything about.
I think our exchanges are producing clarity about the issues that separate us, if not agreement on them, and that is good. After reading and reflecting on your email message, it occurs to me that we are arguing somewhat at cross purposes.
You focus in your message very much on the "restriction" I have imposed that there cannot be a negative output in any line of production relative to the quantity of that input required in the system as a whole, but I do not think that is what separates us. Let me try to explain.
I start from Marx's claim that capitalism rests on the exploitation of the working class and that the ever-increasing wealth of the capitalist class is the direct consequence of that exploitation. I think Marx is correct about that, and I think he has correctly explained this on-going exploitation as the historical result of the separation of the great majority of men and women from access to or command over the land, the forests, the mines, the oceans, and even the knowledge and craft skill needed to wrest a living from nature. Marx thought that capitalism is mystified, in that it presents the appearance of equal uncoerced exchange in the marketplace between workers and employers, so that it is puzzling how capitalists can keep accumulating more and more capital while the workers who actually create that capital by their labor remain propertyless. Marx's solution to this puzzle is the distinction between labor and labor-power and the concomitant introduction of the concept of surplus labor value. Thus far, I would imagine, although I do not know, that we would agree.
When I began to study this subject more closely, I found that one can set up labor value equations that demonstrate that the labor value of the physical surplus in each cycle of production, a surplus that the capitalists appropriate in the money form of profit, exactly equals the surplus labor value extracted from the workers in the process of production. This seems quite dramatically to prove the correctness of Marx's claims, at least in the simple case in which there is equal organic composition of capital in all lines of production.
But it occurred to me that one can equally well set up iron-value equations or corn-value equations [or Botox, Gummi Bear, apples, or broccoli value equations], and that every single result provable about labor-value equations can, without exception, be proved in each of those alternate systems of equations. The distinction between labor and labor-power, which Marx thought was the key to unraveling the mystery, plays no role in the construction of the equations. There is of course no meaningful distinction between iron and iron-power or corn and corn-power, but that does not in any way invalidate the conclusions drawn in those systems of equations.
Now, when I arrived at this result, I did not conclude that Marx was wrong in claiming that capitalism rests on the exploitation of the working class. Not at all. I concluded that we need to find a more successful way of modeling what happens in capitalism, a way that captures the historical separation of workers from the means of production and that cannot be replicated for iron, corn, or any other non-labor input into the productive process. My rather tentative and [admittedly] rudimentary efforts can be found in the essay to which I have several times alluded, "A Critique and Reinterpretation of Marx's Labor Theory of Value."
Let me repeat. I do not think that Marx contradicted himself. Quite to the contrary, I think when we cast his claims in mathematical form we can demonstrate that many of them [not all, to be sure] are correct. The problem is, all of the same claims, without exception, are also true of 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 can be replicated for labor-values simply by adjusting the example and the notation appropriately. Thus, the supposed contradictions you generate can be generated as well, under the same assumptions, for labor-values.
There is a question to which I do not give much thought, but that agitates many people interested in this stuff. If I reject the Labor Theory of Value as Marx formulated it, can I call myself a Marxist? Well, Marx is long dead and the copyright has run out on that term, so I think it is in the public domain. I call myself a Marxist for two reasons. The first is that he remains my principal inspiration and guide in my on-going efforts to understand the world in which I live. The second is that it irritates people.
It remains only to thank you, Alan Freeman, and Chris Byron for taking the time to engage with me on these matters. I have enjoyed the back and forth and have learned from it.
All the best,