Monday, April 29, 2024


  • Prof. Rowena Ball teaches a course on indigenous mathematics at Australian National University.
  • Prof. Caroline Fohlin, an economics professor at Emory University, is arrested for being assaulted by rioting police.
  • Prof. Tim Garrett questions the units of measurement in aggregate production functions. Aggregate production functions are not laws of nature, and those not in a broken discipline should not be thrown by questions about units of measurement. Maybe some production functions make sense as limit cases of linear combinations of Leontief production functions.
  • Daniel Kahneman has died.
  • Deirde McCloskey asserts, without cogent argument, that the labor theory of value is wrong. In what units do you imagine the marginal product of capital is measured?
  • Andy Merrifield has an article, "Gramsci and his friend 'S'", in Monthly Review.
  • Branko Milanović reminisce about a neo-Ricardian study group in communist Yugoslavia.

Update on 1 May: Added link to Andy Merrifield essay,

Saturday, April 27, 2024

Marxian Political Economy As Forward-Looking

Every child knows a nation which ceased to work, I will not say for a year, but even for a few weeks, would perish. Every child knows, too, that the masses of products corresponding to the different needs required different and quantitatively determined masses of the total labor of society. That this necessity of the distribution of social labor in definite proportions cannot possibly be done away with by a particular form of social production but can only change the mode of its appearance , is self-evident. No natural laws can be done away with. What can change in historically different circumstances is only the form in which these laws assert themselves. And the form in which this proportional distribution of labor asserts itself, in the state of society where the interconnection of social labor is manifested in the private exchange of the individual products of labor, is precisely the exchange value of these products. -- Karl Marx to Dr. Kugelmann, 11 July 1868

The above quotation is a pithy statement of a pre-analytical vision. The ideas underlying this vision are interesting, independently of what you may think about the details of Marx's theory of value.

One can start to explicate these ideas with a one-commodity model. Accordingly, consider an economy in which one commodity, corn, is produced. Suppose production takes one year. Let a0 be person-years of labor needed to produce a bushel corn. Let a be the bushels of seed corn needed to produce a bushel corn. Assume labor is necessary to produce corn:

a0 > 0

Assume that a surplus product is produced, in that more than a bushel corn is produced for every bushel of seed that is planted:

0 < a < 1

The table below shows how each person-year of workers hired by the capitalists are allocated.

Distribution of a Work in the Current Year
Labor TimePurpose
1 - aTo produce (1 - a)/a0 commodities to consume at the end of the current year.
a (1 - a)To produce capital-goods to be used to produce (1 - a)/a0 commodities to consume at the end of the next year.
a2 (1 - a)To produce capital-goods to be used to produce capital goods to produce (1 - a)/a0 commodities to consume at the end of two years hence.
a3 (1 - a)To produce ... (1 - a)/a0 commodities to consume at the end of three years hence.
. . .. . .

Recall the sum of a geometric series:

1 + a + a2 + a3 + . . . = 1/(1 - a)

So some algebra shows that the labor expended at a moment of time for the purposes shown in the table is indeed one person-year.

This is very simple, of course. The heterogenous nature of capital goods is not shown, even though such heterogeneity is essential for the full articulation of these ideas. In a capitalist economy, nobody is in charge of ensuring that the labor force is allocated so as to produce commodities for consuming now and in the future. The social division of labor comes about through participants responding to prices, orders, contracts, and so on, as they perceive them. A structure of production exist at any moment of time, refracting (not necessarily consistent) plans and expectations about what can be sold in the future.

Even in this simple example, variations can be introduced. Suppose the economy is expected to grow. And suppose that one expects technical progress to reduce one or both coefficients of production at some rate. Then the allocation of labor would not be as in the table. Pasinetti's vertically hyper-integrated sectors help in the analysis here.

Another question is if the plans implicit in the allocation of labor at a moment in time will be realized in the years to come. This realization depends on the mix of decisions to consume and save, now and in time to come. But those decisions are constrained by income, which depends on the decisions to hire workers for wages today. An independent equilibrium does not exist that is just being followed by agents in the economy. Instead, possible and actual future paths are being laid down, tile by tile, plank by plank. Thus, as Paul Davidson has argued, Post Keynesians have an appreciation of the distinction between uncertainty and risk that economists of the Austrian school lack.

Thursday, April 25, 2024

Austrian School Claims About The Period Of Production And Capital

1.0 Introduction

Economists of the Austrian school generally retain some concept that lower interest rates incentivize capitalists or entrepreneurs to adopt more lengthy production processes, in some sense, while still rejecting aggregate physical measures of roundaboutness or capital intensity. This post collects some quotations of economists of the Austrian school or Austrian-adjacent saying such or saying something confused about the Cambridge Capital Controversy. I want to recall this post.

2.0 Hayek on the Mythology of Capital

Hayek's 1936 paper is, I think, often cited by Austrian economists. I can agree with the following:

"The basic mistake – if the substitution of a meaningless statement for the solution of a problem can be called a mistake – is the idea of capital as a fund which maintains itself automatically, and that, in consequence, once an amount of capital has been brought into existence the necessity of reproducing it presents no economic problem. According to Professor Knight, 'all capital is normally conceptually, perpetual,' 'its replacement has to be taken for granted as a technological detail,' and in consequence 'there is no production process of determinate length, other than zero' or 'all history,' but 'in the only sense of timing in terms of which economic analysis is possible, production and consumption are simultaneous.'" Hayek 1936: 201-202.

I think Bohm-Bawerk has a metaphor of capital as like a lake, with a stream flowing in and another one out. The streams may have the same volume of water flowing at the same rate, but the depth of the lake still matters.

Here is a less well-posed objection Hayek has to Knight:

"it is asserted that 'making an item of wealth more durable' or 'using a longer period of construction,' i.e. lengthening the time-dimension of investment in either of the two possible ways, is only one among an 'accurately speaking, infinite number' of possible ways of investing more capital, which are later even described as 'really an infinite number of infinities.'" Hayek 1936: 202

And here Hayek clearly makes a mistake:

"An increase of capital will always mean an extension of the time dimension of investment, that capital will be required to bring about an increase of output only in so far as the time dimension of investment is increased." Hayek 1936, p. 204

Hayek is considering the analysis of the choice of technique in a given state of technical knowledge:

"It should be quite clear that the technical changes involved, when changes in the time structure of production are contemplated, are not changes in technical knowledge." Hayek 1936: 205

And here Hayek rejects Böhm Bawerk's measure of the period of production:

"It is not proposed, and is in fact inadmissible, to reduce the description of the range of periods for which the different factors are invested to an expression of a single time dimension such as the average period of production." Hayek 1936: 206

3.0 de Soto on Reswitching

I skip ahead to this century. Here is a deeply confused quotation:

"growth in voluntary saving always causes, in prospective terms, a ‘lengthening’ of the productive structure, irrespective of whether techniques which were only profitable at higher interest rates are readopted in certain new investment processes - all initial factors (land, labor, and existing capital goods) are subjectively deemed to be 'original means of production' which merely determine the starting point of the production process. It is therefore irrelevant whether or not the new investment process incorporates techniques which, considered individually, may have been profitable at higher rates of interest." de Soto (2006)

Considering which techniques are cost minimizing at different rates of interest is an analysis conducted in a comparision of long period positions. It is questionable if it even makes sense to talk about an interest rate on money in an intertemporal equilibrium, that being the model in which initial quantities of capital goods are given. Some fans of Austrian economics have recently injected confusion into the entry on the Cambridge Capital Controversy. De Soto is certainly a 'reliable source', though, in Wikipedia terms.

4.0 Yeager on the CCC

Leland Yeager was, at least, sympathetic to the Austrian school. He re-introduced something like a period or production, where that period depends on prices:

"The paradoxes dissolve when we recognize that the amount of that factor required in a physically specified production process does indeed depend on its own price." (Yeager 1976)

I do not think his definition is clear. He calls this measure 'waiting':

"We have to recognize waiting as a factor of production—the tying-up of value over time." (Yeager 1976)

And he is clear about how it is dependent on prices:

"the amount of waiting required in accomplishing a physically specified purpose does depend on its own price." (Yeager 1976)

In their response to comments on their retrospective, Cohen and Harcourt say, as I recall, that Yeager misunderstood the issues. Traditional marginalist theory is about the allocation of given resources. Those given resources are land, labor, and capital. What does it mean to talk about a given quantity of capital in the theory? Yeager's waiting does not help answer this question.

At any rate, Yeager recognizes consumption-reversal remains a challenge:

"One paradox not cleared up to my full satisfaction concerns consumption... It seems inadequate to reply that labor is not the only factor of production and that the higher output per man in [a] technique ... does not, at all interest rates, mean higher output in relation to labor and waiting together." (Yeager 1976)

Yeager claims that not fully specifying a traverse limits the CCC:

"Standard theory need not be embarrassed by stories that do not even say how the interest rate is determined and changed, why one economy might be in a steady state employing one technique and an otherwise similar economy in a steady state employing another, or how an economy might make a transition between such states." (Yeager 1976)

I conclude with one more quotation:

"the concept of an aggregate of physical capital is inherently fuzzy. Some capital goods are always being worn out and scrapped, and new ones are always being constructed. Whether the aggregate is growing or shrinking or staying unchanged may be hard to say, especially since unforeseen changes in technology and tastes are always occurring and raising or lowering the market values and the genuine usefulness of particular capital goods." (Yeager 1976)

5.0 Cachanosky and Lewin

Cachanosky and Lewin champion an old measure of the period or production:

"It is the (present-) value-weighted amount of time involved in the investment. As such, it is a money-value of time measure. It can be easily show that it is also the elasticity of the NPV with respect to the discount factor f. Therefore, Duration (D) can be interpreted as a measure of 'roundaboutness' and also of the sensitivity of the value of the investment to changes in the interest rate." (Lewin and Cachanosky 2019b)

I know this measure from Hicks' Value and Capital. They also cite Macaulay, a researcher in finance about contemporary with Hicks' work. Duration depends on prices. Fratini recalls that this measure requires a division of zero in an equilibrium. I have noticed a lack of appreciation of the wage-rate of profits frontier in some literature from Austrian school economists.

Anyways, they present Duration in the context of Austrian business cycle theory:

"In its most generic form, the ABCT posits a scenario in which, because of an unsustainably low discount rate, many investors mistakenly invest in unsustainable (ultimately unprofitable) ventures. A surge of investments characterized by higher Durations as a result of the lower rate of discount, is followed eventually by a surge of business failures reversing this trend, bouncing back to lower Duration, safer, investments. Regardless of whether the Duration of some investments rise more or less than others, thus changing the ranking of ventures in terms of their Durations, investors are in general choosing higher duration investments." (Lewin and Cachanosky 2019b)

I am not sure quite what is being claimed in that last sentence, especially with the phrase, "in general".

Anyways, they resist explicitly equating Duration to a measure of the quantity of capital, although I thought that was the point:

"our definition of capital does not suggest that more capital and less labor is implied by an increase in Duration. These are the very aggregate concepts that are rejected by our approach." (Lewin and Cachanosky 2019b)

Consumption reversal might still be an issue for Cachanosky and Lewin.

6.0 Conclusion

I do not know how much more literature I want to look at. Above, I have nothing to say about Hayek's triangles or Hayek (1941). I skip over Roger Garrison's more recent book, too, and much more. Apparently, Cachanosky and Lewin have an even more recent book where they might have a response to Fratini.

  • Cachanosky, N and P. Lewin. (2018). The role of capital structure in Austrian business cycle theory. Journal of Private Enterprise, 8(2): 268–280.
  • de Soto, J. H. (2006). Money, Bank Credit, and Economic Cycles, 1st English ed. (trans. by M. A. Stroup) Auburn: Ludwig von Mises Institute.
  • Fratini, S.M. (2019a) A note on re-switching, the average period of production and the Austrian business-cycle theory. Review of Austrian Economics. 32 (4): 363-374
  • Fratini, S.M. (2019b) Re-switching and the Austrian business-cycle theory: A rejoinder. Review of Austrian Economics. 32 (4): 368-389.
  • Hayek, Friedrich A. (1936). The mythology of capital. Quarterly Journal of Economics 50: 199-228.
  • Hayek, Friedrich A. (1941). The Pure Theory of Capital. Chicago: University of Chicago Press.
  • Lewin, P. and Cachanosky, N. (2019a) Austrian capital theory: A modern survey of the essentials. Cambridge: Cambridge University Press.
  • Lewin, P. and Cachanosky, N. (2019b) Re-switching, the average period of production and the Austrian business-cycle theory: A comment on Fratini. Review of Austrian Economics. 32 (4):375-382.
  • Yeager, Leland B. (1976). Capital paradoxes and the concept of waiting. In Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (Ed. by Mario Rizzo). Lexington: D. C. Heath.

Monday, April 22, 2024

A Perverse Switch Point For Neoclassical Economics, Non-Perverse For Austrians

Figure 1: The Wage-Rate of Profits Frontier
1.0 Introduction

This post completes a demonstration that the economic life of a machine is independent of the capital-intensity of a technique. I here fill in the upper right of a two-by-two table. I have previously filled in the upper-left and lower right entries. And I also have an example for the lower left.

2.0 Technology

Tables 1 and 2 present coefficients of production for processes which can be combined to produce a new output of corn. The example has the structure of one from Salvatore Baldone. Corn is assumed to be the sole consumer good and the numeraire. In the first process, labor works with corn input to produce a machine with a physical life of three years. Labor works with seed corn and machines of the specified age, in each of the remaining processes, to produce a unit of corn and machines a year older. The machine is discarded after being operated in the last process.

Table 1: Inputs for The Technology
New Machines0100
One-Year Old Machines0010
Two-Year Old Machines0001

Table 2: Outputs for The Technology
New Machines1000
One-Year Old Machines0100
Two-Year Old Machines0010

3.0 Choice of Technique

Three techniques exist for producing a net output for corn. The Alpha, Beta, and Gamma technique differ in the economic life of the machine. In Alpha, the economic life of the machine continues to be one-year, while it remains its full physical life of three years in Gamma. Figure 1, at the top of this post, displays the wage curves for the three techniques. Gamma is cost-minimizing at a low rate of profits. Beta is cost-minimizing at an intermediate rate of profits, and Alpha is cost-minimizing at a high rate of profits. The wage curves for the Alpha and Beta techniques intersect at a low rate of profits within the frontier.

Perhaps this example is clarified by looking at prices. As shown in Figure 2, the price of a new machine is positive for the whole range of feasible rate of profits in the system of equations for each technique. Figure 3 graphs the prices of old machine of each age as a function of the rate of profits. Suppose the machine is operated for its physical life of three years, as under Gamma. The price of a two-year old machine is positive for rates of profits up to a switch point with Beta, at approximately 61 percent. The price of a one-year old machine is positive even for rates of profits slightly higher. Thus, the analysis of the choice of production based on prices confirms that Gamma is cost-minimizing at low rates of profits.

Figure 2: The Price Of A One-Year Old Machine

Figure 2: The Prices Of Old Machines

The price of a two-year old machine under Beta is zero. The price of a one-year old machine, when it is operated for two years, is positive between a rate of profits of approximately 24 and of 73 percent. That is, in a range of high rates of profits where Gamma is no longer cost-minimizing, Beta is cost-minimizing in the indicated range. Finally, Alpha is cost-minimizing in the highest range of profits, when the prices of one-year old and two-year old machines is negative under both Beta and Gamma.

If the physical life of a machine were two years, this example would be one of a reswitching. Around the switch point between Alpha and Beta at approximately 73 percent, a lower rate of profits is associated with a decreased value of capital per worker and an increased net output of corn per worker. On the other hand, around this switch point, a lower rate of profits is associated with an increased economic life of the machine.

4.0 Conclusion

This example fills in the upper right of this table. Table 1. The economic life of a machine is independent of the capital intensity of the techniques in which the machine is operated.

Friday, April 19, 2024

A Letter From Marx To Engels In 1858 Outlining His Critique Of Political Economy

I have previously repeated some transcriptions from the correspondence Marx and Engels. I tried to concentrate on some formulations from Engels of ideas important in Marxism, Marx stating what is important and novel in Capital, or outlines of the project, particularly concentrating on the so-called transformation problem. This long letter certainly belongs in this collection.

Marx's ideas were fairly well-developed in 1858. Here he has promised Duncker, a publisher, to write what eventually became A Contribution to the Critique of Political Economy. After delay, he only delivered to the publisher the first part of what he was aiming for. I have always found this short book less inspiring, as compared with Capital. Capital does not contain anything on advocates of labor notes, though. The introduction is notable for a short statement of historical materialism, with various aphorism. It went through German (Prussian?) censorship, but I have never seen anybody comment on that. Marx thought his work was scientific, I guess, and thus the censors could not object.

Anyways, we see that Marx only published the first of six parts that he had planned, and only the first subpart of that. Volume 3 of Capital has something on land and rent. And one could argue that he incorporated some of his theory of wages into volume 1. But his developed publications do not contain anything explicit on the state, international trade, and the world market. I think, with his work habits, if Marx promised a few pages, you can expect a long chapter. If he promised a chapter, you can expect a book. Or maybe you will never get anything.

I include the start of this letter for completeness. I did not look up what the first two paragraphs are about, other than to see that the battle of Alma was part of the Crimean war.

2 April 1858

Dear Frederick

The Guardian stories highly AMUSING. A correspondent of the Daily Telegraph (DIRECTLY UNDER PAM'S AUSPICES) writes of the great danger of being 'DEAF' in Paris, and says that all 'DEAF ENGLISHMEN' were being hounded by the police as Allsops. Also that ENGLISHMEN were leaving Paris en masse, partly because of police chicanery, partly for fear of an outbreak. For if the latter were to happen and the Bonapartists be victorious, the John Bulls feared they might be massacred by the MADDENED SOLDIERS, whereat the correspondent himself naively comments that IN SUCH A CASE [HE] SHOULD LIKE TO BE ANYWHERE ELSE BUT IN PARIS. This DESERTION by the Bulls AT THIS MOMENT OF COMMERCIAL DEPRESSION is queering the pitch of the Parisian épicier and householdr, whores, etc. Have you seen that 300 million francs have AVOWEDLY 'DISAPPEARED' FROM THE BUDGET, AND NOBODY KNOWS WHAT HAS BECOME OF THEM? There will, BY AND BY, be further REVELATIONS about Bonapartist FINANCE, and then the asses on the Tribune will realise the wisdom of not having published the very ELABORATED ARTICLES I sent them on the subject six months ago.219 The fellows are asses and anything which is not, in the crudest sense, a 'question of the day' they tend to cast aside as UNINTERESTING, only to go and compile the most egregious rubbish about the selfsame subject as soon as it does become à l'ordre du jour.

Nota bene: in the military clubs here it is being rumoured that EVIDENCE has been discovered among the papers left by Raglan that, 1. at the battle of the Alma he rightly suggested to attack the Russians, not from the direction of the coast, but from the opposite flank, and drive them into the sea; 2. that he proposed to advance on Simferopol after the batde of the Alma; 3. that at Inkerman it was only by dint of the most urgent pleas and MENACES that he extorted from Canrobert the order for Bosquet to hasten to his [Raglan's] assistance. It is further said that, if the boasting on the other side of the Channel were to continue, these PAPERS would be published, providing proof that the French were ever ready TO BETRAY THEIR DEAR ALUES. Indeed, a few HINTS which de Lacy Evans dropped in the HOUSE OF COMMONS seem to indicate something of the kind.

I've been so ill with my bilious complaint this week that I am incapable of thinking, reading, writing or, indeed, of anything SAVE the ARTICLES for the Tribune. These, of course, cannot be allowed to lapse since I must draw on the curs as soon as possible. But my indisposition is disastrous, for I can't begin working on the thing for Duncker until I'm better and my fingers regain their VIGOUR and GRASP.

The following is a SHORT OUTLINE OF THE FIRST PART. The whole thing is to be divided into 6 books: 1. On Capital. 2. Landed Property. 3. Wage Labour. 4. State. 5. International Trade. 6. World Market.

1. Capital falls into 4 sections, a) Capital en général. (This is the substance of the first instalment.) b) Competition, or the interaction of many capitals, c) Credit, where capital, as against individual capitals, is shown to be a universal element, d) Share capital as the most perfected form (turning into communism) together with all its contradictions. The transition from capital to landed property is also historical, since landed property in its modern form is a product of the action of capital on feudal, etc., landed property. In the same way, the transition of landed property to wage labour is not only dialectical but historical, since the last product of modern landed property is the general introduction of wage labour, which then appears as the basis of the whole business.

WELL (IT IS DIFFICULT FOR ME TO-DAY TO WRITE), let us now come to the corpus delicti.

I. Capital. First section: Capital in general. (Throughout this section wages are invariably assumed to be at their minimum. Movements in wages themselves and the rise and fall of that minimum will be considered under wage labour. Further, landed property is assumed to be zero, i. e. landed property as a special economic relation is of no relevance as yet. Only by this procedure is it possible to discuss one relation without discussing all the rest.)

1. Value. Simply reduced to the quantity of labour; time as a measure of labour. Use-value—whether regarded subjectively as the USEFULNESS of labour, or objectively as the UTILITY of the product—is shown here simply as the material prerequisite of value, and one which for the present is entirely irrelevant to the formal economic definition. Value as such has no 'substance' other than actual labour. This definition of value, first outlined by Petty and neatly elaborated by Ricardo, is simply bourgeois wealth in its most abstract form. As such, it already presupposes 1. the transcending of indigenous communism (India, etc.), 2. of all undeveloped, pre-bourgeois modes of production which are not in every respect governed by exchange. Although an abstraction, it is an historical abstraction and hence feasible only when grounded on a specific economic development of society. All objections to this definition of value derive either from less developed relations of production or else are based on confused thinking, whereby the more concrete economic definitions from which value has been abstracted (and which may therefore also be seen, on the other hand, as a further development of the same) are upheld as against value in this its abstract, undeveloped form. In view of the uncertainty of messieurs les économistes themselves about the precise relation of this abstraction to later, more concrete forms of bourgeois wealth, these objections were plus ou moins justified.

The contradiction between the general characteristics of value and its material existence in a particular commodity, etc.—these general characteristics being the same as those later appearing in money—gives rise to the category of money.

2. Money.

Some discussion of precious metals as vehicles of the money relation.

a) Money as a measure. A few comments on the ideal measure in Steuart, Attwood, Urquhart; in more comprehensible form among the advocates of labour money (Gray, Bray, etc. An occasional swipe at the Proudhonists). The value of a commodity translated into money is its price. For the moment price appears only in this purely formal distinction between it and value. Thus, in accordance with the general law of value, a specific amount of money merely expresses a specific amount of objectified labour. In so far as money is a measure, the variability of its own value is of no importance.

b) Money as a means of exchange, or simple circulation.

Here we need only consider the simple form of circulation as such. All the other conditions by which it is determined are external to it, and hence will not be considered till later (presuppose more highly developed relations). If the commodity be C and money M then, although simple circulation evinces the two circuits or final points: C—M—M—C and M—C—C—M (this latter constituting the transition to c), the point of departure and the point of return in no way coincide, save by chance. Most of the so-called laws put forward by economists do not consider money circulation within its own confines, but as subsumed under, and determined by, higher movements. All this must be set aside. (Belongs in part to the theory of credit; but also calls for consideration where money appears again, but further defined.) Here, then, money as means of circulation (coin). But likewise as realisation (not simply evanescent) of price. From the simple statement that a commodity, in terms of price, has already been exchanged for money in theory before it is so exchanged in fact, there naturally follows the important economic law that the volume of the circulating medium is determined by prices, not vice versa. (Here, some historical stuff on the polemic concerning this point.) Again it follows that velocity may be a substitute for volume, but that a certain volume is essential to simultaneous acts of exchange in so far as the relation of these themselves is not that of + and —, an equalisation and consideration which will only be touched on at this juncture by way of anticipation. At this point I shall not go further into the development of this section and would only add that the lack of congruence of C—M and M—C is the most abstract and superficial form in which the possibility of crises is expressed. If the law concerning the determination of circulating volume by prices be developed, it will be found that the assumptions made here are by no means applicable to all states of society; hence the fatuity of comparing e.g. the influx of money from Asia into Rome and its effect on prices there tout bonnement with modern commercial relations. On closer examination, the most abstract definitions invariably point to a broader, definite, concrete, historical basis. (OF COURSE, since to the extent that they are definite they have been abstracted therefrom.)

c) Money qua money. This is a development of the formula M—C—C—M. Money, the independent existence of value as opposed to circulation; material existence of abstract wealth. Already manifested in circulation in so far as it appears, not only as a means of circulation, but as realising price. In this capacity c), in which a) and b) appear to be no more than functions, money is the universal commodity of contracts (here the variability of its value acquires importance: value being determined by labour time); it becomes an object of HOARDING. (This would still seem to be an important function in Asia, as formerly in the ancient world and in the Middle Ages GENERALLY. Now persists only in a subordinate capacity within the banking system. In times of crisis money in this form again acquires importance. In this form money considered along with the world-historical DELUSIONS which it engenders, etc. Destructive properties, etc.) As the realisation of all higher forms in which value will appear; definitive forms in which all relations of value are externally concluded. Money, however, once fixed in this form, ceases to be an economic relation which is lost in its material medium, gold and silver. On the other hand, in so far as money comes into circulation and is again exchanged for C, the final process, the consumption of the commodity, again falls outside the economic relation. The principle of self-reproduction is not intrinsic to simple money circulation, which therefore implies something extrinsic to itself. Implicit in money—as the elaboration of its definitions shows—is the postulate capital, i.e. value entering into and maintaining itself in circulation, of which it is at the same time the prerequisite. This transition also historical. The antediluvian form of capital is commercial capital, which always generates money. At the same time the emergence of real capital, either from money or merchant capital, which gains control of production

d) This simple circulation, considered as such—and it constitutes the surface of bourgeois society in which the underlying operations which gave rise to it are obliterated—evinces no distinction between the objects of exchange, save formal and evanescent ones. Here we have the realm of liberty, equality and of property based on 'labour'. Accumulation, as it appears here in the form of HOARDING, is merely greater thrift, etc. On the one hand then, the fatuity of the economic harmonists, modern free traders (Bastiat, Carey, etc.), in upholding this most superficial and most abstract relation of production as their truth, as against the more advanced relations and their antagonisms. Fatuity of the Proudhonists and suchlike socialists, in contrasting the ideas of equality, etc., corresponding to this exchange of equivalents (or presumed AS SUCH), to the inequalities, etc., to which this exchange reverts and from which it emanates. In this sphere, appropriation by labour, the exchange of equivalents, appears as the law of appropriation so that exchange simply returns the same value in another material form. In short, while everything may be 'lovely' here, it will soon come to a sticky end and this as a result of the law of equivalence. For now we come to

3. Capital.

This is really the most important part of the first instalment and one on which I particularly need your opinion. But today I can't go on writing. My bilious trouble makes it difficult for me to ply my pen, and keeping my head bent over the paper makes me dizzy. So FOR NEXT TIME.



K. M.

There is a lot in this letter. In much of Capital, Marx takes wages as at a given level, but not always. The given level does not have to be a physical subsistence. We see the order of exposition is value, money, capital. The simple circulation of commodities, with money as an intermediary, provides the possibility of crises. Marx asserts the theory of endogenous money. Much is given here about presenting his ideas as in opposition to the Ricardian socialists. Marx gestures that his account of exploitation is consistent with justice in exchange.

Saturday, April 13, 2024

The Fundamental Sraffian Theorem

1.0 Introduction

I have been reading Robin Hahnel. Hahnel argues even more strongly than Steedman did that labor values are redundant. And he argues for the importance of the fundamental Sraffian theorem. I think this may be Hahnel's coinage. Anyways' this is my working my way through some of what I think he is saying.

Hahnel has some interesting things to say, not discussed here, about analyzing environmental concerns in a Sraffian framework. I ignore the chapter in Hahnel (2017) on the moral critique of capitalism. Following Eatwell (2019) and others, I hold that mainstream economists do not have a theory of value and distribution, anyways.

2.0 The Setting

Suppose a capitalist economy is observed at a given point in time. n commodities are being produced, each by a separate industry. Suppose the technique in use can be characterized by a row vector a0 and a n x n square matrix A. Let the column vector d denote the quantities of each commodity paid to the workers for a unit of labor.

The jth element of a0 is the amount of labor directly employed in the jth industry in producing one unit of a commodity output from that industry. "We suppose labour to be uniform in quality or, what amounts to the same thing, we assume any differences in quality to have previously been reduced to equivalent differences in quantity so that each unit of labour receives the same wage…" - Piero Sraffa (1960).

The jth column of A is the goods used up in producing one unit of a commodity output. For example, suppose iron is produced by the first industry and steel is produced by the second industry. a1,2 is then the kilotons of iron needed to produce a kiloton of steel. Assume that every good enters directly or indirectly into the production of each commodity. Iron enters indirectly into the production of tractors if steel enters directly into the tractor industry. Assume a surplus product, also known as a net output, exists. That is:

0 < λPF(A) < 1

where λPF(A) is the dominant eigenvalue of the matrix A. The dominant eigenvalue is also known as the Perron-Frobenius root.

3.0 Prices of Production

Suppose the wage purchases the specified bundle of commodities. And also assume the wage is advanced. One can define the input-output matrix with wage goods included:

A+ = A + d a0

I think that Sraffa treats the input-output matrix as A+ in chapter 1 of his book.

The system of equations for prices of production is:

p A+ (1 + r) = p

where p is a row vector, and r is the rate of profits. One can show that, given a surplus product, not including wage goods, a solution exists.

Fundamental Sraffian Theorem: The rate of profits, r, in the system of prices of production is positive if and only if:

0 < λPF(A+) < 1

In fact, the rate of profits is:

r = 1/λPF(A+) - 1

Under these assumptions, the price of each produced commodity is positive with the above rate of profits. And this economically meaningful solution is unique, up to the specification of a numeraire.

4.0 Increased Surplus Product

Suppose one or more of the elements of A+ decrease. Then 1 - λPF(A+), which is strictly positive, increases. The surplus product that capitalists capture is increased by decreased components of the real wage and by decreased commodity inputs into production.

Suppose that the real wage is given and that an innovation results in a new technique, B, being available. This technique might have increased coefficients and decreases in other coefficients, as compared to A. It might even have a new column or delete a column for an industry that is not used to directly produce a wage good. This new technique is adopted at the given wage if and only if:

1 - λPF(B+) > 1 - λPF(A+)

Suppose further that:

1 - λPF(B) < 1 - λPF(A)

Then the maximum rate of profits, at a wage of zero, decreases. Suppose no reswitching exists. I think this is what is meant by Capital-Using, Labor-Saving technical change. This is also known as Marx-biased technical change. Marx's law of the tendency of the rate of profits to fall, presented in volue 3 of Capital, is not justified by this analysis.

5.0 Quantity Flows

This framework can also be used to examine the rate of growth. Suppose employment, at an instant of time, is unity:

L = a0 q = 1

where q isthe column vector of gross outputs. In this formulation, employment increases at the rate of growth.

Let consumption out of the surplus product be in the composition of the column vector e, and let c be the level of such consumption. It is most coherent to take this consumption as not made by the workers:

We could hardly imagine that, when the workers had a surplus to spend on beef. their physical need for wheat was unchanged. -- Robinson (1961)

So prices of production associated with this treatment of qunatity flows are as above.

Let the column vector j represent investment goods. These are part of the surplus product. Then the column vector q of gross outputs satisfies the following equation:

q = A+ q + c e + j

The above is extremely general. I now consider a steady-state rate of growth. Assume constant returns to scale in every industry. The vector of investment goods is in the same proportion as existing capital goods:

j = g A+ q

Here I present a derivation, since I typed this out to check myself. Substituting the specification of investment goods and after some algebraic manipulations, one has:

c e = [I - (1 + g)A+] q

Assuming the rate of growth is less than the maximum, one has:

c [I - (1 + g)A+]-1e = q

Premultiplying by the row vector of labor coefficients, one has:

c a0 [I - (1 + g)A+]-1e = a0 q = 1

The solution of the system of equations for quantity flows is:

c = 1/{a0 [I - (1 + g)A+]-1e}

The maximum rate of growth is:

gmax = 1/λPF(A+) - 1

The level of consumption out of the surplus product is lower, the higher the rate of growth and vice versa. One can also consider the impact on the rate of growth of changes in the elements of the matrix A+. I believe one can prove the following:

Theorem: The steady state rate of growth, g is higher if:

  • Consumption out of the surplus product, where the surplus product does not include wages, is lower.
  • Necessary wages are lower.
  • The dominant eigenvalue, λPF(A), of the input-output matrix is lower.

The theorem highlights dilemmas in development economics. One does not want to obtain a higher rate of growth by lowering wages for those who are already pressed. It does not help for foreign aid to end up in luxury consumption either. In chosing the technique out of a range of possibilities, one would like the one that maximizes the rate of growth. Unless the rate of growth equals the rate of profits, that is, consumption out of the surplus product does not occur, the cost-minimizing technique is unlikely to be efficient in this sense.

6.0 Conclusion

The theory of value and distribution has a family resemblance to modern formulations of classical and Marxian political economy. Labor values are not discussed. It is focused on prices of production. Yet, with its consideration of dynamic changes in dominant eigenvalues, it seems to be consistent with an analysis of the formal and real subsumption of labor to capital. The formulation in this post can easily be generalized in various ways, Hahnel emphasizes inputs from nature and mentions the theory's consistency with homogeneous labor inputs. The analysis of growth should include technical change. I am interested in fixed capital. Some issues arise with general joint production, but the model is open in any case.

  • John Eatwell. 2019. 'Cost of production' and the theory of the rate of profit. Contributions to Political Economy.
  • Robin Hahnel. 2017. Radical Political Economy: Sraffa Versus Marx. Routledge.
  • Joan Robinson. 1961. Prelude to a critique of economic theory. Oxford Economic Papers, New Series. 13 (1): 53-58.

Saturday, April 06, 2024

Keynes And Robinson On Supposed Self-Regulating Markets

Here is John Maynard Keynes in 1926:

"Let us clear from the ground the metaphysical or general principles upon which, from time to time, laissez-faire has been founded. It is not true that individuals possess a prescriptive 'natural liberty' in their economic activities. There is no 'compact' conferring perpetual rights on those who Have or on those who Acquire. The world is not so governed from above that private and social interest always coincide. It is not so managed here below that in practice they coincide. It is not a correct deduction from the Principles of Economics that enlightened self-interest always operates in the public interest. Nor is it true that self-interest generally is enlightened; more often individuals acting separately to promote their own ends are too ignorant or too weak to attain even these. Experience does not show that individuals, when they make up a social unit, are always less clear-sighted than when they act separately.

We cannot, therefore, settle on abstract grounds, but must handle on its merits in detail, what Burke termed 'one of the finest problems in legislation, namely, to determine what the State ought to take upon itself to direct by the public wisdom, and what it ought to leave, with as little interference as possible, to individual exertion.' We have to discriminate between what Bentham, in his forgotten but useful nomenclature, used to term Agenda and NonAgenda, and to do this without Bentham's prior presumption that interference is, at the same time, 'generally needless' and 'generally pernicious.' Perhaps the chief task of Economists at this hour is to distinguish afresh the Agenda of Government from the Non-Agenda; and the companion task of Politics is to devise forms of Government within a Democracy which shall be capable of accomplishing the Agenda. -- John Maynard Keynes, The end of laissez faire. In Essays in Pursuasion, 1931

Here is Joan Robinson in 1962, from a later reprint:

"It is possible to defend our economic system on the ground that, patched up with Keynesian correctives, it is, as he put it, the 'best in sight'. Or at any rate that it not too bad, and change is painful. In short, that our system is the best system that we have got.

Or it is possible to take the tough-minded line that Schumpeter derived from Marx. The system is cruel, unjust, turbulent. but it does deliver the goods, and, damn it all, it's the goods that you want.

Or, conceding its defects, to defend it on political grounds - that democracy as we know it could not have grown up under any other system and cannot survive without it.

What is not possible, at this time of day, is to defend it, in the neo-classical style, as a delicate self-regulating mechanism, that has only to be left to itself to produce the greatest satisfaction for all.

But none of the alternative defenses really sound very well. Nowadays, to support the status quo, the best course is just to leave all these awkwards problems alone." -- Joan Robinson. 1964. Economic Philosophy. Pelican: p. 130.

Thursday, April 04, 2024

A History Of Production Processes In Volume 1 Of Capital

1.0 Introduction

I have written many posts on formal results related to my favorite interpretations of the theory of value and distribution in Marx's Capital. But Marx's work is not solely about formalism. One aspect of volume 1 is a history of production processes up to Marx's day. Much opportunity exists to build on this history. Some have done this in works I have not read much of. I have been reading Soren Mau, and many years ago I read much of Charles Babbage's On the Economy of Machinery and Manufactures. Ian Wright, too, has had something to say about the impersonal force of capital at the level of a totality. I found Harry Cleaver's study guide useful in writing this post, even though I read Capital more analytically than politically.

This post provides a brief overview of aspects of Capital I have not mentioned before. Much more can be be found in volume 1. For instance, I say nothing about business cycles here.

2.0 Primitive Accumulation

Marx does not proceed in chronological order. He concludes volume 1 with a section on primitive accumulation. He describes the enclosure movement, which led to many peasants becoming vagabonds and beggars. And he describes strict laws against such. This leads to a labor force of workers with the double freedom of being free to sell their labor power and of being free from ownership of the means of production. I do not recall much about the transformation of natural economies, in overseas colonies, to capitalist economies. For example, the imposition of money taxes on colonial subjects constrained those subjects to seek waged labor so as to obtain the needed money.

3.0 (Re)producing the Presuppositions of Capitalism

But Marx starts his exposition, more or less, with a system in which production units are coordinated by selling commodities on markets for money. His book is about, from one perspective, how capitalism produces and reproduces its own presuppositions on an expanded scale.

According to Marx, capitalism initially takes over existing processes. He calls this formal subsumption. In the putting-out system, also called the domestic system, a merchant provides handicraft workers in their homes with raw materials to work up. The merchant collects their products and sells them on the market. Even though the workers are physically isolated, this system is the beginning of the aggregation of workers into a labor force.

Chapter 13 describes co-operation, and chapter 14 describes what Marx calls manufacture. Many handicraft workers are brought together under one roof. They might all be executing the same tasks, each transforming raw materials, through several steps, into a single commodity. Or they might be producing different products, perhaps with some vertical integration. The outputs of some workers are semi-finished products used as inputs by other workers.

In chapter 10, Marx writes about struggles over the length of the working day. In the formalism, absolute surplus value is increased if workers can be made to work longer, while requiring the same length of time needed to produce the commodities that they purchase from their wages. Some of this chapter seems to be still relevant in the United States today, where many low-pay workers have more than one job. Can their employers send them home and then call them back in the same day? Do the working days for these jobs sometimes add up to 24 hours? Computer and communication technology allow your employer to call on you at any time.

Marx has an interesting story about how mill owners might have found it in their own interest for laws to be passed regulating hours and working conditions. Each mill owner in Manchester would like to hire healthy workers, overwork them, and then discard them. But if all mill owners are doing this, where are healthy workers to be found? This story could be modeled with game theory, I guess.

Once so many workers are gathered in one place, the production processes which they operate can be 'rationalized'. This redivision and reallocation of tasks is advanced along with the introduction of machinery, as Marx discusses in chapter 15, Machinery and Modern Industry.

When I was young, the Rochester Museum and Science Center had a diorama - probably on the same floor as this one - showing the inside of a mill. A wheel was turned by a waterfall, and a system of gears and pulleys delivered the power to several rows of machines. For Marx, a machine is combination of tools, such as a lever, an inclined plane, a screw, etc., where the motive power might not be a human. The motive power could be water or steam, for example.

The result of this introduction of machinery and the re-organization of tasks is what Marx calls the real subsumption of capital. The pace at which laborers work is regulated by the machine. Automation is such that workers serve the machine, not vice versa. Laborers can no longer competitively duplicate their activities outside of employment bhy capitalists.

The increase in productivity brought about by real subsumption results in the increase of relative surplus value. The length of the working day required to produce the commodities purchased by wages decreases. Even with the same length of the working day and the same basket of wage goods, surplus labor time increases. The increase in relative surplus value is even compatible with a somewhat decreased working day and a somewhat larger basket of wage goods. This increase in relative surplus value is about forces operating behind the back of capitalists. They do not fund innovation so as to decrease the necessary labor embodied in wage goods.

4.0 Extensions and Conclusion

This history can be continued. Peter Drucker is of some importance in the development of the idea of management as a profession. Taylorism, named after Frederick Taylor, the author of Principles of Scientific Management, provides analytical tools for breaking tasks down further and regimenting them. Operations Research (OR) and Command, Control, Communications, and Information (C3I) are some disciplines building on the work of Babbage. For reasons of Information Assurance (IA), even relatively privileged computer programmers do not own the means of production; in the modern corporation, almost insurmountable hoops prevent you from hooking your own devices up to the corporate intranet or sharing files between your work and personnal computer. The history extends to office work and service jobs; it is not confined to factory work.

The result of this history is a division within the workshop and other entities organized in private firms, as well as among many productive enterprises in many industries scattered over a country or many countries. For the most part, no one worker oversees the entire production of a commodity. Rather, each becomes a detail worker. I tend to assume that a Leontief input-output matrix shows the interactions of all industries, but this structure is the result of a historical process. Furthermore, every capitalist is constrained by competition. The domination of capital is not solely about the relationship between individual employers and employees. It is also about an overarching dominating logic. By the way, I know some who take pride, probably rightfully, in their work in this setting.

The question for the socialist is whether this increased productivity can be maintained, with an increased population and developed social relationships among all, while somehow abolishing this domination. Can something like this division of labor be made transparent? If so, how do we get there?