Figure 1: A Pattern Diagram with Joint Production1.0 Introduction

This post completes an example. I analyzed bits of this example
here and
here.
This post may make no sense if you have not read a long series of previous posts
or, maybe, the papers highlighted
here
and here.
I am interested in how and if my approach to analyzing and visualizing variations in the choice
of technique with technical progress extends to joint production. The example suggests fake switch points
do not pose an insurmountable obstacle for such an extension.

2.0 Technology

I repeat the specification of technology.

I postulate an economy in which two commodities, corn and linen, can be produced from inputs of corn, linen, and labor. Managers
of firms know of three processes (Tables 1 and 2) to produce corn

Here is a post from a blog
devoted to cybercommunism. The blogger is glowing about Paul Cockshoot’s work on refuting Hayek’s supposed refutation of the possibility
of a post-capitalist society.
William Milberg
writes about how it is becoming more
common to use the word "capitalism", a word mainstream economists had mostly stopped using.
Herbert Giants and Rakesh Khurana write
about the corrupting effects of neoclassical economics on what is taught in business school and then practiced by corporate elites.
Osita Nwanevu writes,
in The New Republic, about the enthusiasts that showed up at last weekend’s Third MMT Conference.
Lisa Schweitzer studies urban environments. In a blog post, she expresses irritation at Paul Romer’s arrogance, admittedly filtered through a glowing New York Times

I am not sure about the economic logic in this post. Maybe somebody like D’Agata or Zambelli could do
something with this. These ideas were suggested to me by email with a sometime commentator.

I start out with notation for Sraffa’s price system, modified in an unusual way to
allow for persistent variations in the rate of profits among industries:

a0 is a row vector of labor coefficients in each of n industries.
A is a Leontief input-output matrix, where ai, j
is the quantity of the ith commodity needed as input to produce one unit of the jth commodity.
S is a diagonal matrix, where all off-diagonal elements are zero. sj, j is
the markup on non-labor costs in the jth industry.
p is a row vector of prices.
w is the wage.
r is the scale factor for the rate of profits.

The coefficients

Figure 1: Wage Curves and The Price of Corn for the Fluke CaseIntroduction

This post extends a
previous post.
I am basically introducing structural dynamics into an example, by Bidard and Klimovsky of fake switch points.

At a rate of profits of zero in the example, the price of corn is zero for Alpha, one of the two techniques
that is cost-minimizing there and for somewhat higher rates of profits. At a time before the fluke
case, only the Gamma technique is cost-minimizing at a rate of profits of zero. The price of corn,
as calculated with the Alpha technique, is negative at a rate of profits of zero.
Alpha prices become non-negative only for positive rates of profits. This possibility cannot
arise in examples with only single production and the choice of technique analyzed by the

Figure 1: Wage Curves with Corn as Numeraire1.0 Introduction

This post presents an example of a fluke switch point in which the choice of technique cannot be analyzed
by the construction of the wage frontier. Under joint production, the technique that is cost-minimizing,
for a given rate of profits, does not necessarily maximize the wage. Nevertheless, one can still see
what I call a pattern over the wage axis in this case. The example is a generalization of
the numerical example in Bidard & Klimovsky (2004).

2.0 Technology

I postulate an economy in which two commodities, corn and linen, can be produced from inputs of corn, linen, and labor. Managers
of firms know of three processes (Tables 1 and 2) to produce corn and linen. Each process produces net outputs of corn and
linen as a

I happen to have one book by Marty Weitzman (1942 – 2019) on my bookshelf. So I thought I would write a bit about
The Share Economy: Conquering Stagflation.

This is an ill-timed book. It proposes that firms negotiate with workers to pay them a percentage of revenues,
instead of, say, an hourly money wage.
It argues that such a change will address the widespread macroeconomic problem,
throughout the 1970s, of simultaneously high unemployment and high inflation. But, by the time the book came out, stagflation had been "solved", in
an extremely reactionary way.
The countervailing
power
of organized labor
was being abolished. Labor unions were being crushed, and workers would, by and large,
no longer see their wages increase with productivity. Instead of unemployment being addressed,

This list is mostly a matter of aspirational reading.

Maybe I want to read Ted Burczak’s
Socialism after Hayek.
(The Amazon page has one of Herb Gintis’ long reviews.)
Binyamin Appelbaum’s
The Economists’ Hour: False Prophets, Free Markets, and the Fracture of Society
is not even out yet, and already some mainstream economists are whining about it on twitter.
William R. Clark and Vincent Arel-Bundock have a paper,
Independent but not indifferent: Partisan bias in monetary policy at the Fed,
in 2012.
Christopher Gandrud and Cassandra Grafström’s
Does presidential partisanship affect Fed inflation forecasts?
is related.
Mark Buchanan
recommends
that more
attention
be paid to the work of Ole Peters and others at the London Mathematical Laboratory. They have developed
something called

This post gestures to a worrisome argument that could be constructed by combining arguments from certain references. It
is also more about current events than most posts on this blog.

Philip Converse’s argument
that most members of the mass public are ideologically innocent has long been influential among political scientists.
Why should those who have families to raise, bills to pay, and jobs to take up their time pay much attention to
the details of politics?

Barber and Pope (2018) provides recent empirical evidence, from something like a natural experiment,
that conservative Republicans, especially, are unprincipled.
Their results are based on a survey conducted in early 2017, before Trump had a record as governing.
Since Trump does not care to know anything about anything, one

I happen to think the minimum wage in the United States should be raised. I’ll go along with the
consensus of $15 an hour.

I also happen to
know
that, even under ideal conditions, wages and employment cannot be
explained
by supply and demand.

Some economists, who I no (other) reason to disrespect, seem to think my true statement about labor
economics can be discredited by
attacking my motivations.
So they point out how, under (incoherent) neoclassical theory, higher minimum wages can be justified
by, for example, the theory of monopsony.
But my motivations are almost the opposite.
I take the evidence
that neoclassical economics is wrong about labor markets as a launching into the illogic
of mainstream economics.
(Is this
the most recent meta-analysis on minimum wages?)

The attack,

Blair Fix argues that economists
argue in a circle in putting forth the marginal productivity theory of distribution.
I know that there is no such consistent theory anyways. It occurs to me that
process recurrence, as well as the reswitching of techniques, can be used to demonstrate this
inconsistency.

Suppose you completely know the technique being used in an economy to produce its output. And,
which is even more impossible, you know all other possible techniques. I am thinking of
a technique being specified with something like a Leontief input-output matrix, in
physical terms. Assume, counterfactually, that all these techniques exhibit constant
returns to scale. With these assumptions, you know the physical marginal product
of each input into production, whether it is previously

This post, as suggested, extends this
one-good example. I assume a constant returns-to-scale technology, as specified in Tables 1 and 2. Labor is advanced to the capitalists,
and wages are paid out of the surplus at the end of the year (period of production). The capitalists (incorrectly) expect the technology in
existence at the start of the year to continue to exist. I assume prices of (re)production prevail.

Table 1: Inputs for The Technology
InputProcess(I)(II)(III)Labor30 eσ0,1(1 – t)180 eσ0,2(1 – t)(39/2) eσ0,3(1 – t)New Widgets100One-Year Old Widgets010Two-Year Old Widgets001
Table 2: Outputs for The Technology
OutputProcess(I)(II)(III)New Widgets3 eσ1,1(t – 1)(7/4) eσ1,2(t – 1)(237/20) eσ1,3(t – 1)One-Year Old Widgets100Two-Year Old Widgets010
Only a newly produced widget is a

I am being published
in Structural Change and Economic Dynamics. Currently, this link is without my corrections to proofs, I guess.

Research highlights:

Technical progress and variations in industry markups can change characteristics of the labor markets.
A numeric example illustrates the theory of the choice of technique.
In the example, switch points are created and destroyed with varying coefficients of production and varying markups.
Around some switch points, higher wages are associated with greater employment, given the level of net or gross output
Graphical displays are provided for visualizing these results.

Abstract: This article presents an example in which perturbations in relative markups and
technical progress result in variations in characteristics of the labor market.

I know that the idea of a "natural rate" of unemployment or a
non-accelerating inflation rate of unemployment (NAIRU)
makes no
sense.
I cite, for example, James Galbraith’s 1998 book,
Created Unequal: The Crisis in American Pay.
I think Colin Rogers’ 1989
book is related.

Jared Bernstein
gives
the idea of a natural rate of unemployment at the first of four examples of ideas that [mainstream] economists have gotten
wrong for decades. This is not the first
example of a case where Post Keynesians
(and only Post Keynesians(?)) could explain an empirical phenomenon decades in advance.

Figure 1: A Pattern Diagram
I have put up a
working paper
with the post title.

Abstract: This article considers Harrod-neutral technical progress in the context of an analysis of the choice of technique.
In a model of the production of commodities by means of commodities, neutral technical change is compatible with the reswitching of
techniques, capital reversing, process recurrence, and the reverse substitution of labor. A taxonomy of fluke switch points is
applied to an example, illustrating how these phenomena can arise and vanish in the course of neutral technical progress.

I get various fluke switch points, as is typical of my examples. By assuming Harrod-neutral technical change, I
end up with the structure in Figure 2, in one slice of the parameter space.

Figure 2: A

"One of the curious things about our educational system, I would note, is that the better trained
you are in a discipline, the less used to dialectical method you’re likely to be.
In fact, young children are very dialectical; they see everything in motion, in
contradictions and transformations. We have to put an immense effort into training
kids out of being dialecticians."
— David Harvey, Companion to Marx’s Capital: The Complete Edition. Verso (2018).

I do not have children, and I am not sure I understand Harvey’s claim. But one writer
I liked was Jean Piaget.
(I also want to mention Seymour Papert.)

I take from him that children think in a way that can be described
by advanced mathematics. I think, in particular, of topology and
modern
algebra.
The idea is children take time to

Carlo Milana has posted a paper on arXiv. I was prepared to accept this paper’s claims. Economists have developed
price theory. Referring to Sraffian "paradoxes" and "perverse" switch points is a matter of speaking.
There does not exist separate Sraffian and neoclassical versions of price theory. For a result to be "perverse",
it need only contradict outdated neoclassical intuition. But it is as much a part of the mathematical economics
as any other result. (It is another matter that much teaching in microeconomics is inconsistent with the mathematics.)

In equilibrium, the price of the services of each capital good in use is equal to the value of the marginal product
of that good, with all prices discounted to the same moment in time. This discounting implies that the interest
rate

[embedded content]Young Children Policing Group Members
This post presents examples of psychologists inducing stress in experimental subjects, some showing why we need Institutional Review Boards (IRBs).
Some of the older studies involved so much suffering that experimental subjects suffered Post-Traumatic Stress Disorder (PTSD). I recall
that at the end of the 1976 movie, The Tenth Level, about the Milgram experiment, starring William Shatner, the scientists are discussing what they
would do if they were experimental subjects. Would they refuse to torture others? And one says to Shatner/Milgram something like,
"It seems to me, you have already been tested and failed."

Yudkin, Van Bavel, and Rhodes: Almost the only somewhat happy story here. Toddlers are willing to close a fun slide,

This post is about the misrepresentation of Sraffian
capital theory in Lewin and Cachanosky (2019). I cannot
recommend this short book. Presumably, it is meant as
an introduction. But I do not see it as succeeding.
I do not see what a more advanced audience would
get out of it that is not available in a few
recent papers by Lewin and Cachanosky.

Before proceeding to my main theme, let me note that I
agree with some parts of this book, mainly where
Lewin and Cachanosky draw on Ludwig Lachmann,
to parallel themes in Joan Robinson’s emphasis
on historical time.
They state that no physical measurement of capital
exists and that capital is not a factor of production,
with a demand function.
They state, probably as influenced by Jack Birner, that Hayek never set out a coherent
and internally

Figure 1: APP Around Switch Points1.0 Introduction

I take it that the Austrian theory of the business cycle builds on Austrian capital theory. The following two claims
are central to Austrian capital theory:

Given technology, profit maximizing firms adopt a more capital-intensive, more roundabout technique at a lower interest rate.
The adoption of a more roundabout technique increases output per worker.

Originally, Eugen von Böhm-Bawerk proposed a physical measure of the average period of production, but economists of the
Austrian school have been distancing themselves from this position for well over half a century. I have
argued that the
first claim fails, even in a framework without any scalar measure of capital-intensity or the average period of production.

Recently, Nicholas

Those who understand price theory reject the theory of the Austrian Business Cycle (ABC).
I am thinking here that its logical invalidity follows from post-Sraffian capital theory.
It is also wrong because of its reliance on the concept of the natural rate of interest.

Some years ago, I tried to get published a demonstration that ABC theory was in error.
I forget how many journals rejected it. Four or five articles
here
are from this series of revisions.
The rejections from the journals more sympathetic to Post Keynesians
generally said that everybody knows that ABC theory is wrong.
The rejections from the journals more sympathetic to the Austrian school
said that I ought to read more and more obscure literature.
Some of this helpful for understanding of the history of ABC theory,
but

I have been thinking of posting a review of Quiggin’s book, but this is not it. I suppose I should
mention that I am in the acknowledgements.

Jorge Besada raves at the Mises Institute.
Peter Boettke on his blog.
Tyler Cowen lists Quiggin’s book in his current reading.
Diane Coyle on her blog.
David Gordon at the Mises Institute.
Richard Holden at Inside Story.
Arnold Kling on his blog.
"hayekian" raves.

Quiggin has a response to a couple of
the above. By the way, he had a paper,
in 1987, on public choice.

I think any reviewer should note that Quiggin is extremely generous to
Hazlitt’s
Economics in One Lesson. Hazlitt does not mention "opportunity cost". By focusing on this
concept, Quiggin makes Hazlitt seem more coherent than he is. I agree with Quiggin that this coherence does
not

Figure 1: A Pattern Diagram
Consider an example of the production of commodities, in which many commodities are produced within
capitalist firms. Suppose two techniques are available to produce a given net output.
These techniques use the same set of capital goods, albeit in different proportions.
They differ in process in use for only one industry. Given the qualification about
the same capital goods, generic (non-fluke) switch points are the intersection of the
intersection of the wage curves for two techniques that differ in exactly one process.

Suppose that, due to technological progress, some coefficients of production decrease
in the process unique to the Alpha technique.
Figure 1 shows a possible pattern diagram
for this generalization of a previous
example.
Here, switch points

The Growing Importance of Finance in the Post-War U.S. Economy
As I understand it, Marco Rubio takes from Post Keynesians the idea that, during the post-war
golden age, investment decisions
were dominated by industrial firms. But now, they are dominated by financial corporations.
This change has been accompanied by deleterious effects on economic growth, stagnant wages, and
an upward shift in the distribution of income and wealth.
The increasing importance of finance in the economy in the United States, at least, is
illustrated by the above graph. The impact of the global financial crisis is immediately
apparent in 2008.

The distinction between having investment directed by finance or by industry
might not make any sense to you if you think of every investment as like
purchasing a

Ezra Klein
writes about
John Kenneth Galbraith’s concept of countervailing power.
Ingrid Kvangraven and Carolina Alves are
busting myths about heterodox economics. I have written before about economics as a study of the
reproduction of
society.

Ben Holland, of Bloomberg News, writes an article,
Marco Rubio puts out a paper citing obscure left-wing economists. Rubio’s position paper is
here.
I do not find, say, Wynne Godlay, Hyman Minsky, Mariana Mazzucato, and many proponents of Modern Monetary Theory
and Stock-Flow Consistent modeling particularly obscure or left-wing.

Perspectives on Politics, a journal of political science, has a
special issue,
with open access on the causes and consequences of Trump.

1.0 Summary of Defense

Last month, Mike Munger
purports
to "summarize the basic argument for capitalism" (emphasis added).
He acknowledges his argument is superficial. I find it excessively so.
Munger argues that capitalism:

Supports the division of labor
Provides price signals so as to direct production appropriately
Promotes economies to scale

Ultimately, this defense is that capitalism delivers the goods.
Here’s a well-expressed, simple defense that, partially,
argues along these lines:

It is possible to defend our economic system on the ground that,
patched up with Keynesian correctives, it is, as he put it, the
‘best in sight’. Or at any rate that it is not too bad, and change
is painful. In short, that our system is the best system that we
have got.

Or it is possible to

Figure 1: Wage-Rate of Profits Curves
Consider a comparison of comparison of stationary states. Net output is taken
as given, and a unit of net output is the numeraire. Technology consists
of a finite set of techniques. In each technique, net output is produced
from inputs of labor and produced circulating capital goods. No fixed
capital is used, and land of the best quality is in such abundance that
it is free. Also assume constant returns to scale.

One can find a wage-rate of profits curve for each technique.
The cost-minimizing technique at is the technique its wage curve
on the outer envelope, also known as the wage-rate of profits
frontier, at that wage. Switch points are points at which two or
more wage curves intersect (on the frontier). Suppose the same
gross vector

Many years ago, I used to argue, on Usenet, about the Cambridge Capital Controversy. Many mainstream economists
used to ignorantly assert,
when pretending to respond, that an application of the CCC to labor economics
was my idea alone. So I used to demonstrate that this was false by quoting from the literature.
As far as I can see, mainstream economists are still mostly trained into ignorance.

P. Garegnani:

"The idea that demand and supply for factors of production determine distribution has become so deeply ingrained in economic thought that
it is almost viewed as an immediate reflection of facts, and not as the result of an elaborate theory. For the same reason, it is easily
forgotten how comparatively recent that theory is. In the first systematic analysis of value and

Fact: If you use the word "carceral" instead of "prison" your argument immediately becomes more persuasive.

Good praxis is to use words like "praxis" that nobody understands.
— Matthew Yglesias (5 April 2019, on Twitter)

A large academic literature
exists around Antonio Gramsci’s Prison Notebooks. Topics discussed
include the relationship of civil society to the state, hegemony, the contrast between consent and
coercion, class alliances in political parties, Fordism, the contrast between a "war of position" and
a "war of movement", the contrast between organic intellectuals and traditional intellectuals, and
the concept of a passive revolution.

When writing his notebooks, Gramsci had to be concerned with Fascists guards reading them and tearing
them up in displeasure. Thus, he

1.0 Introduction

This post is on current events. The plane crashes of the Boeing 737 Max 8 airplane is
arguably
about
more than a software bug.
I point out in this post that you can read about how the United States’
Federal Aviation Administration (FAA) is supposed to certify software and electronic hardware in airplanes
yourself.
In some sense, this post is not about software bugs, but rather about software engineering certification processes that
fit into a larger systems engineering perspective.

2.0 FAA Resources

The FAA provides lots of resources associated with DO-278C,
Software Considerations in Airborne Systems and Equipment Certification,
the primary document of interest in this context.

You can find an overview of the FAA Airplane Certification Service
here.
Position papers

Arindrajit Dube writes an obituary for Alan Krueger, in Slate.
Maria Cristina Marcuzzo, at INET, highlights Krishna Bharadwaj’s contributions to economics.
Longtime commentator Emil Bakkum’s web page, collecting a variety of resources, is here.
An advocate of Modern Monetary Theory, Brian Romanchuk is apparently writing a book about models supposedly of Dynamic Stochastic General Equilibrium. Some recent posts include:
Questions about time scales in DSGE models. Anticipations have a time scale and so does calendar time as it passes.
A tutorial introduction to the limitations of linear models of business cycles. Basically, they either explode or decay, with possibly sinusoidal variation. Persistent cycles can only exist because of driving noise.
A long summary of problems with DSGE. Some