1.0 Introduction

I wrote this decades ago.

Here is a simple parable. Consider an island with a particularly simple
society with two people, Robinson and Friday. Robinson and Friday live
on one good, call it corn. At the start of our story, Robinson and Friday
have just finished a feast. Both Robinson and Friday have each eaten
food baked out of 50 bushels of corn. Also, Robinson has 50 bushels corn
remaining. Friday, perhaps because he’s newly arrived, has none.

2.0 The Initial Deal

Both Robinson and Friday can see that they must continue to eat in the
future. They understand that their continual survival could be achieved by
planting the remaining corn, saving 50 bushels corn in next year’s harvest,
and living off of the remainder. (In this story, Robinson and Friday are
each able

1.0 Introduction

This post outlines an unoriginal argument against Marx’s version of the Labor Theory of Value (LTV), if that is the
right name.
Somehow, this post was obliquely inspired by Fabio Petri’s recent working paper.

Suppose technology, net output, and the real wage are given. Then the rate of profits and prices of production
are determined.

Suppose that the technology provides a choice of technique. Then the determination of the choice of technique
requires an analysis at the level of prices of production. One can do labor value accounting only after
the determination of the technique in use.

Given the technique and the level of operation of each process, one can then determine the labor value
embodied in the output of each industry. One can then use this labor value

Figure 1: Variation in the Economic Life of a Machine with Technical Progress
Exploration of the effects of perturbations of model parameters in the analysis of the choice of technique has suggested an answer to this
question to me. I am not sure how well-developed the argument in this post is.

The question is raised by empirical results, particularly by Han & Schefold and by Zambelli.
I have previous commented
on Zambelli. Heinz Kurz has recently questioned the reliability of these results. The data come from economies in which fixed
capital is widely used. One can expect old plants that would not be currently reproduced to be operated and to obtain quasi-rents.
Nevertheless, empirical wage curves are surprisingly close to straight lines and reswitching and other ‘perverse’ phenomena

A Beach On The East End Of Oneida Lake
The Iroquois are an example of primitive communism.
This post includes lots of anachronisms, and I use current place names. I had never heard
of the Haudenosaunee before, which apparently is the preferred term.
I find I do not know much
about my neighbors, the Oneidas. The Oneidas were one of the five nations
in the Iroquois confederacy.

I am confused whether primitive capitalism is tied exclusively to hunter-gatherer societies, without a surplus product.
Given the role of the three sisters, that is, corn, beans, and squash, in, say, the Oneida society, I guess they must
have been an agricultural society. I gather that anthropologists have found the concept of a surplus product useful.
Useful questions include who gets the surplus? What do they do

No book-length biography of D. G. Champernowne exists, as far as I can see.
Even his Wikipedia page
is quite terse. Yet he advised and participated in important twentieth-century intellectual developments.

From Hodges biography of Alan Turing, I learned that ‘Champ’ was a friend of his. Champernowne did early work
in programming chess-playing algorithms, along with Turing and Claude Shannon.
Game-playing is one of those disappointing applications of Artifical Intelligence. What seems to work best,
like ChatGPT, uses
lots of processing power,
while ignoring
what experts in the subject matter say.
Anyways, Champernowne was in on the invention of the computer.

Champernowne (1953-1954) published an appreciation and explanation of the English translation of von Neumann’s article on

I have sometimes written retrospectives
about my research program. I have been exploring the results of perturbing parameters in models of the choice of technique.
This is a bit more prospective.

Illustrations of One-Dimension Pattern Diagrams: I have a selection of these written up.
Independence of Economic Life of Machines and Capital-Intensity: I have the analytical results I want. I am being slow to read what I need to connect results up to Austrian capital theory. I have had a much different earlier version rejected by Metroeconomica.
Illustrations of Partitions of Parameter Spaces by Fluke Switch Points: I have had a draft paper like this rejected by the Cambridge Journal of Economics.
Extensive rent with perturbations of markups: I have had a paper based on this rejected by

This is more of my commonplace book, based on reading some of Hayek’s The Pure Theory of Capital.
Hayek rejects Böhm Bawerk’s average period of production, a single number summarizing the capital
intensity of a structure of production. He still strives to say that more capital-intensive techniques
are longer in some non-aggregate sense. I probably will not finish this book. To compare and contrast
this book with J. R. Hicks’ Value and Capital would be of interest.

Hayek correctly takes issue with the treatment of capital as a homogeneous quantity and the explanation
of interest by the supply and demand of capital:

"the attempts to explain interest, by analogy with wages and rent, as the price of the services of some definitely given ‘factor’ of
production, has nearly always led to a

1.0 Introduction

I do not think I have presented an introductory example in a while in which
an increased wage is associated with firms wanting to employ more labor,
given the level of net output. This example is presented as a matter of
accounting for a vertically integrated firm.

Exact calculations with rational numbers are tedious in this example. I expect that if anybody bothers to check this,
they would use a spreadsheet. As far as I can tell, Microsoft Excel uses double precision floats.

2.0 Technology

The managers of a competitive, vertically-integrated firm for producing corn know of the four production processes listed in Table 1.
Corn is a consumption good and
also a capital good, that is, a produced commodity used in the production of other commodities.
In fact, iron,

Marx, in Theories of Surplus Value, quotes James Stuart writing about ‘profit upon alienation’.
When one sells a good one owns, one has alienated it from oneself. In the typical work relation under capitalism,
the managers of firms, that is, the representatives of capitalists, sell the product or services that workers
produce. Workers do not own the goods they produce, for they have previously sold their labor-power.
That is, they have agreed that their product is not owned by themselves, and neither is their labor.

But alienation means something more in Marx’s Paris Manuscripts.
The work of Ludwig Feuerbach is important background here. (By the way,
this post is based mostly on secondary and tertiary literature, I forget which. I have not read most of the Marx and Engels’ works cited

A revolution occurred in price theory about two-thirds of a century ago.
Several scholars independently developed components of this revolution.
This post merely lists selected literature. I have
previously tried to
briefly describe
why some of these authors are precursors.

Ladislaus von Bortkiewicz (1907) On the correction of Marx’s fundamental theoretical construction i the third volume of Capital. Translated and reprinted by Sweezy.
David G. Champernowne (1945-1946) A note on J. V. Neumann’s article on "A model of economic equilibrium". Review of Economic Studies 13 (1): 10-18.
Georg von Charasoff (2010) Das System des Marxismus: Darstellung und Kritik. Berlin: H. Bondy.
V. K. Dmitriev (1974) Economic Essays on Value, Competition, Utility. English Trans.
Walter Isard (1951)

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

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

1.0 Introduction

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

2.0 Hayek on the Mythology of Capital

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

"The basic mistake – if the substitution of a meaningless statement for the solution of a problem can be called a mistake – is the idea of capital as a fund

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.