This post presents a
limited
account
of the history of analyzing prices of production with non-uniform rates of profits.
I start from developments in post Sraffian price theory. D’Agata (2018) and Zambelli (2018b) have
argued that Sraffian prices of production can still be defined when rates of profits have regular and
persistent variations among industries. Barriers to entry or idiosyncratic properties of investment
can result in such variations. Steedman (1981) presents the first formulation in post Sraffian price theory
that I know of in English with systematic variations of the rate of profits among industries.
Roemer (1981: 23-29) provides microfoundations for modeling imperfect competition in linear production models.
He assumes different capitalists have different information

The 2020 "Nobel Prize" in economics goes to Paul Milgrom and Robert Wilson. I suppose
it is nice that economists acknowledge that markets are not natural entities but
need to be constructed. For example, consider the Federal Communications Commission
auction
of the microwave spectrum.

The 2012 "Nobel Prize" went to Alvin Roth and Lloyd Shapley. The 1996 "Nobel Prize",
to William Vickrey (a Post Keynesian, by the way) was also for acution theory. The
2002 prize went to Daniel Kahneman and Vernon Smith. Smith’s work included experiments
with markets constructed in the laboratory.

I do not know much about this field. But I am hoping some journalists know of Philip
Mirowski, an expert on the history of information in economics, and get him
to comment on the award this year.

Figure 1: Prices of Production1.0 Introduction

This post presents a new kind of fluke case in the analysis of the choice of technique, at least new to me.
I call this a pattern for requirements for use, and it can arise only in a case of joint production. My graphs
in this post have some incomprehensible notation, since I am currently exploring perturbing parameters, in
line with my research agenda.
I know that perturbing the requirements for use removes the indeterminancy in this example.

2.0 The Givens

For this example, the data consist of the available technology and the proportions in which the two produced commodities,
corn and silk, enter into the commodity basket specified by the requirements for use. I also choose a numeraire. The example
is a perturbation of problem 8.2 in

This is C27 in Sraffas archives.

97 Fortis Green
London N2
Tudor 0214

6th August 1966

Dear Piero,

I do not know whether you know Roger Simon, who is Secretary of the Labour
Research Department. At all events he is a great admirer and enthusiast of
Gramsci. Thanks to his initiative, plans are afoot (in which I too am
collaborating) to publish a new volume of Gramsci’s works translated into
English and Lawrence & Wishart have agreed, in principle, to undertake publication.

We would very much welcome views and suggestions from you on how this should be
done. The general idea at present is a bigger book than the L & W. 1957 translation (which is
now out of print), including, if appropriate, passages already translated on that occasion.
One line of thought that we are pursuing is

In 1929, John Maynard Keynes and Hubert D. Henderson wrote, Can Lloyd
George Do It? The Pledge Examined. This was published by The Nation
and Athenaeum and is an examination of the pledge by the leader
of the Liberal party, if elected, to dramatically reduce the amount of
unemployment in Great Britain. (I was inspired to look up this work
while reading Zachary Carter’s new book.)

Chapter VI of Keynes and Henderson is concerned with "How Much Employment Will the Liberal Plan Provide?"
The direct employment for each million pounds can be quantified. The authors
divide the resulting indirect employment into two types. The first, in the industries
that directly and indirectly supply road-building, housing, and so on, Keynes
and Henderson think can be quantified:

VI.2 The Importance of

In a blog associated with the Frankfurter Allegmeine, Gerald Braunberger
criticizes
the effects of Sraffian political economy on Italian policy in the 1970s. I
rely on google translate and subject matter expertise to make some sense out of this.
By the way, Bertram Schefold shows up in the comments. I would like
to know more about the motivations behind this. Does Braunberger
think the public is increasingly aware that mainstream economics
is broken?

Before I disagree, I note Braunberger seems well-informed on some points. I know of grumbles
about Garegnani’s treatment of Sraffa’s archives. And I have heard that the Trieste
summer schools were torn between those who emphasized long period logic and
Post Keynesians who emphasized uncertainty, money, and historical time.
On another

Figure 1: A Pattern Diagram
This post illustrates the numeric example used
here.
The example is of an economy in which two commodities, iron and corn, are
produced by workers from inputs of iron and corn. Two processes
are available for each industry, leading to a choice among four
techniques. I analyze stationary states.

I look at prices of production, with a bushel corn as numeraire
and wages paid out of the surplus at the end of the year.
Prices of production are defined so as to allow for markups
in both industries. Figure 1 shows the variation in switch
points on the wage frontier with variations in the ratio of markups.

I am interested in how variations in markups can bring about
qualitative changes favorable to labor pressing for higher
wages. For example, around the switch

I have a working paper.

Abstract: This article extends to unequal rates of profits a derivation of prices of production from a linear program.
A partition of the price-wage space is illustrated in an example with two produced commodities. The variation in the solution
of the LP with perturbations of relative markups is illustrated. This analysis provides an intuitive explanation of
how the reswitching of techniques and of how capital reversing can emerge in non-competitive markets.

I first became aware of David Graeber as a poster on Usenet back in the 1990s.

Many people who have succeeded in this world have no interest in conducting
honest discussions. I found some places where one could have cheerful
talk, including with harsh disagreement. And I found other places not
so much. I probably fit in with the latter.

Sometime in November 1998, a thread arose, "A Donaldism for David Friedman".
David Friedman is Milton’s son and also promotes plutocracy under the
guise of ‘liberty’. The thread was about how participants should
treat other posters who continually lied and said others secretly
wanted to set up a totalitarian dictatorship where they could kill
those who disagreed with them. Graeber was not having any of this:

[Dan Clore wrote:]

David

1.0 Introduction

Piero Sraffa wrote down his ‘first equations’ in 1927, for an economy without a surplus.
D3/12/5 starts with these equations for an economy with three produced commodities.
I always thought that they did not make dimensional sense, but Garegnani (2005) argues
otherwise. This post details Garegnani’s argument, albeit with my own notation.

There are arguments about how and why Sraffa started on his research project I do not
address here. The question is how did he relate what he was doing at
this early date to Marx. In addition to Garegnani, DeVivo, Gehrke, Gilibert, Kurz, and Salvadori
are worth reading here.

2.0 Givens

I assume an economy in a self-replacing state in which n + 1 commodities are produced.

c0,0 is the input of the first commodity used in producing the

Paul Graham jokingly asks, "What phrase signals that the person using it doesn’t understand your field?"
Stephen Gordon and
Alex Tabarrok both
respond with "Neoclassical economics".

Jamie Morgan (ed.) (2016) What is Neoclassical Economics? Debating the Origins, Meaning, and Significance, New York: Routledge.
R. Robert Russell and Maurice Wilkinson (1979). Microeconomics: A Synthesis of Modern and Neoclassical Theory, New York: John Wiley.

I have a new working paper.

The article presents previously unpublished material from file D13/12/111 in Sraffa’s archives. In particular, it reproduces an English
translation of Aurelio Macchioro’s review in Annali dell’Istituto Giangiacomo Feltrinelli, a summary by Christopher Bliss of a
paper that he read to the Cambridge Political Economy Club, a draft response by James Meade, a rejected paper on Marx by Vittorio Volterra
and Moshe Machover, and a paper on the subsistence economy by Gouranga Rao. Correspondence in the Sraffa archives related to
these works is also reproduced.

"Typically 2 the integer is used for counting, whereas 2 the real number is used for measuring.

But in higher mathematics there’s a technical sense in which integers aren’t
real numbers — we say instead that they can be identified with real
numbers." — Timothy Gowers

1.0 Introduction

Numbers, in some sense, are only defined in mathematics up to isomorphisms. This post runs
quickly through some math to explain what this means.

I begin by assuming knowledge of the natural numbers, {0, 1, 2, …},
as characterized by the Peano axioms.
I also assume an understanding of what it means for two natural numbers to be equal, for one
to be greater than another, and for two to be added or multiplied together. Other operations
could be built on top of this structure, as needed.

2.0

These seem to be resources for providing the student with an overview of schools of thought, fields, and
the history of economics.

Exploring Economics is set up by
the Network for Pluralist Economics. Here
is their overview of Post Keynesianism.
Economics Education is a webpage "built by Sam de Muijnck and
Joris Tieleman of Rethinking Economics Netherlands." Here
is their page on feminist economics. Here
is their page on Post Keynesian economics. This
is their page on (original) institutional economics.
The Institute for New Economic Thinking supports
Goncalo Fonseca’s History of Economic Thought web site.
Apparently, the recently departed Mark Hayes, building on work by Philip Aretis and Victoria Chick, had a lot to do with maintaining the
Post-Keynesian Economics Society. Every once

Zach Carter’s The Price of Peace: Money, Democracy, amd the Life of John Maynard Keynes.
James Crotty’s Keynes Against Capitalism: His Economic Case for Liberal Socialism.
Stephanie Kelton’s The Deficit Myth: Modern Monetary Theory and the Birth of the People’s Economy.
Stephen Marglin’s to-be-published Raising Keynes: A Twenty-First-Century General Theory. I think his earlier Growth, Distribution, and Prices parallels Donald Harris’ even earlier Capital Accumulation and Income Distribution in that they both see Sraffa’s price equations, supplemented by dual quantity relations, as a whole model that can be closed by alternative theories. Marglin draws some contrasts in his notes on the literature.
Bill Mitchell, Randy Wray, and Martin Watts’ Macroeconomics.
Matthew Yglesias’s

"One must be able to say at all times – instead of points, straight lines, and planes — tables,
chairs, and beer mugs." — David Hilbert (as quoted by Constance Reid, Hilbert, Springer-Verlag, 1970: p. 57)

Consider the Fibonacci sequence: 1, 2, 3, 5, 8, 13, …
The first two terms in this sequence are 1 and 2. After this, each term is the arithmetic sum of the previous two terms.
Let A be the set of elements in this series. Let s be the function mapping an element in A onto another element of A,
where s(n) is the term in the sequence following n. I want to read s as "successor".
(I do not claim originality for the following use of the Fibonacci series.)

Notice that the set A and the successor function satisfy
the following properties:

1 is in the set A.
For any n in the set A,

… If you speak of a revolution in mathematics, you are likely to be treated to the ironic response,
"Oh, so two
and
two now make
five?"
We can answer: "Why not? Suppose we ask for the delivery of two
articles each weighing two pounds; they are delivered in a box weighing one pound; then in this package
two pounds and two pounds will make five pounds!"

"But you get five pounds by adding three weights, 2 and 2 and 1.""

"True, our operation ‘2 and 2 make 5’ is not an addition in the usual sense. But we
can define the operation to make the result hold true. We can imagine a packaging such
that the operation might be, for instance:

2 and 2 make 5; 2 and 3 make 6 (if the box weighs one pound in each case),
3 and 3 make 8; 3 and 4 make 9 (if the box weighs two pounds), etc.

"The

I have long been convinced that many mainstream economists, however they performed under hazing,
do not understand mathematics.

"T. C. Koopmans, perhaps the greatest defender of the use
of the mathematical tool in economics, countered the criticism
of the exaggeration of mathematical symbolism by claiming
that the critics have not come forward with specific
complaints. The occasion was a symposium held in 1954
around a protest by David Novick. But, by an irony of
fate, some twenty years later one of the most incriminating
corpora delicti of empty mathematization got into print
with the direct help of none other than Koopmans. R. J.
Aumann had already published in Econometrica an article
dealing with the problem of a market in which there are as
many traders as the real numbers, that

I have been exploring Sraffa’s correspondence after the publication of his book.
Here is a letter dated June 18, 1962, from Mathur to Sraffa (D3/12/111: 298):

Dear Mr. Sraffa,

In Nuffield there is a senior research student Edmund Nell who is attached to the faculty of Literae Humaniores[?]
and is researching into the significance of concepts in economics. He is highly interested in the type of analysis
you have proposed, and has been trying to work his way through it. In Oxford there is no other person whom I have
met or heard of who has made a more detailed study of your book.

He would very much like to meet you, to discuss some of his problems, and would be writing to you direct regarding it.
In the meantime, he has asked me to introduce him to you. This letter is meant to

[embedded content]Neoclassical Political Economy
You may have seen the above overly polite video.

I have not done this in a while, even before the pandemic. I used to, when I visited an academic bookstore
or a college library, skim through textbooks, concentrating on introductory or intermediate microeconomics.
Economics is in an extraordinary state, where the textbooks are full of nonsense that has
been known to be logically invalid for half a century.

Here is an example. David D. Friedman (Milton’s son) has made the 1990 or second edition of his
Price Theory: An Intermediate Text
available online. And it contains this manure:

This conclusion is useful for seeing how various changes affect the distribution of income.
Suppose the number of carpenters suddenly increases, due to the

Marx is mostly right.

That is the conclusion one should draw from capital
theory. But honestly understanding how we are fed, clothed, and housed
under capitalism is not what academic economics is about.

Ownership of property in, say, the United States results in the
generation of income. This income takes the form of interest on
debt, dividends, capital gains, rent, and so on. Many of those who
are among the most wealthy often have returns to property ownership
as their only source of income.

Overall, laborers work within a given environment to recreate
the capital goods used up in production and to produce more.
The source of the returns to property ownership comes from
paying workers less than what they produce, over and above
the constantly reproduced capital.
The owners of

1.0 Introduction

One inspiration for this post is stumbling across this
abstract

2.0 Marx

Start with labor coefficients and a Leontief input/output matrix, in physical terms. You can construct this
from make and use tables for your country, given price indices by sectors.

For any existing capitalist economy, I expect that matrix to characterize a more than viable economy. After all the
capital goods used up in producing the final demand in, say, a year are reproduced, some commodities will remain for consuming
and investing.

As with any other matrix, a set of n Eigenvalues and corresponding Eigenvectors can be found for
that matrix. And, if I recall correctly, the maximum Eigenvalue has an associated Eigenvector in which
all elements are non-negative. The components for Sraffa’s

I have been looking at Sraffa’s archives. Scott
Carter was responsible for putting them online, as I understand it. Anyways, I know some contents has been published. What should
I read for transcripts of letters between Robinson and Sraffa? Maybe something by Marcuzzo?

Anyways, here is a 18 June 1960 letter from Robinson to Sraffa (D3/12/111: 340-341)

All the work that I have been doing the last 10 years has been very much influenced by you – both our conservations
in old days and by your Preface. When I went off my head I thought that the idea I had seen in a blinding flash was yours,
because it came to me in terms of Ricardo’s corn economy, but it was connected with TIME and it so appears is very much
akin to your point of view (though one it seems to fit perfectly well.) Since,

I have defined patterns of switch points in considering perturbations of examples of the choice of technique.
For example, I have defined three-technique and four-technique patterns.
An obvious extension is to consider how these patterns arise in models of joint production.
A simplification is to only consider models of fixed capital without superimposed joint production.

This post lays out an example in which, maybe, some parameter values can lead to a three-technique pattern.
I am trying to consider whether I want to allow it to be an interlocked system.
The question arises when I lay out a simple example in which a machine can be used for one or two years.

Accordingly, consider an example with the coefficients of production in Table 1. Corn and new machines are finished goods.
An

[embedded content]Katzner, Bowles, and Resnick on UMass Amherst
Shartly after about 32:30 minutes, Sam Bowles, to laughter, draws a Venn diagram on the board. This is a light talk, and Bowles is explicitly describing
economics from his own experience at the University of Massachusetts at Amherst. Bowles places various economists in various subsets.
I have varied the names a bit in my reproduction below.

Bowles’ Taxonomy
I take the universe to be the set of all economists. Or, maybe, given Bowles includes John Rawls, it is a set of academics concerned with topics
Bowles thinks economists should be concerned with. I take it that this taxonomy is not to apply to all time and space, but maybe only to academics
from about 1970 to now. I explicitly added Kenneth Arrow, Milton Friedman, and

Do economists have anything to say about racism in the United States? Some do.
The Review of Black Political Economy, for example, exists.

Other groups in the United States are often thought of as marginalized.
I have written about
women in economics
before.
As usual, I want to mention the existence of the
International Association for Feminist Economics
and their journal
Feminist Economics.
I also note the existence of
Queer Economics: A Reader
for those economists that might be of a questioning bent.

Discourse in many academic disciplines about the Other often draw on post-modernism, post-structuralism,
and other scary stuff. Some economists have attempted to extend Marxism to engage with postmodernism.
Although I have read a bit of
David Ruccio and Jack Amariglio,
I do not know

This post lists some views on Production of Commodities by Means of Commodities: A Prelude
to a Critique of Economic Theory.

The quantity flows Sraffa takes as given are those observable in an actual economy at a given time, as with a snapshot (Roncaglia 1978).
These quantity flows, on the contrary, are at the level of effectual demand (Garegnani 1990).
These quantity flows are for an economy in a self-replacing state.
The assumption of constant returns to scale is necessary for drawing any interesting conclusions from Sraffa’s work (Samuelson 1990, Samuelson 2000).
Market prices tend towards or orbit around Sraffa’s prices of production in a process akin to gravitational attraction (Garegnani 1990).
Sraffa’s book is an investigation of logical consequences in a system of prices of

[embedded content]John Eatwell On Why Economists Disagee
I like the above lecture by John Eatwell. He concludes by talking about the
partial equilibrium model of supply and demand "that we teach, and we justify it by the general equilibrium model".
He notes that lots of economists
put imperfections in.
The Arrow-Debreu is currently the fundamental model of price theory among mainstream economists.
According to Eatwell, economists fall into
at least five groups.

Those who think revisions are important to retain market rationality and try to find ways to make the model work, for example, with representative agents in Dynamic Stochastic General Equilibrium models.
Those who think reasonable, empirically-based imperfections can be used to produce practical models.
Those who find things that

At this time, the book had long ago been published by Cambridge University Press. I suppose I ought to review
whatever conditions exist on transcribing stuff in the archives. The following is D3/12/111:9.

Routledge & Kegan Paul Ltd.

October 15th 1969

Professor Piero Sraffa,
Trinity College,
CAMBRIDGE

Dear Professor Sraffa,

At the Frankfurt Book Fair last week, Einaudi told me about your "Produzione di merci a mezzo di merci".

I don’t know whether this has been published in English, but if not, we would be very interested in publishing it.

Yours sincerely,

Norman Franklin

My fellow Americans:

We have endured a week such as no Nation should live through: a time of violence and tragedy.

For a few minutes tonight, I want to talk about that tragedy – and I want to talk about the deeper
questions it raises for us all.

I am appointing a special Advisory Commission on Civil Disorders.

Governor Otto Kerner, of Illinois, has agreed to serve as Chairman, Mayor John Lindsay, of New
York, will serve as Vice Chairman…

The Commission will investigate the origins of the recent disorders in our cities. It will
make recommendations – to me, to the Congress, to the State Governors, and to the Mayors –
for measures to prevent or contain such disasters in the future.

But even before the Commission begins its work; and before all the evidence is in, there
are