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Saturday, February 12, 2011


Here are the price equations of our corn/iron/tools model, revised so as to represent workers as petty commodity producers. In order to indicate that capital cannot be transferred from the labor producing "industry" to other lines of production, I introduce a new variable, r, to stand for the rate of "profit," if there is any, in that "industry.

( 0Pl + 30Pc + 15Pi + 0Pt )( 1 + r ) = 150Pl

( 60Pl + 128Pc + 2Pi + 3Pt )( 1 + R) = 240Pc

( 20Pl + 16Pc + 1Pi + 5Pt )( 1 + R) = 60Pi

( 50Pl + 6Pc + 27Pi + 4Pt )( 1 + R) = 16Pt

It is not necessary to specify the real wage because that is implied by the input quantities of the first line of production. This is now a system of four equations in six unknowns: Pl, Pc, Pi, Pt, r, and R. We reduce the number of unknowns to five by stipulating that corn is the money commodity, as before, setting Pc = 1. That still leaves one degree of freedom.

It is not difficult to demonstrate [see the essay referenced above] that r and R vary inversely to one another. That, note, is different, formally speaking, from showing that the wage and the profit rate in the old system vary inversely to one another, although the underlying facts are much the same. A non-zero r means that the workers have somehow managed to extract from the capitalists some portion of the surplus. But this way of representing things, besides making no reference to the Labor Theory of Value, also opens the way to economists like Gary Becker to introduce the notion of "human capital." Workers who, in effect, drive the wage above bare subsistence can either consume the extra in the form of a somewhat less miserable standard of living, or they can -- as Becker might say -- invest in the improvement of their capital stock [themselves] by paying for education, which will allow them to produce a new and higher priced commodity -- namely, skilled labor. This way of thinking, crazy as it is [Marx is brilliant on this], leads naturally to the countless discussions of the "return on investment in education' in the form of higher lifetime earnings.

Notice, by the way, that if we wish to continue with this charade of labor as a commodity produced by a petty bourgeois entrepreneur, we must allow for several labor sectors, each with its own particular "product" [some form of unskilled or skilled labor or educated labor] and with its own rate of return. We can even analyze a failure of some children of the educated workforce to take advantage of the opportunities provided by their parents as their choosing to consume the additional portion of the surplus made available to them instead of investing it, thus reproducing the fairytale about prudent and imprudent capitalists [ants and grasshoppers.] And, of course, the variation in the rates of return in the several labor sectors permits us to talk about the relative exploitation of unskilled workers by much better compensated skilled workers.

The point of all this is to elaborate on the fundamental verruckheit, or craziness, of the manner in which bourgeois ideology [law, economic theory, philosophy, sociology, etc.] mystifies and conceals the exploitative nature of capitalism, making it appear that the failure of the workers to improve themselves is attributable to their imprudence rather than to the disadvantageous position in which they find themselves vis-a-vis capital.

[A propos, Susie and I saw "Company Men" last night, an interesting movie about the effects of the economic crisis on three privileged and advantaged corporate executives -- Ben Affleck, Chris Cooper, and Tommy Lee Jones, with a nice turn by Kevin Costner. It is worth seeing, I think.]

It is not difficult to show, formally, that the total profit appropriated by the corn, iron, and tools sectors is equal to what is lost to the labor sector by its inability to shift its capital to a more profitable line investment.

I have now come to the end of my story, even though there is a very great deal more to be said about Marx's theories, some of which I have said at length in my two books and several articles on him. Let me explain why I have taken so very much time and expended so much effort expounding and analyzing the Labor Theory of Value, only in the end to show [with arguments original to Vegara and myself] that the theory is incorrect.

Part of the reason, to be totally honest, is that I simply find the analytics of the theory fascinating and elegant. My entire life has been spent taking impossibly difficult theories [such as those in Kant's First Critique] and clarifying them in my own mind until I can present them to others as clear, simple, elegant, and beautiful. My second reason is to rescue Marx from the unfounded criticism that he is -- in the infamous words of Paul Samuelson -- a "minor post-Ricardian autodidact." I was so offended by those words when I first read them that I felt a need to show, clearly and simply, that they were just not true. My third reason is that I believe one cannot really come to grips with the profound truth at the heart of Marx's critique of capitalism without first working through this theoretical story and becoming completely clear on its precise status and limits. Speaking simply for myself, I could not have been led to an understanding of the ironic structure of Marx's critique, and the core irrationality of treating workers as though they are participants in a free market of exchange among producers and consumers, had I not first made my peace, intellectually, mathematically, and theoretically with Marx's own attempts to capture that craziness.

I hope this tutorial has been useful to some of you. as I feared, it went on for a very long time, so long, I imagine, that I lost a number of readers along the way. But I have enjoyed writing it, and it will live forever in cyberspace, in the weird way things have of surviving in that realm.


Daniel said...

Professor, thank you so much. I was looking forward to the next instalment every day and I appreciate your clarity of style and the mixture of 'hard' and 'soft' theory. Unfortunately, your moneybags book is nowhere to be found in the UK, is there any chance you could make it available as an e-book?
With gratitude,
Daniel Rubinstein
London South Bank University

J.Vlasits said...

Thank you again for a great tutorial!

Matthew J. Brown said...

I've kept up with the tutorial and have very much enjoyed it. Thank you! Very interesting, and I'm very inclined to go read more of your work on Marx now.

skholiast said...

Possibly you lost some readers along the way, but you also picked some up, myself included. I salute your astonishing trepidation. It's a pleasure to read you "live," as it were, after going back to your Defense of Anarchism & your tolerance essay many times.

Anonymous Philosophy ABD said...

Daniel, try here:

and you'll find:

"# Title: Moneybags must be so lucky : on the literary structure of Capital
# Further information: Robert Paul Wolff.
# Publisher Details: Amherst : University of Massachusetts Press
# Creation Date: 1988
# Format: 82 p. ; 23 cm.
# Language: English
# Author: Robert Paul Wolff
# Subjects: Marx, Karl, 1818-1883. Kapital ; Marx, Karl, 1818-1883. Kapital -- Literary style ; Capital
# Identifier: ISBN0870236156 (alk. paper);ISBN0870236164 (pbk. : alk. paper)
# Source: OLIS
# Type: Book
# Snippet: Moneybags must be so lucky : on the literary structure of Capital / "

Unknown said...

Professor, thank you very much. I have enjoyed it thoroughly. I have a couple of questions, but suspect they are based on a misunderstanding. I will pass them along if I figure it out.

I would like to know how your theory has been received and whther you have encountered any common criticisms.

I very much look forward to the next series of tutorials. Thanks again.

Chris said...

Daniel check, it's there.

Thank you professor.

Chris said...

Found a link to several copies of the book. The cover is rather amusing.

john c. halasz said...

The are two problems here. There is the question of why labor-value should be chosen as a unit-of-account, when, formally speaking. any other basic input would yield the same result, that the numaire produces a surplus of output over its inputs. But there's a still more basic problem: why should the corn/iron model economy result in any surplus at all? The answer is that it is simply arbitrarily stipulated at the outset. But how is that different from the claim that any equivalence between labor-value and monetary price is an arbitrary stipulation and thus merely tautologous?

Of course, the corn/iron model is too rudimentary to be any actual economy, though one could jigger it so that the entirely consumable surplus were outputted as corn, (and, yes, I'm aware that the model is expandable to N-sectors with X- different choice of techniques-of-production). And, yes, any economy that produces a consumable surplus can re-invest some portion of that surplus in expanding production and output, thus increasing the consumable surplus. But the problem with the model is the static equilibrium conception of such "growth" in the model, which simply is a reiteration of the same input "recipes". But over greater accumulations of the same output from the same inputs will result simply in diminishing returns: there is only some much corn that anyone can eat.

john c. halasz said...

(Cont.) What is being represented by such a "balanced" growth model is the role of the reproduction schema. Since sectors/firms produce for each other long "before" they produce for final consumption demand, in order for any surplus-producing economy to sustain itself, let alone to grow, those produced inputs to production must be reproduced in their relevant proportions. This is a fundamental constraint on the economy's production system, one which is imposed on rather than derived from market processes, which may or may not be market mediated, (since markets can be at least partly replaced by vertically integrated firms). But because of the problem of diminishing returns, the process of "balanced" growth can't simply be one of reiterations of the "same" inputs producing increased outputs.(Nor is the sustainability of consumption and its distribution an irrelevant consideration). Rather the primary source of economic "growth" is, ceteris paribus, improvements in the technical means-of-production, innovation in processes and products, which raise the productivity of labor and increase the consumable/distributable surplus. Which means that the reciprocal input proportions of an economies reproduction schema, ceteris paribus, are constantly themselves changing, within and across production/business cycles.

Which is, indeed, a source of "trouble", since Marx is not intent on explaining why the process of economic growth is always balanced, based on an equilibrium of investment allocation, but rather on the long-run disequilibrium dynamics of the process of growth and the expansion of capital. Nor does the trouble necessarily derive from minimum subsistence wages, since with expanded output, rising real wages are needed to generate increased sales by capitalists, since aggregate demand is primarily wage-based. (That's one of those "contradictions"). It's the rooted asymmetry between profits and wages, rather than absolute or constant levels, that's the main driver in a profit-seeking system. (Just as there is a distinction to be made between absolute and relative immiseration, there is a corresponding distinction between absolute and relative surplus-value, with Marx' intent, I think, being that absolute immiseration only predominantly takes hold in depressions.)

john c. halasz said...

So now back to the first problem:
why labor-values as a unit-of-account and standard of value or numaire for the "system". After all, Sraffa's neo-Ricardan model eliminates labor as an input in favor of technical coefficients of production, that is, various "recipes" of inputs, each of which, within and between sectors, constitutes a discrete "technique of production", the choice of which is based on which is the cost-minimizing one, and only considers wages in terms of the inverse ratio between wages and profits in the distribution of the surplus-product as output, and the variable effects that might have, rather than a crucial input. And, indeed, if labor values are held to be constant and minimal, as merely the subsistence cost for the re-production of labor-power, then they might virtually be eliminated from the "picture", since such a constant and low cost as an input might not be what accounts for the variations and differentials between productive sectors.

Initially, labor-values were invoked A) to account for how commodities could be exchanged at equivalent "values", through a system of "natural prices" in long-period equilibrium, through the amount of labor "embodied" in each commodity. Such a system of "natural prices" is then supposed to account for the distribution of market incomes. And B) to explain the existence and intelligibility of profits, given that all commodities are exchanged at equivalent "values", through the distinction between labor-value and labor-power and the corresponding distinction between value and surplus-value. And it seems that the claims of A do require a B-type account.

I'll pause here to reflect that any overall schema of economic explanation is going to require some kind of unit-of-account and some kind of standard of "value", as reflecting preferences for "efficiency", the economizing of means/inputs in relation to output. Without insisting on any one such standard of "value", it will amount to something like a "principle of least effort", almost as the obverse of the thermodynamic definition of "work", whereby a technique-of-production that cost less overall effort to produce its output will be proffered to one that costs more effort, (which will likely be reflected in money prices as cheaper or dearer).

john c. halasz said...

(Cont.) As a first approximation, the amount of labor-effort required to produce something seems a reasonable choice of a standard of "value". But Marx is not simply repeating Ricardo, but rather systematically "critiquing" him. So A) his account is not quite Ricardo's one of embodied labor as a constant. Rather in Marx' account labor-values are determined by abstract, average, socially necessary labor time, which is not abstracted/extracted directly through the intentionality or activity of laborers, but rather through the competitive processes of markets, in which, crucially, there is a large supply of commodified labor-power compelled to sell itself "freely" to employers on the markets. But B) Marx doesn't hold to Ricardo's "natural prices" as identifiable with "value", but rather replaces "natural prices" with "cost-prices of production". And because, as indicated above, constant technical change is constantly changing the reproduction schema in a productive economy, cost-prices of production themselves are constantly changing about, (such that it is at least difficult to make out the long-period equilibrium assumption behind "natural prices").

The upshot is that Marxian labor-values are not the same constant, "embodied" labor-values of Ricardo. If Marx hold labor-values "constant" (per capital and ceteris paribus) that then means that a new labor-value which is twice as as productive as an old labor-value is nonetheless the "same", (though the unit "embodiment" of the labor-value of output has decreased, together with the unit cost of labor in output prices, which themselves also decline). And thus the labor "embodied" in older production gets devalued or depreciated just as much as the obsolete capital stocks it "embodies".

The upshot then is that in Marx' version labor-values tend to diverge from rather than converge on monetary prices. And that "contradictory" divergence between the two units-of-account plays a large role in Marx' explanation of the long-run disequilibrium and crises-ridden tendencies by which industrial capitalist economies "develop".

john c. halasz said...

One further reflection on the concept of economic "value" and why some such concept might be needed. "Value" is a matter of the relation and ratios "internal" to the economic system in any given state. That is, a piece of land, a machine-tool, a box of chocolates, might all exist independently, but they only acquire specific (and possibly even measurable) "value" through the nexus of the systematic relations which are imposed on them. Thus the land acquires its "value" through the coal or ore that is extracted from it, the machine-tool from the materials it is capable of transforming, the box of chocolates from the wages of workers who want to please their sweethearts on St. Valentine's Day, etc. That quite materially and causally distinct "things" can enter into a system of relations. by which they, each and all, partakes of a common substance, "value", is strange and requires explanation. (Nowadays, with general systems theory, it's more readily grasped that materially diverse and unconnected things can enter into a system through their informational properties or aspects and the exchange or communication of such information). But the key point is that such "value" is reasonably objective, relative to the existence of the economic system itself, and has cumulative effects of the dynamics of the system. That is, it is not decomposable into its separate individual atomic components or constituents. (I actually have no idea what the neo-classical standard of value is, if any. "Revealed preference" has always struck me as a tautology, and subjective utility preference functions as at once positivistically psychologistic and idealistic, i.e. non-explanatory "explanations". Perhaps opportunity costs is meant to play the role, though I don't see how they are consistently derived, rather than just invoked).

At any rate, the question as to why labor-value should provide a standard of "value", whether or not Marx' LTV is "correct", can be addressed by reflecting that it is the only input, amongst formally equivalent ones, that possesses the property of intentionality. It is only when labor has dug the minerals out of the land, worked the machines in factories, chosen to spend its wages on chocolates, etc. that the nexus of "value" is brought together and activated, however deformed and occluded the role of labor might be in that same system. None of the other inputs, whatever their independent, objective existence can create and transform "value" by generating and transforming such a system in the first place. Even the other key ingredient for increased material surpluses, the development of the technical means of production, not only crucially depends on human knowledge, know-how and experience, but depends on the value-states of the system, that is, technological conversions of the means of production will only occur at economic rates determining their "value".

I haven't gotten to the matter of whether Marx' LTV has been proven "incorrect" or inconsistent or not, and whether or why that might matter, let alone into all those thorny issues about the "transformation problem" and the "tendential law of the falling rate-of-profit". But I'll leave off for now, to attend to real matters, (hoping, of course, that some other, much more adept commenter might contribute and relieve me of any such heavy burden.)

john c. halasz said...

O.K. So no one else wants to discuss the issues further or offer criticisms or arguments. So be it. I'll try and haplessly and hopelessly continue the effort, nevertheless. In dribs and drabs.

Where I left of was the contention that "value" has a kind of objective existence within the "system", (both of Marx and of the actual economy), and that value, as a unit-of-account, diverges from money-prices.

It might be useful to distinguish to kinds of "equilibrium". The first is the most basic classical theorem or principle of economics: that the equalization of the rate-of-profit across all sectors through the (re-)allocation of investment results in a state of "general equilibrium" in an economy, which is tantamount to the optimal utilization of all "resources", not least commodified labor-power, toward the maximal output, given initial constraints, on the long-period assumption . The other "partial equilibrium" account is that there is always a "formula" of price/quantity by which markets will "clear" in accordance "the law of supply and demand", in any given short-period. And the latter forms a nexus between markets for all resources and assets, by which the first is to be brought about and "guaranteed".

So why does Marx posit apparently two different units of account, money-prices and labor-values?

Because value-relations are shown forth precisely when market prices don't "clear".

john c. halasz said...

So back to basics. I said before that Marx takes the money price of labor-power as initially "fair" and equivalent, (which doesn't necessarily involve the decomposition of the money-wage into a basket of wage-good staple commodities). That's not where the divergences between "value" and prices "originates".

The Vol.! account is not an account of a petty commodity producers' economy,- (since the focus is on the emergence of a fully-fledged industrial capitalist economy, and small-scale, "craft" commodity production belongs to the margins of pre-capitalist economies, just as the Physiocrats had it),- nor is it exactly an account of an industrial capitalist economy, when the "organic composition of capital" is exactly equal, since such a stipulative condition hasn't yet come up. Rather Marx starts with the basic core, the commodity form, and gradually unfolds its further spiraling implications, in Vol.! and after. Vol.1 is "represents" a conceptual level of exposition, rather than any account of any actual economy, (even though the "whole" of "Capital" is already implicitly there). And the key point is that Marx shows in the basic set-up of Vol.1 that the source of profit is the difference between the monetary price of labor-power and the monetary product of its output, which is to say, the extraction of additional labor-time from labor-power, such that some units of labor-value become "surplus-value" rather than being recycled into the exchange-of-equivalents which comprises the basic premises of the "system". That's an explanation at once of the M-C-M' circuit, by which money "magically" produces more money, and the accumulation of "real" capital stocks. Hence labor-values, as units-of-account, are extracted and "shadow" monetary units-of-account. But which is the real "value", especially given that both are equally "real" and objective in their effects?

But that's just the point: the vagaries of the two units-of-account that hang in the balance, "contradictorily", counter-valingly, make up the subsequent adventures of "Capital".

(To be continued, haphazardly. "Same Bat-time! Same Bat-station!")

john c. halasz said...

Oh, one last small point, (mostly as a note to myself): the extraction of surplus-labor-values occurs under "market" competitive pressures, but actually takes place "outside" markets, but rather "within" extra-market production-organizations.

Utopian Yuri said...

Thank you so much for this series! Although I can't say I understand it in all of its complexity, I have met my shorter-term goal of beginning to engage with the theory. I got myself a copy of Understanding Marx in furtherance of my long-term goal.

john c. halasz said...

So at production/work sites throughout the economy, the extraction of surplus-value takes place, which explains the intelligibility and existence of profit. That this does not occur directly from market exchanges is one of the reasons this fact can be obscured. In turn, profits are only realized from the sale of output on markets, only after total value has been produced and surplus-value extracted. And only then is surplus-value recirculated and distributed in the form of profits, rents, interest, fees, taxes, etc. Capital investment is realized and profits are obtained from revenues from the sale of output, but without these priors, there would be no profit, and hence no tendency toward the equalization of rates-of-profit across sectors amounting to "general equilibrium".

(It is a matter of some small importance that wages are advanced ex ante prior to the realization ex post of investment, not just because they show up on the other side of the "equation" as consumption demand and because profits receive their seeming "justification" from this advance against the assumption of the risk that profits won't be realized from the sale of output above cost, but because wages are paid in terms of the value-relations prevailing in the earlier production period, whereas in the subsequent production period, technical change will have increased productivity and output, which is part of the asymmetry between profits and wages).

Thus the source of profit in the exploitation of labor, which I will comment on again later. But for now, I will point out that the relation between Capital and Labor is at the core of Marx systematic thinking, because the "class struggle" doesn't just concern the (re-)distribution of output and incomes, but is even more over the conditions and control of production/work, which occurs "behind the scenes" as far as market-based "society" is concerned. And it is itself a "contradictory" process, since Capital and Labor are both opposed and antagonistically cooperative through its various phases.

john c. halasz said...

But for now what need emphasis is the relentlessly expansionary "imperative" of an industrial capitalist, profit-driven system, across time and space, intensively as it penetrates, commodifies, and restructures ever more spheres of social life, and extensively as it seeks out ever more resources and territories for its operations. "Globalization" is built into its DNA.

Across successive production periods, there is an ever-increasing accumulation of capital stocks, "dead labor", which must be re-valorized through being "combined" with further exploitation of living labor. Profits from the realization of investments need to find opportunities for re-investment, (else the accumulation of such money-profits will simply bid up the prices on the extant stock of capital "assets", and thereby eliminate their profitability). So surplus-value must be re-produced continuously through the further expansion of value.

However, due to the intensive competition between particular capitals, capitalists who invest in technically improved capital stocks, which lower output prices and unit labor costs, will increase market share and drive competitors into bankruptcy. But that will also reduce the required labor-time to produce output and decrease employment, even as, temporarily profits rise, even as output prices fall, (and remaining workers might receive an increase in real wages, due to falling prices and a temporarily increased surplus from which to pay wages). Those extra workers will eventually need to be employed in more labor-intensive sectors, even as older out-competed capital stocks need to be liquidated at a loss. Meanwhile, the threshold for effective investment rises, due to increased capital-intensity in production, even though the costs of capital goods will eventually come down, by the same process by which output-prices for final consumption goods declined.

This is not simply a stable "equilibrium" process. Nor is it a "linear" process of ever-increasing capital intensity, since labor and capital will need to be re-deployed in other sectors. But the combination of increased capital costs, lowered output prices and decreased employment and thus wage-based consumption demand will put the squeeze on temporarily increased profits for competitive "winners", even as the profits of "losers" disappear together with the value of their capital stocks, such that a new round of competitive consolidation will ensue, within and across sectors. As Marx put it, competition breeds monopoly and monopoly breeds competition.

I think it's out of the attempt to comprehend and "chart" these "contradictory" dynamics that Marx adheres to "value" terminology, not out of any slavishly dogmatic adherence to prior theoretical sources.

john c. halasz said...

O.K. So here is perhaps the place to deal with the thorny "transformation problem. After the turn of the last century, a neo-classical economist called Bortkiewicz, following on the first neo-classical response to Marx' work by the Austrian economist Boehm-Bawerk, produced a reading of the issue that claimed to demonstrate that Marx attempted solution to the problem was mathematically wrong and that therefore Marx' LTV was inconsistent. And if Marx' theory is formally inconsistent, then it's simply wrong, refuted, not a possible candidate theory for the "truth" and can be safely ignored and replaced with something else. Later Sraffan criticisms of Marx' LTV were added to the lists, though Sraffa was ironically mostly concerned to demonstrate the systematic inconsistency of neo-classical marginalist theories and re-raise the basic questions about economic "value".

The problem concerns differing "organic compositions of capital", i.e. the degree of capital intensity vs. labor intensity, in different sectors of production. If more labor-value is being directly extracted in some sectors, while other sectors rely on increasing accumulations of capital stocks, and surplus-value is derived from extracted labor-time, how is the fundamental theorem of the equalization of the rate-of-profit across all sectors to work? After all, on a crude reading, it would be precisely the less capital-intensive sectors that would extract the most labor-value, and thereby enjoy the highest rate of surplus-value and profit over against the capital-intensive sectors, which is counter-intuitive, since why then would capital-intensive sectors attract investment?

Supposedly, then, labor-value inputs need to be transformed into cost-prices of production, the Marxian equivalent of Ricardan "natural prices", in order for the equalization of profits to obtain. And Marx then claims that three aggregate equalities most obtain: total value = total prices, total surplus-value = total money profit and value rate-of-profit = money rate-of-profit. But it is claimed that all three equalities can't mathematically obtain together. Further, since it is the cost-prices of production that are the actual determinants of equilibrium, labor-values are redundant, and drop out of the explanation.

john c. halasz said...

However, the above criticism is a mis-reading of the actual "transformation problem" and ironically enough, it's exact inversion. In the first place, the "problem" is not how to convert labor-values into prices, but rather how to convert the values and prices that obtain under the the stipulation of equal "organic compositions of capital" across all sectors, which obtains in Vol.!, as Marx lays out the basic workings of the system, into the values and prices that obtain, as the system realistically develops, under unequal compositions between sectors. And Marx' claim is not that one must first obtain cost-prices of production before one can determine distribution, but rather one must first determine the distributions of surplus-value, (between profits rents, interest, etc.), before one can determine cost-prices of production. IOW though labor-values are directly extracted differentially at production/work sites across sectors, the price system will redistribute them, such that the "equilibriating" rate-of profit (and the 3 value/price equalities) obtain, with more concentrated capital-intensive sectors effectively drawing labor-values from more dispersed labor-intensive ones. Thus Marx' actual account is a complex account of price-formation and its dynamics, that's much different from the simplistic aggregation of partial equilibria of the marginalists. Further, though particular investment decisions at discrete point in time are determined by cost-prices of production, technical change is constantly and dynamically changing the formation of such prices, such that there is little point in determining a total set of such prices at "equilibrium" in each slice of time. (Which accounts for Marx' seeming relative lack of concern with specifying a solution for a "complete" set of such prices).

john c. halasz said...

Bortkiewicz, following neo-classical assumptions, re-normalized each production as at equilibrium, which then allowed him to accuse Marx of "double-counting", which only results from his own assumptions. And which rather negates Marx' point, since the latter was concerned to demonstrate the long-run disequilibrium dynamics of the system, not to uphold its perfectly self-equilibriating regulation. (Marx used the classical assumption of equilibrium to undermine it: oops! another "contradiction). Bortkiewicz further subtly confused and conflated prices with physical quantities in assuming a simple constant reproduction schema, against Marx intention. (If it once took 1 hour of labor to produce one unit of output, but now an hour produces 2 units, physical output has doubled, but labor-value remains the same, with the labor-value in each unit of output now being 1/2 of what it was, whereas B. thinks that a doubling of physical output is a doubling of "value"). And B. then plugged the output prices, under the assumption of simple constant reproduction, back in as initial input prices, when, given a capital goods sector, the value composition of output prices changes from one production period to the next.

In googling to refresh my memory on this issue, I found this web page, which, though slightly unclear at the end, is basically clear and mathematically simple, in illustration the solution to the "transformation problem", according to the TSS interpretation:

john c. halasz said...

So if labor-values don't directly translate into nominal money-prices, and if they don't correspond to any measure of physical output, (other than labor-time itself), such that, as physical output expands, the quantity of unit labor-value "embodied" in it shrinks, even though value is nonetheless said to be expanding in further processes of production, just what are labor-values and what is their point?

Let's start with why consumption demand is mostly wage-based,(or, more generally, dependent of production incomes). Wealthy capitalists are wealthy because of their ownership of large capital stocks. From the profits thereof, they can finance their lavish consumption, but their wealth far exceeds anything that they could consume with it. Any individual capitalist could sell his capital assets, and thereby live even "larger", but all capitalists can't do so at once, since that would collapse the value of their capital stocks, (as with a stock market crash), and thereby relieve themselves of their wealth. (Similarly, a capitalist who borrows too much against his wealth might expose himself to bankruptcy, so that some other capitalist takes over his wealth, whereas one who has sold, since he can't immediately consume so much wealth, must save it in the form of financial "assets", which are just claims on capital stocks and their profits, once again). But the capital stocks themselves, which are the source of their wealth, can't be eaten or consumed. Rather capital stocks can only be "consumed" in the process of production and realized through revenues from the sale of output. Michael Kalecki, the co-discoverer of the principle of real aggregate effective demand, put it in a punchy slogan: workers spend what they get, whereas capitalists get what they spend. On the other hand, when there is rising income inequality, (as in the U.S. nowadays where the top 10% receive 50% of the income and consume 40% of output), that is actually a sign of stagnation and dis-investment, since, though the production of luxury and especially status and positional goods might command high profit margins, (since higher top-end incomes will bid up their prices), they make less use of the overall capital stock, which also must be re-configured for such output, which means de-valuing stocks oriented toward more basic consumption.

So profits concern mainly investment demand and don't serve as a reliable basis of broad-based consumption demand, by which capital stocks are realized and valorized through the sale of output.

john c. halasz said...

(Cont.) On the other hand, the key to the whole system is the Capital/Labor relation. Expressed in purely economic terms, capital and labor are at once complements and substitutes for each other. Capitalist competition might drive capitalists to invest in improved, productivity-enhancing capital stocks, thereby gaining market-share, increasing output and reduced costs and prices, and driving out competition. (Secondarily, rising wage-cost pressures might also induce the same). But the "value" of such capital investment is always "measured" in terms of the labor-value it displaces, while also always requiring new labor-value to put it into operation. "Officially", capital assets form a nexus to be traded off against one another on the market, in accordance with the general rate-of-profit and its equilibrium equalization. But at a more basic level, labor-values and capital investment are being constantly "traded off" against each other, (though this is not simply a market operation), and labor-value is required to make up the "value" of capital.

IOW labor-value, in its admixture with capital investment, is always required to valorize capital stocks, and with increased capital intensity, labor-value must likewise be "expanded". To make the point clear, suppose the production system of the entire economy were completely automated, produced by capital stocks alone, such that pushing a few buttons on a remote-control were all that it required to produce total output, without any admixture of labor-value. Then either a) there would be no wage-incomes to purchase output, or b) output would be distributed without regard for labor-input, "free of charge". What then would be the "value" of capital stocks? A reductio ad absurdum.

The most basic point here is that the key driver of the entire industrial capitalist system is the "imperative" to maintain the "value" of capital by means of the rate-of-profit. Which is a very bumpy ride, indeed!

john c. halasz said...

So maybe now on to perhaps the thorniest and most contentious issue in Marx: "the tendential law of the falling rate-of-profit". Two preliminary remarks: 1) the idiom is Hegelian, such that the "law" is a tendency, a potentiality, which might interact with other such countervailing "laws" to determine (i.e. specify) variable outcomes, rather than a being a deterministic "covering law". And 2) AFAIK the referenced rate-of-profit is stated primarily in "value" terms, (S/C+V), and is directed toward profits-of-production, though equally it concerns the economy-wide rate-of-profit and its supposed equilibriating function.

The "law" is partly a complex and multi-sided thesis about technical change and the development of technology under the auspices of capitalism. As competition drives capitalists to adopt technical improvements in their means-of-production, the capital-intensity of production rises, though that doesn't occur all at once and equally between sectors, but rather through successive rounds of competitive consolidation and at differential rates across interacting sectors. (And it partly depends on contingent discoveries in knowledge and technology). However, as technically improved, productivity-enhancing capital stocks take hold, (raising temporarily the rate-of-profit of innovative capitalists), several consequences ensue: a) older capital stocks get driven out and produces losses, b) output prices are lowered, and as that runs against demand elasticities, unit profit margins decrease, c) though b implies higher real wages, workers become unemployed, as fewer are needed, but need eventually to be re-deployed elsewhere in less productive sectors, so consumption demand is impaired, And d) surviving, successful capitalists now face higher fixed capital costs, but as the same cost-lowering dynamic takes hold in capital-goods sectors, initially competitive fixed costs face competitive depreciation from historical cost to replacement cost.

Hence, as technical means-of-production improve and competitive consolidation occurs, capitalists face rising constant investment costs, (C in the value-rate-of-profit), which itself depreciates with time, increased output (at lower V) at lowered prices, but declining wage-based demand.

The economy-wide "value" rate-of-profit includes the losses of bankrupt competitors, the increase in C for incumbents, the increase in output together with lowered output prices, and the decrease in V, which also means lowered wage-based consumption demand.

Obviously, something must be done!

john c. halasz said...

So the profit-driven system tends to run into the ground. Increasing C, together with increasing output and thus lowered output prices by which profits from C are to be realized. Needless to say, increasing V wouldn't help with the value equation, as, though rising wages might help with the demand side, it would also lower the profit side.

The only "solution" is to expand "value",- to redeploy labor and much else,- in order to maintain surplus-value.

Unknown said...

Hello Professor, I have learned much from your tutorial (and from your blog in general). My understanding is that capitalism creates wealth by exploiting the unique characteristics of Labor as an input. This resonates with my own experiences and reflections; however, I am left wondering what are the alternatives? How does Socialism generate wealth without also exploiting these unique characteristics?

Robert Paul Wolff said...

Brian, let me try to sort out your question. First of all, human beings create wealth by mixing their labor with nature in collective, purposive ways. That will remain as true under socialism as it is under capitalism [or any other social formation.] In this very general sense of "exploit," human beings exploit nature, they exploit their caacity for labor, they exploit their intelligence -- i.e., they use all these productively. Capitalism appropriates the lion's share of the annual social surplus by "exploiting" labor in a quite different sense of the term, namely by depriving workers of access to the means of production save on its terms, thus compelling workers to labor for a wage that does not enable them to purchase the surplus they have created by their work. In a socialist economy, workers will still work, and in that sense "exploit" nature and their own capacity for productive labor, but they will do so on terms that they set collectively. No one will be able to appropriate the surplus simply by controlling the means of production.

Is that clearer?

Unknown said...

I see. Yes, that helps -- thanks again!