Hayek introduced his triangles in his lectures for his book Prices and Production. The first edition was
in 1931 and the second in 1935. He attempted a more general treatment of capital theory in
his 1941 book, The Pure Theory of Capital. I want to claim that Hayek knew that
he could not draw his triangles under these more general assumptions. And that
he knew that capital theory needed more development than he was able to give.

Jack Birner knows this, although I do not know a reference off-hand. I want to say that
Roger Garrison knows this too, that he presents his diagrams of trianlges in his 2001 book,
Time and Money: The Macroeconomics of Capital Structure, mainly
for their heuristic and pedagogical value. He says something like this in the following:

"…The widely recognized

Samuel Bowles on how "Marx’s representation of the power relationship between capital and labour in the firm is an essential insight"
Economics in the Rear-View Mirror on renewal of Paul Sweezy’s instructorship.
Manoucher Parvin, in 1992, asks, "Is teaching neoclassical economics as the science of economics moral?"
Alexander Douglas on micro-founded macro.
A review of Fredric Jameson’s new book, in Jacobin earlier this month.
A review of Fredric Jameson’s new book, in the September issue of Harper’s.

Figure 1: Wage Curves for the Two Techniques1.0 Introduction

Economists following the Austrian school often represent the structure of production with Hayekian
triangles (Hayek 1931, Rothbard 1962, Skousen 1990, Garrison 2001, Machaj 2017). Typically,
goods of the highest order are produced with unaided labor or other unproduced original resources.
(Fillieule (2007), in which a Hayekian triangle is constructed with an infinite stream of unproduced inputs, is an exception.)
Rarely, is a model of the production of commodities by means of commodities, as in Sraffa (1960), considered.
This post illustrates how to construct a Hayekian triangle with such a model, in the case with circulating capital.

It also illustrates how the use of such triangles to tell the stories that Austrian

The following are the first three paragraphs of the introduction
to the Wealth of Nations:

"The annual labor of every nation is the fund which
originally supplies it with all the necessaries and
conveniencies of life which it annually consumes, and
which consist always either in the immediate produce of that labour,
or in what is purchased with that produce from other nations.

According, therefore, as this produce, or what is purchased with
it, bears a greater or smaller proportion to the number of those who
are to consume it, the nation will be better or worse supplied with
all the necessaries and conveniencies for which it has occasion.

But this proportion must in every nation be regulated by two
different circumstances: first, by the skill, dexterity, and judgment
with which

This is more for my commonplace book. The first two quotations are part of a symposium with Morishima and Samuelson:

"This paper will suggest that the meaning of
the relationship between values and prices
described in Capital has been widely misunderstood.
Commentators as eminent as Mrs. Robinson
and Professor Samuelson have sought in the transformation
discussion issues which Karl Marx never
meant it to contain. Writers on ‘the transformation
problem’ since L. Bortkiewicz have focussed on an
issue that is largely peripheral; and others like E.
B6hm-Bawerk have asserted that there is a contradiction
between the analyses of Volumes I and III
which is certainly not to be found there unless lne
reads into them an interpretation different from
that which Marx repeatedly emphasized.

Many of my examples illustrate simple structures of production for models in which commodities are produced with commodities.
Economists following the Austrian school often illustrate the structure of production with Hayekian triangles.
Accordingly, this post illustrates a Hayekian triangle with a model in which commodities are produced out of commodities.
I consider the case in which only circulating capital exists. This post is a rewrite of
this one.

The following are taken as given for the technique in use:

A: The nxn Leontief input-output matrix in physical terms. Assume all commodities are basic and the economy is productive.
a0: The n-element row vector of direct labor coefficients.
d: An n-element column vector that is in the proportions in which commodities are consumed.

This is for my commonplace book.

"It is true that some lengthy or roundabout processes are physically efficient. But so are some short processes. Lengthy processes
are not physically efficient because they are long. Some, probably most, lengthy processes would be physically very inefficient,
for there are such things as spoiling or wasting with time.
With a given labour force there is a definite limit to the quantity of labour embodied in roundabout processes which can
be used to advantage. Apart from other considerations, there must be a due proportion between the amount of labour
employed in making machines and the amount which will be employed in using them. The ultimate quantity of value will
not increase indefinitely, relatively to the quantity of labour employed, as the

I have expressed an appreciation
before of the section in Capital on commodity fetishism.
Perhaps this section stands up
to a critique of Marx’s theory of value.

"But Marx had drawn a nightmare picture of what happened to human life under capitalism, when everything was
produced only in order to be exchanged; when true qualities and uses dropped away, and the human power of making
and doing itself became only an object to be traded. Then the makers and the things made turned alike into commodities,
and the motion of society turned into a kind of zombie dance, a grim cavorting whirl in which objects and people
blurred together till the objects were half-alive and the people were half-dead. Stock-market prices acted back
upon the world as if they were independent powers, requiring

1.0 Introduction

This post illustrates a derivation of prices of production, based on certain properties of duality
theory as applied to linear programming. I strive to be more concise and elementary
than previous expositions.
This exposition is based on John Roemer’s Reproducible Solution (Analytical Foundations of Marxian Economic Theory,
Cambridge University Press, 1981).

You will find no utility maximization or supply and demand functions below. I have no need for such hypotheses.
Nevertheless, one can read this derivation as consistent with marginalism.

2.0 Technology and Endowments

Two commodities, iron and corn, are produced in this example. Managers of firms know a technology consisting
of the processes defined in Table 1. Each column shows the inputs and outputs for a

I picked up the novel that the following quotation is from because I think I recall Kress participating in
conversations on Usenet years ago. This novel ended up more a political argument than I expected. It is
for Genetically Modified Organisms (GMOs), done right. We should rather strive for plants for food
resistant to insects, not resistant to pesticides, for example. I assume that Kress agrees with
her heroine.

"He had spent the two-week winter vacation from school, which somehow got extended to
nearly another week, with Jake in Los Angeles…

He left an eleven-year old nerd, dress in Levi’s, a tee that said CHESS PLAYERS HAVE
GREAT MOVES, and a baseball cap. He returned looking like a thirty-two-year-old
investment banker trying to be cool, dressed in a $300

1.0 Introduction

Where do prices come from in mainstream economics? As far as I know, some hard questions were raised half a century ago.
They still have not been answered, I gather.

2.0 No Agent Makes Prices

Consider competitive markets, as defined in marginalist economics for most of the twentieth century.
This implies that agents in the market take prices as given.

From Steve Keen, I know that if only a countable infinity of consumers and firms exist, the agents are
systematically mistaken. Despite their beliefs, they are not atomic, and their actions in varying quantities
bought or sold affect prices.
For agents not to be systematically mistaken,
an uncountable infinity of consumers and firms must
exist.

I have noted Emmanuelle Benicourt
making similar
points before.

Figure 1: Variation in the Cost-Minimizing Technique with Selected Coefficient of Production
This post reports on some work with
Steedman’s corn-tractor model.
I have yet to find an instance of triple-switching. I have found a case of reswitching, though.

Figure 1 above and Table 1 below show how switch points vary with perturbations of the labor needed to produce a bushel of corn
in the corn industry with Type I tractors. Only one switch point exists in region 1. Around this switch point a lower rate of
profits is associated with the production and use of Type I tractors, an increase in consumption per labor-year, and a
decrease in labor inputs in the corn industry per bushel produced. In other words, this switch point conforms to obsolete
marginalist intuition.

Table 1: Regions

Ludwig
Von Mises
expanded his erroneous 1920 essay into a book,
Socialism: An Economic and Sociological Analysis. The first
edition was published in 1922 and the second edition in 1932.

Since Von Mises is attempting to be more comprehensive, he treats
the socialist advocacy of free love in an early chapter.
Being au courant, he writes about Freud. He argues that the bourgeois
idea of marriage as a contract, binding on both husband and wife,
is an improvement on what came before.

But I find it hard to get beyond passages like those below.
Here, Von Mises confines women to her supposed role in
propagating the human race, as in Margaret Atwood’s The Handmaid’s Tale:

"The radical wing of Feminism, which holds firmly to this standpoint,
overlooks the fact that the expansion of woman’s

1.0 Introduction

I would like to illustrate triple switching, in
the corn-tractor model,
with one of my one-dimensional diagrams.
I have a triple-switching example,
from Bertram Schefold, but the wage-rate of profit frontier is not visually striking in it.
Such an example would not be worthy
of a research paper.
But perhaps I could modify a section of my
recent working paper
to submit somewhere. Besides, posing a new problem might motivate me to update my computing technology.

2.0 Technology

The corn-tractor model
is a fixed capital model, an adaption of
the Samuelson-Gargenani model.
Labor and tractors are used to produce new tractors. Labor and tractors are also used to produce corn.
Corn is the consumption good and the numeraire. Table 1 shows the coefficients of production for a

Louis-Philippe Rochon on Paul Davidson.
James Galbraith, Thomas Palley, and Matias Venengo on Paul Davidson.
The Economist on Donald Harris. Response in letters to the editor (Both behind paywall).
The Washington Post on policy advice from Donald Harris for Jamaica (Behind paywall).
Maybe I want to read Vanessa Wills’ Marx’s Ethical Vision, which may be in tension with views I have set out.
Gordon Katic on the insidious elitist upshot of behavioral economics.

A mistaken theory claims prices convey information about relative scarcities. Friedrich Hayek uses an example of tin.
According to this theory, a higher wage incentivizes investments in less labor-intensive techniques and to
shifting production towards less labor-intensive commodities. Likewise, a lower interest rate incentivizes
investments toward more capital-intensive techniques and to shifting production towards more capital-intensive commodities.

A number of attempts have been made to elaborate this theory and to formalize this vision:

One can measure capital-intensity by aggregating the prices of capital goods used, per person-year of labor employed, in producing a commodity.
Around switch points, a lower interest rate is associated with the adoption of a more capital-intensive

I have demonstrated that Von Mises fails
to identify problems with central planning.
This post merely documents Von Mises being mistaken.
He erroneously says that an economic decision cannot be made over
alternative methods of producing a given good,
without market prices for capital goods and resources.

"The director wants to build a house. Now, there are many methods
that can be resorted to. Each of them offers, from the point
of view of the director, certain advantages and disadvantages with
regard to the utilization of the future building..; each of them requires
other expenditures of building materials and labor… Which method should the director choose;
He cannot reduce to a common denominator the items of various
materials and various kinds of labor to be expended. Therefore

In re-reading Robinson, I often find her succinctly summarizing a theory, often developed later.
Here is a quotation from one of my favorite books by her:

"The argument is sometimes advanced that evidence shows that, in reasonably prosperous countries,
the percentage of unemployment is never seen to vary very much, averaging good times with bad,
over the long run … But even for prosperous countries the evidence is largely an optical illusion.
Capitalist industry does not employ the whole work force in any country.
Domestic service, paid or unpaid, jobbing work and small-scale trade, and, in most countries,
agriculture, hold a reservoir of labour which fills up when regular employment is not expanding
as fast as the population. The question of whether people are happier in these

The title claim is not surprising. But it occurs to me that it follows from how I
model prices of
production, given stable relative profit rates
among industries. I am not original with this modeling. My contribution is analying the choice of technique and exploring how this analysis
varies with perturbations of relative markups.

In the price equations, s1r, s2r, s3r, and so on are the rate of profits
in the various industries. I call r the scale factor for the rate of profits.
Given the technique and a given wage in terms of a given numeraire, one can find prices and the scale factor for the rate of profits.
The scale factor is a declining function of the wage. The cost-minimizing technique at a given wage is the technique for the
wage curve on the outer frontier at that wage. At a

1.0 Introduction

This post is an update, based on suggestions from a user on reddit.
I have explained this before.
Suppose one insists socialism requires central planning.
In his 1920 paper, ‘Economic calculation in the socialist commonwealth’, Ludwig Von Mises claims
that a central planner requires prices for capital goods and unproduced resources to successfully plan an economy.
The claim that central planning is impossible without market prices is supposed to be a matter of scientific principle.

Von Mises was mistaken. His error can be demonstrated to follow from the theory of linear programming and
duality theory. This application of linear programming reflects a characterization of economics
as the study of the allocation of scarce means among alternative uses. This post

1.0 Introduction

I have explained this before.
Suppose one insists socialism requires central planning.
In his 1920 paper, ‘Economic calculation in the socialist commonwealth’, Ludwig Von Mises claims
that a central planner requires prices for capital goods and unproduced resources to successfully plan an economy.
The claim that central planning is impossible without market prices is supposed to be a matter of scientific principle.

Von Mises was mistaken. His error can be demonstrated to follow from the theory of linear programming and
duality theory. This application of linear programming reflects a characterization of economics
as the study of the allocation of scarce means among alternative uses. This post demonstrates that Von Mises was
mistaken without requiring, hopefully,

I have another working paper,
Visualizing variations in the analysis of the choice of technique, at the Centro Sraffa. The abstract follows.

Abstract: This article describes a diagram that depicts how the analysis of the choice technique varies with
perturbations of selected parameters in models of the production of commodities. Fluke switch points partition the graph.
Three examples are provided, of circulating capital with markup pricing, of fixed capital with structural economic dynamics,
and of intensive rent with markup pricing.

1. Introduction

Elsewhere on the internet, I have been explaining my understanding of some rudiments of the political
economy of Karl Marx.

Marx’s concept of surplus value is a generalization of the concept of profit, in some sense.
Surplus value takes in all returns to ownership, whether they be profits, interest, rent, and so on.
Surplus value arises from the distinction between the use value and the exchange value of labor power,
a peculiar commodity. Because capitalists own the means of production, they can ensure through
their domination of the workers, that laborers work longer than the time needed to reproduce
their means of subsistence.

2. A Simple LTV as the Setting of Marx’s Theory

Marx explains the generation of surplus value in volume 1 of Capital. For the sake of

[embedded content]Automation Of Chinese Ports
With automation, many processes for production and distribution now execute with minimal
human oversight. How can the labor theory of value, as in volume 1 of Capital,
be compatible with this?

Marx has some comments on this subject in the Grundrisse:

The exchange of living labour for objectified labour – i.e. the positing of social labour in the form of the
contradiction of capital and wage labour – is the ultimate development of the value-relation and of
production resting on value. Its presupposition is – and remains – the mass of direct labour time,
the quantity of labour employed, as the determinant factor in the production of wealth. But to the
degree that large industry develops, the creation of real wealth comes to depend less on

"There is in every society or neighbourhood an ordinary or average rate, both of wages and profit, in every different employment
of labour and stock…

There is likewise in every society or neighbourhood an ordinary or average rate of rent…

These ordinary or average rates may be called the natural rates of wages, profit and rent, at the time and place in
which they commonly prevail.

When the price of any commodity is neither more nor less than what is sufficient to pay the rent of the land,
the wages of the labour, and the profits of the stock employed in raising, preparing, and bringing it to market,
according to their natural rates, the commodity is then sold for what may be called its natural price…

The actual price at which any commodity is commonly sold, is called

So my computer crashed. I hadn’t backed it up in a while. But, even so, my backup failed, too.
I am currently paying for some specialist organization to restore the data, and they are on their third attempt.
The cost seems a lot for an individual, but I feel like I need a lot that is on it.

I am going to buy a new computer, and I have been slow about this. Until I do this, I will not
be able to post any mathematical examples. I think that I have posted enough that I can
recreate these examples.
But I have lost draft introductions and conclusions not in posts. This is always my difficulty, and what
I had should probably have rewritten those parts anyways.

I have also lost code, some for applications I do not recall. I have lots of PDFs, some for works I have also in books.
I had

Infinite are the arguments of Marxists. This very selective survey needs references.

A first difficult is that everybody knows Marx has something to do with the Soviet Union. Many
come to reading Capital with certain preconceptions. A couple comments in the book, for analytical reasons, contrast capitalism and
feudalism and a post-capitalist
economy with common ownership. But the book is about capitalism. The book contains expressions of outrage, often ironical.
But is capitalism criticized for being unjust?
And the labor theory of value, for Marx, is not about what workers
should be paid.

I tend to read Marx as developing
a theory
for political economy, a theory about how capitalism works.
But should such a thing as Marxian political economy even exist? "A critique of political

Overview

Paul Davidson took Keynes’ General Theory of Employment Interest and Money seriously.
The interpretation in mainstream textboooks misses important points.
Keynes’ book was about theory, not primarily about (short-run?) fiscal or monetary policy.
Keynes does not explain persistent unemployment from imperfections or sticky or rigid money wages or prices.
A general theory is one that has less axioms
than the special case treated by, say, Marshall. Davidson identified,
specifically, three axioms relaxed or rejected by Keynes:

Neutrality of money. For Keynes, money is non-neutral in all runs.
Gross substitution. Money has no substitutes; it cannot be produced from labor.
Ergodicity. Important time series in economics can be non-ergodic. Numerical probabilities cannot necessarily

Michael Harrington was a great socialist in the United States. This is not to say that he did not make some political
missteps, at least at Port Huron.
Isserman’s biography seems to have Michael making political missteps throughout the 1950s and 1960s.
His son Alexander had exposure to some hard-to-understand ideas before he got to college:

My older son, Alexander, began to read Dostoevsky on his own when he was about fifteen and once told a college professor
who was explaining Hegel’s dialectic in terms of thesis, antithesis, and synthesis that Hegel didn’t use those terms and that
he should read the section on Master and Servant in the Phenomenology of Spirit for the real theory.
— Michael Harrington. 1988. The Long-Distance Runner: An Autobiography. New York: Henry Holt and

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