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.

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.

Salut.

Your

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.

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. a_1,2 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 < λ_PF(A) < 1

where λ_PF(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 < λ_PF(A⁺) < 1

In fact, the rate of profits is:

r = 1/λ_PF(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 Profit

Suppose one or more of the elements of A⁺ decrease. Then 1 - λ_PF(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 - λ_PF(B⁺) > 1 - λ_PF(A⁺)

Suppose further that:

1 - λ_PF(B) < 1 - λ_PF(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:

g_max = 1/λ_PF(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, λ_PF(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.

References

• 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.

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.

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?

Perverse Switch Point For Austrian Economics

Figure 1: The Wage-Rate of Profits Frontier

This post continues a series of posts demonstrating that the change in the economic life of a machine at a switch point is independent of the change of the capital intensity of the technique at a switch point. I here fill in the lower left in a a two-by-two table.

The wage curves above are for the an example with the same structure as in the previous post in this series.This is a 'one-good' model. The manager of firms know three processes to produce a widget, also known as a machine. In the first process, labor and a new widget are used to produce new widgets and a one-year old widget. In the second process, labor and a one-year old widget are used to produce new widgets and a two-year old widget. In the last process, labor and a two-year old widget are used to produce new widgets. The output coefficients, b_1,2 and b_1,3, specify how many new widgets are produced by the second and third widgets. New widgets are the only commodities that can be consumed. The numeraire is a new widget.

The choice of technique arises because managers of firms can choose different economic lifetimes for the machine. Free disposal is assumed.

One can create a system of equations for the quantity flows for each technique. The net output is one new widget. The solution shows at what level each process is operated. It also shows how many widgets of each age are advanced as capital goods and how much labor is employed, per net output.

One can also create a system of equations for prices of production for each technique. Wages are paid out of the surplus, and the same rate of profits is obtained in operating each process. Figure 1 shows the wage curves for the example, for the specified parameters, b_1,2 and b_1,3. The cost-minimizing technique is on the outer frontier.

Around the single switch point, the value of capital per worker is higher at a lower rate of profits. This is a negative real Wicksell effect, a formalization of the notion of capital deepening. A greater output per worker is associated with a lower rate of profits. So, as far as real Wicksell effects go and unlike the previous one, this example conforms to obsolete marginalist teaching.

But consider the economic life of a machine. Around the switch point, a lower rate of profits is associated with a shorter economic life of a machine. And operating the machine for a shorter time results in a greater net output per worker. A choice of a shorter life of a machine can be associated with either more or less output per worker.

The machine operates at non-constant efficiency in the example. Whether the efficiency is increasing or decreasing over various years cannot be defined, in general, in models with multiple inputs for the machine. Furthermore, the change in the properties of the analysis of the choice of technique do not need to arise from perturbing parameters for processes in which the machine is operated. These changes can arise from perturbing other processes in multicommodity models.

Figure 2: A Parameter Space for the Example

Perturbing the parameters b_1,2 and b_1,3 cannot create an example with a switch point falling into the upper right of my two-by-two table (Figure 2). Thus, I need to consider either a model with a different structure or perturbing additional parameters in ths one-good model.

Keynes And Marx

1.0 Introduction

John Maynard Keynes had some amusing jibes against Marx, but does not provide any substantial argument against the theory in Marx's Capital. In fact, one can draw parallelisms between elements of Keynes' and Marx's theories. This post provides a brief start on justifications for these assertions.

2.0 Jibes

Keynes' most explicit and most well-known statement about Marx is probably this:

"How can I accept a doctrine which sets up as its bible, above and beyond criticism, an obsolete economic textbook which I know to be not only scientifically erroneous but without interest or application for the modern world? How can I adopt a creed which, preferring the mud to the fish, exalts the boorish proletariat above the bourgeois and the intelligentsia vho, with whatever faults, are the quality in life and surely carry the seeds of all human advancement? Even if we need a religion, how can we find it in the turbid rubbish of the Red bookshops? It is hard for an educated, decent, intelligent son of Western Europe to find his ideals here, unless he has first suffered some strange and horrid process of conversion which has changed all his values." - Keynes, 1931

This is from his essay, 'A short view of Russia'. One might also want to look at the essays, 'Am I a Liberal?' and 'Liberalism and Labour'. These three were all republished in Essays in Pursuasion. The latter two are more about party politics in Britain in the 1920s.

3.0 The General Theory, Including Drafts

Keynes distinguished, in drafts of the General Theory, between three types of economies. He designated the first type as a barter of co-operative economy. The second type is a neutral entrepreneur economy or a neutral economy, for short. This type is summarized by Marx's symbols C-M-C and acts like the first type. Agents exchange commodities for commodities, with money acting as an intermediary, but having no independent effect on the course of events. A monetary theory of production, though, deals with a money-wage economy, also known as an entrepreneur economy. This type is characterized with Marx's symbols M-C-M'. Money matters in all runs. I rely on secondary literature which I do not reference below.

Another parallelism between Keynes and Marx is in the choice of units:

"In dealing with the theory of employment I propose, therefore, to make use of only two fundamental units of quantity, namely, quantities of money-value and quantities of employment. The first of these is strictly homogeneous, and the second can be made so. For, in so far as different grades and kinds of labour and salaried assistance enjoy a more or less fixed relative remuneration, the quantity of employment can be sufficiently defined for our purpose by taking an hour's employment of ordinary labour as our unit and weighting an hour's employment of special labour in proportion to its remuneration; i.e. an hour of special labour remunerated at double ordinary rates will count as two units. We shall call the unit in which the quantity of employment is measured the labour-unit; and the money-wage of a labour-unit we shall call the wage-unit." -- Keynes. 1936.

The above seems close to Marx's theory of value.

4.0 After The General Theory

I pick two examples of others drawing on parallels between Keynes and Marx. Perhaps the above section heading is unfair to Kalecki. When he visited Cambridge, the Keynesians found that he was in on all their jokes. Kalecki divides the economy into a sector producing consumer goods and a sector producing investment goods. He was aware of Rosa Luxemburg, and Luxemburg built on Marx's schemes of simple and expanded reproduction.

Joan Robinson (1953) makes the point about units of measurement that I note above. She had a lot more to say about Marx.

5.0 Conclusion

Many have had lots more to say about the relationship of the ideas of Keynes and Marx. One question is whether Marx was wrong to claim that the development of capitalism will lead to its own demise, perhaps in the depth of a great depression. Does not Keynes provide the political tools to keep capitalism going indefinitely? Some Marxists rejected Keynesianismn on these grounds.

Another question is about long-run theory. Keynes' General Theory is not confined to the short run. No need exists for the labor market to eventually clear. Sraffa provides a theory of prices consistent with a non-clearing labor market, and he takes output as given. Should there not be a theory that integrates the approaches of Keynes and Sraffa? But this has been on the agenda for decades.

Lots more can be said.

References

• Michal Kalecki, 1943. Political aspects of full employment, Political Quarterly.
• John Maynard Keynes, 1931. Essays in Persuasion.
• John Maynard Keynes, 1936. The General Theory of Employment, Interest and Money. Harcourt, Brace and Company.
• Joan Robinson, 1953. An open letter from a Keynesian to a Marxist.