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

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