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.

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

I have been re-creating some of my
past
analyses.
The graphs in this post look a bit different because I impose a requirement that the relative markups sum to unity.

2.0 Technology

Consider an economy which produces three commodities, iron, steel, and corn, with the technology specified in Table 1.
Two processes are available for producing each commodity. The coefficients of production in a column specify
the person-years of labor, tons of iron, tons of steel, and bushels of corn required to produce a unit of output of the given industry.

Table 1: The Technology

Figure 1: Wages Curves for Example of Intensive Rent1.0 Introduction

This post modifies an example
from Antonio D’Agata.
Two types of land exist,
each specialized for producing a specific commodity.

In the example, some wage curves slope upwards, which is not possible in a model with circulating
capital alone. The cost-minimizing technique is not found from the outer frontier of the wage curves.
For one range of the rate of profits, no cost-minizing technique exists, even though a
feasible technique exists in that range with a positive wage and positive prices. If the wage
is taken as given, more than one cost-minizing technique exists in the range of wages
where a cost-minimizing technique exists.

This example does not illustrate variation in the order of rentability with
the wage

1.0 Introduction

Broadly speaking, the history of political economy contains
two approaches
to value and distribution. For purposes of this post, I do not distinguish between
classical and Marx’s political economy. Institutionalists and those who know about
German historical schools, for example, might have a complaint about being ignored.

This post is quite unoriginal. I thought I would just record these properties
of two approaches.

2.0 Marginalism

Marginalist economics is about the allocation of given resources among alternatives.
In marginalism, the theory of value and distribution is almost co-extensive with
economic theory. The givens, for the theory of value and distribution, are:

Endowments, including distribution of endowments among households.
Tastes or preferences of

I have thought about what would be the minimal structure of an example that
combines
extensive and intensive rent. I want to include a commodity produced without land, as well as an agricultural
commodity.

This post considers a simpler example. An analysis of extensive rent includes
the identification
of the order of efficiency and the order of rentability, given the wage or the rate of profits.
I take the concept of these orders from Alberto Quadrio Curzio.
Can these orders be defined in a model of intensive rent? What would the minimum structure
of an example be in which to explore this question? I continue to insist on including
an industrial commodity with negligible inputs of land.

I suggest Table 1 provides the technology for such an example. Each
column specifies the

John Cassidy on Donald Harris in the Mew Yorker.
Dean Dettloff on The Catholic case for communism in America.
Enrico Bellino and Gabriel Brondino, Circular vs. one-way production processes: two different views on production and income distribution, in Review of Political Economy. I want to recall this for my work on Hayekian triangles.
Bob Murphy and David Glasner on the Sraffa-Hayek debate. (They spend to much time on monetary policy before getting to the debate.)
Leland Yeager and Steve Hanke. 2024. Capital, Interest, and Waiting: Controversies, Puzzles, and New Additions to Capital Theory. I probably will not order this.
Pierangelo Garegnani. 2024. Capital Theory, the Surplus Approach, and Effective Demand. Appears to now be available.

Figure 1: Extensive Rent Example As Relative Market Power Varies Between Industry And Agriculture
This post is an elaboration on this past post.

The analysis of the choice of technique varies with perturbations of relative markups in industry
and agriculture. Figure 1 depicts this variation, while Figure 2 is an enlargement of the lower
range of the relative markup in industry. The heavy solid lines in Figure 1, other than the
horizontal line at the top, are switch points on the inner frontier of the wage curves. They
divide the space into areas in which the cost-minimizing technique is labeled in bold. The dashed
lines are intersections on the outer frontier of the wage curves. The order of fertility varies
across dashed lines. The dotted lines are intersections of rent curves. The

The following is a list of publications I expect to see in the first volume of Sraffa’s
collected works:

Monetary inflation in Italy during and after the war (This is Sraffa’s dissertation).
The current situation of Italian banks. Manchester Guardian. 1922.
The bank crises in Italy. Economic Journal. 1922.
On the relations between cost and quantity produced. Annali di economia 1925. (I think an English translation is in the Cambridge Journal of Economics.)
The laws of returns under competitive conditions. Economic Journal. 1926.
Increasing returns and the representative firm. Economic Journal. 1930. (This is a symposium with Robertson and Shove.)
An alleged correction of Ricardo. Quarterly Journal of Economics. (with L. Einaudi).
Dr. Hayek on money and capital. Economic

Figure 1: Choice of Technique with Extensive Rent and Competitive Markets1.0 Introduction

I am making some slow progress on recreating
past
posts.
For variation, I here take the wage as given.

If I write this up more formally, I intend not to try to relate it to Marx’s concept of absolute rent.
The point is to illustrate the following comment with long-lasting variations in market power
between industry and agriculture:

"The complexity of the outcomes with the potential existence of conflict or concordance among
the three major economic categories (earners of wages, profits, and rents) profoundly modifies
the traditional analysis of profits
and wages." — Alberto Quadrio Curzio and Fausta Pellizzari. Rent, Resources, Technologies, Springer,2010: 34.

This story illustrates how the

This is another post for my commonplace book. It is extraordinary difficult to get a rational
explanation for the marginal revolution. Trying to imitate nineteenth-century physics seems
to be part of it.

"Marx implicitly assumes the the whole of social reproduction is mediated through the
exchange of commodities, including the reproduction of labor power, that is, the reproduction of
people themselves. We can view the labor that produces what productive workers consume as the labor necessary
for the reproduction of society and the labor that capitalists appropriate in the form of surplus value
as the surplus labor time of society, in the sense that only the necessary labor time would be
required to enable reproduction of people and productive facilities on the same scale.
Thus the

Here is a list of books by Marxists that have stood the test of time.
I am being impressionistic and probably idiosyncratic. I am more interested in analysis of what is than political organizing.
What should be added? Removed?

Frederick Engels, Anti-Dühring, 1877. I think German comrades learned Marxism during the second international more from this thick tome. I recommend other works for introductions these days.
Vladimir Lenin, What is to be Done?, 1902. Lenin lays out a strategy and defines a vanguard party. And the Bolsheviks are in power at the end of 1917.
Rosa Luxemburg, The Accumulation of Capital, 1913. Luxemburg argues that capitalism needs a less advanced sector (or maybe military purchases from the state) to provide demand. Growth paths can be defined by Marx’s scheme

This post is for my commonplace book. I have been reading
Enrico Bellino and Gabriel Brondino’s
"Circular vs. one-way production processes: two different views on production and income distribution"
(Review of Political Economy, 2024).

Bellino and Brondino draw a distinction between a circular model of production and
a one-way model. In the latter, a finite, dated series of non-produced inputs (for example, labor)
results in the production of the output. This dichotomoy is distinct from
the distinction
between a theory focusing
on the reproduction of society
and a theory focusing on the allocation of scarce resources.

Bellino and Brondino argue that, if subsistence wages enter into the costs of production,
the one-way model becomes a circular model of production.

The one-way model

Figure 1: Hayekian Triangles for The Two Techniques1.0 Introduction

This post is a variation on this one.

2.0 Technology and Net Output

Suppose technology is as characterized by the coefficients of production in Table 1.
All techniques are characterized by single production, no fixed capital, and no joint production.
In the Alpha technique, the first corn-producing process is operated. The second corn-producing
process is operated in the Beta technique. The ale-producing process is operated in both techniques.

Table 1: Regions
InputCorn IndustryAle IndustryProcess IProcess IIProcess IIILabor1 person-yr.275/464 person-yrs.1 person-yr.Corn1/10 kilo-bushels113/232 kilo-bushels2 kilo-bushelsAle1/40 kilo-liters1/200 kilo-liters2/5 kilo-litersOUTPUTS1 kilo-bushel1 kilo-bushel1 kilo-liter