Labor Values And Invariants

1.0 Introduction

This post is an attempt to work through some linear algebra that some have used to understand Karl Marx's Capital. I have recently explained how, in a simple model, prices of production are equal to labor values if the organic composition of capital does not vary among industries. That special case is the setting of volume 1.

In capitalism, workers rent themselves out to their employers. They work longer, under the dominion of capital, than needed to produce the commodities which they purchase with their wages. Marx explains the returns to ownership (profits, interest, rent, etc.) by the distinction between the use value and the exchange value of labor power.

This post removes the special case assumption. It considers certain relationships between the system of labor values and the system of prices of production. These relationships are highlighted towards the start of volume 3. I ignore Hegel, on his head or otherwise.

2.0 Quantity Flows

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.

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.

Let y be the column vector of net outputs and q the column vector of gross outputs, both in physical terms. In Leontief's work, y is taken as given. Gross outputs and net outputs are related as:

y = q - A q

Or:

q = (I - A)^-1 y

The labor force needed to produce this net product is:

a₀ q = a₀ (I - A)^-1 y = 1

I have taken units in which labor is measured to be such that this labor force is unity. Employment is such that the net output is produced, the capital goods in producing the net output are reproduced, the capital goods used in producing those capital goods are reproduced, and so on.

3.0 Labor Values

Let e_j be the jth column of the identity matrix. The labor force needed to produce this net output is:

v_j = a₀ (I - A)^-1 e_j

That is, the (direct and indirect) labor needed to produce a net output of one unit of the jth commodity is v_j. The row vector of labor values is:

v = a₀ (I - A)^-1

4.0 Prices of Production

At any time, market prices are such that different industries are making different rates of profits. Under competitive conditions, without barriers to entry in the various industries, a kind of leveling process is going on.

One can imagine a vector of prices such that this leveling process is already completed with the observed technique and wage. Let p be that row vector of prices of production, with all industries obtaining the same rate of profits.

I need an assumption about the composition of commodities purchased from the wage, w, since I want to explore the labor value embodied in the wage. Accordingly, assume that the wage is a proportion of the final product. The wage ranges from zero to unity, inclusive. The physical composition of the wage is w y. Wages are advanced. Define:

A^*(w) = A + w y a₀

I gather the vector operation at the end of the above expression is the outer product. Prices of production satisfy the equation in the following display:

p A^*(w) (1 + r) = p

where r is the rate of profits. That is, p is a price vector consistent with the observed technique and wage.

By the Perron-Frobenius theorem, the eigenvalue of A^*(w) with the maximum modulus is real, positive, and does not exceed unity. The corresponding rate of profits is non-negative. The eigenvector consists of all positive entries. Thus a solution exists for the above equation. Furthermore, the wage and the rate of profits are related by a decreasing function. The maximum wage occurs at a rate of profits of zero. The maximum rate of profits is finite and occurs at a wage of zero.

Prices of production have been found up to a scaling factor. They are generally not proportional to labor values, as Ricardo and Marx knew.

5.0 Invariants

The scale for prices of production can be fixed by specifying a numeraire. Consider, instead, the imposition of an identity between the system of labor values and the system of prices of production.

5.1 Case 1: Total Gross Output

The labor value of gross output is equal to the price of gross output if and only if:

v q = p q

Imposing the above condition fixes the scale for prices.

5.2 Case 2: Total Net Output

Alternatively, the labor value of net output is equal to the price of net output if and only if:

v y = p y = 1

I have taken advantage above of the scaling of units of labor time. This invariant is my favorite of the three invariants considered here.

5.3 Case 3: The Rate of Profits

The labor value of advanced capital is v A^*(w) q, while its price is p A^*(w) q. The labor value of profits is:

(1 - w) v y = (1 - w)

The rate of profits does not differ between the system of labor values and the system of prices if and only if:

(1 - w)/[v A^*(w) q] = (1 - w) p y/[p A^*(w) q]

6.0 Concluding Observation

The above post has defined three invariants, each equating a sum or ratio of labor values to the corresponding sum or ratio in the system of prices of production. Only one invariant can generally hold, though, in the given model. This has led to quite a bit of literature arguing that one of these or other invariants is central to Marx's argument.

Some have another approach. They adopt another model in which all three invariants hold. In fact, more than one such model has been developed.

An approach I find of interest looks at a special composition of final output. Whatever the composition of the final output, one can iterate by looking at the composition of the capital goods used in producing that final output. A number of iterations leads to a composite commodity of close to the output of something like Marx's industry of average organic composition of capital.

Or one can retain an interest in how labor is allocated among industries, while exploring prices of production with an arbitrary numeraire. The fundamental theorem of Marxism holds in this setting. Must one draw quantitative relationships between the system of labor values and the system of prices of production?

Others might want to explore the historical and empirical evolution of the parameters of the model in the post and related models.

Reference

• Francis Seton. 1957. The 'Transformation Problem'. Review of Economic Studies 24 (3): 149-160.

Utility Maximization A Tautology?

Economists proved over half a century ago that certain stories are unfounded in the theory. For example, one might think that if some workers are involuntarily unemployed, a drop in real wages would lead to a tendency for the labor market to clear. The Cambridge Capital Controversy revealed some difficulties. In response, some economists turned to the Arrow-Debrue-McKenzie model of intertemporal equilibria in which it is not clear that one could even talk about such concepts. The Mantel-Sonnenschein-Debreu theorem shows that this model lacks empirical content. Utility theory provides a closure for some models. Formally, one can demonstrate the existence of equilibria under certain assumptions. But existence does not get one very far.

My purpose of this post is to note that some saw utility theory as a useless tautology at the time of the marginal revolution:

"It is interesting, in this connection, that the earliest critics saw in the theory of marginal utility what we have called a behaviourist theory of choice ... and used exactly the same arguments against it which will be used below against this latter version. Thus [John] Cairnes wrote about Jevon's theory: 'What does it really amount to? In my apprehension to this, and no more - that value depends upon utility, and that utility is whatever affects value. In other words, the name "utility" is given to the aggregate of unknown conditions which determine the phenomenon, and then the phenomenon is stated to depend upon what this name stands for.' Jevon's theory was believed to say no more than this: 'that value was determined by the conditions which determine it - an announcement, the importance of which, even though presented under the form of abstruse mathematical symbols, I must own myself unable to discern'. Some Leading Principles of Political Economy, 1874, p. 15.

[John] Ingram took the same view in A History of Political Economy, 1888, ed. by Ely, 1915, p. 228 and passim. Cairnes, Ingram, and other early critics of marginal utility had, however, directed their criticism also against the mathematical method generally, and the discussion went soon into other channels. The marginalists met the criticism by claiming to be proponents of logical and mathematical method and their tautological psychology thus escaped its well-deserved criticism." -- Gunnar Myrdal (1953) The Political Element in the Development of Economic Theory (trans. by Paul Streeten, Routledge & Kegan Paul, p. 231.

Obviously, Cairnes and Ingram could not have known about results demonstrated a century later. Utility theory manages simultaneously to not say anything about market phenomena, to not be good armchair theorizing, and to be empirically false at the level of the individual.

Elsewhere

• Solidarity Federation
• Francisco Nunes-Pereira and Mário Graça Moura. On the survival of a flawed theory of capital: mainstream economics and the Cambridge capital controversies, Cambridge Journal of Economics. Concludes mainstream economists continue to use flawed aggregate production functions because of an instrumentalist methodology and conformism.
• . Colin Rogers. Whitehead’s fallacy of misplaced concreteness and the unfortunate uselessness of all monetary-macro theory micro-founded on Walrasian-Pareto general equilibrium theory, Cambridge Journal of Economics. Argues that neo-Walrasian general equilibrium theory cannot support monetary theory, despite the practices of mainstream economists.
• Theo Santini and Ricardo Azevedo Araujo. Vertical integration, technical progress and structural change,Cambridge Journal of Economics. Builds on the theory of vertical integration to develop measures of technical progress.
• The Levy Institute podcast. John Harvey talks to James Galbraith in the first episode.
• Reading Capital with comrades, a podcast. I'm not sure lectures work in this format.
• Pitchfork Economics, a podcast.
• An interview with Nick Hanauer and his new co-written book.

Two Special Cases For The Labor Theory Of Value

1.0 Introduction

A simple labor theory of value holds in two special cases.

1. The rate of profits in the system of prices of production is zero.
2. The vector of direct labor coefficients is an eigenvector of the Leontief input-output matrix corresponding to the maximum eigenvalue.

I do not know if I've worked through this alone before. A more rigorous approach would prove the uniqueness of the solution.

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.

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). I guess the idea is that relative wages are more or less stable.

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.

2.1 Quantity Flows

Let y be the column vector of net outputs and q the column vector of gross outputs, both in physical terms. In Leontief's work, y is taken as given. Gross outputs and net outputs are related as:

y = q - A q

Or:

q = (I - A)^-1 y

The labor force needed to produce this net product is:

L = a₀ q = a₀ (I - A)^-1 y

One might as well take units in which labor is measured to be such that this labor force is unity. Employment is such that the net output is produced, the capital goods in producing the net output are reproduced, the capital goods used in producing those capital goods are reproduced, and so on.

2.2 Labor Values

Let e_j be the jth column of the identity matrix. The labor force needed to produce this net output is:

v_j = a₀ (I - A)^-1 e_j

That is, the (direct and indirect) labor needed to produce a net output of one unit of the jth commodity is v_j. The row vector of labor values is:

v = a₀ (I - A)^-1

(I could put an aside here about geometric series and an infinite sum of labor time, assuming the current technology was used forever in the past.)

The employment needed to produce a given net output is the sum of the labor values of the individual commodities in net output, v y. One can think of this post as showing one way of decomposing the observed net output and employed workers. With this way of thinking, no assumptions have been made about returns to scale.

Labor values support one way of doing accounting in models like this. One could ask about how much employment would have decreased or increased if final demand had been decreased or increased by some specified quantities of specified commodities.

2.3 Prices of Production

Take y as numeraire. At any time, market prices are such that different industries are making different rates of profits. Under competitive conditions, without barriers to entry in the various industries, a kind of leveling process is going on.

One can imagine a vector of prices such that this leveling process is already completed with the observed technique and wage. Let p be that row vector of prices of production, with all industries obtaining the same rate of profits:

p A (1 + r) + w a₀ = p

where r is the rate of profits and w the wage. That is, p is a price vector consistent with the observed technique and wage. Since y is numeraire, one has:

p y = 1

The point is to show that prices of production are labor values in special cases.

3.0 The First Special Case: No Profits

Assume that the rate of profits is zero. The claim is that prices of production are labor values.

First, consider the equation for the numeraire:

v y = a₀ (I - A)^-1 y = a₀ q

By assumption, the amount of labor employed is one unit. So using labor values for prices satisfies the equation for the numeraire. Furthermore, if the rate of profits is zero, the wage is unity. (One might do a bit of algebra here.)

I want to show:

v A + a₀ = v

But this is true if and only if:

a₀ = v (I - A)

Or:

a₀ (I - A)^-1 = v

But this is the definition of labor values. So if the rate of profits is zero, prices of production are labor values.

4.0 The Second Special Case: Equal Organic Compositions Of Capital

Suppose that:

a₀ A = λ a₀

where λ is the eigenvalue with the maximum modulus. By the Perron-Frobenius theorem, this eigenvalue is positive and less than unity. All of the elements of the vector of direct labor coefficients are positive.

Under this special case, the solution to the price equations is:

p = v

and:

r = R (1 - w)

where:

R = (1 - λ)/λ

Suppose:

v = (1/(1 - λ)) a₀

By the definition of labor values:

v (I - A) = a₀

Or:

(1/(1 - λ)) (a₀ - a₀ A) = a₀

Using the special case assumptions, one has:

(1/(1 - λ)) (a₀ - λ a₀) = a₀

Thus, in this special case, labor values are directly proportional to direct labor coefficients.

I want to show:

v A(1 + ((1 - λ)/λ)(1 - w)) + w a₀ = v

Or:

(1/(1 - λ)) a₀ A((1/λ) - ((1 - λ)/λ)w) + w a₀ = (1/(1 - λ)) a₀

Or:

(λ/(1 - λ)) a₀((1/λ) - ((1 - λ)/λ)w) + w a₀ = (1/(1 - λ)) a₀

But the left-hand side is simply (1/(1 - λ)) a. So labor values are prices of production in the special case. Furthermore, prices of production do not vary with distribution in this case.

5.0 Conclusion

Suppose the organic composition of capital does not vary among industries. That is, the vector of direct labor coefficients is the specified eigenvector of the Leontief input-output matrix. So prices of production associated with the observed technique and net output are labor values. How does capital obtain profits in this special case? This is Marx's question in the first volume of Capital.

Objections to the lack of realism of this special case and to the conditions needed to define prices of production are not on point. If you have a theory explaining returns to capital, it should apply in this special case. The question, I gather, is more salient if you think there is something fair about commodities being priced at labor values.

The answer cannot be entrepreneurship, since the returns to entrepreneurship are a non-equilibrium phenomenon. For half a century, economists have known that the answer cannot be supply and demand of capital. For that answer, one must have a unit in which capital can be measured independently of prices. I suppose one can create a self-consistent model with intertemporal utility maximization by households, including households whose income is entirely from returns to ownership. But the mechanics of how such a model works disagree with traditional notions of substitution and scarcity.

A valid answer, it seems to me, must invoke some concept of power. This answer need not be exactly Marx's. The Post Keynesian theory of growth, in which large corporations set the rate of growth, might be part of an answer applicable in some times and places.

Orwell Remembers Revolution

Pablo Picasso's Guernica

This post has long quotations, as is typical of a commonplace book.

Where did socialism work? In Barcelona, Spain, and, more generally Aragon and Catalonia, from August 1936 to April 1937. This was the anarchist version, and was resisted by all governments, including the Soviet Union.

The right staged their coup against the Republic in July 1936. Orwell went to Spain in December, and he wanted to kill fascists. He describes it as almost happenstance that he ended up in the militia under the Party Of Marxist Unity (POUM). This party contained, among others, followers of Trotsky and did not follow Stalin's line. Orwell describes how he found Barcelona:

"This was in late December 1936, less than seven months ago as I write, and yet it is a period that has already receded into enormous distance. Later events have obliterated it much more completely than they have obliterated 1935, or 1905, for that matter. I had come to Spain with some notion of writing newspaper articles, but I had joined the militia almost immediately, because at that time and in that atmosphere it seemed the only conceivable thing to do. The Anarchists were still in virtual control of Catalonia and the revolution was still in full swing. To anyone who had been there since the beginning it probably seemed even in December or January that the revolutionary period was ending; but when one came straight from England the aspect of Barcelona was something startling and overwhelming. It was the first time that I had ever been in a town where the working class was in the saddle. Practically every building of any size had been seized by the workers and was draped with red flags or with the red and black flag of the Anarchists; every wall was scrawled with the hammer and sickle and with the initials of the revolutionary parties; almost every church had been gutted and its images burnt. Churches here and there were being systematically demolished by gangs of workmen. Every shop and café had an inscription saying that it had been collectivized; even the bootblacks had been collectivized and their boxes painted red and black. Waiters and shop-walkers looked you in the face and treated you as an equal. Servile and even ceremonial forms of speech had temporarily disappeared. Nobody said 'Senior' or 'Don' or even 'Usted'; everyone called everyone else 'Comrade' and 'Thou', and said 'Salud!' instead of 'Buenos dias'. Tipping was forbidden by law; almost my first experience was receiving a lecture from a hotel manager for trying to tip a lift-boy. There were no private motor-cars, they had all been commandeered, and all the trams and taxis and much of the other transport were painted red and black. The revolutionary posters were everywhere, flaming from the walls in clean reds and blues that made the few remaining advertisements look like daubs of mud. Down the Ramblas, the wide central artery of the town where crowds of people streamed constantly to and fro, the loudspeakers were bellowing revolutionary songs all day and far into the night. And it was the aspect of the crowds that was the queerest thing of all. In outward appearance it was a town in which the wealthy classes had practically ceased to exist. Except for a small number of women and foreigners there were no 'well-dressed' people at all. Practically everyone wore rough working-class clothes, or blue overalls, or some variant of the militia uniform. All this was queer and moving. There was much in it that I did not understand, in some ways I did not even like it, but I recognized it immediately as a state of affairs worth fighting for. Also I believed that things were as they appeared, that this was really a workers' State and that the entire bourgeoisie had either fled, been killed, or voluntarily come over to the workers' side; I did not realize that great numbers of well-to-do bourgeois were simply lying low and disguising themselves as proletarians for the time being." (Chapter I)

Orwell finds equality within the militia, despite ranks and orders:

"At this time and until much later the Catalan militias were still on the same basis as they had been at the beginning of the war. In the early days of Franco's revolt the militias had been hurriedly raised by the various trade unions and political parties; each was essentially a political organization, owing allegiance to its party as much as to the central Government. When the Popular Army, which was a 'non-political' army organized on more or less ordinary lines, was raised at the beginning of 1937, the party militias were theoretically incorporated in it. But for a long time the only changes that occurred were on paper; the new Popular Army troops did not reach the Aragon front in any numbers till June, and until that time the militia-system remained unchanged. The essential point of the system was social equality between officers and men. Everyone from general to private drew the same pay, ate the same food, wore the same clothes, and mingled on terms of complete equality. If you wanted to slap the general commanding the division on the back and ask him for a cigarette, you could do so, and no one thought it curious. In theory at any rate each militia was a democracy and not a hierarchy. It was understood that orders had to be obeyed, but it was also understood that when you gave an order you gave it as comrade to comrade and not as superior to inferior. There were officers and N.C.O.S. but there was no military rank in the ordinary sense; no titles, no badges, no heel-clicking and saluting. They had attempted to produce within the militias a sort of temporary working model of the classless society. Of course there was no perfect equality, but there was a nearer approach to it than I had ever seen or than I would have thought conceivable in time of war.

But I admit that at first sight the state of affairs at the front horrified me. How on earth could the war be won by an army of this type? It was what everyone was saying at the time, and though it was true it was also unreasonable. For in the circumstances the militias could not have been much better than they were. A modern mechanized army does not spring up out of the ground, and if the Government had waited until it had trained troops at its disposal, Franco would never have been resisted. Later it became the fashion to decry the militias, and therefore to pretend that the faults which were due to lack of training and weapons were the result of the equalitarian system. Actually, a newly raised draft of militia was an undisciplined mob not because the officers called the private 'Comrade' but because raw troops are always an undisciplined mob. In practice the democratic 'revolutionary' type of discipline is more reliable than might be expected. In a workers’ army discipline is theoretically voluntary. It is based on class-loyalty, whereas the discipline of a bourgeois conscript army is based ultimately on fear. (The Popular Army that replaced the militias was midway between the two types.) In the militias the bullying and abuse that go on in an ordinary army would never have been tolerated for a moment. The normal military punishments existed, but they were only invoked for very serious offences. When a man refused to obey an order you did not immediately get him punished; you first appealed to him in the name of comradeship. Cynical people with no experience of handling men will say instantly that this would never 'work', but as a matter of fact it does 'work' in the long run. The discipline of even the worst drafts of militia visibly improved as time went on. In January the job of keeping a dozen raw recruits up to the mark almost turned my hair grey. In January the job of keeping a dozen raw recruits up to the mark almost turned my hair grey. In May for a short while I was acting-lieutenant in command of about thirty men, English and Spanish. We had all been under fire for months, and I never had the slightest difficulty in getting an order obeyed or in getting men to volunteer for a dangerous job. 'Revolutionary' discipline depends on political consciousness — on an understanding of why orders must be obeyed; it takes time to diffuse this, but it also takes time to drill a man into an automaton on the barrack-square. The journalists who sneered at the militia-system seldom remembered that the militias had to hold the line while the Popular Army was training in the rear. And it is a tribute to the strength of 'revolutionary' discipline that the militias stayed in the field-at all. For until about June 1937 there was nothing to keep them there, except class loyalty. Individual deserters could be shot - were shot, occasionally - but if a thousand men had decided to walk out of the line together there was no force to stop them. A conscript army in the same circumstances - with its battle-police removed - would have melted away. Yet the militias held the line, though God knows they won very few victories, and even individual desertions were not common. In four or five months in the P.O.U.M. militia I only heard of four men deserting, and two of those were fairly certainly spies who had enlisted to obtain information. At the beginning the apparent chaos, the general lack of training, the fact that you often had to argue for five minutes before you could get an order obeyed, appalled and infuriated me. I had British Army ideas, and certainly the Spanish militias were very unlike the British Army. But considering the circumstances they were better troops than one had any right to expect." (Chapter III)

When Orwell gets leave in April 1937, he finds Barcelona is back to normal, but with some omnious overturns. He reflects on his time in the POUM militia:

"The essential point is that all this time I had been isolated - for at the front one was almost completely isolated from the outside world: even of what was happening in Barcelona one had only a dim conception - among people who could roughly but not too inaccurately be described as revolutionaries. This was the result of the militia-system, which on the Aragon front was not radically altered till about June 1937. The workers' militias, based on the trade unions and each composed of people of approximately the same political opinions, had the effect of canalizing into one place all the most revolutionary sentiment in the country. I had dropped more or less by chance into the only community of any size in Western Europe where political consciousness and disbelief in capitalism were more normal than their opposites. Up here in Aragon one was among tens of thousands of people, mainly though not entirely of working-class origin, all living at the same level and mingling on terms of equality. In theory it was perfect equality, and even in practice it was not far from it. There is a sense in which it would be true to say that one was experiencing a foretaste of Socialism, by which I mean that the prevailing mental atmosphere was that of Socialism. Many of the normal motives of civilized life - snobbishness, money-grubbing, fear of the boss, etc. - had simply ceased to exist. The ordinary class-division of society had disappeared to an extent that is almost unthinkable in the money-tainted air of England; there was no one there except the peasants and ourselves, and no one owned anyone else as his master. Of course such a state of affairs could not last. It was simply a temporary and local phase in an enormous game that is being played over the whole surface of the earth. But it lasted long enough to have its effect upon anyone who experienced it. However much one cursed at the time, one realized afterwards that one had been in contact with something strange and valuable. One had been in a community where hope was more normal than apathy or cynicism, where the word 'comrade' stood for comradeship and not, as in most countries, for humbug. One had breathed the air of equality. I am well aware that it is now the fashion to deny that Socialism has anything to do with equality. In every country in the world a huge tribe of party-hacks and sleek little professors are busy 'proving' that Socialism means no more than a planned state-capitalism with the grab-motive left intact. But fortunately there also exists a vision of Socialism quite different from this. The thing that attracts ordinary men to Socialism and makes them willing to risk their skins for it, the 'mystique' of Socialism, is the idea of equality; to the vast majority of people Socialism means a classless society, or it means nothing at all. And it was here that those few months in the militia were valuable to me. For the Spanish militias, while they lasted, were a sort of microcosm of a classless society. In that community where no one was on the make, where there was a shortage of everything but no privilege and no boot-licking, one got, perhaps, a crude forecast of what the opening stages of Socialism might be like. And, after all, instead of disillusioning me it deeply attracted me. The effect was to make my desire to see Socialism established much more actual than it had been before. Partly, perhaps, this was due to the good luck of being among Spaniards, who, with their innate decency and their ever-present Anarchist tinge, would make even the opening stages of Socialism tolerable if they had the chance." (Chapter VIII)

Here is something about the atomsphere:

"But besides all this there was the startling change in the social atmosphere - a thing difficult to conceive unless you have actually experienced it. When I first reached Barcelona I had thought it a town where class distinctions and great differences of wealth hardly existed. Certainly that was what it looked like. 'Smart' clothes were an abnormality, nobody cringed or took tips, waiters and flower-women and bootblacks looked you in the eye and called you 'comrade'. I had not grasped that this was mainly a mixture of hope and camouflage. The working class believed in a revolution that had been begun but never consolidated, and the bourgeoisie were scared and temporarily disguising themselves as workers. In the first months of revolution there must have been many thousands of people who deliberately put on overalls and shouted revolutionary slogans as a way of saving their skins. Now things were returning to normal." (Chapter IX)

And then on 3 May 1937, the Assault and Civil Guards attacked the anarchists in Barcelona, starting at the Telephone Exchange which the Anarchists ran. The militia for the POUM was, more or less, on the side of the anarchists. The communists were on the side of suppressing the workers' revolution. The May days changed Orwell's plans and how you got along with others:

"In the hotel the horrible atmosphere of suspicion and hostility had grown worse now that the fighting was over. In the face of the accusations that were being flung about it was impossible to remain neutral. The posts were working again, the foreign Communist papers were beginning to arrive, and their accounts of the fighting were not only violently partisan but, of course, wildly inaccurate as to facts. I think some of the Communists on the spot, who had seen what was actually happening, were dismayed by the interpretation that was being put upon events, but naturally they had to stick to their own side. Our Communist friend approached me once again and asked me whether I would not transfer into the International Column.

I was rather surprised. 'Your papers are saying I'm a Fascist,' I said. 'Surely I should be politically suspect, coming from the P.O.U.M.'

'Oh, that doesn't matter. After all, you were only acting under orders.'

I had to tell him that after this affair I could not join any Communist-controlled unit. Sooner or later it might mean being used against the Spanish working class. One could not tell when this kind of thing would break out again, and if I had to use my rifle at all in such an affair I would use it on the side of the working class and not against them. He was very decent about it. But from now on the whole atmosphere was changed. You could not, as before, 'agree to differ' and have drinks with a man who was supposedly your political opponent. There were some ugly wrangles in the hotel lounge. Meanwhile the jails were already full and overflowing. After the fighting was over the Anarchists had, of course, released their prisoners, but the Civil Guards had not released theirs, and most of them were thrown into prison and kept there without trial, in many cases for months on end. As usual, completely innocent people were being arrested owing to police bungling." (Chapter X)

Orwell goes back to the front, is shot, and goes to the hospital in Barcelona. He is lucky to get out of Spain without, at least, being arrested by the Republican government.

I want to recall that chapters V and X1 are Orwell's attempt to give a historical overview, that is, they are about politics, no longer a memoirist's eyewitness testimony.

Variation On An Example From Schefold

Figure 1: Variation in the Economic Life of a Machine with Technical Progress

This post varies the coefficients of production in an example from Bertram Schefold. I wanted to have 'nice' fractions at a time of zero. Qualitatively, this looks like a previous post.

Reviewers for a recent rejection of an article with another fixed capital example objected to this type of model. I need to relate technical progress to a well-known type (Harrod-neutral, Marx-biased, or whatever) or produce some evidence that this sort of modeling is reasonable.

Table 1 presents the technology for this example. Machines and corn are produced in this economy. Corn is the only consumption good. New machines are produced from inputs of labor and corn. Corn is produced from inputs of labor, corn, and machines. A machine can be worked for two years. After the end of the first year of its working life, it is known as an old machine. I assume each process requires a year to complete and exhibits constant returns to scale.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)
Labor	(7/25) e- σ t	3 e- φ t	(14/5) e- φ t
Corn	(4/25) e- σ t	(4/25) e- φ t	(2/3) e- φ t
New Machines	0	1	0
Old Machines	0	0	1
Outputs
Corn	0	1	1
New Machines	1	0	0
Old Machines	0	1	0

The managers of firms need not run the machine for two years. They could discard the machine after only one year. (I assume free disposal.) I call Alpha the technique in which the machine is run for one year, and Beta the technique in which the machine is run for its full physical year of two years. The managers will be cost-minimizing if they run the machine for only one year if the price of an old machine is negative. Prices are found as prices of production, with an external specification of the wage or the rate of profits.

Figure 1 above and Table 2 below illustrate the analysis of the choice of technique. Until time reaches the pattern over the axis for the rate of profits, it is cost-minimizing to operate the machine for only one year. In Region 2, the machine is operated for two years when wages are low, and for one year when wages are higher. Region 3 is an example of reswitching. Eventually, it is cost-minimizing to operate the machine for two years, for all feasible wages.

Table 2: The Wage Frontier in Selected Regions in Parameter Space

Region	Switch Points	Cost-Minimizing Techniques
1	None	Alpha
2	One	Beta, Alpha
3	Two	Beta, Alpha, Beta
4	None	Beta
5	One	Alpha, Beta

Figure 2 partitions the parameter space such that the characteristics of the variations in the choice of technique technique do not vary within each region. Each region is bounded by thick (non-dotted) lines. Suppose that technical progress in producing and using machines is steady. That is, σ and φ have some fixed values. The dotted line in Figure 2 illustrates a path in logical time for such a thought experiment. The 45 degree line corresponds to the case in which σ and φ are equal, as in Figure 1. The numbering of the regions in Figures 1 and 2 and in Table 2 correspond.

Figure 2: A Parameter Space

Stepping through this example does not provide any qualitative differences from previous posts. Reswitching in models of fixed capital can be manifested as the return of a period of truncation. Around a switch point, a lower wage need not be associated with greater employment for a given net output. And so on.

Bertrand Russell On Bolshevism In 1920

Many to the left of liberals, that is, socialists, communists, and anarchists of various stripes, were opposed to the Soviet Union since its founding. Another example is Bertrand Russell. This is from the preface to his The Practice and Theory of Bolshevism, first printed in November 1920:

"The Russian Revolution is one of the great heroic events of the world's history. It is natural to compare it to the French Revolution, but it is in fact something of even more importance. It does more to change daily life and the structure of society: it also does more to change men's beliefs. The difference is exemplified by the difference between Marx and Rousseau: the latter sentimental and soft, appealing to emotion, obliterating sharp outlines; the former systematic like Hegel, full of hard intellectual content, appealing to historic necessity and the technical development of industry, suggesting a view of human beings as puppets in the grip of omnipotent material forces. Bolshevism combines the characteristics of the French Revolution with those of the rise of Islam; and the result is something radically new, which can only be understood by a patient and passionate effort of imagination.

Before entering upon any detail, I wish to state, as clearly and unambiguously as I can, my own attitude towards this new thing.

By far the most important aspect of the Russian Revolution is as an attempt to realize Communism. I believe that Communism is necessary to the world, and I believe that the heroism of Russia has fired men's hopes in a way which was essential to the realization of Communism in the future. Regarded as a splendid attempt, without which ultimate success would have been very improbable, Bolshevism deserves the gratitude and admiration of all the progressive part of mankind.

But the method by which Moscow aims at establishing Communism is a pioneer method, rough and dangerous, too heroic to count the cost of the opposition it arouses. I do not believe that by this method a stable or desirable form of Communism can be established. Three issues seem to me possible from the present situation. The first is the ultimate defeat of Bolshevism by the forces of capitalism. The second is the victory of the Bolshevists accompanied by a complete loss of their ideals and a régime of Napoleonic imperialism. The third is a prolonged world-war, in which civilization will go under, and all its manifestations (including Communism) will be forgotten.

It is because I do not believe that the methods of the Third International can lead to the desired goal that I have thought it worth while to point out what seem to me undesirable features in the present state of Russia. I think there are lessons to be learnt which must be learnt if the world is ever to achieve what is desired by those in the West who have sympathy with the original aims of the Bolsheviks. I do not think these lessons can be learnt except by facing frankly and fully whatever elements of failure there are in Russia. I think these elements of failure are less attributable to faults of detail than to an impatient philosophy, which aims at creating a new world without sufficient preparation in the opinions and feelings of ordinary men and women.

But although I do not believe that Communism can be realized immediately by the spread of Bolshevism, I do believe that, if Bolshevism falls, it will have contributed a legend and a heroic attempt without which ultimate success might never have come. A fundamental economic reconstruction, bringing with it very far-reaching changes in ways of thinking and feeling, in philosophy and art and private relations, seems absolutely necessary if industrialism is to become the servant of man instead of his master. In all this, I am at one with the Bolsheviks; politically, I criticize them only when their methods seem to involve a departure from their own ideals." -- Bertrand Russell

I have not got very far into this short book itself. Some of the above sounds to me a bit like Richard Wolff. The Soviet Union was an experiment, conducted at great human cost. We should learn from its successes and failures. We can and will do better.

Examples Of One-Parameter Pattern Diagrams

Figure 1: Variation in the Economic Life of a Machine with Technical Progress

I have invented graphs for visualizing how the analysis of the choice of technique varies with perturbations of parameters in models of prices of production. This post presents some examples of one type of diagram. One must click on a link with each graph, I guess, to fully understand what is being depicted.

Figure 1 is an extension of an example from Betram Schefold (21 May 2020). This example concerns technological progress and the economic life of a machine in an example of pure fixed capital.

Figure 2 is from an example of two produced commodities with stable relative markups in the two industries (19 September 2020).

Figure 2: The Effects of Variations in Relative Markups

Figure 3 is from another example of fixed capital (3 November 2020). This is a two-commodity model in which machines are used in both sectors

Figure 3: Recurrence of Truncation without Reswitching

Figure 4 is from an example in which the consumption good can be produced with only circulating capital or with a machine with a physical life of two years (1 December 2020).

Figure 4: Triple Switching with Fixed Capital

Figure 5 is from an example in which a machine can last three years (12 December 2020).

Figure 5: An Extension of an Example of Fixed Capital from Salvatore Barone

Figure 6 is from a three-commodity example of non-competitive markets with variations in markups in one industry (11 May 2021).

Figure 6: Variation of Switch Points with the Markup in the Steel Industry

Figure 7 is from the same three-commodity example, but with variations in the markup in another industry (18 May 2021).

Figure 7: Variation of Swith Points with the Markup in the Iron Industry

Figure 8 is an example with extensive rent and technological progress (3 July 2021). This example concerns which type of land is marginal and thus rent-free.

Figure 8: Structural Dynamics with Extensive Rent

Figure 9 is from an illustration of an example to find fluke switch points (28 August 2021).

Figure 9: Technical Progress in An Illustration of an Algorithm to Find Fluke Switch Points

Figure 10 extends an extension of an example from Antonio D'Agata (30 December 2021).

Figure 10: Structural Dynamics in an Example with Intensive Rent

Figure 11 is from an example with extensive rent and markup pricing (29 September 2023).

Figure 11: Variation with Ratio of Markups in Industry to Agriculture

These diagrams were generated out of a research program that I have stumbled upon.

Austrian Economists Rediscovering Sraffa

Some recent papers by economists of the Austrian school rediscover some aspects of post-Sraffian price theory. Others would benefit from more knowledge of post-Sraffian price theory. But the authors do not know this.

Fillieule (2007) is a rediscovery of Sraffa's standard commodity. He sets out a special case of Hayekian triangles in which an infinite series of datad labor inputs are used to produce current net output. "Only circulating capital is taken into account", and "the proportion between capital goods and originary factors is the same in all stages." Fillieule, unlike Sraffa, has wages advanced instead of being paid out of net output. He gestures at Sraffian subsystems. Production at any year can be viewed as decomposed into producing the net output, producing the capital goods needed to produce net output one year hence, producing capital goods needed for the production of the capital goods that go into producing net output two years hence, and so on.

Consider the analysis of the choice of technique. Different techniques have different standard commodities. One must pick one numeraire in the analyis. The numeraire cannot simultaneously be two different standard commodities. I do not know if these observations undermine Fillieule's conclusions.

Mateusz Machaj (2015) responds to the Fillieule (2007) and Hülsmann (2011). He emphasizes intertemporal labor intensity and considers variations in the amount of labor (originary factors more generally) hired at each stage of production. It is unclear to me how such variations can be independent of one another. Those working in the direct production of corn are presumably producing for immediate consumption and seed corn for the production of seed corn for use in production next year. In other words, some ratio of their labor is simultaneously going into production at every stage of production illustrated in a Hayekian triangle. I doubt Machaj's 2017 book resolves this question.

Howden (2016) is a response to Machaj (2015). Howden rejects that one can analyze a change in the rate of profits without considering individual savings and investment decisions. He adopts an outdated supply (savings) and demand (investment) approach to explaining interest rates and fails to see that an open model can be considered. Howden correctly notes that Machaj's description of changes in the amount of labor applied at specified stages is unmotivated. But he sticks to obsolete physical notions of roundaboutness. His article is full of quotations for ideas that some, including Austrian-school economists, would say have been transcended:

"the assertion that artificial reductions to the interest rate cause an unsustainable lengthening in the structure of production is the central tenet of the Austrian theory of the business cycle."

Machaj (2017a) is a reply to Howden (2016).

Manish (2018) is a response to Machaj (2017b) and defends the Pure Time Preference Theory (PTPT) theory of the rate of interest. I am not sure that it makes sense for a general preference for present goods over future goods outside a steady state, when relative quantities are changing. Nor am I sure that the Austrian approach of imputing values to higher order goods can explain interest rates without presuming interest rates.

Granot (2019) is a rediscovery of price Wicksell effects. He finds that for a given technique, the average period of production varies non-monotically with the interest rate. This result was explained by Sraffa in Section 48, pages 44-45, of his book.

Harwick (2022) and Iborra (2021) reference me. A previous version of Milana (2023) did reference me. He still references Osborne. Even though Harwick sticks unknowingly to considering one-way models from originary factors - no consideration of production of commodities by means of commodities for him, I can find something to agree with. He thinks simple models are a good way to approach capital theory. One should not start with the most general model. For me, the most general model would be one of general joint production, multiple types of labor, no simplifications of simple fixed capital, multiple types of land on each of which many types of agricultural commodities can be grown, and so on.

References

• Renaud Fillieule. 2007. A formal model in Hayekian macroeconomics: the proportional goods-in-process structure of production. Quarterly Journal of Austrian Economics. 10: 193-208.
• Er'el Granot. 2019. An overlooked scenario of "reswitching" in the Austrian structure of production. Quarterly Journal of Austrian Economics. 22 (4): 509-532.
• Cameron Harwick. 2022. Unmixing the metaphors of Austrian capital theory. The Review of Austrian Economics 35 (2): 163 - 176.
• David Howden. 2016. The interest rate and the length of production: a comment. Quarterly Journal of Austrian Economics. 19 (4): 345-358
• Jörg Guido Hülsmann. 2011. The structure of production reconsidered. Working paper.
• Rafael Garcia Iborra. 2021. A financial analysis of reswitching. Revista Procesos de Mercado 18 (1): 220 - 244.
• Mateusz Machaj. 2015. The interest rate and the length of production: an attempt at refomulation. Quarterly Journal of Austrian Economics. 18 (3): 272-293.
• Mateusz Machaj. 2017a. Interest and the length of production: a reply. Quarterly Journal of Austrian Economics. 20 (2): 164-170.
• Mateusz Machaj. 2017b. Money, Interest, and the Structure of Production: Resolving Some Puzzles in the Theory of Capital. Lexington.
• G. P. Manish. 2018. A brief defense of Mises's conception of time preference and his pure time preference theory of interest. Quarterly Journal of Austrian Economics. 21 (2): 95-109.
• Carlo Milana. 2023. Refuting Samuelson's capitulation on the re-switching of techniques in the Cambridge capital controversy. The Review of Austrian Economics. Not yet assigned to an issue.

A Parameter Space for an Example of Harrod-Neutral Technical Progress

Figure 1: A Two-Dimensional Parameter Space

The above is for this example. I wish somebody would be inspired by this to write it up with mathematical proofs. What I see here is found by numerical methods.

Figure 1 shows a partition of the parameter space based on fluke switch points. The dashed line shows the temporal path in the previous post. Each of the solid lines are parallel affine functions, with a slope of unity. A proof that these slopes are unity should be able to handle a model with any number of produced commodities.

Milovan Djilas On The Soviet Union As State Capitalism

What to make of the Soviet Union? Apparently, the description of it as state capitalism goes back to Lenin. Djilas description of it as such is central to his best-known book:

"Abstract logic would iпdicate tћat tће Communist reyolution, when it achieves, under different conditions and Ьу state compulsioп, the same things achieved Ьу industrial revolutions and capitalism in the West, is nothing but а form of state-capitalist revolution. The relationships which are created Ьу its victory are state-capitalist. This appears to Ье even шоrе true because the new regime also regulates all political, labor, and other relationships and, what is more important, distributes the national income and benefits and distributes material goods which actually have been transformed iпto state property.

Discussion on whether or not the relationships in tће U.S.S.R. апd in other Communist countries are state-capitalist, socialist, or perhaps something else, is dogmatic to а coпsideraЬle degree. However, such discussion is of fundamental importance.

Even if it is presumed that state capitalism is nothing other than the 'antechamber of socialism,' as Lenin emphasized, or that it is the first phase of socialism, it is still поt опе iota easier for the people who live uпder Communist despotism to endure. lf the character of property апd social relationships brought about Ьу thе Communist revolution is streпgthened and defined, tће prospects for liЬeration of the people from such relationships become more realistic. If the people are поt conscious of the nature of the social relationships iп which they live, or if tћеу do not see а way in which they сан alter them, their struggle cannot ћаvе any prospect of success.

If the Communist revolution, despite its promises апd illusions, is state-capitalist iп its undertakings witћ state-capitalist relationships, tће only lawful and positive actioпs its fuпctionaries сап take are the опеs tћat improve their work апd reduce the pressure апd irrespoпsiЬility of state admiпistratioп. Тће Coшmunists do not admit iп theory tћat they are workiпg in а system оf state capitalism, but their leaders behave tћis way. Тћеу coпtшually boast about improviпg tће work of tће admiпistration апd about leadiпg tће struggle 'agaiпst bureaucratism.'

Moreover, actual relationships are not those of state capitalism; these relationships do поt provide а method of improving the system of state admiпistration basically.

Iп order to establish the пature of relatioпships which arise iп thе course of thе Communist revolution and ultimately become estaЬlished iп the process of industrialization and collectivizatioп, it is пecessary to peer further iпto the role and manner of ореrаtiоп of tће state under Communism. At present, it will be sufficient to point out that in Communisш the state macћineтy is not tће instrument wћiсћ really determines social and property relatioпships; it is only tће instrument Ьу which these relatioпsћips are protected. In truth, everythiпg is accomplished in thе nаше of thе state and througћ its regulations. Тће Communist Party, iпcluding tће professional party bureaucracy, stands above the regulations and behind every siпgle one of thе state's acts.

It is the bureaucracy whiсћ formally uses, adшinisters, and controls Ьоtћ пationalized анd socialized property as well as the entiтe lifе of society. Тће role of tће bureaucracy in society, i.e., monopolistic administration and control of national income and пational goods, consigпs it to а special privileged positioп. Social relatioпs resemЬle state capitalism. Тће more so, because tће carryiпg out of industrialization is effected not with tће ћеlр of capitalists but with the ћеlр of tће state machine. In fact, this pгivileged class perfoтms tћat functioп, using tће state machiпe as а cover апd as ап iпstrurneпt.

Ownership is пothing other tћan tће right of profit and control. If оnе defines class benefits Ьу this right, thе Communist states have seen, in the final analysis, thе origin of а пеw form of ownership or of а new ruling and exploiting class.

In reality, the Communists wете uпаЬlе to act differently from аnу ruling class that preceded them. Believiпg that they were building а new and ideal society, tћеу built it for themselves in tће only way they could. Their revolution and their society do not appear eitћer accidental or unпatural, but appear as а matter of course for а particular country and for pгescriЬed peгiods of its developmeпt. Because of this, no matter ћоw extensive and inhuman Communist tyranny ћаs been, society, in the course of а certain period - as long as industrialization lasts - has to and is аЬlе to endure this tуrаппу. Furthermore, this tyranny no longer appears as something inevitaЬie, but exclusively as ан assurance of the depredations and privileges of а new class.

In contrast to earlier revolutions, the Commuпist revolution, conducted in the nаше of doiпg away with classes, has resulted in the most complete authority of any siпgle пеw class. Everything else is sham and an illusion." -- Djilas (1957)

As I understand it, party functionaries were assigned to state offices. In this way, the party formed a parallel to the official government. Furthermore, these party members became the owners of collectivized property, that is, they controlled it. This is the new class.

Djilas says that communist revolutions differed from previous revolutions in that they were not a matter of an already hegemonic class coming to power. The post-revolution institutions had not already grown up in old society, but had to be created and imposed by force, by the communist party. The leaders believed they were creating a classless society. But, after the revolution, they created a class to bring about a needed industrialization, at great cost.

References

• Milovan Djilas. 1957. The New Class: An Analysis of the Communist System.
• Vladimir Lenin. 1918. The chief task of our day. 'Left-wing' childishness and the petty-bourgeois mentality. Collected WorksVol. 27: 323-354.
• Vladimir Lenin. 21 April 1921. The tax in kind (the significance of the new policy and its conditions). Collected WorksVol. 32: 329-365.

Elsewhere: Data On Capitalism And Other Systems

The first is a distateful counting of the victims of capitalism in the twentieth century. The second concludes that no-longer-actually-existing socialism was about as efficient as western countries. The last argues that general prosperity first declined with the introduction of capitalism.

• Salvatore Engel-DiMauro. 2021. Anti-communism and the hundres of millions of victims of capitalism. Capitalism Nature Socialism 32(1): 1-17.
• Peter Murrell. 1991. Can neoclassical economics underpin the reform of centrally planned economies?. Journal of Economic Perspectives 5(4): 59-76. This issue has a symposium on transition economies, with other interesting articles.
• Dylan Sullivan and Jason Hickel. 2023. Capitalism and extreme poverty: a global analysis of real wages, human height, and mortality since the long 16th century. World Development 161: 1-18.

Here are a couple of other links:

• Louis-Philippe Rochon argues that we should not teach neoclassical ewconomics to undergraduates.
• The P2P Foundation seems like an interesting approach.

Another Example of Harrod-Neutral Technical Progress And The Choice Of Technique

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time

This post presents an example in which some coefficients of production vary from those in example. Reswitching, capital reversing, and the reverse substitution of labor do not arise in this example.

Table 1 shows the coefficients of production for this example. The labor coefficients vary identically with the the labor coefficients in the previous example. a_2,1(a), a_3,1(a), a_2,1(b), a_3,1(b), a_1,2(c), a_3,2(c), and a_1,2(d) are all larger in this example.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	(15/2) e-φt	32 e-σt	(13/2) e-φt	60 e-σt	(15/2) e-φt	55 e-σt
Iron	1/6	2/5	1/20	1/10	1	0
Steel	1/20	1/20	1/4	3/10	0	1/4
Corn	1/15	1/15	1/15	0	0	0

Table 2 repeats the definition of the techniques of production. As in the previous example, the Alpha and Theta techniques each undergo Harrod-neutral technical progress.

Table 2: Techniques

Technique	Processes
Alpha	a, c, e
Beta	a, c, f
Gamma	a, d, e
Delta	a, d, f
Epsilon	b, c, e
Zeta	b, c, f
Eta	b, d, e
Theta	b, d, f

As usual, prices of production are defined for each moment in time. Given the wage or the rate of profits, one can find the cost-minimizing technique. Figure 1, at the top of this post, and Figure 2 depict how the dependence of the cost-minimizing technique on distribution varies with time. These graphs are drawn for the specified rate of technical progress. The variation of the cost-minimizing technique with distribution is invariant in each numbered region, although the specific rate of profits, for example, at which a switch point occurs does vary.

Figure 2: Variation in the Maximum Rate of Profits and the Cost-Minimizing Technique with Time

At the maximum rate of profits, the wage is zero. Variations in labor coefficients do not matter. In this case, the Beta technique remains cost-minimizing for all time at a wage of zero. The cost-minimizing technique at the maximum wage varies from Alpha to Theta, as the pure technique with the faster growth in technical progress becomes dominant. Beta and Theta vary in the iron-producing and steel-producing processes. Ultimately, at the extreme right of the graphs, two switch points exist as distribution varies.

I guess these two examples illustrate general properties of Harrod-neutral technical progress in the case where all techniques require the production of the same commodities and all of these commodities are basic in the sense of Sraffa. Fluke cases will arise over time. So-called 'perverse' switch points need not arise, but can.

A Characterization Of Neoliberalism From Wendy Brown

I have been reading Brown (2015). She acknowledges neoliberalism is difficult to define:

"Three decades out, rich accounts by geographers, economists, political theorists, anthropologists, sociologists, philosophers, and historians grappling with these questions have established that neoliberalism is neither singular nor constant in its discursive formulations and material practices. This recognition exceeds the idea that a clumsy or inapt name is draped over a busy multiplicity; rather neoliberalism as economic policy, modality of governance, and order of reason is at once a global phenomenon, yet inconstant, morphing, differentiated, unsystematic, contradictory, and impure, what Stuart Hall calls a 'field of oscillations' or Jamie Peck calls 'unruly historical geographies of an evolving interconnected project.' Neoliberalism is a specific and normative mode of reason, of the production of the subject, 'conduct of conduct,' and scheme of valuation, yet in its differential instantiations and encounters with extant cultures and political traditions, it takes diverse shapes and spawns diverse content and normative details, even different idioms.

Thus the paradox of neoliberalism as a global phenomenon, ubiquitous and omnipresent, yet disunified and nonidentical with itself. This dappled, striated, and flickering complexion is also the face of an order replete with contradiction and disavowal, structuring markers it claims to liberate from structure, intensely governing subjects it claims to free from government, strengthening and retasking states it claims to abjure. In the economic realm, neoliberalism aims simultaneously at deregulation and control. It carries purpose and has its own futurology (and futures markets), while eschewing planning. It seeks to privatize every public enterprise, yet valorizes public-private partnerships that imbue the market with ethical potential and social responsibility and the public realm with market metrics. With its ambition for unregulated and untaxed capital flows, it undermines national sovereignty while intensifying preoccupation with national GNP, GDP, and other growth indicators in national and postnational constellations."

Brown's emphasis is on how neoliberalism remakes the self. Under neoliberalism, people are all regarded as independent entrepreneurs, each trying to increase their human capital. This conception extends to areas that do not necessarily have anything to do with money. How much time should invest in relationships? What best practices should parents adopt in raising their children?

This way of thinking about people contrasts with an older notion of the utility-maximizing consumer. Our preferences form a field that we move around in through exchange. I think John Stuart Mill is important for articulating a pre-marginalist view of economic man. Homo economicus has a history and has varied over the development of political economy.

Brown and Marcuse both share a concept about how capitalism corrupts our non-working time. In One Dimensional Man, Marcuse deplores the prevalence of instrumental reason. For Brown, the neoliberal concept of the self is not a member of a social class. In the neoliberal view, we no longer have workers and capitalists. We are longer examples of homo politicus. I think of Hannah Arendt as an idealized picture of political man, what we could be reasoning together in the public square, in the agora. Brown also mentions homo legalis, the subject of right and an emphasis of Foucault and his concept of governability.

Reference

• Wendy Brown. 2015. Undoing the Demos: Neoliberalism's Stealth Revolution. Zone Books.

Harrod-Neutral Technical Change And The Choice Of Technique

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time

1.0 Introduction

I thought I would revisit the application of my analysis of fluke switch points to an example of Harrod-neutral technical change. Two techniques are assumed to experience Harrod-neutral technical change. The same commodities are produced with both techniques. No capital goods are produced for one technique that are unproduced in the other. Consequently, the techniques have no processes in common. At least two processes must be available in each industry. So more than two techniques must exist.

I think these ideas could be worked up into something. I will probably spend some time toying with the example.

2.0 Technology

This economy produces a single consumption good, called corn. Corn is also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. So three industries exist. One produces iron, another produces steel, and the last produces corn. Two processes exist in each industry for producing the output of that industry. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce a unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year. The technology is specified for a specific moment in time, and improves over time.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	(15/2) e-φt	32 e-σt	(13/2) e-φt	60 e-σt	(15/2) e-φt	55 e-σt
Iron	1/6	2/5	1/200	1/100	1	0
Steel	1/200	1/400	1/4	3/10	0	1/4
Corn	1/300	1/300	1/300	0	0	0

A technique consists of a process in each industry. Table 2 specifies the eight techniques that can be formed from the processes specified by the technology. If you work through this example, you will find that to produce a net output of one bushel corn, inputs of iron, steel, and corn all need to be produced to reproduce the capital goods used up in producing that bushel.

Table 2: Techniques

Technique	Processes
Alpha	a, c, e
Beta	a, c, f
Gamma	a, d, e
Delta	a, d, f
Epsilon	b, c, e
Zeta	b, c, f
Eta	b, d, e
Theta	b, d, f

The Alpha and Theta techniques each undergo Harrod-neutral technical progress. The labor coefficients for the Alpha technique decrease at the the rate φ and those for the Theta technique decrease at the rate σ. The other techniques consist of a mixture of processes from these two techniques.

3.0 Prices of Production

A system of equations can be set out for prices of production, for each technique,at any moment of time. I assume that net output consists of a bushel corn, and that this net output is the numeraire. Wages are paid out of the surplus product after the harvest. Given competitive conditions, the same rate of profits are obtained in each industry.

These assumptions are sufficient to determine the wage and the prices of produced commodities, for each technique, at the given moment in time, as a function of the rate of profits.

4.0 The Choice of Technique

The cost-minimizing technique at a moment of time can be found by constructing the wage frontier as the outer envelope of the wage curves for the eight techniques. Given the rate of profits, the cost-minimizing technique maximizes the wage. Given the wage, it maximizes the rate of profits.

Figure 1, at the top of this post, and Figure 2 depict how the dependence of the cost-minimizing technique on distribution varies with time. These graphs are drawn for the indicated rates of neutral technical progress in the Alpha and Theta techniques. Figure 1 graphs the maximum wage and the wage at each switch point on the frontier. Figure 2 graphs the rate of profits, both the maximum and at each switch point on the frontier. Figure 2 also shows the rate of profits at switch points between -100 percent and zero. The thin vertical lines partition time into numbered regions. Each partition corresponds to a fluke switch point.

Figure 2: Variation in the Maximum Rate of Profits and the Cost-Minimizing Technique with Time

The ranking of techniques by the maximum rate of profits does not vary with time. At the maximum rate of profits, the wage is zero. Variations in labor coefficients do not matter. In this case, the Alpha technique remains cost-minimizing for all time at a wage of zero. It is not necessary, in general, that the cost-minimizing technique at a zero wage, be one of those experiencing Harrod-neutral technical change. For other coefficients of production, the Beta technique, for example, could be cost-minimizing at a zero wage.

In general, the cost-minimizing technique at the maximum wage starts with the technique with the slowest rate of neutral technical progress. Over time, the cost-minimizing technique becomes the technique with the largest rate of technical progress.

In the example, the Alpha technique is cost-minimizing at the start of time, whatever the distribution of income. Region 1 illustrates this lack of dependence of the cost-minimizing technique on distribution. the Alpha technique remains cost-minimizing for all time at a wage of zero. Since the rate of Harrod-neutral technical progress is assumed to be greater for the Theta technique, eventually Theta is cost-minimizing at the maximum wage. One can see the effects of technical progress with the exponential growth of the maximum wage in Figure 2.

Consider Region 7 in the Figures. At a non-fluke switch point, only one process changes in the cost-minimizing technique. As the wage increases, the corn-producing process changes at the switch point between Alpha and Beta. At the second switch-point with increasing wages, the cost-minimizing process in steel production changes. Finally, at the switch point between Delta and Theta, the cost-minimizing process in in iron production changes.

In Region 6, which process changes first, with increasing wages, in iron and steel production varies. The iron process varies at the switch point between Beta and Zeta. At a higher wage, the steel process in the cost-minimizing technique varies at the switch point between Zeta and Theta. The partition between Region 6 and Region 7 has a fluke switch point in which the iron and steel-producing processes change simultaneously.

Region 2 exhibits reswitching between the Alpha and Beta techniques. The switch point at the lower wage is an example of capital-reversing, also known as a positive real Wicksell effect. Around this switch point, a higher wage is associated with the employment of more labor per unit of net output. It also exhibits the reverse substitution of labor. In Regions 2, 3, and 4, the labor coefficient in Process f exceeds the labor coefficient in Process e. A higher wage at this switch point between Alpha and Beta is associated with greater employment per unit of gross corn output.

5.0 Conclusion

The introduction of switch points and the variation in the cost-minimizing technique at the maximum wage is, in some sense, a general property of technology formed out of techniques experiencing Harrod-neutral technical progress. With time, switch points are introduced as fluke cases. These fluke cases need not create examples of reswitching, capital-reversing, reverse labor substitution, or process recurrence. But they do in the example.