Here is John Stuart Mill stating a principle that sounds noble, and then
immediately making a strange caveat.

"The object of this Essay is to assert one very simple principle, as entitled to govern
absolutely the dealings of society with the individual in the way of compulsion and
control, whether the means used be physical force in the form of legal penalties, or the
moral coercion of public opinion. That principle is, that the sole end for which
mankind are warranted, individually or collectively, in interfering with the liberty of
action of any of their number, is self-protection. That the only purpose for which
power can be rightfully exercised over any member of a civilized community, against
his will, is to prevent harm to others. His own good, either physical or moral, is not

This blog, over years,
presents a
welter of
fluke cases.
I created many of the numerical examples to illustrate the reswitching of techniques, capital reversing, or
some such so-called ‘perversity’. Fluke cases can be combined. For example, a fluke switch point at a rate of
profits of zero can also be a fluke switch point at which three wage curves intersect. Or two switch points on
the wage frontier can both be fluke switch points at which four wage curves, not necessarily the same, intersect.
Numerical examples remain to be developed for some possibilities.

Selected Fluke Cases
Pattern of switch points over the wage axisPattern of switch points for the reverse substitution of laborPattern of switch points over the axis for the rate of profitsReswitching pattern of switch

In Mark Twain’s novels, Huckleberry Finn is just a kid in what you might
think is the most despised group in society. His mother ran away, and his father, who
rarely is home to look after him, is the town drunk. Huck does not go
to school, dresses in rags, and often sleeps outside in some barrel
down by the waterfront. But Huck is quite conscious that some hard-working
adults are looked down on worse than him by respectable people.

‘That’s all right. Now, where you going to sleep?’

‘In Ben Roger’s hayloft. He lets me, and so does his pap’s
nigger man, Uncle Jake. I tote water for Uncle Jake whenever he wants
me to, and any time I ask him he gives me a little to eat if he
can spare it. That’s a mightly good nigger, Tom. He likes me,
becuz I don’t ever act if I was above him. Sometime

The Four Circuits of Capital
Marx describes
three circuits of capital
in the opening chapters of Volume 2 of Capital.
But when I draw a diagram, as above, a fourth circuit seems to be missing. So I have
added the circuit of advanced capital.

The circuit of advanced capital begins with commodities, consisting
of means of production and labor power, in the hands of or under
the direction of capitalists. They have purchased these commodities
with monetary advances. The capitalists, at this point, care
about the use values of these commodities, and they have
purchased them to be in specific proportions.

The sphere of circulation is left behind in the next step in the circuit.
Workers apply labor to the means of production, under the formal and
real subsumption of capital, to produce

Figure 1: Convergence to a Pattern of Switch Points over the Axis for the Rate of Profits1.0 Introduction

This post illustrates how to find fluke switch points. As usual, I proceed by example, in this case, as taken from
my paper
in Structural Change and Economic Dynamics.

2.0 Technoplogy

In this example of
a capitalist economy, two commodities, iron and corn, are produced. One process is known for producing iron. In the iron industry, workers use inputs of iron and corn to produce an output of iron.
The output of the iron industry is one ton with the inputs shown in Table 1.
Two processes are known for producing corn.
Each corn-producing process shown in Table 1 produces an output of one bushel corn from inputs of labor power, iron, and corn.
Assume constant returns to scale.

Table

Ben Franklin was one the founding fathers of the United States. He participated in the
constitutional convention. He was the first Postmaster General. He did experiments with electricity,
when the Leyden jar was a new thing. There is a story about flying a kite in a thunderstorm.

He also wrote about the wealth of nations:

"Finally, there seem to be but three ways for a nation to acquire wealth. The first is by war, as
the Romans did, in plundering their conquered neighbors. This is robbery. The second by commerce,
which is generally cheating. The third by agriculture, the only honest way, wherein
man receives a real increase of the seed thrown into the ground, in a kind of continual miracle, wrought by
the hand of God in his favour, as a reward for his innocent life and his virtuous

Figure 1: A Pattern Diagram1.0 Introduction

Aside, perhaps from the above visualization, nothing novel is presented in this post. It follows
an example presented by Freni (1991). I know of this example from problems 7.7 and 7.29 in
Kurz and Salvadori (1995). The oddities of this example can be seen in an earlier and
more complicated example from D’Agata (1983).

This is an example of intensive rent. When the requirements for use are large enough, capitalists will use more than one process
to produce a commodity on homogeneous land. The scarcity of land is expressed in the emergence of rent. This example, though,
is a challenge to Sraffa’s work. The cost-minimizing technique is a unique function of the wage, but it is not a unique
function of the rate of profits. The wage frontier is not

[embedded content]John Eatwell On The Bomb Sraffa Planted At The Foundations Of EconomicsJames Galbraith on Dismal Economics, reviewing books by Mason Gaffney and Fred Harrison, Stephen Marglin, Alessandro Roncaglia, and Robert Skidelsky.
Jane Gleeson-White, in the Guardian, on accounting, unpaid care work, and the biosphere.
A blog post pointing out Bob Murphy’s confusions and mistakes on the implications of the Cambridge Capital Controversy for the Austrian school. Compare and contrast with here.

To me, this is an easy question. SNALT, for a capitalist economy, is:

L = a0 (I – A)-1y

The notation is from Luigi Pasinetti’s Lectures on the Theory of Production.
The idea can be empirically applied with data from national income and product
accounts (NIPAs), using techniques explained in, for example,
Ronald Miller and Peter Blair’s Input-Output Analysis

Figure 1: Wage Curves and Rent1.0 Introduction

I might as well illustrate an example with extensive rent and reswitching. I find it incredible that
the agents in these sorts of models understand the implications of, say, a variation of the
distribution of income for their self-interests.
Nevertheless, I try to note the consequences of variation in the distribution of income
and perturbations of model parameters on prices of production. And I do not
worry too much about disequilibria.

2.0 Technology and Requirements for Use

Consider a capitalist economy in which two commodities, iron and corn, are produced. One process is known for producing iron.
In the iron industry, workers use inputs of iron and corn to produce an output of iron. The output of the iron industry is one ton with
the

"Let us take the process of circulation in a form under which it presents itself as a simple and direct exchange of commodities.
This is always the case when two owners of commodities buy from each other, and on the settling day the amounts mutually owing
are equal and cancel each other. The money in this case is money of account and serves to express the value of the commodities
by their prices, but is not, itself, in the shape of hard cash, confronted with them. So far as regards use-values, it is clear
that both parties may gain some advantage. Both part with goods that, as use-values, are of no service to them, and receive others
that they can make use of. And there may also be a further gain. A, who sells wine and buys corn, possibly produces more wine,
with given labour-time, than

Figure 1: Variation in Switch Points with Time1.0 Introduction

This post continues my effort to understand how fluke cases can partition parameter spaces in models of prices of production
with extensive rent.
Some background for this post is
here,
here,
and here.

2.0 Technology

The technology is described by the coefficients of production in Table 1.
I assume that requirements for use are such that they cannot be satisfied by cultivating
only two types of land. After fully cultivating two types, the third type must also be
introduced into cultivation, at least partially.
See this post for a slightly longer description
of the technology.

Table 1: The Coefficients of Production
InputIron IndustryCorn IndustryIIIIIIIVLabora0,1 = 1a0,2 = 1/2a0,3 = 3a0,4(t) = 2.0743 e-0.03648 tType 1

[embedded content]A Propertarian Getting The Better Of The Wrong Side Of The Argument
I have been looking at some debates on YouTube. Not only is there a culture of twitch streamers debating.
There are some, such as Noah Cortez
"Booksmarts", critiquing debates.
By the way, here is a video
providing an overview of (Resnick and) Wolff’s academic work, seemingly inspired
by the prominence Wolff is gaining with his YouTube presence.

I suppose that this post is aspirational, and some of these points can be argued over.
I guess, this post is related.
I’d like for the debaters to:

Recognize that such a debate topic is orthogonal to a debate on socialism versus capitalism. Thus, Barone’s
economic calculation problem is not on-topic, without an argument.
Know the distinction between use value

"I know not how I may seem to the world, but as to myself
I seem to have been only like a boy playing on the sea-shore
and diverting myself in now and then finding a smoother pebble
or a prettier shell than ordinary, whilst the great ocean of truth
lay all undiscovered before me." — Isaac Newton (apocryphal?)

For the past couple of years, I have been pursuing a
research program that I seem
to have stumbled upon. I am looking for fluke switch points, where these fluke
switch points partition certain parameter spaces. The analysis of the choice
of technique is supposed to be qualitatively invariant, in some sense,
in each region formed by these partitions, but varies among regions.

I have tried to define a
taxonomy
for such fluke switch points.
Using an
example,
I have explored

Figure 1: Wage Curves for Fluke Case for r-Order of Fertility1.0 Introduction

This post illustrates two fluke cases that can arise in a model with land and extensive rent. I
call these a pattern of switch points for the r-order of fertility and a pattern of
switch points for the w- order of fertility.
I have previously described a
fluke case in the order of rentability, which can be either over the wage axis or over
the axis for the rate of profits.
These fluke cases can arise in an analysis in which
a parameter space is partitioned by fluke cases such that in each of the resulting regions
the analysis of the choice of technique does not qualitatively vary, in some sense.

2.0 Introduction

The technology is described by the coefficients of production in Table 1.
Let there be T1 = 100

This transcription is taken from here.

Dear Sir:

Replying to your note of the 14th of last month, may I thank you for your kindness in sending me your work on Marx;
I had already read it with great interest in the issue of the Archiv which Dr. H. Braun was good enough to send me,
and was pleased for once to find such understanding of Capital at a German University.
Naturally I can’t altogether agree with the wording in which you render Marx’s exposition. Especially the definitions
of the concept of value which you give on pages 576 and 577 seem to me to be rather all-embracing: I would first
limit them historically by explicitly restricting them to the economic phase in which alone value has up to now been known,
and could only have been known, namely, the forms of society in

Figure 1: A Partition of a Slice of the Parameter Space1.0 Introduction

This post presents another example from Woods (1990). It
is a modification of this example.

That previous example demonstrates that the order of fertility – the order in which lands of various types
and that support different processes of production are taken into cultivation – varies with distribution.
If the wage were different, the order of fertility could be different. Furthermore, the order of rentability – the order
of lands from high rent to low rent – also varies with distribution. The order of fertility is not necessarily the
order of rentability.

This post demonstrates another issue in the order of fertility. It depends, in this sort of open model, if one takes
the wage or the rate of profits as given.

[embedded content]Victor Magarino Debating "Ubersoy" On The Labor Theory Of Value
The above is one in a series (Richard Wolff versus "Destiny", Slavoj Zizek versus Jordan Peterson) in which the pro-capitalist/anti-socialist
side is represented by somebody seemingly almost completely ignorant of the topic they are pretending to discuss. Magarino needs a better
interlocutor. I can find some related debates on YouTube with a more level playing field.

That said, I think Magarino needs a better answer to the question in this post title. I do not think that this
question is answered by pointing out that some work is needed to maintain the vats while wine is aging. J. R. McCulloch
was supposedly extremely confused on this question when it was first(?) posed.

Wine illustrates two challenges

Figure 1: A Partition of a Slice of the Parameter Space1.0 Introduction

This post tells a story in which owners of a certain type of land find the amount of their land needed to produce net output declines.
Wages stay constant, and the rent for some landlords increases. This example is generalized from Woods (1990).

2.0 Technology

This an example (Table 1) of a capitalist economy in which two commodities, iron and corn, are produced. One process is known for producing
iron. In the iron industry, workers use inputs of corn to produce an output of iron. Three processes are known for producing corn.
Each corn-producing process operates on a specific type of land. These processes can be thought of as examples of joint production.
Their outputs are corn and the same quantity of land used

[embedded content]A History Lecture Focusing on Cantor, Dedekind, Gödel, Turing, etc.Norman Wildberger’s next video in the above series is here. This professor, who has some dissenting views, explicitly tells his class that he does not belive in any of what he is teaching here. I wish, in trying to introduce this, he was more clear on the distinction between provability and truth. You do not get much even on lives here, much less on what minor events in the world induced Gödel to leave Vienna for Princeton.
Virginie Pérotin on What do we really know about woker co-operatives. Richard Wolff’s organization, Democracy at Work, provides an overview.
Sebastian Gechert et al. have published Measuring capital-labor substitution: the importance of method choices and publication biases.

1.0 Introduction

I have previously considered some
points
on which Marx is vulnerable. In this post, I mention three mistakes.
I take the first from Joan Robinson and probably the second point too.
I take the third from Ajit Sinha. The second is perhaps the least original.

You can find lots of stupid stuff and nonsense about Marx. Pointing
out these particular mistakes is
beyond many. To have an opinion about these points, one must
read Marx. One might even accept that Marx is mistaken on these
points, yet find his general vision correct.

2.0 The Rate of Profits in Volume 1 of Capital

Marx defines the rate of profits in his system of labor
values as:

r = s/(c + v)

where c is constant capital, v is variable capital,
and s is surplus value. All are measured in value.

Some

Figure 1: Switch Points Varying With Perturbations In Markup In Iron Industry
I have created an example
with three produced commodities and a choice of technique.
The three produced commodities are called iron, steel, and corn. Corn is taken to be the numeraire and the only
commodity purchased by households for consumption.
Markups are assumed to vary among industries, even
when prices of production prevail.

I was able to locate various fluke switch points in that example. The fluke switch points partition the
space of relative markups, as shown in Figure 2. Consider a 45 degree line in this space sloping upward,
with s3/s1 equal to s2/s1.
This corresponds to perturbing the markup in the iron industry, with unchanged markups in the
steel and corn industries. Figue 1, at the top of this

Figure 1: Variation of Switch Points with the Markup in the Steel Industry1.0 Introduction

I want to continue to analyze
this
example.
This example does not do everything I would like with a three-commodity example. Specifically,
I do not have a case of triple-switching in the parameter space I explore in this post.
That space of relative markups, in a model with n industries, has (n – 1) dimensions.
And it is partitioned by (n – 2)-dimensional manifolds, where each manifold corresponds to
a fluke switch point. Whether or not reswitching, capital-reversing, or the recurrence of techniques exist
depends on relative markups. This post illustrates in an example with three produced commodities.

2.0 Technology

This economy produces a single consumption good, called corn. Corn is also a

"In that early and rude state of society which precedes both the accumulation of stock and the appropriation of
land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the
only circumstance which can afford any rule for exchanging them for one another. If among a nation of hunters,
for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should
naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days or two
hours labour, should be worth double of what is usually the produce of one day’s or one hour’s labour…

…As soon as stock has accumulated in the hands of particular persons, some of them will naturally employ it in setting
to work

[embedded content]A Debate on Socialism versus Capitalism
I suppose Destiny entered this debate in good faith. But why did he have to lie about what Wolff was saying?
Wolff certainly never repudiated the labor theory of value in his opening remarks. And later
Wolff explicitly argued that the Democrats are not socialist. One may not understand or
agree with Wolff, but why lie?

Apparently "Destiny" feels he lost badly and has been trying to find somebody
less
eminent
to contrast his ignorance with.
(I also stumbled upon a debate last December between
"Socialism Done Left" and Victor Magarino.)
Maybe it is not too interesting to watch somebody
with a twitch stream try to educate himself.
I probably have all sorts of disagreements with those here drawing on Cockshott and Cottrell or
on

Brad DeLong and Noah Smith chat about the Cambridge Capital Controversy
on their
podcast,
Hexapodia is the key insight.
Noah says it was only mentioned in one of
his classes on macroeconomics, but seems to say he was never formally taught it.
Given his summary near the start of this discussion, he has obviously
read something about it.
Brad thinks the language used by the MIT economists in the 1960s was
badly and inaccurately phrased and poorly suited to shed light.
He says he had trouble figuring out why anybody would disagree that
a single aggregate index could not be rigorous and theoretically justified.
So this discussion, if I understand correctly, could be expected to
fit well with the name of their podcast. But maybe not.

Brad distinguishes between the ownership of physical

Zach Carter has an appreciation
of Joan Robinson’s work on imperfect competition, with a bit about the role of Cambridge circus
in helping Keynes write the General Theory. Paul Krugman,
gatekeeper, reacts:

"Nice appreciaton of Joan Robinson, although no mention of her later role. Sad to say,
as a student I mainly encountered her through the ‘Cambridge capital controversy’,
a huge intellectual muddle. Somehow Robinson and others managed to convince themselves
that the moral legitimancy of capitalism rested on the existence of a well-defined
measure of ‘capital’ that had a well-defined marginal product. What followed
was a tortured debate that illuminated nothing much, and eventually just faded away.
Oh well. But Zach Carter is right: we value thinkers for their best work,
not their

Figure 1: Wage Curves for the Example1.0 Introduction

The Cambridge Capital Controversy (CCC) applies to models both of competitive industries and of non-competitive industries.
Around a switch point exhibiting capital-reversing, a higher wage is associated with greater employment per unit of
net output produced. It is not merely a question of what technology is available. It is also a matter of
the power of firms among industries to extract value from their workers, their upstream suppliers, and their
downstream buyers. And of the countervailing power to resist such exercise of power. Can you cite
literature in Industrial Organization (IO) that explicitly recognizes the logical consequences of the CCC
for IO?

This post presents an example of a fluke switch point, or rather two fluke

I have a working paper at the Centro Sraffa.

Abstract:
This article considers structural economic dynamics, in models with fixed capital and a choice of technique,
of the production of commodities. Fluke switch points are described and cataloged. For fluke switch points,
parameter perturbations create a qualitative change in how the choice of technique varies with distribution.
Techniques are presented for visualizing partitions of parameter spaces such that the analysis of the choice
of technique does not vary within each region. Implications are drawn about the choice of the truncation of
the operation of (or the economic life of) machines and about the adoption of roundabout techniques.

[embedded content]An Introduction to Algebraic Geometry
I have been looking for fluke switch points in certain parameter spaces of coefficients for polynomial equations.
Bertram Schefold has pointed out to me that I may want to look into algebraic geometry. This may be beyond me. I
consider what I have been doing as exploratory mathematics, and I have been relying on numerical algorithms.
I started with thinking that there is a parallel to bifurcation theory. But Barkley Rosser convinced me that
I should not use that terminology without an explicit dynamic system, presumably of market prices.
These two
threads
on Math Overflow suggest I might want to look at
Bertrametti et al. Lectures on Curves, Surfaces and Projective Varieties. I need a physical book for this, I think, not just a