Welcome

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Selected Biographies Of Karl Marx

Selected Biographies

Author	Year	Title
Gustav Gross	1885	Karl Marx: Eine Studie
William Liebknecht	1896	Karl Marx, Biographical Memoirs
Paul Lafargue	1905	My Recollections of Karl Marx
Various	1908	Karl Marx: In memoriam
Jonathan Spargo	1910	Karl Marx: his life and work
Clara Zetkin	1913	Karl Marx und Sein Lebenswerk
Franz Mehring	1918	Karl Marx: The story of his life
Otto Ruhle	1926	Karl Marx: Leben und Werk
David Riazanov	1927	Karl Marx and Frederick Engels: an introduction to their lives and works
Institute of Marxism-Leninism of the Central Committee of the CPSU		Karl Marx: a biography
E. H. Carr	1934	Karl Marx: A study in fanaticism
Boris Nicolaevsky	1936	Karl Marx: Man and Fighter
Karl Korsch	1938	Karl Marx
Isaiah Berlin	1939	Karl Marx: His Life and Environment
Leopold Schwarzschild	1947	The Red Prussian: the life and legend of Karl Marx
David McLellan	1973	Karl Marx: a biography
Fritz J. Raddatz	1975	Karl Marx: Eine politische biographie
Francis Wheen	1999	Karl Marx: A life
Jonathan Sperber	2013	Karl Marx: A nineteenth century life
Gareth Stedman Jones	2016	Karl Marx: greatness and illusion
Michael Heinrich	2018	Karl Marx and the Birth of Modern Society (1st of 3 volumes.)

Karl Marx was a great man. In other words, he had a huge impact on the world. Many, as seen above, have written biographies. I try to give the original year of publication. I am inconsistent about whether or not I translate the title.

Early biographies tend to be memoirs, based on recollections and oral stories, with little documentation. Later, biographies tend to be more intellectual histories. I have read the Mehring biography and the Lafarge memoir. Most of what I have read about his life were in studies of his thought, that are not included above. Examples include Shlomo Avineri, Ernest Mandel, and Takahisi Oishi. Some around the mid twentieth century focus on being pro or against the Soviet Union. The last couple of decades have seen academic works with lots of documentation.

References

• Lenin. 1915. Karl Marx. Collected Works, V. 21
• Segrillo, Angelo. 2019. Two centuries of Karl Marx biographies. LEA Working Paper, No. 4.

Some Quotations On What You Deserve

When one achieves at least partial enlightenment, one will realize that one's income does not necessarily reward productivity, effort, or any other virtue.

"For we each of us deserve everything, every luxury that was ever piled in the tombs of the dead kings, and we each of us deserve nothing, not a mouthful of bread in hunger. Have we not eaten while another starved? Will you punish us for that? Will you reward us for the virtue of starving while others ate? No man earns punishment, no man earns reward. Free your mind of the idea of deserving, the idea of earning, and you will begin to be able to think." -- Ursula K. Leguin, The Dispossessed.

"Pity? It's a pity that stayed Bilbo's hand. Many that live deserve death. Some that die deserve life. Can you give it to them, Frodo? Do not be too eager to deal out death in judgment. Even the very wise cannot see all ends. My heart tells me that Gollum has some part to play in it, for good or evil, before this is over. The pity of Bilbo may rule the fate of many." -- J. R. R. Tolkien, The Fellowship of the Ring

"'Deserve's' got nothing to do with it." -- Clint Eastwood (as William Munney), Unforgiven

"By way of attempting to give the reader some general impression of the way people lived together in those days, and especially of the relations of the rich and poor to one another, perhaps I cannot do better than to compare society as it then was to a prodigious coach which the masses of humanity were harnessed to and dragged toilsomely along a very hilly and sandy road. The driver was hunger, and permitted no lagging, though the pace was necessarily very slow. Despite the difficulty of drawing the coach at all along so hard a road, the top was covered with passengers who never got down, even at the steepest ascents. These seats on top were very breezy and comfortable. Well up out of the dust, their occupants could enjoy the scenery at their leisure, or critically discuss the merits of the straining team. Naturally such places were in great demand and the competition for them was keen, every one seeking as the first end in life to secure a seat on the coach for himself and to leave it to his child after him. By the rule of the coach a man could leave his seat to whom he wished, but on the other hand there were many accidents by which it might at any time be wholly lost. For all that they were so easy, the seats were very insecure, and at every sudden jolt of the coach persons were slipping out of them and falling to the ground, where they were instantly compelled to take hold of the rope and help to drag the coach on which they had before ridden so pleasantly. It was naturally regarded as a terrible misfortune to lose one’s seat, and the apprehension that this might happen to them or their friends was a constant cloud upon the happiness of those who rode.

But did they think only of themselves? you ask. Was not their very luxury rendered intolerable to them by comparison with the lot of their brothers and sisters in the harness, and the knowledge that their own weight added to their toil? Had they no compassion for fellow beings from whom fortune only distinguished them? Oh, yes; commiseration was frequently expressed by those who rode for those who had to pull the coach, especially when the vehicle came to a bad place in the road, as it was constantly doing, or to a particularly steep hill. At such times, the desperate straining of the team, their agonized leaping and plunging under the pitiless lashing of hunger, the many who fainted at the rope and were trampled in the mire, made a very distressing spectacle, which often called forth highly creditable displays of feeling on the top of the coach. At such times the passengers would call down encouragingly to the toilers of the rope, exhorting them to patience, and holding out hopes of possible compensation in another world for the hardness of their lot, while others contributed to buy salves and liniments for the crippled and injured. It was agreed that it was a great pity that the coach should be so hard to pull, and there was a sense of general relief when the specially bad piece of road was gotten over. This relief was not, indeed, wholly on account of the team, for there was always some danger at these bad places of a general overturn in which all would lose their seats.

It must in truth be admitted that the main effect of the spectacle of the misery of the toilers at the rope was to enhance the passengers' sense of the value of their seats upon the coach, and to cause them to hold on to them more desperately than before. If the passengers could only have felt assured that neither they nor their friends would ever fall from the top, it is probable that, beyond contributing to the funds for liniments and bandages, they would have troubled themselves extremely little about those who dragged the coach.

I am well aware that this will appear to the men and women of the twentieth century an incredible inhumanity, but there are two facts, both very curious, which partly explain it. In the first place, it was firmly and sincerely believed that there was no other way in which Society could get along, except the many pulled at the rope and the few rode, and not only this, but that no very radical improvement even was possible, either in the harness, the coach, the roadway, or the distribution of the toil. It had always been as it was, and it always would be so. It was a pity, but it could not be helped, and philosophy forbade wasting compassion on what was beyond remedy.

The other fact is yet more curious, consisting in a singular hallucination which those on the top of the coach generally shared, that they were not exactly like their brothers and sisters who pulled at the rope, but of finer clay, in some way belonging to a higher order of beings who might justly expect to be drawn. This seems unaccountable, but, as I once rode on this very coach and shared that very hallucination, I ought to be believed. The strangest thing about the hallucination was that those who had but just climbed up from the ground, before they had outgrown the marks of the rope upon their hands, began to fall under its influence. As for those whose parents and grand-parents before them had been so fortunate as to keep their seats on the top, the conviction they cherished of the essential difference between their sort of humanity and the common article was absolute. The effect of such a delusion in moderating fellow feeling for the sufferings of the mass of men into a distant and philosophical compassion is obvious. To it I refer as the only extenuation I can offer for the indifference which, at the period I write of, marked my own attitude toward the misery of my brothers." -- Edward Bellamy, Looking Backwards

"I once had occasion to talk with one of the shipwrecked survivors of La Bourgogne and he told me that he had been lucky enough to get into a lifeboat in which a number of men had got away; if more had been taken in, the boat would have capsized and sunk. The men in safety on board, armed with jack-knives and hatchets, had hacked off the hands of those who, clinging to the sides of the boat, were endeavoring to scramble in out of the sea. The knowledge of being one of those in the lifeboat, of being safe, whilst others round me are drowning, that feeling became intolerable to me. People argue with me but I am not sufficiently expert to answer them subtly, I only cling tenaciously to the one fact that I cannot accept a place in a lifeboat in which only a limited number of people are saved. If I could feel, at least, assured that it was the best who were saved, it might not be so bad, but what makes me most indignant is when somebody says to me 'What are you grumbling at? You must admit that it is very comfortable in the lifeboat.'" -- André Gide, The God that Failed

"But he answered one of them, 'I am not being unfair to you, friend. Didn’t you agree to work for a denarius? Take your pay and go. I want to give the one who was hired last the same as I gave you. Don't I have the right to do what I want with my own money? Or are you envious because I am generous?' So the last will be first, and the first will be last. -- Matthew 20: 13-16

A Letter From Marx To Engels In 1868 On The Transformation Problem

In this letter, Marx outlines the three volumes of Capital. I know about this letter from Fred Moseley's Money and Totality (2016). Is this where scholars learned about Marx's mother (-in-law?) saying, "If only Karl had accumulated capital instead of writing about it"? The context is a discussion, in a couple of previous letters, of the effects of inflation on the rate of profits. This letter is more evidence that Marx was quite conscious of the transformation problem. (Theories of Surplus Value is definitive evidence.) I think Marx's distinction between vulgar and classical political economy, on commodity fetishism, on the illusions created by competition is central to his political economy. It is not an idea to be found in Ricardo. Marx also has a more elaborate taxonomy of capital than Ricardo does.

London

30 April 1868

Dear Fred,

For the CASE under discussion it is immaterial whether m (the surplus value) is quantitatively > or < than the surplus value created in the given branch of production itself. E.g., if 100m/(400c + 100v) = 20%, and this becomes, owing to a fall in the value of money by 1/10, = 110m/(400c + 110v) (assuming that the value of the constant capital sinks), it is immaterial if the capitalist producer pockets only half of the surplus value which he himself produces. For the rate of profit for him then = 55m/(400c + 110v) > than the former 50m/(400c + 100v). I retain m here in order to show qualitatively in the expression itself where the profit comes from.

But it is proper that you should know the method by which the rate of profit is developed. I shall therefore give you the process in the most general outline. In Book II, as you know, the process of circulation of capital is presented on the basis of the premisses developed in Book I. I.e. the new determinations of form which arise from the process of circulation, such as fixed and circulating capital, turnover of capital, etc. Finally, in Book I we content ourselves with the assumption that when, in the valorisation process, 100 pounds becomes 110 pounds, it finds the elements into which it is converted anew already in existence in the market. But now we investigate the conditions under which these elements are to be found in existence, that is to say, t he social intertwining of the different capitals, of parts of capital and of REVENUE (=m).

In Book III we then come to the conversion of surplus value into its different forms and separate component parts.

I. Profit is for us, for the time being, only another name for or another category of surplus value. As, owing to the form of wages, the whole of labour appears to be paid for, the unpaid part of it seems necessarily to come not from labour but from capital, and not from the variable part of capital but from the total capital. As a result, surplus value assumes the form of profit, without there being any quantitative difference between the one and the other. It is only an illusory manifestation of surplus value.

Further, the part of capital consumed in the production of a commodity (the capital, constant and variable, advanced for its production, minus the utilised but not consumed part of fixed capital) now appears as the cost price of the commodity, since for the capitalist that part of the value of the commodity that it costs him is its cost price, while the unpaid labour contained in the commodity does not enter into its cost price, from his point of view. The surplus value = profit now appears as the excess of the selling price of the commodity over its cost price. Let us call the value of the commodity W and its cost price K; then W = K + m, therefore W — m = K, therefore W > K. This new category, cost price, is very necessary for the details of the later analysis. It is evident from the outset that the capitalist can sell a commodity at a profit below its value (as long as he sells it above its cost price), and this is the fundamental law for comprehending the equalisations effected by competition.

Therefore, while profit is at first only formally different from surplus value, the rate of profit is, by contrast, at once really different from the rate of surplus value, for in one case we have m/v and in the other m/(c + v), from which it follows from the outset, since m/v > m/(c + v), that the rate of profit < than the rate of surplus value, unless c = 0.

In view of what has been developed in Book II, it follows, however, that we cannot compute the rate of profit on the commodity product of any period we select, e.g. that of a week, but that m/(c + v) denotes here the surplus value produced during the year in relation to the capital advanced during the year (as distinct from the capital turned over). Therefore, m/(c + v) stands here for the annual rate of profit.

Then we shall first examine how variations in the turnover of capital (partly depending on the relation of the circulating to the fixed portions of capital, partly on the number of times the circulating capital turns over in a year, etc., etc.) modify the rate of profit while the rate of surplus value remains the same.

Now, taking the turnover as given, and m/(c + v) as the annual rate of profit, we examine how the latter can change, independently of changes in the rate of surplus value, and even of its total amount.

Since m, the total amount of surplus value, = the rate of surplus value multiplied by the variable capital, then, if we call the rate of surplus value r and the rate of profit p', p' = rv/(c + v) Here we have the 4 quantities p', r, v, c, with any 3 of which we can work, always seeking the 4th as unknown. This covers all possible cases of movements in the rate of profit, in so far as they are distinct from the movements in the rate of surplus value and, TO A CERTAIN EXTENT, even in its total amount. This has, of course, hitherto been inexplicable to everybody.

The laws thus found - very important, e.g., for understanding how the price of the raw material influences the rate of profit - hold good no matter how the surplus value is later divided among the producer, etc. This can only change the form of appearance. Moreover, they remain directly applicable if m/(c + v) is treated as the relation of the socially produced surplus value to the social capital.

II. What were treated in I as movements, whether of capital in a particular branch of production or of social capital - movements changing its composition, etc. - are now conceived as differences of the various masses of capital invested in the different branches of production.

Then it turns out that, assuming the rate of surplus value, i.e. the exploitation of labour, as equal, the production of value and therefore the production of surplus value and therefore the rate of profit are different in different branches of production. But from these varying rates of profit a mean or general rate of profit is formed by competition. This rate of profit, expressed absolutely, can be nothing but the surplus value produced (annually) by the capitalist class in relation to the total of social capital advanced. E.g., if the social capital = 400c + 100v, and the surplus value annually produced by it = 100m, the composition of the social capital = 80c + 20v, and that of the product (in percentages) = 80c + 20v | +20m = 20% rate of profit. This is the general rate of profit.

What the competition among the various masses of capital — invested in different spheres of production and differently composed — is striving for is capitalist communism, namely that the mass of capital employed in each sphere of production should get a fractional part of the total surplus value proportionate to the part of the total social capital that it forms.

This can only be achieved if in each sphere of production (assuming as above that the total capital = 80c + 20v and the social rate of profit = 20m/(80c + 20v) the annual commodity product is sold at cost price + 20% profit on the value of the capital advanced (it is immaterial how much of the advanced fixed capital enters into the annual cost price or not). But this means that the price determination of the commodities must deviate from their values. Only in those branches of production where the percentual composition of capital is 80c + 20v will the price K (cost price) + 20% on the capital advanced coincide with the value of the commodities. Where the composition is higher (e.g. 90c +10v), the price is above their value; where the composition is lower (e.g. 70c + 30v), the price is below their value.

The price thus equalised, which divides up the social surplus value equally among the various masses of capital in proportion to their sizes, is the price of production of commodities, the centre around which the oscillation of the market prices moves.

Those branches of production which constitute a natural monopoly are exempted from this equalisation process, even if their rate of profit is higher than the social rate. This is important later for the development of rent.

In this chapter, there must be further developed the various causes of equalisation of the various capital investments, which appear to the vulgar conception as so many sources of profit.

Also to be developed: the changed form of manifestation that the previously developed and still valid laws of value and surplus value assume now, after the transformation of values into prices of production.

III. The tendency of the rate of profit to fall as society progresses. This already follows from what was developed in Book I on the change in the composition of capital with the development of the social productive power. This is one of the greatest triumphs over the pons asini [asses' bridge] of all previous political economy.

IV. Until now we have only dealt with productive capital. Now there enters modification through merchant capital.

According to our previous assumption the productive capital of society = 500 (millions or billions, n'importe [it doesn't matter]). And the formula was 400c + 100v + 100m. The general rate of profit, p', = 20%. Now let the merchant capital = 100.

So, the 100m has now to be calculated on 600 instead of 500. The general rate of profit is thus reduced from 20% to 16 2/3%. The price of production (for the sake of simplicity we will assume here that all of the 400c, i.e. the whole fixed capital, enters into the cost price of the annual output of commodities) now=583 1/3. The merchant sells at 600 and therefore realises, if we ignore the fixed portion of his capital, 16 2/3% on his 100, as much as the productive capitalists; or, in other words, he appropriates 1/6 of the social surplus value. The commodities — en masse and on a social scale - are sold at their value. His 100 pounds (apart from the fixed portion) only serve him as circulating money capital. Whatever the merchant swallows over and above that, he gets either simply by trickery, or by speculation on the oscillation of commodity prices, or, in the case of the actual retailer, as wages for labour - wretched unproductive labour that it is - in the form of profit.

V. We have now deduced profit to the form in which it appears in practice, according to our assumptions 16 2/3%. Next comes the division of this profit into entrepreneur's gain and interest. Interest-bearing capital. The credit system.

VI. Transformation of surplus profit into rent.

VII. At last we have arrived at the forms of manifestation which serve as the starting point in the vulgar conception: rent, coming from the land; profit (interest), from capital; wages, from labour. But from our standpoint things now look different. The apparent movement is explained. Furthermore, A. Smith's nonsense, which has become the main pillar of all political economy hitherto, the contention that the price of the commodity consists of those three revenues, i.e. only of variable capital (wages) and surplus value (rent, profit (interest)), is overthrown. The entire movement in this apparent form. Finally, since those 3 items (wages, rent, profit (interest)) constitute the sources of income of the 3 classes of landowners, capitalists and wage labourers, we have the class struggle, as the conclusion in which the movement and disintegration of the whole shit resolves itself.

Our young couple [Paul and Laura Lafargue] back again since last week, very love-sicK. Apartment for them near Primrose Hill, where they moved in this evening.

Enclosed letters from Kugelmann, etc. I have sent Schily what he wanted, but not in the childish way he requested. In a few days I shall be 50. As that Prussian lieutenant said to you: '20 years of service and still lieutenant'. I can say: half a century on my shoulders, and still a pauper. How right my mother was: 'If only Karell had made capital instead of etc'.

Salut.

Your

K. Marx

Of carbuncles only a very small trace on the right thigh, but will probably vanish without trace.

Ernest Jones has made a fool of himself by his lukewarm and nisi priiis [half-hearted] way of defending Burke. Burke has at least won a victory in forcing the old jackass Bramwell to abandon the hypocrisy of TEMPER, and allowing his mean dog's soul to rampage free of carrière [reins].

Here we see that, for Marx, prices of production reflect the redistribution of surplus value. Marx takes cost prices as untransformed values throughout. Ho also brings up the tendency of the rate of profit to fall. Following Okishio, I do not think this law follows from Marx's premises. Marx describes what Resnick and Wolff call subsumed class processes. Finance shares in surplus value through interest payments. Landlords can obtain absolute and relative rent. And retailers, employing unproductive labor, obtain a return to their capital, which Marx does not count as productive capital. I think this outline is consistent with the order of presentation Marx discusses in the introduction to the Grundrisse.

Elsewhere

Cordelia Belton at Red May

• Matthew Sitman and Sam Adler-Bell's Know Your Enemy podcast.
• Benedict and Kevin's Not Your Grandmother's Book Club podcast.
• Brendan Cooney and Andrew Kliman's Radio Free Humanity podcast.
• Doug Henwood on McCarthyism.
• Peter Boetkke and Rosolino Candela On the feasibility of technosocialism.
• An old essay of mine on a Sraffian interpretation of Marx.

Rate Of Profits As A Weighted Sum Of Value Rate Of Profits

1.0 Introduction

Stefano Perri has a working paper, "Sraffa's response to Eaton's review: a note on the standard commodity and Marx's general profit rate". In this post, I present the analysis rewritten in matrix notation. The claim is, more or less, that the rate of profits in the system of prices of production is the weighted average of the rates of profits, by industry, in the system of labor values. Each weight is the product of the labor value of capital advanced in that industry and the quantity of the gross output of that industry in the standard system.

This post is unsatisfying. I end up with a claim that I do not see how to prove offhand.

2.0 Parameters and Assumptions

The setting is a model of circulating capital, with wages advanced and specified as a given commodity basket. Let A be the n x n Leontief input-output matrix, with a_i,j being the quantity of the ith commodity used as an input in producing the jth commodity. Each row of A represents the inputs of a commodity in the various industries, while each column represents an industry. Let a₀ be the n-element row vector of direct labor coefficients. a_0,j is the quantity of labor employed in manufacturing the jth commodity

The units of measurement for the commodities are chosen such that one unit is produced in each industry. That is, iron ore might be measured in units of 253 million tons, while red winter wheat might be measured in units of 1.6 billion bushels. (I am making such numbers up.) The gross output is then u, a unit column vector. Employment is measured such that total employment is one unit:

a₀ u = 1

Net output, y, is a column vector:

y = u - A u

Assume the Leontief matrix is indecomposable and productive. These assumptions assure the existence of the Leontief inverse (I - A)^-1.

Net output is divided between wages and profits here. Assume wages are advanced and specified in physical terms by the column vector d. Wages are bounded above by net output:

d ≤ u - A u

Since both commodities that function as capital goods and wage goods are advanced, one can form a new matrix:

A* = A + d a₀

Each column of A* is the total commodities advanced in an industry.

3.0 Labor Values

The data determine the labor value embodied in each commodity. Consider the jth commodity. Let e_j be the jth column in the identity matrix. Suppose this is the net output of the economy produced with this technique, where q is now the gross outputs of the economy:

e_j = q - A q

The labor value embodied in this commodity is found from the vector of direct labor coefficients and the Leontief inverse:

ν_j = a₀ q = a₀ (I - A)^-1 e_j

The row vector of labor values is then:

ν = a₀ (I - A)^-1

The reproduction of the net output of the jth industry requires workers distributed across all industries to be reproducing the capital goods used up in making this net output, the capital goods used up in making those capital goods, and so on. Labor values reflect a notional vertical integration of the observed quantity flows, with the observed technique. One can ask how much employment would be increased by a sustained increase in a given industry. So-called employment multipliers answer this question.

One can evaluate the commodities advanced in production with labor values. The labor value of the constant capitals is a row matrix, C:

C = ν A

One can also evaluate the labor value of the commodities which the workers purchase with their wages. The labor value of variable capital is a row matrix, V:

V = ν d a₀

Let T be a diagonal matrix with

t_j,j = C_j + V_j

Each entry along the diagonal is the sum to the constant and variable capital advanced in the corresponding industry.

Let Π be a diagonal matrix in which the elements along the diagonal are the value rate of profits for the industries. Postulate that workers add the same value in each industry, despite the varying amounts of capital equipment with which they work. One then has, as a matter of accounting, the following equality in the system of labor values:

(C + V)(I + Π) = ν

Multiply on the right by the inverse of T:

(C + V)(I + Π) T^-1 = ν T^-1

Multiplication, when restricted to diagonal matrices, is commutative. Hence, one has:

(C + V) T^-1 (I + Π) = u^T (I + Π) = ν T^-1

Or:

[(1 + π₁), ..., (1 + π_n)] = [ν₁/(V₁ + C₁), ..., ν₁/(V_n + C_n)]

The sum of unity and the value rate of profits in each industry is the labor value of the output of that industry, normalized by the capital advanced.

4.0 Standard System

Here, as I understand it, Sraffa defines the standard system with the Leontief matrix including the commodities the advanced wage goods. The gross outputs of the standard system, q*, are defined as follows:

A* q* (1 + r) = q*

Employment in the standard system is unity.

a₀ q* = 1

Gross outputs are an eigenvector, with 1/(1 + r) as the Perron-Frobenius root of the matrix A*.

The net output of the standard system, y*, is defined as:

y* = q* - A* q*

Net output is then:

y* = (r/(1 + r) q*

Net output of the standard system, being proportional to gross outputs, is also an eigenvector.

5.0 Prices of Production

Prices of production are defined as:

p A* (1 + r) = p

Prices of production are a left-hand eigenvector of A* for the same eigenvalue, the Perron-Frobenius root of A*. Take the net output of the standard system as numeraire:

p y* = 1

At this point, the gross output of the standard system and the rate of profits for the system of prices of production have been defined.

One can multiply the row vector defined above, of the sum of unity and the value rate of profits by the column vector T q*:

u^T (I + Π) T q* = ν T^-1 T q*

Or:

u^T (I + Π) T q* = ν q*

I claim that the labor value of the gross outputs of the standard system is the sum of unity and the rate of profits in the system of prices of production:

ν q* = 1 + r

One should be able to find a proof of a few lines for this claim.

6.0 Conclusion

The weighted sum of unity added to the value rate of profits, by industry, is unity added to the rate of profits in the system of prices of production. These weights are the element-by-element product of the labor values of the capital advanced in each industry and the gross outputs from the standard system.

Böhm-Bawerk On The Close Of Marx's System

1.0 Introduction

I have previously quoted authorities disparaging Böhm-Bawerk's pamphlet examining the supposed contradiction between volumes 3 and 1 of Marx's Capital. I refer to Karl Marx and the Close of His System, first published in German, in 1896. Engels brought out volume 3 of Marx's Capital in 1894. Böhm-Bawerk's treatment, although it ultimately misses the point, is important from a historical angle:

"...the historical importance of Böhm-Bawerk's criticism of Marx ... should not lead us into the error of falsely evaluating the work itself. The truth is that in its essentials Karl Marx and the Close of His System is not a particularly remarkable performance." -- Paul M. Sweezy, from the editor's introduction.

I find I also agree with Andrew Kliman. A good bibliography on the transformation problem would be much longer than below, with more recent work.

Böhm-Bawerk's major work is set out in three volumes. The first, History and Critique of Interest Theories is a work of massive scholarship. In the second, Positive Theory of Capital and Interest, Böhm-Bawerk sets out his own failed theory of capital and its returns. Although he does not view capital as a social relation, he sets out the problem of explaining the returns to capital in an insightful manner. I think the categorization in his history influenced Joseph Schumpeter in his History of Economic Analysis.

2.0 Outline of The Close Of Marx's System and First Two Chapters

The Close, after an introduction, has two chapters of exposition of Marx. The third chapter contains Böhm-Bawerk's main critique. A fourth chapter is about how Marx came to make his supposed mistake, and the last chapter is focused on Werner Sombart.

In the introduction, Böhm-Bawerk notes Engel's prize essay competition in the introduction to volume 2 and the awarding of prizes in volume 3 of Capital. Both Marxists and non-Marxists consider the problem treated here of some importance. You can find many Marxists subsequently decrying this focus, to the detriment of other issues.

Chapter 1, the first chapter of exposition, is about volume 1 of Capital. The exposition is narrow. Nothing is said about the form of value, commodity fetishism, the drive to increase absolute and relative surplus value, the consequent changes in technology and organization of capitalist organizations, or the illusions created by competition.

Chapter 2 skips over volume 2, to focus on a few chapters in volume 3. He presents Marx's tables showing how surplus value is redistributed over spheres of varying capital intensity to form prices of production. Like Marx, he evaluates inputs of constant and variable capital at labor values, not at prices of production. He does NOT note that Marx says a possibility of error exists here:

"The foregoing statements have at any rate modified the original assumption concerning the determination of the cost price of commodities. We had originally assumed that the cost price of a commodity equalled the value of the commodities consumed in its production. But for the buyer the price of production of a specific commodity is its cost price, and may thus pass as cost price into the prices of other commodities. Since the price of production may differ from the value of a commodity, it follows that the cost price of a commodity containing this price of production of another commodity may also stand above or below that portion of its total value derived from the value of the means of production consumed by it. It is necessary to remember this modified significance of the cost price, and to bear in mind that there is always the possibility of an error if the cost price of a commodity in any particular sphere is identified with the value of the means of production consumed by it. Our present analysis does not necessitate a closer examination of this point." -- Karl Marx, Capital vol 3, chap 9

Böhm-Bawerk does say that the price of production of a commodity produced with average organic composition of capital is the same as its (labor) value. He quotes Marx as asserting that simple commodity production prevails in a pre-capitalist historical period.

3.0 The Third Chapter

In chapter 3, Böhm-Bawerk provides his criticisms, somewhat disjointedly. In some sense, he does not see a need to do this, since he thinks a contradiction between volume 1 and volume 3 is never resolved:

"I cannot help myself; I see here no explanation and reconciliation of a contradiction, but the bare contradiction itself. Marx's third volume contradicts the first. The theory of the average rate of profit and of the prices of production cannot be reconciled with the theory of value."

He mistakenly thinks the point of the labor theory of value, in volume 1, is to explain relative prices:

"the chief object of the 'law of value' ... is ... the elucidation of the exchange relations of commodities"

But it is to explain why there is a return to capital:

"To explain the general rate of profits, you must start from the theorem that, on average, commodities are sold at their real values, and that profits are derived from selling them at their values, that is, in proportion to the quantity of labor realized in them. If you cannot explain profit upon this supposition, you cannot explain it at all. This seems paradox and contrary to everyday observation." -- Karl Marx, Value, Price, and Profit

Much of Böhm-Bawerk's criticisms of Marx are merely unknowing echoes of Marx's criticisms of his predecessors in classical political economy. I refer here to Theories of Surplus Value, sometimes called the fourth volume of Capital.

Anyways, Böhm-Bawerk organizes his rebuttals around four arguments he finds in Marx:

1. Total prices equal total values.
2. The law of value governs the movement of prices.
3. The law of value rules in a pre-capitalist reign of simple commodity production.
4. "The law of value regulates the prices of production at least indirectly and in the last resort."

Böhm-Bawerk accepts that total prices equals total values:

"...therefore, it is quite true that the total price paid for the entire national produce coincides exactly with the total amount of value or labor incorporated in it [,a] tautological declaration..."

He does have some carping, including the complaint that nobody ever trades this total gross output against something or other.

I skip discussion of the second argument, on price dynamics.

In discussing simple commodity production, Böhm-Bawerk takes the opportunity to contrast his own theory about the period of production and waiting. Why should this theory not apply to simple commodity production?

In discussing Marx's fourth argument, Böhm-Bawerk thinks it reasonable to accept Marx's premise that the sum of total variable capital and total surplus value does not vary with wages. He does not see that, since this sum is the labor value of net output when profits are zero and his acceptance of a tautology in Marx's first argument, the capital replaced in producing the net output must be equal to its labor value in the system of prices of production. Böhm-Bawerk has some carping here, too, in which he mistakenly asserts that capital income can be reduced to a finite series of dated labor inputs, with the first term one in which a good of higher order is produced with unassisted labor.

We are almost home. Böhm-Bawerk recognizes prices of production vary with wages. Some may rise and some may fall. He insightfully notes that the total of the prices of wage goods may therefore deviate from the total labor value of this aggregate.

But, Böhm-Bawerk, finds coherent Marx's application of the rate of profits from the labor value system to the system of prices of production. Given Marx's premises, the rate of profits in the system of prices of production is the ratio of surplus value in the economy as a whole to the total labor value of the capital advanced. Much of the further literature on the so-called transformation problem questions the internal consistency of the volume 3 argument.

4.0 Sundry Observations on The Fourth Chapter

Böhm-Bawerk finds Marx's order of exposition incredibly weak and says this cannot be how Marx came to accept his theory of value. He reads marginalist functions into Marx's use of 'supply' and 'demand'. He recognizes that Marx knew about the transformation problem before publishing volume 1. In this point, he is advanced beyond some later commentators.

5.0 Conclusion

Philip Wicksteed was another early marginalist who reesponded to Marx. Other early treatments of the so-called transformation problem or of Ricardo or Marx's system include works by Ladislaus Bortkiewicz, Vladimir Dmitriev, Georg von Charasoff, Wolfgang Mühlpfordt, and Mikhail Tugan-Baranovsky. Maurice Potron, as I understand it, was the first to apply the Perron-Frobenius theorems to linear economic systems. John Von Neumann drew on Robert Remak in formulating his growth model. Aside from Wicksteed, these authors advanced an objective theory of value, in the tradition of classical or Marxist political economy, in some sense.

I do not see any contradiction in the inequality of relative prices of production and of labor values. On the other hand, Böhm-Bawerk will not lead you to question whether Marx's invariants can all hold simultaneously if capital inputs are transformed. Nor does he pose the so-called transformation problem such that you can see how Charasoff's urkapital (original capital) or Sraffa's standard commodity solve it. For understanding the transformation problem, Böhm-Bawerk is not helpful.

Reference

• Eugen von Böhm-Bawer. 1949. Karl Marx and the Close of His System (ed. by Paul Sweezy).Orion Editions.
• Eugen von Böhm-Bawerk. 1959. Capital and Interest (Three volumes). Libertarian Press.
• Andrew Kliman. 2007. Reclaiming Marx's "Capital": A Refutation of the Myth of Inconsistency Lexington Books.
• Fred Moseley. 2016. Money and Totality: A Macro-Monetary Interpretation of Marx's Logic in Capital and the End of the 'Transformation Problem'. Brill.
• Paul A. Samuelson. 1971. Understanding the Marxian notion of exploitation: a summary of the so-called transformation problem between Marxian values and competitive prices. Journal of Economic Literature 9 (2): 399-431.