Figure 1: A Wage Frontier With Two Fluke Switch Points
This post is a rewrite of this,
without the attempt to draw a connection to structural economic dynamics.

This post presents an example with circulating capital alone. Table 1 presents the technology for an economy in which two commodities,
iron and corn, are produced. Managers of firms know of one process for producing iron and two for producing corn.
Each process is specified by coefficients of production, that is, the required physical inputs per unit output.
The Alpha technique consists of the iron-producing process and the first corn-producing process. Similarly, the Beta
technique consists of the iron-producing process and the second corn-producing process. At any time, managers of firms face a problem of the choice of

Socialism became a mass movement in many European countries about the time of the
heyday of the Second International. Many leaders of these movements and those
struggling for leadership produced works of scholarship, albeit often with
an activist spirit. I think of, for example:

Eduard Bernstein. The Preconditions of Socialism and the Tasks for Social Democracy.
Nikolai Bukharin. The Economic Theory of the Leisure Class.
Richard B. Day and Daniel F. Guido (eds.). 2018. Responses to Marx’s Capital. Brill
Rudolph Hilferding. Böhm-Bawerk’s Criticism of Marx.
Rudolph Hilferding. Finance Capital.
Karl Kautsky. The Social Revolution.
Karl Kautsky. The Path to Power.
Antonio Labriola. Essays on the Materialist Conception of History.
Rosa Luxemburg. The Accumulation of Capital.

1.0 Introduction

In a common model, probability theory assigns a number between zero and
one to events. But
some events cannot be assigned a probability, even zero.
Nobody understands probability, in some sense.

This post is not about economics, although these ideas
do have an application in mainstream economics.
It is not at all novel. This is one of my favorite proofs in all of math, typically taught sometimes after an
introductory mathematical analysis class. My undergraduate class in probability and statistics
only alluded to measure theory.

2.0 An Introduction to Probability and a Overview

Suppose one has some sort of repeatable experiment, like rolling a pair of dice, dealing out a five-card poker hand,
or spinning a spinner. The set of all possible outcomes is the sample

1.0 Introduction

A question has arisen elsewhere. Why, except for an interlude during the post war golden age,
has a nineteenth century orthodoxy dominated economics departments and treasury departments
around the world? Here I do not investigate the details of this orthodoxy
or if it does dominate.

2.0 An Authoritarian Point of View

Some people believe that some are better than others. They want
to live in a world
where those at the top tell those below what to do, and those below jump.

One might think that it would be hard to find people willing to explicitly articulate
these feelings in public. But you can find, if you look, Republican
candidates for elected offices saying
it was a mistake to allow woment to vote
or that interracial marriage should be outlawed.

Some who support

[embedded content]An Experiment in Game Theory
Game Theory provides a formal treatment of well-specified
situations in which the outcome depends on the choices of
several agents who may have conflicting interests.

Abstractly, a player chooses a strategy, where a strategy
specifies the player’s move in every situation that may arise
in the game. For example, a strategy for white in chess specifies,
roughly white’s move for every board configuration in which
it is his turn. This example is rough because white’s play
will prevent certain configurations from arising, and his
strategy need not provide a move for those unreachable
configurations. A game tree is a useful representation for
a game in extensive form. I think this definition of a
strategy elides important issues of algorithms

William Petty began classical political economy in the 17th century. Classical economics was developed through the work of the physiocrats and such
writers as Adam Smith, David Ricardo, and Karl Marx. Marx was also a critic.

About a century and a half ago, economists mistakenly accepted the marginal revolution. Jevons, Menger, and Walras had precursors,
but they were regarded as cranks. Marx, however, posed a political problem. Some might mention Henry George here, or maybe even
Silvio Gesell. Better have an imitation of physics than talk about the ideas of those opposed to capitalists.

Lionel Robbins made clear in the 1930s, when the theory plainly did not apply, that marginalist economics is about the
allocation of scarce resources. Land and labor can be taken as given at a moment

Anton Pichler, Marco Pangallo, R. Maria del Rio-Chanona, François Lafond, and J. Doyne Farmer have an article Forecasting the propagation of pandemic shocks with a dynamic input-output model. This is a non-equilibrium, simulation model applying Leontief’s input-output analysis. I suppose this is applied Sraffianism.
For the use of Leontief input-output models in modeling natural disasters, one could do worse than look at the work of Adam Rose.
Steve Keen responds to this year’s Nobel prize. Diamond and Dybvig (1983) is a well-referenced thought experiment with mathematics. The lessons it teaches are wrong.
Matt McManus writes about Ludwig von Mises. He does not say much about the socialist calculation debate.
Jan Toporowski writes about Oscar Lange.

I have found a common misrepresentation from many, including mainstream economists, is that critics of their
models do not understand them or the role of the assumptions. Those mainstream economists rely
on an incoherent essay
from Milton Friedman to dismiss criticism of the realism of assumptions.

My favorite criticism, though, is that their conclusions do not follow from their assumptions.
I like to show this by
constructing
numerical
examples
that contradict their teaching.

On the other hand, some do criticize the realism of assumptions. I have seen some complain that the economy is
never in equilibrium. It is unrealistic to assume equilibrium. I often find this unconvincing.

One can go back at least as far as Adam Smith, the distinction he draws between market
prices and

[embedded content]Richard Wolff Interviews George DeMartino (About 15:15)George DeMartino’s The Tragic Science: How Economists Cause Harm (Even as They Aspire to do Good)
Stanford Encyclopedia Philosophy entry on analytical Marxism.
One version of Marx-Engels Collected Works at the Antonie Pannekoek Archive.
Maybe I should order Ludo Cuyvers’ Neo-Marxism and Post-Keynesian Economics: From Kalecki to Sraffa and Joan Robinson

Empirically, prices are fairly close to proportional to labor values. But that is
neither here nor there as far as the correctness of Marx’s theory of value. To
see that, you have to get to the last footnote in chapter 5 of Capital.
(Most "refutations" of Marx are based on ignorance of the first few pages of
chapter 1.)

From the foregoing investigation, the reader will see that this statement only
means that the formation of capital must be possible even though the price and value
of a commodity be the same; for its formation cannot be attributed to any deviation of
the one from the other. If prices actually differ from values, we must, first of all, reduce
the former to the latter, in other words, treat the difference as accidental in order that
the phenomena may be observed in their

I want to write an inadequate appreciation of Saul Kripke, a great analytical philosopher.
The Guardian has an obituary.

I start from an example of a pratical use of his work. Chin and Older (2011) use modal logic to specify and reason about the
security properties of (computer) systems. One wants to be able to assert who (or what) has access to certain data and who can
grant access. Certain states of a system should never arrive.

A Kripke structure, as presented in Chin and Older (2011), is a three-tuple consisting of:

A set W, known as the set of all possible worlds.
An interpretation I, that maps each proposition to a subset of W. Informally, I(p) is the set of worlds in which the proposition p is true.
A function J that maps the name of each principal to a set of ordered pairs

Apparently, Lincoln responded to this congratulations from the International Workingmen’s Association:

Sir,

We congratulate the American people upon your re-election by
a large majority.

If resistance to the Slave Power was the reserved watchword of
your first election, the triumphant warcry of your re-election is,
Death to Slavery.

From the commencement of the Titanic-American strife the
working men of Europe felt instinctively that the star-spangled
banner carried the destiny of their class. The contest for the
territories which opened the dire epopee, was it not to decide
whether the virgin soil of immense tracts should be wedded to the
labour of the emigrant, or prostituted by the tramp of the
slave-driver?

When an oligarchy of 300,000 slave-holders dared to inscribe,
for

Here is Jean Jacques Rousseau:

"…whether those who command are necessarily
better than those who obey, and if strength of body or of mind, wisdom or virtue are always found in particular
individuals, in proportion to their power or wealth:
a question fit perhaps to be discussed by slaves in the hearing
of their masters, but highly unbecoming to reasonable and free men in search of the truth."
— Jean Jacques Rousseau, Discourse on Inequality (1755).

Early developers of political economy were not slavish. Here
is Adam Smith explaining that returns to capital and land
are the result of value added by labor not paid
out in wages.

"In the early and rude state of society…
the whole produce of labour belongs to
the labourer; and the quantity of labour commonly employed in

This is the start of Section 5, "Strikes and combinations of workers", in the second
chapter of The Poverty of Philosophy:

"’Every upward movement in wages can have no other effect than a rise in the price of corn, wine, etc.,
that is, the effect of a dearth. For what are wages? They are the cost price of corn, etc.; they
are the integrant price of everything. We may go even further: wages are the proportion of the elements
composing wealth and consumed reproductively every day by the mass of the workers. Now, to double wages …
is to attribute to each one of the producers a greater share than his product, which is contradictory
and if the rise extends only to a small number of industries, it brings a general disturbance in exchange;
in a word, a dearth…. It is impossible, I

This post draws attention to the existence of a vast web of existing organizations that, perhaps, operate partly outside and partly inside a capitalist logic.
These standards organizations define technologies vital to keeping our society running. I think I would find it interesting
for some scholar interested in council communism or syndicalism to look into these. The examples I list are perhaps
idiosyncratic, out-of-date, and reflect my personal history with computing.

Here is a list of some of the organizations I have in mind:

American National Standards Institute (ANSI)
International Electrotechnical Commission (IEC)
Institute of Electrical and Electronics Engineers (IEEE)
Internet Engineering Task Force (IETF)
International Standards Organization (ISO)
International

1.0 Introduction

I recently stumbled across McKiernan (2017), an Austrian response to Sraffa’s book.
This is a weird working paper. He works through Sraffa, with apparently no
knowledge of all the textbooks
explaining the book.
McKiernan correctly notes that Sraffa provides little context about
his points. And the mathematics is not always explicit. Naturally, McKiernan
makes mistakes. If he ever revisits this, I think he would want to break
it up into several papers. (Fabra (1991) is the strangest published response
to Sraffians of which I know.)

I only want to focus on one point, Sraffian subsytems. But before doing that, let
me at least point out something insightful in McKiernan’s paper.
He points out one of what I later call a fluke case:

However, Sraffa makes no note of cases

1.0 Introduction

Over a half-century ago, economists reached a consensus. The model in which employment
and real wages are explained by the intersection of a downwards-sloping labor
demand function and a supply function is incoherent, not even wrong.
This incoherence was demonstrated under the assumptions of perfect competition
and of firms that have adjusted their plant and other capital
inputs. I do not know what Greg Mankiw
and Jonathan Gruber
are doing, but it certainly is not education.

Anyways, I have not recently gone through a simple example, without some of my innovations.
Maybe I will repost this some time with graphs and more references.

2.0 Technology

Consider a very simple vertically-integrated (representative) firm that produces a
single consumption good, corn, from

A Bad Reproduction Of An Engraving Of Quesnay In Kuczynski And MeekIntroduction

This folder consists of:

A 20 Sep. 1965 letter from Marguerite Kuczynski to Piero Sraffa. Sraffa’s handwritten annotation suggests his response is not in the archives.
Handwritten notes made by Sraffa.
An 18 Oct. 1965 letter from Marguerite Kuczynski to Piero Sraffa.
A 25 Nov. 1965 handwritten draft letter from Piero Sraffa to Marguerite Kuczynski.
An 18 Dec. 1965 letter from Marguerite Kuczynski to Piero Sraffa.
A typed copy of a 10 Feb. 1966 letter from Piero Sraffa to Marguerite Kuczynski.
A 26 Feb. 1966 letter from Marguerite Kuczynski to Piero Sraffa.
A 2 Dec. 1971 letter from Marguerite Kuczynski to E. A. G. Robinson.
A 9 Mar. 1972 letter from Marguerite Kuczynski to Piero Sraffa.

INET has a collection of links in memory of Lance Taylor.
Alex Thomas has a focused review of A Reflection on Sraffa’s Revolution in Economic Theory, which was edited by Ajit Sinha.
John E. King has an overview in Jacobin, of Paul Sweezy’s work.
Ian Birchall, also in Jacobin, tells us about Daniel Guérin. I have read his Anarchism, but I am currently reading Iain McKay’s Proudhon collection.
Monthly Review reposts Ksenia Arapko’s review of Michael Heinrich’s How to Read Marx’s ‘Capital’. I found that not knowing the first edition, which variants Marx added in the French edition, and so on, I did not really know the opening chapters.
I want to note the existence of symposia on intangible capital and on human capital in the summer 2022 issue of the Journal of Economic

This is about Shove’s review of The Socialist Tradition. Apparently Gray does
not take those important in the development of economic thought seriously.
Since Piero Sraffa is neither the recipient nor the sender, and the topic is not his work, maybe the editors of
his collected works should not include this.

8, Abbotsford Park,
Edinburgh. 10.
3rd November, 1946

Dear Shove,

(If the fact that we occupied adjacent seats on the occasion of one of my rare visits to the Annual Meeting of the Economic Society
justifies this assumption of familiarity) – I should like, if I may, to exchange friendly greetings on the excuse of your
review of my Socialist Tradition.

First of all I should like to say as a sheep before the shearers is dumb, so in general a reviewee ought to open not his

[embedded content]First Lecture For MIT Microeconomics
I associate Jonathan Gruber with Obamacare. I think the Affordable Care Act is totally insufficient
and a great advance. If politicians hire you to model the effects of some policy change,
might you want to use, more or less, the most widely accepted techniques?
I am also appreciative that I can watch this.

When you are teaching, should you present claims in the most romantic way possible?

"That is why I can teach you the entire field of microeconomics, which is really sort of – macro is kind of a
fun application – micro is really economics."
(around 9:20)

Thinking of (micro)economics as a matter of constrained optimization is only one approach. I like the idea of
investigating the conditions needed for a capitalist economy
to

This is C/294 in the Sraffa archives. Rudiger Soltwedel had his own letterhead.

D 66 Saarbrucken 3, 28. Febr. 1968
Waldhausweg 7
Evangelisches Studentenheim

Professor Piero Sraffa
Trinity College
Cambridge

Dear Sir,

I am student of economics at the University of Saarbrucken and I just began my finals work for my diploma.

The topic of this study that Prof. E. Schmen formulated is your essay and its title is exactly that of your book: ‘Sraffa’s production of commodities by means of commodities’.

My task is to state the intention of your book and to explain its relation to input-output analysis.

After looking around in literature I only found three reviews (AER: Reder; Ec. Journ.: Harrod; Jorn. Of Pol. Econ.: Quandt; all 1961) but nothing beyond that.

I would be very

This letter is an item removed from printed books in Sraffa’s library. It is labeled
Sraffa I/38 in the archives where I stumbled into it.

15th Oct, 75

Centre for Economic Studies,

Nehru University,

New Delhi 57

Dear Piero Sraffa,

How are you? A lot of things have happened since my return in July to Delhi. Personally, my health was
not too good for some time but has now stabilised somewhat. I had considerable teaching load this
term and have had to devote a lot of time to preparation of lectures etc. I am now writing up a part
of my lectures material – mainly on classical theories of value and distribution. My intention is to
focus on conceptual development and the shift to the supply and demand approach and the implications of
such a methodological shift. What I intend to

Figure 1: Wage Curves and Rent for an Example of Intensive Rent
The analysis of the choice of technique has above always been based on the construction of a wage-rate of profits
frontier. Given a technology in which requirements for use can be satisfied, prices of production for
an eligible technique are uniquely determined by the given rate of profits. If the rate of profits
is in a range where such prices are non-negative for at least one technique, one of the techniques
is uniquely cost-minimizing, except at switch points. This property does not necessarily hold in models of general
joint production. The first subsection of the first non-introductory chapter on joint production in Bidard (2004) has the title "Not amused".
An examination of local perturbations in an example of intensive

Figure 1: Wage Curves and Rent for an Example of Extensive Rent
The analysis of the choice of technique in models of extensive rent can be based on the construction of wage curves,
even though the outer envelope does not represent the cost-minimizing technique. The orders of fertility and rentability
are emphasized here. The order of fertility is the order in which different qualities of land are introduced into
production as requirements for use expand. The order of rentability specifies the sequence of different qualities of lands
from high rent per acre to low rent per acre. Both orders may vary with the distribution of income. Table 1 presents
coefficients of production for an example. Technical progress is assumed to reduce coefficients of production in each
of the corn-producing

Figure 1: A Wage Frontier With A Fluke Switch Point
A fluke example with fixed capital illustrates the emergence of the reswitching of techniques. Table 1 presents coefficients of production
in a perturbation of an example from Schefold (1980). With the first process, workers, under the direction of mangers of firms,
manufacture new machines. The remaining two processes are used to produce corn. The last process requires an input of an old machine,
which is jointly produced with corn by the second process. Corn is both a consumption good and a capital good, insofar as it
is an input into all three processes. Technology improves in this example, as usual, with an exponential decline in
specified coefficients of production.

Table 1: The Coefficients of Production
InputMachine IndustryCorn

Figure 1: A Wage Frontier With Two Fluke Switch Points
This post presents an example with circulating capital alone. Table 1 presents the technology for an economy
in which two commodities, iron and corn, are produced. One process is known for producing iron, and two are
known for producing corn. Each process is specified by coefficients of production, that is, the required inputs
per unit output. The Alpha technique consists of the iron-producing process and the first corn-producing process.
Similarly, the Beta technique consists of the iron-producing process and the second corn-producing process. At any
time, managers of firms face a problem of the choice of technique.

Table 1: The Coefficients of Production
InputIron IndustryCorn IndustryAlphaBetaLabora0,1 = 1a0,2α = 0.7174 e-σ ta0,2β

I did not always think that mainstream economists are mostly socialized to be unlettered knaves, deficient in
mathematics and logic. It took decades
of empirical evidence.

These links are mostly to tedious and petty stuff, more for my own archiving. Lots of weird stuff comes from non-economists.
Sometimes you will find a poster not necessarily defending me, but trying to get some other poster to say
something substantial. Some, like Tim Lambert, do not even seem to care about economics. The misrepresentations
by mainstream economists of what they and others say is not confined to discussions with me. Some serious people, like David Graeber,
appear in these discussions independent of me.

Poor teaching of econ (August 2007)
Failure of neoclassical economics (January, 2006).
Baumol,

The Babbitt family
started in America with Edward Bobet, who died in 1675.

We have now come to that time of terror and disaster to the settlers the uprising of the Indians, known as King Phillip’s War.
It can easily be imagined how many anxious hours were passed by Edward and Sarah Bobet, so far removed from the garrison stockade,
with their large family of children. Judging by the quantities of Indian relics found on his home farm it would seem that it was
a peculiarly favorite haunt of the Indians before Bobet bought it. Finally their position became too dangerous to admit of
further delay and being warned of the commencement of hostilities, on June 25, 1675, they took refuge in the garrison at Taunton,
leaving behind the home which had been the fruit of so much labor in the

I do not know if I will keep on, but I thought I might present a series of
posts expanding on this one.
By the way, I should have said there that the maximum rate of profits is the reciprocal of the
organic composition of capital in Sraffa’s standard system, not the actual system.

Sraffa’s model is descriptive, based on objective data that can be observed for one production period. This data,
at least through the first three chapters of
The Production of Commodities by Means of Commodities, consists of:

The gross quantities produced over the production period, in physical units.
The proportion of labor employed in each industry.
The commodities that are used as inputs in each industry.
The wage, expressed as a proportion of the value of the net output produced in the period.