Table 1: Lower Rate of Profits around a Switch Point
Tradional Marginalist Story’Perverse’ Marginalist Story
Traditional Austrian StoryGreater net output per workerSmaller net output per worker
More roundabout techniqueMore roundabout technique
Switch pt. in region 2, 1st in region 52nd switch point in region 3, 2nd in region 6
‘Perverse’ Austrian StoryGreater net output per workerSmaller net output per worker
Less roundabout techniqueLess roundabout technique
1st in region 3, 1st and 3rd in region 6, switch point in region 72nd switch point in region 5

My examination
of triple-switching
in the corn-tractor model allows for
drawing some conclusions about Austrian capital theory.

The corn-tractor model, like the Samuelson-Garegnani model, is useful for investigating certain
aspects of

Why, under capitalism, do periods of persistent unemployment arise?
Robert Lucas says the problem is to explain why workers do not to want to work:

"A theory that does deal successfully with unemployment needs to address two
quite distinct problems. One is the fact that job separations tend to take
the form of unilateral decisions – a worker quits, or is laid off or fired – in
which negotiations over wage rates play no explicit role.
The second is that workers who lose jobs, for whatever reason, typically
pass through a period of unemployment instead of taking temporary work
on the ‘spot’ labor market jobs that are readily available in any economy.
Of these, the second seems to me the more important: it does not
‘explain’ why someone is unemployed to explain why he does not have a
job

Figure 1: Partitioning a Part of the Parameter Space with Fluke Cases

1.0 Introduction

This post is a continuation of the first example here.
I examined a perturbation of two parameters of that example.
I ended up with a more perspicacious
partition of the parameter space than here.

2.0 Technology

Table 1 merely repeats the parameters for the fluke case that I started with. This case has switch points on the
axis for the rate of profits and on the wage axis. A third switch point exists at an intermediate rate
of profits.

Table 1: Parameters for Technology for First Example
ParameterType I TractorsType II Tractors
Tractor input per tractor (a)≈ 0.3062262/5
Labor input per tractor (b)≈ 233.696720
Years tractors last in tractor industry (n)12

Tractor input per bushel

Duncan Foley participated in a 2003 conference comparing and contrasting
general equilibrium theory with long period models developed by
advocates of the Cambridge capital critique. This is from the
wrap-up discussion on the last day.

"I am in a somewhat peculiar position because due to certain idiosyncrasies of my
education I never learned ‘neoclassical economics’. The economic theory that I learned wasfrom Herbert Scarf
and it was couched entirely in terms of the abstract general equilibrium model with n commodities,
abstract production sets, and so forth. Someone has defined economic intuition as what
you learn in your first course in economics, and since I did not learn the same things as
many other people, my intuition is not the same. My economic intuition was always that there

Figure 1: Wage Curves for an Example With Tractors Lasting One and Two Years

1.0 Introduction

This post presents two examples in the
corn-tractor model.
These examples are double fluke cases. Each has three switch points. One is on the wage axis, and another
is on the axis for the rate of profits.
Perturbations of parameters of each example can result in triple-switching.

The corn-tractor model is a fixed capital model, an adaption of the Samuelson-Gargenani model. The consumption good, corn,
can be produced by labor working with any one of a number of different types of tractors. Each type of tractor is produced
by labor with an input of that type of tractor. Each type of tractor lasts for a specified number of years in the production
of new tractors and of corn. Its lifetime can

This passage suggests to me that, in economics, one
cannot expect to find event regularities from
surface level data:

"The really important difference between us and our natural science colleagues
is illustrated by the fact that we never reach down to constants like the speed
of light and of sound in a particular medium, or the specific weights of atoms
and molecules. We have nothing corresponding to the universally valid measurements
of energy, voltage, amperes, and so on. The regularities we find do not have
the firm, general, and lasting validity of ‘laws of nature.’

If we economists, for instance, establish by observation the income or
price elasticity for, say, sugar, our findings are valid for only a specific
group of consumers in a single community or region at a particular

I have written up a series of post as a research paper:
first post,
second,
third,
fourth,
fifth,
sixth,
seventh.
Here I present the abstract and most of the introduction.

Abstract:
Empirical research indicates that the reswitching of techniques, as well as multiple switching with more switch points,
is rare. This article explores parameter spaces in the analysis of the choice of technique to suggest why
reswitching and triple-switching might be hard to find in empirical data. An example illustrates that the emergence
of triple-switching requires specific evolutions of coefficients of production. Further evolution of technology removes
the possibility of triple-switching. The example also illustrates that the roundaboutness of a technique is
independent of the capital-intensity of a

Here is a story about David Hilbert torwards the end of his career:

"Otto Neugebauer, now an associate professor, was placed at the
head of the Mathematical Institute. He held the famous chair for exactly one day,
refusing in a stormy session in the Rector’s office to sign the required
loyalty declaration. The position of the head of the Mathematical Institute
passed to Weyl. Although his wife was part Jewish, he was one of those
who thought that something might yet be salvaged. All during the bitter
uncertain spring and summer of 1933 he worked, wrote letters, interviewed
officials of the government. But nothing could be changed.

By late summer nearly everyone was gone. Weyl, vacationing with his
family in Switzerland, still considered returning to Göttingen in the hope
that

Figure 1: Actual and Stylized Partitions of Parameter Space with Triple-Switching

This post is a continuation
of
this
series
of
posts.

The partitioning of the parameter space by fluke switch points in these posts can be combined into one picture.
The left pane in Figure 1 illustrates. The dashed line is a ray from the origin, discussed below.
I find this complete picture for this example hard to perceive by eye. The right pane
provides a highly stylized presentation of the partitions, rotated and stretched. The partitions
are not straight lines on the left. The boundary between regions 1 and 5 is tangent to the boundary
between regions 1 and 2 at the point of intersection. The boundary between regions 3 and 4 is
likewise tangent to the boundary between regions 2 and 4 where they

Apparently, many mainstream economists assert that anything worthwhile in economics will be published in one of a few journals.
The following is a selection of some articles from these well-respected journals, as I understand it:

American Economic Review

Donald J. Harris. 1973. Capital, distribution, and the aggregate production function. AER. 63(1): 100-113.
David Laibman and Edward J. Nell. 1977. Reswitching, Wicksell effects, and the neoclassical production function. AER, 67(5): 878-888.

Economica

Murray Milgate. 1976. On the origin of the notion of ‘intertemporal equilibrium’. Economica. New series 46(181): 1-10.

Journal of Economic Literature

G. C. Harcourt. 1969. Some Cambridge controversies in the theory of capital. JEL. 7(2): 369-405
A.

Figure 1: Extra Profits at Gamma Prices for the Sixth Double-Fluke Switch Point
This post is a continuation of
this
series
of
posts.

In the last double-fluke case, the three switch points between Alpha and Gamma coincide as a
ingle switch point. Figure 1 illustrates, while Figure 2 depicts how the parameter space is
partitioned around this double-fluke case. Region 7, in which one switch point occurs, is connected. At the point corresponding to the double-fluke case, the two boundaries between regions 6 and 7 are tangent.
Schefold’s example is at a point, (φ t, σ t)=(1,1⁄2), in the thin
wedge for region 6 in Figure 2. I did not find that points in the parts
of region 6 in previous posts had more visually compelling wage frontiers than the point that Schefold found

Figure 2:

Marx, like Adam Smith and Walt Rostow, had a stages theory of history. Feudalism was succeeded by
capitalism, and capitalism is to be succeeded by socialism. Socialism is to arise first in the most advanced capitalist countries.
(The theory of history is not my favorite part of Marxist theory.)

Russia, in 1917, was a semi-feudal country with peasants as the largest class. I guess China
was the same, before Mao. A Marxist would not expect socialism to be successful in either country.

I think Lenin and the Bolsheviks agreed with this thesis when they first came to power.
They expected their revolution to kick off revolutions elsewhere in Europe.
And their expectations seemed to be initially met, what with the Spartacist uprising in Germany, Hungary, and so on.

Lenin, knowing that

Figure 1: Partitions of the Parameter Space Around the Double-Fluke Switch Points
This post is a continuation of this
series
of posts.

The fourth and fifth double-fluke cases, in order of an increasing φ t, are symmetrical. The
fourth case has two switch points between Alpha and Gamma. One is on the wage axis. The wage
curves are tangent at the other switch point, at a positive rate of profits below the maximum.
Alpha is cost-minimizing at all feasible rates of profits. Gamma is cost-minimizing only at the switch points.
The fifth case also has two switch points between Alpha and Gamma. One is on the axis
for the rate of profits, and the wage curves are tangent at the other switch point. Gamma
is cost-minimizing at all feasible rates of profits. Alpha is cost-minimizing only at the

Figure 1: Extra Profits at Gamma Prices for the Third Double-Fluke Switch Point
This post is a continuation of this
series of
posts.

The next double-fluke case to be considered arises for parameters on intersection of the upper and lower boundaries
of regions 3 and 5. Figure 1 illustrates this case, while Figure 2 depicts local perturbations of this double-fluke case.
Perturbations that lead to either of the switch points at the extremes of the rate of profits no longer being at a feasible rate result in reswitching, as in regions 3 and 5. One switch point, as in region 2, results from perturbations
in which both fluke switch points no longer being at a feasible rate of profits. But consider a perturbation
n which both switch points occur at a positive rate of profits below the

Because of its treatment of capital. Other answers are possible.

This post draws heavily on the work of Pierangelo Garegnani.
I start with a (parochial) definition of economics:

"Economics is the science which studies human behavior as a relationship between ends and
scarce means which have alternative uses." — Lionel Robbins (1932)

The scarce means are the factors of production: land, labor, and capital. Land and labor are in
physical terms, in units of acres and person-years, respectively. They can be aggregated or disaggregated, as you wish.

But what is capital?
Some early marginalists, such as Knut Wicksell took it as a value quantity, in units of dollars or pounds sterling.
Maybe I should rather say, it is given in numeraire units.
Capital is taken as given in quantity, but

Figure 1: Extra Profits at Gamma Prices for the Second Double-Fluke Switch Point
This post is a continuation of this
series of posts.

A switch point in which wage curves are tangent on the axis for the rate of profits is a double-fluke case
symmetrical to the double-fluke case in the previous post.
As shown in Figure 1, this case arises in this example as well. The roles of the Alpha and Gamma techniques are reversed. Alpha is always cost-minimizing, while Gamma is cost-minimizing only at the switch point.

This symmetry extends to partitions of the parameter space, as seen in Figure 2. A locus
corresponding to a switch point at which wage curves are tangent bounds a region, 1 or 4, in
which no switch points exist. Reswitching occurs in regions 3 and 5, which are on the other
side of

Consider the introduction of new, advanced machinery into a capitalist
economy. This will raise productivity and be good for the population
as a whole. It will displace workers, at least temporarily, who
were previously making the product of the machine with handicraft production
or now obsolete machines with lower productivity.
But the production of the machines requires workers too. So, ignoring
short-run frictions, will the workers not remain as well off?

David Ricardo believed something like this at one point in his life.
But he had come to the opposite conclusion when he revised his Principles
for the third edition. And he was forthright in saying so.
Some of the displaced workers will be more or less permanently unemployed.
By the way, this was not a matter of coming to agree

Figure 1: The Wage Frontier for a Double-Fluke Switch Point
This post is an expansion of a previous one.
That post defines the technology and the price system for the three techniques conprising
the technology. In Alpha, labor and corn inputs are used to produce corn.
Beta and Gamma are more roundabout.
In each, Labor and corn are first used to make a machine that lasts two years
and can be used to produce corn each year. In Beta, the machine is discarded after being
operated one year.
The machine is operated for its full life of two years in Gamma.
The technology varies over time. One pararemter specifies the decrease
in coefficients of production for Alpha.

The solutions of the price system for a technique yields a wage curve.
Figure 1 plots the wage curves for the three techniques

I take the following long quote from Bohm-Bawerk.

"The entire sum of originary productive forces at Crusoe’s disposal … is a day’s labor
which we shall assume to be a 10-hour workday… Let us assume that the fruit harvest [is] enough
to enable our castaway to gather the subsistence minimum in nine hours a day, and enough in 10 hours to furnish
him with adequate sustenance for complete health and vigor… Crusoe now has a choice between two lines of
conduct. One alternative is … to consume each day the fruits gathered by a full 10 hours’ work… The other
alternative is to restrict himself to the subsistence minimum… In that event – but only in that event – he has
a tenth hour open in which he makes hunting equipment for future use… Before there can be any
real formation of capital,

Figure 1: Triple Switching with Strucutral Economic Dynamics1.0 Introduction

I have been using fluke switch points to partition two-dimensional slices of parameter spaces.
I know, I think, how reswitching can appear and disappear. But I am confused
how more switch points can appear. So this post is a start on exploring a triple-switching
example.

I have stumbled upon two examples of triple-switching, so to speak. I have not yet
replicated Steedman’s claim that triple-switching can arise in his corn-tractor model.
But then, in my first explorations I had different types of tractors lasting for the
same number of years. So I turn to an example from Schefold, which I
have explored previously.

I expect to find numerical examples of phenomena that I have not yet seen. For example,

Figure 1: A Larger Parameter Space
This post is an expansion on the first
example here.
It presents shortly a more comprehensive analysis of the variation in the choice of technique in the example
of circulating capital in Section 2. Local perturbations of two coefficients of production are examined there.
Figure 1 partitions a larger part of the space defined by these two coefficients of production.
Table 1 exhibits how the cost-minimizing technique varies with the rate of profits in each region.

Table 3: Ranges of the Rate of Profits by Region
RegionRangeTechniqueNotes10 ≤ r ≤ r1BetaReverse substitution of labor at switch point.r1 ≤ r ≤ rα,maxAlpha20 ≤ r ≤ r1BetaSwitch point is ‘non-perverse’.r1 ≤ r ≤ rα,maxAlpha30 ≤ r ≤ rβ,maxBetaNo switch point.40 ≤ r ≤ rβ,maxBetaNo switch point.50

I take it for granted that marginalism became accepted partly because Marx had used the best
in classical political economy in his account of why socialism would and should transcend
capitalism. This post presents some who have argued for or asserted the same.

I start by summarizing an argument from Antonia Campus. Campus argues that the marginalists
in the 1870s did not have an accepted theory of production, cost, and price. Only in the
1890s did the marginal productivity theory of distribution become accepted. Now that that
theory has been demolished, in the 1960s, we are back into the confusion of the 1870s, with every
person his own capital theorist.

"With the publication in 1867 of Volume 1 of Capital, Ricardo’s theory of
distribution and value had in fact reappeared, not in

Figure 1: The Demand for Labor1.0 Introduction

Wages and employment are not determined in competitive markets by the interaction of well-behaved supply and
demand curves, as portrayed in much introductory economics. At least, no reason exists to thinks so. Every
once in a while I like to recall
that this is an implication of the Cambridge Capital Controversy.

2.0 Technology

Consider a very simple competitive capitalist economy in which corn and iron are produced from inputs of labor, iron, and corn.
All production processes in this example require a year to complete. The managers of firms know of two processes for
producing corn and two processes for producing iron (Table 1).
The processes a and b, for producing corn, require the tabulated inputs to be available
at the beginning of

A 2019 profile of Stephen Marglin in the Harvard Crimson.
William Morris, the author of News from Nowhere, wrote the Manifesto of the Socialist League.
David O’Connell explains, in Jacobin, that Catholic orthodoxy is quite radical on the economy.
Jack London’s How I became a socialist.

Figure 1: A Parameter Space1.0 Introduction

This is a re-creation and elaboration of a
previous post.

The analysis of the choice of technique, in models of circulating and fixed capital, can be 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 a feasible technique, including the wage, 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. These properties do not necessarily hold in models of general joint production.
An examination of local perturbations in an example of intensive rent illustrates surprising

I have been using fluke switch points to partition parameter spaces into
regions. In each region, the analysis of the choice of technique does not
qualitatively vary.

Fluke switch points have been discussed in the literature on the analysis
of the choice of technique. Mostly, these mentions dismissal fluke cases,
on the correct grounds that they only occur at an accidental point in
the parameter space.

Here is a statement from one contribution to the famous QJE symposium:

"Cases with multiple roots or cases in which the curves cross only at end points … can be
classified as irrelevant since the F[actor] P[rice] F[rontier] (envelope) is unchanged by their
exclusion." — Bruno, Michael, Edwin Burmeister, and Eytan Sheshinski. 1966. The nature and implications of the reswitching of

Figure 1: A Parameter Space1.0 Introduction

I have been reconstructing some of my examples. The first example in this post
is from here.
I am thinking of writing a draft article, as mentioned here.
While I am at it, I thought I would also work through the examples
in Garegnani (1966) and Bruno, Burmeister & Sheshinski (1966),
both from the symposium in the
Quarterly Journal of Economics of that year.

2.0 The Emergence of the Reverse Substitution of Labor

This section 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

5.0 Fluke Cases

This post is a continuation of this one.
This is a numeric example of intensive rent.
Here I present five fluke
cases before depicting how the analysis of the choice of technique varies
with the full range of relative markups in agriculture.

5.1 Switch Point at Maximum Scale Factor for Epsilon

In the first fluke case, the wage curves for Alpha and Delta intersect
at the maximum scale factor for the rate of profits for Delta (Figure 7).
Figure 8 displays the graphs of the rent curves.
At any larger scale factor, rent in Delta would be negative.
This fluke case is associated with a
qualitative change in the range of the scale factor for the rate of profits in which no cost-
minimizing technique exists. The wage frontier consists of the wage curves for the Delta
and

Figure 1: Variation of the Technique with the Markup in Agriculture1.0 Introduction

This post is the start of a recreation of a
previous post, with a requirement that relative markups lie on a simplex.

These two posts are intended to explain Figure 1, above, which presents a summary of the results of the analysis
of the choice of technique, given any level of the relative markup in agriculture, as compared with the relative
markups in the non-agricultural industries. My presentation is long enough that I break in down into a couple of posts.

The numerical example illustrates that the interest of landlords are affected by persistent barriers of entry in
industry and agriculture, as well as class struggle between workers and capitalists. Other classes care about
attempts among

Ramon Llul was a medieval scholar who invented social choice theory (specifically, the Borda count), as seen in a manuscript discovered in 2001(?). (Other discoveries.)
A review of Steve Paxton’s Unlearning Marx: Why Soviet Failure was a Triumph for Marx. Maybe I want to read this.
Pierangelo Garegnani’s Capital Theory, the Surplus Approach, and Effective Demand.