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Saturday, December 31, 2016


I M Flaud [!!] offers the following comment on the first part of my discussion of expropriation and exploitation:  “Perhaps the definition of labor value is incomplete, if by linear algebra anything true about labor value is true about iron value or corn value. To put it differently, if some assertion one is expressing about X-values in some restricted language L come out "the same" whether X is labor, iron or corn, then this is evidence that L cannot express essential features of labor that distinguish it from iron and corn.”

That is exactly, precisely the correct conclusion.  Bravo!  It is the conclusion to which I came after I had proved the inadequacy of the Labor Theory of Value to explain the manifest fact that in a capitalist economy the workers get screwed [a technical term – sorry for the jargon.]  “Clearly,” I said to myself, “workers in a capitalist economy are getting the short end of the stick, but Marx’s explanation, invoking the distinction between labor and labor-power and all the rest, is wrong.  So what is the explanation?  What is more, how can we capture in our explanation the central feature of capitalism to which Marx devotes so much time in the opening chapters of Capital, namely its mystification of what is going on?”

So I went back to Marx’s text and looked again.  And there it was, as plain as day.  The workers in a capitalist economy get only a portion of what they produce by their skill and labor, because by a long historical process of expropriation, they have been denied ownership of their own means of production – of their tools, of their machinery, even of their skills – until all they have left is their labor, which if they wish to live they are compelled to sell in the marketplace as though it were a commodity whose natural price is the cost of its reproduction.  Why don’t farmers get to eat all the food they grow, after setting aside what is needed for seed?  Because they do not own the land and the farm tools.  Why don’t factory workers get to wear the clothing they make or to sell it to buy the food they need?  Because they do not own the wool or the cotton or the thread or the machinery with which they turn these materials into clothing.

How, I asked, can we capture this situation in a set of formal equations that explains exactly how the workers are getting screwed and simultaneously explains why in a capitalist economy it seems as though the workers are getting a fair return for their labor?  Here is what I came up with:

If we look carefully at the price equations in a simple capitalist model, we see [I go into this at length in my article] that formally speaking, labor is not modeled differently from any other input on the left side of the equations.  Oh, to be sure, we use the letter L or l to stand for “labor” but that is just a labeling convention, not a formal distinction.  No wonder everything we show about labor also can be shown for iron or corn or cloth.  They are all represented formally in precisely the same way in the equations.  But in the real world, there is a fundamental structural difference, which we ought to be able to capture mathematically.

Consider:  The ideology of capitalism says the worker is a legally free producer of the commodity labor.  OK.  Then in our system of price equations, let us have an equation for the labor producing industry as well as equations for the corn, iron, and cloth producing industries.  [Notice that in this approach, there is no need to formulate labor value equations.]  Now, in each equation, there is a term [1 + π ] which stands for the profit mark-up.  [π or the Greek equivalent of p is the one standard symbol for the profit rate.]  And the profit rate is the same in every industry because competition and the movement of capital in pursuit of the highest rate of return equilibrates the profit rate.  If a capitalist who makes high end jewelry for sale to the carriage trade is making 5% on his invested capital while a junk dealer is making 8%, then the quality jeweler will move his capital out of gems and into junk, because in a capitalist economy, all any good honorable capitalist cares about is his rate of return, not the social acceptability of his product.  [You understand that I am laboring mightily to communicate the math in as palatable a fashion as possible.]

But there is a big problem with the labor sector.  The worker, who is in this model a labor manufacturer, cannot move his capital to a sector with a better rate of return, because his capital is his body, and the only way he can cash in his capital and move it is … by cashing it in, which is to say dying!  So the worker, who by an historical process of expropriation has been deprived of his true capital, his tools and skills and land and raw materials, is compelled to remain in the labor producing business.  In other words, the worker has no choice but to get a job working for a capitalist.

When we set up the equations along these lines, with a separate rate of return in the labor equation, we find that the prices, and hence the rates of return, in the other sectors are skewed up by virtue of the fact that one huge sector, the labor sector, is frozen and cannot move its capital to compete [and thus drive down the prices and the rate of return] in all the other sectors.

How much does the labor sector lose by this structural rigidity?  Well, not surprisingly, what the labor sector loses is exactly mathematically equal to what all the other sectors gain.  In short, profit in a capitalist economy is the extra value taken from the workers by virtue of the fact that they have been deprived of their ownership of their capital.  Which is to say:


That, my friends, is the connection between exploitation and expropriation.


F Lengyel said...

The relative immobility of labor is compounded in the US economy by tying employment to health insurance. This is a structural reason for capitalist opposition to universal health care, the Affordable Care Act, etc, since such risk pooling arrangements shift relative rates of return in favor of labor. I will read your mathematical account (incidentally, I have a PhD in the subject--a foolish investment.) It's not surprising that Republicans want to dismantle the ACA and provide nothing to replace it.

Robert Paul Wolff said...

It is quite elementary math -- undergraduate stuff. But it passes for something in the parts of the Academy I inhabit. A good point about the effect of universal health care on labor mobility, although for other reasons france, with universal health care, has very low labor mobility, a problem they have been unable to deal with politically.

Why has it turned out to be a foolish investment?

F Lengyel said...

Applied mathematics doesn't have the same criteria for success as pure mathematics. I was disappointed by the relative lack of mathematical sophistication of the left--your book on formal methods in political philosophy led me to your site. Too much of the literature amounts to capitalist apologetics, or it remains silent on background assumptions. (There are exceptions, such as John Quiggen's Economics in Two Lessons--at least he makes opportunity cost the central organizing principle.) During the financial crisis I found myself in a discussion with a very senior Israeli game theorist on the subject of political economy. He mostly avoided the subject he said, at least professionally, since for him it concerned the control of natural resources and intellectual property, He didn't think game theory had much to say about it-as if it amounted to studying asymmetric zero-sum games that certain elites happen to be systematically winning against the rest of the population. But I think that was a missed opportunity.

I wasn't aware of low labor mobility in France.

Why was my PhD a foolish investment? Without being too specific, I was relegated to low-academic-value technical support work--I no longer volunteer, even for friends. Changing that impression would have been like retraining Pavlov's dogs. I had to leave.

Danny said...

let us agree to disagree on what is as plain as day.

Danny said...

I want to protest that I think 'real' economics is interesting, call me crazy. Ooops, I've already been called crazy, and that hurts my feelings. Indeed, maybe it's true. And it *is* true, if this makes any sense at all:

'Consider: The ideology of capitalism says the worker is a legally free producer of the commodity labor. OK.'

OK! ;)

'the labor sector, is frozen and cannot move its capital to compete [and thus drive down
the prices and the rate of return] in all the other sectors.'

Noting that the theory implied, here, is that the crucial factor in explaining why prices usually cannot be maintained at arbitrary set levels, is 'competetion'. But even people who would not deny this may nevertheless forget it when asking such questions as:
'Will lower production costs be passed on to the consumers in lower prices?' Actually, as I recall, Karl Marx pointed out that cost-lowering new technology *compels* the capitalist to charge lower prices, as a result of market competition. So, is technology the only reason for prices to be forced down by competition? No, competition is the key to the operation of the price-coordinated economy. Another example: when the airline industry in the United States went several years after 2001 without a single major plane crash, comptetition among
insurance companies forced the premiums charged to airlines to decline.

Competition, forces prices toward equality. competition, causes capital, labor, and other resources to flow where their rates of return are highest. And that is, where the unsatisfied demand is greatest. And that is, until the returns are evened out through competition, much like water seeking its own level.

Again, water seeks its own level. Sticking with the conceit, I might add that waves and tides are among the ways in which water seeks its own level, without being frozen at that level. So okay, there are these fluctuations, and they are relative to one another, and they are what move resources from places where their earnings are lower to where their earnings are higher. Or, again, from where the supply is greatest, relative to the demand, to where there is the most unsatisfied demand.

I'd emphasize, here, that I don't think you necessarily must introduce some notion of some ideal pattern of allocation of resources that should remain the same, and I don't see 'clear as day' that prices should remain the same over time.

Danny said...

Maybe we look at the price of petroleum in the world market. And with it the price of gasoline. We might consider, in this context, the notion of volitional pricing. I mean, of course, economics interactions are sometimes played into moral dramas. There are often complaints blaming high rental prices on “greedy landlords”, low wages on “bad employers” and rising oil prices on “unscrupulous traders” and “unscrupulous oil dealers”.

One may argue that prices are set volitionally, by the choice of the seller alone, or with massive weighting towards the seller. One may say that this is 'plain as day'.

The fact that prices fluctuate over time, and occasionally have a sharp rise or a steep drop, misleads some people into concluding that prices are deviating from their 'real' values. And maybe that is their usual level under usual conditions, or somesuch, and find find it to be 'plain as day' that this is 'more real', or I dunno, 'more valid' than
their much higher/lower levels under different conditions. Maybe people are selling their homes for less than their 'real' value' when a large employer goes bankrupt in a
small community, or simply moves away to another region or country.

Anyways, I started by mocking the suggestion that I consider that the ideology of capitalism says the worker is a legally free producer of the commodity labor. Mocking was the idea, but why am I mocking? Is this perhaps not utterly perspicuous. Well, so many words there are quite informally defined, while being terribly abstract. 'Commodity labor'. 'capitalism'. 'Legally free'. 'Producer'. 'Ideology'. Heck, even 'the worker'. I am asked to consider this, and I get no further than considering whether it means anything at all. Certainly it is not a Adam Smith's kind of a strawman, to my eyes. I ask for indulgence if I am belaboring an obvious point, here..

Anonymous said...

I was disappointed by the relative lack of mathematical sophistication of the left--your book on formal methods in political philosophy led me to your site.

The left and only the left has serious problems, it seems.


Anyway, this blog by Robert Vienneau (not your anonymous commenter) may be of interest:

Jerry Fresia said...

Indeed, brilliant contribution. For me this may be one of your best blogs ever; light bulbs turning on in my head. I'm not math adversed but I think by not using math in this blog, your concise summary simply draws in the reader. It did me! (Ironically, I suspect that the mobility issue was far more acute when Marx was writing.)

LFC said...

How does the historical process of expropriation deprive the worker of his skills, i.e., the specific things he's learned how to do?

Doesn't someone w skills that the contemp. capitalist economy values -- say, statistical or mathematical competence, or the ability to write software code -- have more bargaining power in the labor marketplace than someone w skills that are less valued, e.g. the ability to interpret a poem?

LFC said...

p.s. glancing now at your earlier post "Marx without Marx," I see you point out that many of the workers' traditional skills atrophied or disappeared w the introduction of machinery, so factory workers lacked skills their predecessors as artisans etc had.

Granted, and that answers to some extent the historical question. But it doesn't answer how this applies to a contemporary or at least partly 'post-industrial' capitalist economy.

Robert Paul Wolff said...

LFC, I have indeed answered the historical question [or rather Marx has. Much f CAPITAL is devoted to that answer]. I am now writing an additional post that addresses the second question.

Anonymous said...

So division of labor, or, in other words, the laborer's making use of his or her comparative advantage, actually works against laborers as a whole, is that right?

Also, the economy is a zero sum game?

Willard said...

Expropriation may correlate to the belief in GRRRROWTH:

> In 2015, according to PSZ [], the richest 1% of people in America received 20.2% of all the income in the nation. Ten points of that 20.2% came from equity income, net interest, housing rents, and the capital component of mixed income. Which is to say, 10% of all national income is paid out to the 1% as capital income. Let me reiterate: 1 in 10 dollars of income produced in this country is paid out to the richest 1% without them having to work for it.

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