Figure 1: The Wage-Rate of Profits Frontier1.0 Introduction

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

2.0 Technology

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

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.

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

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

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

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

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

Figure 1: The Wage-Rate of Profits Frontier1.0 Introduction

This is one in 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 want to illustrate
each entry in a two-by-two table in a previous post.
The example in this post has two switch points. One fits the traditional Austrian and neoclassical stories, as in the entry in the upper-left
of the table. The other switch point is ‘perverse’ in both ways, as in the entry in the lower right.

2.0 Technology

The example is of a ‘one-good’ economy, in which the produced commodity has a physical lifetime of three years when used
in production. When the commodity is newly produced, it can also be used by

Matt McManus on Thomas Sowell.
A review of Adam Shatz’s biography of Frantz Fanon.
Nathan Robinson interviews Kohei Saito on degrowth.
I have not read Bob Rowthorn on neo-ricardianism in decades. I wish NLR made PDFs of old articles freely available.

Table 1: Lower Rate of Profits Around A Switch Point
Traditional Marginalist Story’Perverse’ Marginalist StoryTraditional Austrian StoryNegative real Wicksell effect, greater net output per workerPositive real Wicksell effect, smaller net output per workerLonger economic life of machineLonger economic life of machine’Perverse’ Austrian StoryNegative real Wicksell effect, greater net output per workerPositive real Wicksell effect, smaller net output per workerShorter economic life of machineShorter economic life of machine
I have been thinking about perturbations of coefficients in a model
of fixed capital. This research can be redirected to find examples to fill in the above two-by-two table.
Under obsolete marginalist teaching, a lower rate of profits encourages firms to addopt more

This post is basically complaining that I cannot keep up.

I think I am fairly informed on Karl Marx. I do not read German, and I have not even read some early works.
My area of concentration is reading Capital as a work of mathematical economics, which cuts against the
subtitle and, maybe,
de-emphasizes a break
with classical, especially, Ricardian political economy.

More generally, I thought Marx generally praises the tremendous increase of productivity brought about by the bourgeoisie.
He downplays the accompanying environmental degradation. Imperialism extends capitalism into non-European colonies.
Marx deplores the violence, but thinks rationalization of such societies is progress.

As I understand it, some of the literature below challenges these ideas. This is partly because

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

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

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

1.0 Introduction

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

The rate of profits in the system of prices of production is zero.
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

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

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.

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

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

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

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.

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.

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

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. a2,1(a), a3,1(a),
a2,1(b), a3,1(b), a1,2(c), a3,2(c),
and a1,2(d) are all larger in this example.

Table 1: The Technology
InputIronIndustrySteelIndustryCornIndustryabcdefLabor(15/2) e-φt32 e-σt(13/2) e-φt60 e-σt(15/2) e-φt55 e-σtIron1/62/51/201/1010Steel1/201/201/43/1001/4Corn1/151/151/15000
Table 2 repeats the definition of the techniques of

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

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time1.0 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

[embedded content]Hakim on the Economic Calculation Problem
Reactionaries often bring up the Economic Calculation Problem (ECP) as a fatal objection
to socialism, considered as entailing central planning. Ludwig Von Mises put this forth in 1920 as an argument in principle
that central planning is guaranteed to be highly inefficient. He postulates that the planning authority knows
the prices of consumer goods and all technical possibilities, including the endowments of originary factors of production.
But without prices of intermediate goods, the planning authority cannot make rational decisions about how to produce
commodities. Like Enrico Barone,
Von Mises insists the planning authority must re-introduce prices for intermediate goods and a market for ‘capital’.

Friedrich Hayek changed

I feel each of these three needs more than I am able to say. I find intriguing radicals attacking
communist parties from the left, as Negri and others (Autonomia) did in Italy in the 1960s and 1970s.
I draw on those who have all sorts of arguments with Solow. I find him witty.
Thirwall I associate with Nicholas Kaldor and development economics.

Antonio Negri (1933 – 2023). Repost of 2015 interview from Democracy Now. Libcom page of works related to Negri.
Robert Solow (1924 – 2023): MIT obituary. Russell Sage Foundation obituary. 1987 Nobel announcement.
Tony Thirwall (1941 – 2023). Repost of an obituary from John McCombie.

I claim that what mainstream economists teach about what Keynes wrote is often false and nonsenical.
Unfortunately, this is quite impressionistic in that I do not give examples
of these misrepresentations.
I am writing here only about the General Theory.
I suppose some mainstream economists might respond that they do not teach about Keynes at all.

Some say Keynes work was about policy, not theory. Keynes specifically says otherwise in the first sentences
of the preface to his major work:

"This book is chiefly addressed to my fellow economists. I hope that it will be intelligible to others.
But its main purpose is to deal with difficult questions of theory, and only in the second place with
the applications of this theory to practice. For if orthodox economics is at fault, the error

Socialist and coomunist parties have formed various internationals over the course of centuries.
I consider a
declaration of the Socialist International, adopted at its First Congress held in Frankfort-on-Main on 30 June-3 July 1951
an authoritative statement of "The Aims and Tasks of Democratic Socialism".
This declaration was re-affirmed in 1962.
The declaration starts as follows:

1. From the nineteenth century onwards, capitalism has developed immense productive forces. It has done
so at the cost of excluding the great majority of citizens from influence over production. It put the rights
of ownership before the rights of man. It created a new class of wage-earners without property or social rights. It sharpened the struggle between the classes.

Although the world contains