Reswitching in a Model of Extensive Rent

My article with the post title is now available at the Bulletin of Political Economy (Volume 16, issue 2, pp. 133-146). The abstract follows:

Abstract: This article presents an example of the reswitching of the order of fertility and of the order of rentability. Whether or not these orders differ from one another varies with distribution for certain parameter ranges in the example. This analysis emphasizes that more rent per acre is not necessarily associated with more fertile land and that the ranking of lands by fertility cannot, in general, be determined from only data on physical inputs and outputs for the available processes.

Variations in the Economic Life of Machines

These posts demonstrate, in a model of fixed capital, that the cost-minimizing choice of the economic life of a machine need not conform to traditional Austrian and marginalist theory. The cost-minimizing choice of technique around a switch point might associate a shorter economic life of a machine with an increased capital intensity. This counter-intuitive variation of the economic life of a machine is independent of capital reversing and the re-switching of techniques, both of which are also illustrated in these posts.

These posts build on the Cambridge capital controversy (CCC). A lower rate of profits may be associated with a decreased value of capital per worker, a decreased ratio of the value of capital to output, and a decreased sustainable steady state of consumption per worker (Harcourt 1972). Capital is not a factor of production, and an equilibrium rate of profits, assuming competitive conditions, is generally not equal to the marginal product of capital (Harris 1973). The unfounded idea in the background is that, in a supply-and-demand explanation of prices and distribution, an increased relative supply of a factor of production supposedly drives its price down and incentivizes entrepreneurs to adopt techniques, out of a given technology, that use that factor more intensively. All sides to the CCC accepted that this theory lacks rigorous foundation:

"Such an unconventional behavior of the capital/output ratio is seen to be definitely possible. ... Moreover, this phenomenon can be called 'perverse' only in the sense that the conventional parables did not prepare us for it" (Samuelson 1996).

Han and Schefold (2006) and Zambelli (2018) have recently found some examples of such 'perverse' switch points, albeit not many, in empirical data obtained from national income and product accounts. Kurz (2021) raises some challenges to this empirical work.

Much of the discussion in the CCC focused on models with only circulating capital. Bidard (2004), Pasinetti (1980), and Schefold (1989) are canonical references in post Sraffian price theory to fixed capital. The economic life of a machine, in the general case of non-constant efficiency, varies with distribution. Steedman (2020) considers a model with an infinite number of alternative types of machines, each being the only basic commodity in the technique in which it used. Machines operate with constant physical efficiency, for possibly a different number of years in industry and agriculture. He finds that a machine with a shorter life can be adopted at a lower interest rate, independently of capital-reversing. In contrast, this article considers variation in the economic life of a single machine. The results established here and by Steedman can be seen as complementary.

The method of analysis is based on comparing stationary states, where prices of production prevail. These models are open, with distribution taken as exogenous. The numeric example is simple enough such that net output consists of a single consumption good, called 'corn'. Corn also functions as circulating capital, while a machine with a physical life of three years represents fixed capital. Both corn and new machines are basic commodities, in the sense of Sraffa. Although no attempt is made to represent production by a series of dated labor inputs, the economic life of the machine seems to be of interest for claims among economists developing capital theory along the lines of the Austrian school. Economists of this school have argued that a greater willingness to defer consumption leads to a greater supply of capital, a lower interest rate, and a greater period of production. In these posts, a greater period of production is identified with a longer economic life of a machine.

The application of perturbation analysis to the analysis of the choice of technique, to identify fluke cases, and to explore how switch points vary with technological change is relatively novel. A fluke case is such that almost any perturbation of model parameters disturbs its qualitative properties. Kurz and Salvadori (1995) is a classic textbook for the analysis of the choice of technique. Vienneau (2018, 2019, 2021, 2024a, and 2024b) extends this analysis to consider the effects of perturbing selected model parameters. In these posts, applying this approach to a single numeric example uncovers surprising variation in the economic life of a machine, including its non-monotonic variation with the rate of profits with neither capital-reversing nor the re-switching of techniques.

Harwick (2022) has noted that some followers of the Austrian school have recently tried to consider Austrian capital theory separately from business-cycle theory. Lewin and Cachanosky (2019) consider a financial measure of capital-intensity, namely the average duration of an investment project. Around any switch point, an increased Duration is associated with a lower interest rate. As emphasized by Fratini (2019), an increased capital intensity, in this sense, is associated with reduced net output per worker around a so-called 'perverse' switch point. Even so, any measure of capital intensity that always increases with a lower rate of profits around a switch point can be associated with a reduction in the economic life of a machine.

Capital-intensity is assessed in these posts by evaluating the price of inputs, either for a given net output or per worker. A reduction in the economic life of a machine is consistent with an increase in capital-intensity. This association between a shorter economic life and greater capital-intensity can arise around a switch point in which a smaller rate of profits results in the adoption of a more capital-intensive technique, with a consequent greater net output per worker. It can also arise around a 'perverse' switch point in which a less capital-intensive technique is adopted at a lower rate of profits. Neither type of switch point is a fluke case, as can be seen by contrasting such switch points with genuine fluke cases.

On The Uselessness Of Economists

If you believed something different, you wouldn't be sitting where you are sitting

Suppose one wants to discuss capitalism versus socialism or some smaller matter. One might think the discipline of political economy, now known as economics would be helpful. But it is not.

What is taught in most universities in the United States was shown to be nonsense more than half a century ago. I find it hard to account for this except on the grounds of political ideology. I realize that most academic economists and their students that persist do not experience themselves as propagandists. And it does take some study to master the mathematical models, even if they are incoherent.

Obviously, exceptions exist. I am most aware of the economics departments at the University of Massachusetts at Amherst, the New School, the University of Missouri at Kansas City, and the University of Utah. And I think the situation might be different in some other countries. At least, they can list some prominent universities like the above. Furthermore, in taking courses in academic economics, one should learn something useful about how national products and income accounts are kept. Many economists might think they are doing measurement without theory, that these theoretical incoherences that I go on about do not matter to them. And there are many partial models that might be useful in a narrow context.

These sort of questions should have clear answers: For some model, what are the parameters and and what are the variables found in the solution? For each parameter or variable, what are the units of measure? Lately, I have been recommending a John Eatwell lecture on the bomb that Piero Sraffa placed at the foundations of economic theory. Working through Kurz and Salvadori's 1995 textbook is also a good way to understand my favorite devasting criticism of marginalist economics.

Smith's natural prices, Ricardo's prices of production, and Marshall's normal prices all characterize a long-period position or equilibrium, depending on the theory. Marginalist economics is about the allocation of given resources. The quantity and initial distribution of capital goods are among the givens, at least in Walras' formulation. Supply and demand are supposed to clear in all markets in equilibrium, and the capitalists obtain the same rate of profits in all markets. This model is ovedetermined and inconsistent. Walras was mistaken.

Taking the numeraire quantity of capital and its initial distribution as given was another incorrect marginalist approach. The physical composition of capital is supposed to be endogeneous. But prices of capital goods are found as solutions of the model. The quantity of capital is simultaneously inside and outside the model. Knut Wicksell realized this approach does not work. And waiting or abstinence cannot explain profits either.

So from about 1930 to the 1970s, marginalists abandoned long period theory in their most general models. The Arrow-Debreu-McKenzie model of intertemporal equilibrium is the cumulation of this trend. In the model, commodities are distinguished by physical properties, when they are available, and the state of the world. Prices are established in forward markets, found at the start of time.

This is a model of supply and demand in some sense. Households maximize utility subject to constraints. Plans are precoordinated, and all markets clear for all time. On the other hand, one can not draw well-behaved supply and demand schedules at the level of the market, as is shown by the Sonnenschein-Debreu-Mantel theorem.

Economists cannot explain how any economy would get in or approach such an equlibrium. Franklin Fisher investigated this question. Fabio Petri notes that the givens of initial quantities of capital equipment would change if production goes on while the economy is in disequilibrium. The equilibria consistent with the givens are not the equilibria that would be approached. The model does not depict tendencies in any possible capitalist economy.

Given an equilibrium, however, the forward prices embody predictions of what spot prices would be. Mainstream economics, when talking about dynamics, often mean the time paths of these spot prices. A conceptual problem arises here. If markets can open and close later, the model is not the Arrow-Debreu-McKenzie model. Anyways, the rate of profits is not the same among industries at any time period, since prices are typically not stationary.

Mainstream economists have basically given up, as I understand it, on trying to develop any general approach to explaining prices and distribution in a capitalist economy. I think the textbooks are not clear on this point. I like some of the bits of mathematics, such as game theory, in some of these textbooks.

Why study this stuff? Even though academic economists are mostly trapped in an intellectual ghetto, they still have a connection to what ideas are hegemonic. And the disciple of economics provides a puzzle for the sociology of 'knowledge' and the philosophy of science. If academic economists were merely useless, the world would be improved.

How To Find Fluke Switch Points

Figure 1: Convergence of Newton Method

This post steps through an algorithm for finding a fluke switch point. I used a different example when I tried to explain this before. Today, I use an example building on my draft ROPE Article.

Consider Figure 3 in this post, repeated below as Figure 2. Let s₁ = s₂ = 1. I want to find s₃, the markup in the corn industry, such that the wage curves for Gamma, Delta, Eta, and Theta intersect at a single switch point. One wants to find a function one of whose zeros is the desired markup.

Figure 2: Variation of Switch Points with the Markup in the Corn Industry

This economy produces a single consumption good, called corn. Corn is also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. So three industries exist. One produces iron, another produces steel, and the last produces corn. Two processes exist in each industry for producing the output of that industry. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce a unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	1/3	1/10	5/2	7/20	1	3/2
Iron	1/6	2/5	1/200	1/100	1	0
Steel	1/200	1/400	1/4	3/10	0	1/4
Corn	1/300	1/300	1/300	0	0	0

A technique consists of a process in each industry. Table 2 specifies the eight techniques that can be formed from the processes specified by the technology. If you work through this example, you will find that to produce a net output of one bushel corn, inputs of iron, steel, and corn all need to be produced to reproduce the capital goods used up in producing that bushel.

Table 2: Techniques

Technique	Processes
Alpha	a, c, e
Beta	a, c, f
Gamma	a, d, e
Delta	a, d, f
Epsilon	b, c, e
Zeta	b, c, f
Eta	b, d, e
Theta	b, d, f

Given the markups s₁, s₂, and s₃, the wage and prices under Gamma are rational functions of the scale factor for the rate of profits:

w_γ(r) = (f₃ r³ + f₂ r² + f₁ r + f₀)/(g₂ r² + g₁ r + g₀)

p_γ,1(r) = (u₂ r² + u₁ r + u₀)/(g₂ r² + g₁ r + g₀)

p_γ,2(r) = (v₂ r² + v₁ r + v₀)/(g₂ r² + g₁ r + g₀)

Since corn is the numeraire, its price is unity. The coefficients of the polynomials are functions of the coefficients of production for the first, second, and first processes in the iron, steel, and corn industries, respectively, and of the markups.

The Delta technique differs from Gamma in the process for producing corn. The extra profits obtained in operating the second corn-producing process at Gamma prices are:

h₁(r)/(g₂ r² + g₁ r + g₀) = 1

- [(a_f,1,3 p_γ,1(r) + a_f,2,3 p_γ,2(r) + a_f,3,3)(1 + s₃r)

+ a_f,0,3 w_γ(r)]

A switch point between Gamma and Delta is found as an appropriate zero of h₁(r), which is a cubic polynomial. Denote r₁(s₃) as the zero sought for the fluke case.

The extra profits obtained in operating the second iron-producing process at Gamma prices are:

h₂(r)/(g₂ r² + g₁ r + g₀) = p_γ,1(r)

- [(a_b,1,1 p_γ,1(r) + a_b,2,1 p_γ,2(r) + a_b,3,1)(1 + s₁r)

+ a_b,0,1 w_γ(r)]

An appropriate zero of h₂(r) is a switch point between Gamma and Eta. Denote r₂(s₃) as the zero sought for the fluke case.

Consider the following function:

h(s₃) = r₂(s₃) - r₁(s₃)

A zero of h(s₃) is such that the wage curves for Gamma, Delta, Eta, and Theta intersect at a single switch point. At a switch point for Gamma, Delta, and Eta, neither extra profits nor extra costs will be obtained in operating either iron-producing and corn-producing processes. Since the same steel-producing process is operated in all four techniques, Theta is also cost-minimizing at this switch point.

One can find such a zero by applying Newton’s method to two initial guesses, as illustrated in Figure 1 at the top of the post. Some experimentation allows one to determine two initial guesses, s⁰₃ and s¹₃, for the markup in the corn industry and for which roots of the cubics are wanted. The slope of a linear approximation to the function whose zero is sought is:

m_{i + 2} = [h(sⁱ₃) - h(s^{i + 1}₃)]/(sⁱ₃ - s^{i + 1}₃), i = 0, 1, 2, ...

The intercept with the ordinate is:

b_{i + 2} = h(s^{i + 1}₃ - m_{i + 2} s^{i + 1}₃, i = 0, 1, 2, ...

The next iteration is:

s^{i + 2}₃ = - b_{i + 2}/m_{i + 2}, i = 0, 1, 2, ...

In my experience, Newton's method converges fairly rapidly in this application of finding fluke switch points.

"Deserves got nothing to do with it"

This post echos another quotation from somebody who understands something about how rewards are distributed under capitalism.

"In every other country capitalism, competitive and monopolistic, displays the same defects and applies similar political and economic remedies in order to save its life from the new revolutionary attacks of socialism and communism. Regarded more narrowly from my own standpoint of criticism, what has occurred is a display and condemnation of the unequal and unfair character of all markets. For nowhere are the bargaining powers of supply and demand on an equal footing, and everywhere the individual buyers and sellers, whether of goods or services, are so unequal in their 'need' to sell and buy that the advantage accruing from sales at any given price give widely different advantages to those who participate. In other words, whether under monopoly or so-called competitive conditions, markets are intrinsically unfair modes of distribution.

This is my most destructive heresy, and therefore the one for which I have least succeeded in gaining attention, even in the form of hostile criticism, from the orthodox economists. The defence of capitalism consists mainly in ignoring positive attacks and in concentrating upon the errors, follies, and divided counsels of its assailants. Among the business and professional classes and their economic supporters the conviction holds that any property or income legally acquired represents the productive services rendered by its recipient, either in the way of skilled brain or hand work, thrift, risks, or enterprise, or as inheritance from one who has thus earned it. The notion that any such property or income can contain any payment which is excessive, or the product of superior bargaining power, never enters their minds. Writers to The Times, protesting against a rise in the Income Tax, always speak of their 'right' to the income they have 'made,' and regard any tax as a grudging concession to the needs of an outsider, the State.

So long as this belief prevails all serious attempts by a democracy to set the production and distribution of income upon an equitable footing will continue to be met by the organized resistance of the owning classes, which, if they lose control of the political machinery, will not hesitate to turn to other methods of protecting their 'rights.'" -- J. A. Hobson, Confessions of an Economic Heretic

Variation With Markups Of The Analysis Of The Choice Of Technique With Intensive Rent

Figure 1: Variation of the Technique with Markup in Agriculture

This post is a continuation a of a previous example.

I suppose this is the first example in post Sraffian price theory which combines intensive rent and markup pricing. I do not plan on trying to publish it, in a stand-alone article. D'Agata (1983) sets some coefficients to zero to simplify it for his purposes. I would like a range of parameters where I get reswitching or capital-reversing. I have found a case where, given the wage, the cost-minimizing technique is not unique away from switch points. I would like an example where some of the locii in Figure 2 below intersect.

I might as well repeat the data. Table 1 shows the coefficients of production. Only one type of land exists, and three processes are known for producing corn on it. Following D'Agata, assume that one hundred acres of land are available and that net output consists of 90 tons iron, 60 tons steel, and 19 bushels corn. The net output is also the numeraire.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Steel	Corn
	I	II	III	IV	V
Labor	1	1	1	11/5	1
Land	0	0	1	1	1
Iron	0	0	1/10	1/10	1/10
Steel	0	0	2/5	1/10	1/10
Corn	1/10	3/5	1/10	3/10	2/5

All three commodities must be produced for any composition of net output. Table 2 lists the available techniques. Only Alpha, Delta, and Epsilon are feasible for these requirements for use. Not all land is farmed and only one corn-producing process is operated under Alpha. Two corn-producing processes are operated together under Delta and Epsilon.

Table 2: Techniques

Technique	Processes
Alpha	I, II, III
Beta	I, II, IV
Gamma	I, II, V
Delta	I, II, III, IV
Epsilon	I, II, III, V
Zeta	I, II, IV, V

In the non-competitive case, the relative markups in different industries are taken as given. Let the rates of profits be in proportions of s₁, s₂, and s₃, respectively.

Figure 1, at the top of the post, shows the variation in the analysis of the cost-minimizing technique with perturbations of the markup up in agriculture. In drawing this figure, markups in iron and corn production, s₁ and s₂, are assumed unity. At the intersection between the Alpha and Delta wage curves, the rent for Delta is zero. The scale factor at this switch point is the maximum for the Delta technique. At a switch point between Alpha and Epsilon in regions 1, 2, 3, and 4, the rent for epsilon is zero. The scale factor at such a switch point is the maximum scale factor for Epsilon. In regions 5 and 6, the maximum scale factor for Epsilon is the scale factor for which the wage turns negative.

A fluke case exists off to the right where the wage curves for Alpha at Delta intersect at the maximum scale factor for the rate of profits for Alpha. At that switch point, Delta has a scale factor for the rate of profits of zero percent and a rent of zero. The fluke case partitioning regions 2 and 3 is one where the wage curves for Alpha and Epsilon intersect at the scale factor where the wage for Delta first turns positive. The fluke case partitioning regions 3 and 4 is one in which the wage curves for Alpha, Delta, and Epsilon all intersect at a single switch point.

The fluke cases partition regions 4 & 5 and 5 & 6 change some characteristics of the range of the scale factor of the rate of profits in which no cost-minimizing technique exists. At the fluke case partitioning regions 4 and 5, the wage curves for Alpha and Epsilon intersect at the maximum scale factor for Alpha. I have previously provided an analysis of the fluke case dividing regions 5 and 6. Maybe I should not consider these two fluke cases since they arise, in some sense, for switch points off the frontier.

Anyways, Table 2 shows how the analysis of the choice of technique varies among the numbered regions. If wants to look at these results in some detail, one can relate the variation in the analysis of the choice of technique to the fluke cases.

Table 2: The Cost-Minimizing Technique in Selected Regions in Parameter Space

Region	Range for Scale Factor	Cost-Minimizing Techniques
1	0 ≤ r ≤ R*,ε	Epsilon
	R*,ε ≤ r ≤ Rα	Alpha
2	0 ≤ r ≤ R*,ε	Epsilon
	R*,ε ≤ r ≤ Rδ	Alpha
	Rδ ≤ r ≤ R*,δ	Alpha and Delta
	R*,δ ≤ r < Rα	None. Wage for Alpha positive.
3	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ R*,ε	Delta and Epsilon
	R*,ε ≤ r ≤ R*,δ	Alpha and Delta
	R*,δ ≤ r < Rα	None. Wage for Alpha positive.
4	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ r*	Delta and Epsilon
	r* ≤ r ≤ R*,δ	None. Wage for Alpha, Delta, Epsilon positive. Rent for Delta and Epsilon positive.
	R*,δ ≤ r < R*,ε	None. Wage for Alpha and Epsilon positive. Rent for Epsilon positive.
	R*,ε ≤ r < Rα	None. Wage for Alpha positive.
5	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ r*	Delta and Epsilon
	r* ≤ r ≤ R*,δ	None. Wage for Alpha, Delta, Epsilon positive. Rent for Delta and Epsilon positive.
	R*,δ ≤ r ≤ Rε	None. Wage for Alpha, Epsilon positive. Rent for Epsilon positive.
	Rε ≤ r < Rα	None. Wage for Alpha positive.
6	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ r*	Delta and Epsilon
	r* ≤ r ≤ Rε	None. Wage for Alpha, Delta, Epsilon positive. Rent for Delta and Epsilon positive.
	Rε ≤ r ≤ R*,δ	None. Wage for Alpha, Delta, positive. Rent for Delta positive.
	R*,δ ≤ r < Rα	None. Wage for Alpha positive.

Figure 2, for completeness, illustrates the partition of the parameter space of markups, where the ratios of markups in iron and steel need not be the same. Figure 1 illustrates what happens along a vertical line in Figure 2 at s₂/s₁ is unity. I realize it is hard to see region 4 and to distinguish its boundaries in Figure 2.

Figure 2: Partition Of Parameter Space

I do not draw any great conclusions. This example demonstrates my visualization techniques and perturbation analysis can be applied to an example where the cost-mninimizing technique is not found from a frontier of wage curves. The non-uniqueness and non-existence of a cost-minimizing technique arises in D'Agata's original example.

An Alpha Vs. Delta Pattern For The r-Order Of Fertility With Intensive Rent And Markup Pricing

Figure 1: Wage Curves and Rent for an Example of Intensive Rent

This post is a continuation of a previous example.

This is a fluke case insofar as the Alpha and Delta wage curves intersect at the scale factor for the rate of profits that is the maximum possible for the Epsilon technique. 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 technology, endowments, requirements for use, and techniques are as previously defined. Requirements for use can only be satisfied by the Alpha, Delta, and Epsilon techniques.

I continue to consider markup pricing. The rate of profits is (s₁ r), (s₂ r), and (s₃ r) in the iron, steel, and corn industries. In determining which technique is cost-minimizing, r, the scale factor for the rate of profits is taken as given.

Figure 1, at the top of this post, depicts the wage and rent curves for the different techniques. The wage curves for the cost-minimizing techniques lie on the wage frontier. The wage frontier consists of the wage curves for the Delta and Epsilon techniques up to the switch point between them. The wage frontier ends there. No technique is cost-minimizing between this switch point and the maximum scale factor for the rate of profits for Alpha.

Table 1 goes into more detail on the wage curves than aqnybody probably cares about. I introduce some notation that I will find useful in later posts. R_δ is the scale factor for the rate of profits at which the wage is zero for Delta. R_*,δ is the scale factor for the rate of profits at which the rent is zero for Delta. This is a fluke case because R_*,δ is equal to R_ε. Anyways, in the first range for the scale factor, only the Alpha and Epsilon techniques have wage curves that are eligible to lie on the wage frontier; the wage curve for the Delta technique lies below the axis for the scale factor for the rate of profits. In the next two ranges, all three wage curves are eligible. In the last range of the scale factor, only the wage curve for Alpha is eligible. The rent curve for Delta and the wage curve for Epsilon lie below the axis for the scale factor.

Table 1: Cost-Minimizing Techniques

Lower Bound on r	Upper Bound on r	Techniques
0 percent	Rδ	Alpha has a positive wage
		Delta has a negative wage
		Epsilon has a positive wage and positive rent
		Epsilon is uniquely cost-minimizing
Rδ	r*	Alpha has a positive wage
		Delta has a positive wage and positive rent
		Epsilon has a positive wage and positive rent
		Delta is non-uniquely cost-minimizing
		Epsilon is non-uniquely cost-minimizing
r*	R*,δ	Alpha has a positive wage
		Delta has a positive wage and positive rent
		Epsilon has a positive wage and positive rent
		No cost-minimizing technique exists
R*,δ	Rα	Alpha has a positive wage
		Delta has a positive wage and negative rent
		Epsilon has a negative wage and positive rent
		No cost-minimizing technique exists

I plot extra profits for each process for each technique to demonstrate my claims about which technique is cost-minimizing. Figure 2 shows extra profits for each process at Alpha prices. Extra profits are zero for the three processes comprising the technique. The last corn-producing process can always pay extra profits for any scale factor, while the penultimate process can pay extra profits for any scale factor greater than that at the intersection of the Alpha and Delta wage curves and not exceeding the maximum scale factor for the Alpha technique. The Alpha technique is never cost-minimizing.

Figure 2: Extra Profits with Alpha Prices

Figure 3 plots extra profits for each process for the Delta and Epsilon techniques. Since four of the five processes in the technology are operated for each technique, four of the five processes obtain extra profits of zero for all scale factors between the limits for each technique. If the Delta technique were in operation at a scale factor greater than at the switch point between Delta and Epsilon, farmers would start to operate the fifth process, moving away from the Delta technique. If the Epsilon technique were in operation in this range, farmers would start to operate the fourth technique. A market algorithm would not coverge to any technique for a scale factor for the rate of profits greater than that at the switch point between Delta and Epsilon and not exceeding the maximum scale factor for the Alpha technique.

Figure 3: Extra Profits with Delta or Epsilon Prices

For a smaller markup in agriculture than in this fluke case, three interesting ranges of the scale factor exist where no technique is cost-minimizing. In the first, the Alpha, Delta, and Epsilon techniques can all pay positive wages and non-negative rents, with positive prices. In the second, only the Alpha and Delta techniques can pay positive wages and a non-negative rent. In the third, the Alpha technique can pay a positive wage, while the Delta technique cannot pay a positive rent.

For a larger markup than in the fluke case, the second interesting range of the scale factor has changed. The Delta technique can no longer pay a positive rent. Instead, the Alpha and Epsilon techniques can pay positive wages and non-negative rents, with positive prices.

Elsewhere

• An appreciation of Rob A. Bryer, a Marxist scholar of accounting.
• I stumbled upon a You Tube channel and web site for the International Marxist Tendency. I do not know what I think about variants of Trotskyism.
• Alessandro Roncaglia contrasts theories of crises in which tendencies exist in competitive markets towards equilibrium and in which such tendencies need not exist.
• Some have YouTube channels trying to explain the strange ideas that mathematicians have come up with:
• An Infinite Series episode explaining the existence of an infinite number of different size infinities. This PBS show was actually finite.
• Numberphile on the same topic.
• Josh is clear that we have to define how to extend our notation when talking about infinity.
• Bri the math guy on the Saint Petersburg Paradox. He is very much about encouraging the student.
• Not so serious.
• Grant Sanderson on Newton's method and fractals.

Economics, An Extraordinary Discipline

It seems to me that mainstream economists are socialized into ignorance and anti-scholarly norm. Plenty of economists exist that so many economists dismiss as 'fringe', and yet these dismissed economists excel on any scholarly criteria. It is not just that mainstream economists do not know of vast bodies of scholarship, produced by academics around the world. They also do not know that what they believe has long ago been shown to be without foundation. I have gone on like this before.

I might as well list the sort scholarly criteria I have in mind. I am thinking of economists with doctorates from well-known universities, who have published numerous journal articles and books from academic presses. They have edited such books and garnered many citations. They have supervised doctorate dissertations, where their students go on to other universities to do the same. They have been visiting professors at universities around the world, and maybe have occupied a named chair. They have been head of their department or otherwise provided successful service in academic administration. They have founded or co-founded journals and have been on the board of editors of various journals. They have provided policy advice and received festschrifts from those who have built on their work. They have written textbooks.

I should provide a small list of examples of scholars who rank on multiple criteria like the above:

• Paul Davidson
• John Eatwell
• Ian Steedman

I could expand this list, but I figure I do not want to embarrass too many with such fulsome praise.

This state of affairs may have something to do with abolishing the history of economic thought and any study of methodology. I do not expect recent mainstream economists to have read Smith's Wealth, Marx's Capital, or Keynes' General Theory. Sraffa's PoCbMoC is simultaneously an epoch-making book and virtually unknown. Fred Lee's A History of Heterodox Economics Challenging the mainstream in the twentieth century documents purges of economics departments.

I think mainstream economics are socialized to believe some questionable claims, based on rumors. For example, Marx was discredited by the marginal revolution. They cannot be expected to know of work in mathematical economics during the 1970s and 1980s formalizing Marx and empirical work that built on it. They'll believe Keynes was shown to be wrong by stagflation in the 1970s. The phrase 'bastard Keynesianism' is unknown, as are earlier theories of stagflation. The Arrow-Debreu-McKenzie model of intertemporal equilibrium is simultaneously the foundation of price theory and no longer central to economics.

But perhaps my perception of the sociology of economics is all wrong.

A Pattern For The r-Order Of Fertility With Intensive Rent And Markup Pricing

Figure 1: Wage Curves and Rent for an Example of Intensive Rent

The first man who, having enclosed a piece of ground, bethought himself of saying, 'This is mine', and found people simple enough to believe him, was the real founder of civil society. From how many crimes, wars and murders, from how many horrors and misfortunes, might not anyone have saved mankind by pulling up the stakes, filling in the ditch, and crying to his fellows, 'Beware of listening to this imposter; you are undone if you once forget that the fruits of the earth belong to us all, and the earth itself to nobody.' -- Jean Jacques Rousseau

1.0 Introduction

This post is a continuation of a previous example. Three commodities, iron, steel, and corn, are produced commodities. A single type of land exists, and three processes are available for producing corn on land.

The choice of technique corresponds to the selection of which processes are used in agriculture. Only the Alpha, Delta, and Epsilon techniques are feasibles for the given endowment of land and the requirements for use. Under Alpha, the land is only partially farmed. Land is not scarce and obtains no rent. Under Delta and Epsilon, the land is fully farmed, with two corn-producing processes being operated side-by-side. The second of these processes varies between Delta and Epsilon.

2.0 Choice of Technique

Prices of production are assumed to prevail, but markups over costs vary between industry and agriculture.

Figure 1 illustrates the wage and rent curves for this example. For a non-negative scale factor for the rate of profits up to the first switch point point, the Epsilon technique is cost-minimizing. At this switch point, the rent on land for Epsilon is zero, while it is positive for any smaller non-negative scale factor. This switch point is a fluke in that it is also the scale factor for the rate of profits at which the wage first turns positive for the Delta technique.

Between this first switch point and the switch point between Alpha and Delta, both the Alpha and Delta techniques are cost-minimizing. At the second switch point, the rent on land for Delta is zero. For a scale factor somewhat larger than at this switch point, no technique is cost-minimizing. Delta and Epsilon are feasible, but rent is negative for both of them. The wage for Epsilon is also negative. Alpha, on the other hand, is feasible, can pay a positive wage, and has a non-negative (zero) rent. Prices of iron, steel, and corn for Alpha are also positive in this range. Yet Alpha is not cost-minimizing.

Table 1: Cost-Minimizing Techniques

Lower Bound on r	Upper Bound on r	Techniques
0 percent	r*	Alpha has a positive wage
		Delta has a negative wage
		Epsilon has a positive wage and positive rent
		Epsilon is uniquely cost-minimizing
r*	r**	Alpha has a positive wage
		Delta has a positive wage and positive rent
		Epsilon has a positive wage and negative rent
		Alpha is non-uniquely cost-minimizing
		Delta is non-uniquely cost-minimizing
r**	rα, max	Alpha has a positive wage
		Delta has negative rent
		Epsilon has negative wage and negative rent
		No cost-minimizing technique exists

Table 1 summarizes these claims about which techniques are cost-minimizing for which ranges of the scale factor for the rate of profits. Figure 2 graphs extra profits for each process at Alpha prices. Extra profits are the difference bewteen the price of the commodity produced by the process and the costs for commodity inputs, rent, and wages. The costs of inputs of iron, steel, and corn incur the going rate of profits for that industry, including markups. Extra profits can be positive or negative. As a check on the calculations, one can maybe see from the graph that extra profits are zero, neither positive nor negative, for the three processes comprising the Alpha technique. For a non-negative scale factor less than at the first switch point, extra profits can be made at Alpha prices by growing corn with the fifth process in the technology. For a scale factor exceeding that at the second switch point, but below the maximum, extra profits are obtained by growing corn with the fourth process in the technology. Thus, Alpha is only cost-minimizing between the switch points.

Figure 2: Extra Profits with Alpha Prices

Figure 3 shows the extra profits obtained for each process for the Delta and Epsilon techniques, in the left and right panes respectively. Extra profits are only graphed for each for the range of the scale factor for the rate of profits for which both the wage and rent is non-negative. Since four of the five processes are operated in Delta, or in Epsilon, extra profits are non-zero for only one process in each graph. And you can see both techniques are cost-minimizing for the full range of the graphed scale factor in each case.

Figure 3: Extra Profits with Delta or Epsilon Prices

3.0 Conclusion

For a markup in agriculture slightly lower than for the fluke case, a range of the scale factor for the rate of profits exists in which the Delta and Epsilon techniques are both cost-minimizing. For a markup slightly higher, no such range, not even a single point, exists. For the whole range of the scale factor in which the Delta technique exhibits a positive rate of profits and a positive rent, the Alpha technique is also cost-minimizing. And when the Alpha technique is cost-minimizing, the class of landlords cannot exist.

Ludwig Von Mises Wrong On Capital Theory

We compare the conditions of two isolated market systems A and B. Both are equal in size and population figures, the state of technological knowledge, and in natural resources. They differ from one another only in the supply of capital goods, this supply being larger in A than in B. This enjoins that in A many processes of production are employed with which the output is greater per unit of input than with those employed in B. In B one cannot consider the adoption of these processes on account of the comparative scarcity of capital goods. Their adoption wouId require a restriction of consumption. In B many manipulations are performed by manual labor which in A are performed by labor-saving machines. In A goods are produced with a longer durability; in B one must abstain from producing them although the lengthening of durability is obtained by a less than proportionate increase in input. In A the productivity of labor and consequently wage rates and the standard of living of the wage earners are higher than in B. -- Ludwig Von Mises Human Action, Chapter XVIII, Section 4

The above seems to be simply wrong, insofar as any sense can be made of it. What does it mean to say the supply of capital goods is larger on one island than another? These are heterogeneous quantities. Presumably some capital goods would be only made on one island, and other capital goods might be made only on the other. Von Mises even almost recognizes this in his remark about "labor-saving machines". Even if the same types of capital goods were made on both islands, it need not be the case that the quantities are uniformly larger on one island. In adapting production to final output, some quantities of some capital goods might be larger on one island while quantities of other capital goods might be smaller.

But put these objections aside. Remarks about "output is greater per unit of input" and a "higher standard of living of the wage earners" might give us a tautological definition of "the supply of capita1 goods". To simplify and to consider, for the sake of argument, a case in which some of these terms have a sharp meaning, suppose both islands A and B are in a stationary equilibrium, what Von Mises considers an evenly rotating economy. Suppose all labor is homogeneous and net output is in the same proportions.

Is the adoption of labor-saving machines, as compared to manual labor, associated with a greater output per unit of labor input? Is the use of capital goods for a longer period of time also associated with a greater output per unit of labor input? We know from numerical examples, the answer to the second question is otherwise.

Von Mises is not operating with a tautological definition of more or less capital goods, in which a greater supply results in a greater standard of living. He also makes assertions about physical properties of these capital goods. And, as a simple matter of logic - that praxeology he goes on about - he is wrong about these entailments.

A Three-Technique Pattern With Intensive Rent And Markup Pricing

Figure 1: Wage Curves and Rent for an Example of Intensive Rent

1.0 Introduction

This post is one in a series exploring variations of an example from Antonio D'Agata (1983).

This post demonstrates that at least one of my fluke cases can appear in a model of intensive rent by varying a parameter specifying relative markups among sectors. This post is only a start of exploring the parameter space of relative markups in a specific numeric example of intensive rent.

Suppose the rate of profits is given, subject to the constraint that the ratios of the rate of profits in agriculture to that in other industries are as specified. Then the wage can be one of two distinct levels. When the wage is at the lower level, then the rent per acre is higher and vice versa. On the other hand, an increased wage, when it is at the lower level is associated with an increased rate of profits.

2.0 Technology, Requirements for Use, Endowments, and Relative Markups

Table 1 presents coefficients of production in an example from D'Agata (1983). Only one type of land exists, and three processes are known for producing corn on it. The scarcity of land is shown by the possibility of two corn-producing processes being operated side-by-side in the cost-minimizing technique.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Steel	Corn
	I	II	III	IV	V
Labor	1	1	1	11/5	1
Land	0	0	1	1	1
Iron	0	0	1/10	1/10	1/10
Steel	0	0	2/5	1/10	1/10
Corn	1/10	3/5	1/10	3/10	2/5

Following D'Agata, assume that one hundred acres of land are available and that net output consists of 90 tons iron, 60 tons steel, and 19 bushels corn. The net output is also the numeraire. All three commodities must be produced for any composition of net output. Table 2 lists the available techniques. Only Alpha, Delta, and Epsilon are feasible for these requirements for use. Not all land is farmed and only one corn-producing process is operated under Alpha. Two corn-producing processes are operated together under Delta and Epsilon.

Table 2: Techniques

Technique	Processes
Alpha	I, II, III
Beta	I, II, IV
Gamma	I, II, V
Delta	I, II, III, IV
Epsilon	I, II, III, V
Zeta	I, II, IV, V

In the non-competitive case, the relative markups in different industries are taken as given. Let the rates of profits be in proportions of s₁, s₂, and s₃, respectively.

3.0 Prices of Production

Prices of prodution can be defined for each technique. Each process operated in a technique contributes an equation in which the going rate of profits are obtained for that industry. The rate of profits in producing iron is s₁ r. In steel, it is s₂ r, and it is s₃ r in the corn-producing processes. As in past posts, I call r the scale factor for the rate of profits.

For example, the following equations specify prices of production for the Delta technique:

(p₁ a_1,1 + p₂ a_2,1 + p₃ a_3,1)(1 + s₁ r) + w a_0,1 = p₁

(p₁ a_1,2 + p₂ a_2,2 + p₃ a_3,2)(1 + s₂ r) + w a_0,2 = p₂

(p₁ a_1,3 + p₂ a_2,3 + p₃ a_3,3)(1 + s₃ r) + ρ c₃ + w a_0,2 = p₃

(p₁ a_1,4 + p₂ a_2,4 + p₃ a_3,4)(1 + s₃ r) + ρ c₄ + w a_0,3 = p₃

In these equations, p₁, p₂, and p₁ are the prices of iron, steel, and corn. The wage is denoted by w, and ρ denotes rent per acre. The techology provides the coefficients of production in this system of equation. The specification of the numeraire specifies another equation.

90 p₁ + 60 p₂ + 19 p₃ = 1

One degree of freedom remains. I take the the scale factor for the rate of profits as externally given in this post.

In solving the above system, a linear combination of the two equations for corn-producing processes can be taken such that rent drops out. Prices of iron, steel, and corn and the wage can be found first. Then one can obtain rent per acre from either one of the corn-producing processes. Only ranges of the scale factor are considered in which prices, the wage, and rent are non-negative.

4.0 Choice of Technique

A technique is cost-minimizing, at a given scale factor for the rate of profits, if it is feasible and extra profits cannot be obtained by operating any process outside the technique. In evaluating a process to see if extra profits can be obtained by running it, one uses the prices of production determined by the technique and the scale factor for the rate of profits. Extra profits in the processes comprising the technique are zero, neither positive nor negative.

Figure 2: Extra Profits for Alpha Prices

Figure 2 shows that Alpha is cost-minimizing only at the scale factor for the rate of profits. If the scale factor were less than this, extra profits would be gained by combining the last corn-producing process with the first. That is, starting from the Alpha technique, capitalists in agriculture would adopt the Epsilon technique. As demonstrated by the right pane in Figure 3, Epsilon is cost-minimizing for any positive scale factor for the rate of profits up to that at the switch point. Delta is cost-minimizing from a scale factor for the rate of profits where the rate of profits turns positive up to the switch point.

Figure 3: Extra Profits for Delta and Epsilon Prices

Above the switch point, the rate of profits for Alpha is positive up to a certain maximum. In this range, extra profits can be made by operating process IV. The Beta technique would be selected if this process entirely replaced the corn-minimizing technique in Alpha. But Beta is not feasible. On the other hand, processes III and IV are operated side-by-side in the Delta technique. But in this range for the scale factor for the rate of profits, Delta obtains a negative rent. So no cost-minizing technique exists for a scale factor for the rate of profits greater than that at a switch point.

Table 3: Cost-Minimizing Techniques

Lower Bound on r	Upper Bound on r	Techniques
0 percent	11.1 percent	Delta has a negative wage
		Epsilon has a positive wage and positive rent
		Epsilon is uniquely cost-minimizing
11.1 percent	43.9 percent	Delta has a positive wage and positive rent
		Epsilon has a positive wage and positive rent
		Delta is non-uniquely cost-minimizing
		Epsilon is non-uniquely cost-minimizing
43.9 percent	65.5 percent	Delta has negative rent
		Epsilon has a positive wage and negative rent
		Alpha has a positive wage
		No cost-minimizing technique exists

Table 3 summarizes this analysis of the cost-minimizing technique for this fluke case with markup pricing and intensive rent. Before the switch point, the wage frontier consists of both the wages curves for the Delta and Epsilon techniques. The wage frontier does not exist after the switch point. D'Agata's original example, with competitive markets, also illustrates the possibility of a range of the rate of profits with multiple cost-minimizing techniques away from a switch point. And he also notes the possibility of the non-existence of a cost-minimizing technique.

5.0 Conclusion

Fluke cases are associated with qualitative change in the analysis of the choice of technique. Such fluke cases can be brought about by technological improves, that is, changes in coefficients of production. This numerical example illustrates that one of these fluke cases can also be brought about changes in market power between agriculture and industry. In this fluke case, three wage curves intersect at a single switch point.

If agriculture does not have quite as much market power as in the example, a range of the scale factor for the rate of profits exists where both Alpha and Delta are cost-minimizing. For the higher wage, landlords cannot exist since land is not scarce and obtains no rent. This variation in whether or not land is scarce with variations in distribution is not about net output. The level and composition of net output is taken as fixed in the above analysis. The fluke case is associated with the disappear of the range of the rate of profits in which Alpha is cost-minimizing. If agriculture has more market power than in the example, Alpha is never cost-minimizing.

This particular example of markup pricing and intensive rent can be further explored. What other fluke cases exist? What happens if the iron and steel industries do not have the same market power?

Reference

• D'Agata, Antonio. 1983. The existence and unicity of cost-minimizing systems in intensive rent theory. Metroeconomica 35: 147-158'

Franz Fanon On The Need For People And Leaders To Learn

Optimism of the will leads me to hope that, with the misery we endure and cause, someday some people, including leaders of political movements and parties, will gain some wisdom. As I understand it, Frantz Fanon generalized principally from Algeria.

The settler is not simply the man who must be killed. Many members of the mass of colonialists reveal themselves to be much, much nearer to the national struggle than certain sons of the nation. The barriers of blood and race-prejudice are broken down on both sides. In the same way, not every Negro or Moslem is issued automatically a hallmark of genuineness; and the gun or the knife is not inevitably reached for when a settler makes his appearance. Consciousness slowly dawns upon truths that are only partial, limited, and unstable. As we may surmise, all this is very difficult. The task of bringing the people to maturity will be made easier by the thoroughness of the organization and by the high intellectual level of its leaders. The force of intellect increases and becomes more elaborate as the struggle goes on, as the enemy increases his maneuvers and as victories are gained and defeats suffered. The leaders show their power and authority by criticizing mistakes, using every appraisal of past conduct to bring the lesson home, and thus insure fresh conditions for progress. Each local ebb of the tide will be used to review the question from the standpoint of all villages and of all political networks. The rebellion gives proof of its rational basis and expresses its maturity each time that it uses a particular case to advance the people's awareness. In defiance of those inside the movement who tend to think that shades of meaning constitute dangers and drive wedges into the solid block of popular opinion, the leaders stand firm upon those principles that have been sifted out in the national struggle, and in the worldwide struggle of mankind for his freedom. There exists a brutality of thought and a mistrust of subtlety which are typical of revolutions; but there also exists another kind of brutality which is astonishingly like the first and which is typically anti-revolutionary, hazardous, and anarchist. This unmixed and total brutality, if not immediately combated, invariably leads to the defeat of the movement within a few weeks.

The nationalist militant who had fled from the town in disgust at the demagogic and reformist maneuvers of the leaders there, disappointed by political life, discovers in real action a new form of political activity which in no way resembles the old. These politics are the politics of leaders and organizers living inside history who take the lead with their brains and their muscles in the fight for freedom. These politics are national, revolutionary, and social and these new facts which the native will now come to know exist only in action. They are the essence of the fight which explodes the old colonial truths and reveals unexpected facets, which brings out new meanings and pinpoints the contradictions camouflaged by these facts. The people engaged in the struggle who because of it command and know these facts, go forward, freed from colonialism and forewarned of all attempts at mystification, inoculated against all national anthems. Violence alone, violence committed by the people, violence organized and educated by its leaders, makes it possible for the masses to understand social truths and gives the key to them. Without that struggle, without that knowledge of the practice of action, there's nothing but a fancy-dress parade and the blare of the trumpets. There's nothing save a minimum of readaptation, a few reforms at the top, a flag waving: and down there at the bottom an undivided mass, still living in the middle ages, endlessly marking time. -- Frantz Fanon, The Wretched of the Earth, Chapter 2: Spontaneity: its strengths and weaknesses

I think by 'violence' Fanon (and Georges Sorel before him) are talking about organized direct action.

Elsewhere

The First Of A Robert Paul Wolff Series Of Lectures On Marx

• Wolff raises the question of why Marx writes like he does in the first volume of Capital. The rest of Wolff's lectures:
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Seth Ackerman, in Jacobin, on Marxist crisis theory.
• Nathan Robinson pans Thomas Sowell.
• Unlearning Economics disagrees with Sabine Hossenfelder. (Her original video.)

Marx Against A Simple Labor Theory Of Value

Marx distinguishes, at least, between market prices, prices of production, and labor values. For the first volume of Capital, Marx assumes market prices bob around or tend to labor values, not prices of production. I think Marx nowhere says he is assuming the organic composition of capital does not vary among industries. He adopts the labor theory of value in when considering capitalist production as a whole so as to address the question of how owners of capital are able to regularly obtain a profit. He wants this explanation to apply when capitalists are not cheating each other. Nor are they cheating the workers.

I have noted before a few passages in the first volume where Marx demonstrates that he is making a simplification, to be dropped in volume 3. Consider the following:

"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 purity, and our observations not interfered with by disturbing circumstances that have nothing to do with the process in question. We know, moreover, that this reduction is no mere scientific process. The continual oscillations in prices, their rising and falling, compensate each other, and reduce themselves to an average price, which is their hidden regulator. It forms the guiding star of the merchant or the manufacturer in every undertaking that requires time. He knows that when a long period of time is taken, commodities are sold neither over nor under, but at their average price. If therefore he thought about the matter at all, he would formulate the problem of the formation of capital as follows: How can we account for the origin of capital on the supposition that prices are regulated by the average price, i. e., ultimately by the value of the commodities? I say 'ultimately', because average prices do not directly coincide with the values of commodities, as Adam Smith, Ricardo, and others believe." -- Marx, Capital, volume 1, last footnote in chapter 5.

Marx above distinguishes between what he will come to call prices of production and labor values. Labor values, for Marx, are important for the economy as a whole. But individual prices are attracted by prices of production, not labor values. Or again:

"The calculations given in the text are intended merely as illustrations. We have in fact assumed that price = values. We shall, however, see, in Book III, that even in the case of average prices the assumption cannot be made in this very simple manner." -- Marx, Capital, volume 1,last footnote in chapter 9, section 1

He is explicit above that the calculations are examples, not literally true. But the occassion of this post was when I stumbled across the following:

"The law demonstrated above now, therefore, takes this form: the masses of value and of surplus value produced by different capitals - the value of labour power being given and its degree of exploitation being equal - vary directly as the amounts of the variable constituents of these capitals, i.e., as their constituents transformed into living labour power.

This law clearly contradicts all experience based on appearance. Everyone knows that a cotton spinner, who, reckoning the percentage on the whole of his applied capital, employs much constant and little variable capital, does not, on account of this, pocket less profit or surplus value than a baker, who relatively sets in motion much variable and little constant capital. For the solution of this apparent contradiction, many intermediate terms are as yet wanted, as from the standpoint of elementary algebra many intermediate terms are wanted to understand that 0/0 may represent an actual magnitude. Classical economy, although not formulating the law, holds instinctively to it, because it is a necessary consequence of the general law of value. It tries to rescue the law from collision with contradictory phenomena by a violent abstraction. It will be seen later how the school of Ricardo has come to grief over this stumbling-block. Vulgar economy which, indeed, 'has really learnt nothing', here as everywhere sticks to appearances in opposition to the law which regulates and explains them. In opposition to Spinoza, it believes that 'ignorance is a sufficient reason'." -- Marx, Capital, volume 1, Chapter 9, Rate and mass of surplus value.

I would like to say volume 1, being the only volume of Capital Marx published in his lifetime, should be central in understanding his theory. The above is another demonstration in opposition to this view, at least as far as the analysis of capital goes. In a even larger project, Marx intended to "examine the system of bourgeois economy in the following order: capital, landed property, wage-labour; the State, foreign trade, world market." It is arguable that some of these steps were incorporated into Capital, but he never arrived at the last three.

No where in this post do I address Marx's curious rhetoric. He talks about real illusions, uses Hegelian terminology, and a lot of fierce irony.

As a throwaway comment, let me note one area where I think Marx is weak. Why do the workers consitute a universal class? Why did Marx think the next social revolution would be the last, ending humanity's prehistory? He provides a philosophical derivation of the role of the working class in such early works as Critique of Hegel's Philosophy of Right and The German Ideology. This derivation in tension with the empiricalism that one should build on the materialist theory of history. Since then, we have seen Lenin and Mao look at the role of the peasants in revolutions in less developed areas of the world. Franz Fanon looked at the global south and the revolutions accompanying decolonization. Michael Hardt and Antonio Negri talk about the 'multitude'. You may have noticed that I do not talk much about praxis. But do workers around the world still have a privileged position in hopes for social change?

Jeremy Rudd: "Why I hate economics"

Jeremy Rudd addresses the Cambridge Society for Economic Pluralism

Jeremy Rudd has written:

Mainstream economics is replete with ideas that 'everyone knows' to be true, but that are actually arrant nonsense. For example, 'everyone knows' that:

• aggregate production functions (and aggregate measures of the capital stock) provide a good way to characterize the economy's supply side;
• over a sufficiently long span - specifically, one that allows necessary price adjustments to be made - the economy will return to a state of full market clearing; and
• the theory of household choice provides a solid justification for downward-sloping market demand curves.

None of these propositions has any sort of empirical foundation; moreover, each one turns out to be seriously deficient on theoretical grounds¹. Nevertheless, economists continue to rely on these and similar ideas to organize their thinking about real-world economic phenomena. No doubt one reason why this situation arises is because the economy is a complicated system that is inherently difficult to understand, so propositions like these - even though wrong - are all that saves us from intellectual nihilism. Another, more prosaic reason is Stigler's (1983, p. 541) equally nihilistic observation that 'it takes a theory to beat a theory.'

Is this state of affairs ever harmful or dangerous? One natural source of concern is if dubious but widely held ideas serve as the basis for consequential policy decisions².

¹ For a useful brief against production functions, see Felipe and Fisher (2003); for the case against capital aggregates, see Brown (1980). The idea that the inherent stability of the economy is a concomitant of general-equilibrium theory is difficult to entertain seriously after giving Fisher (1983) close study; see Grandmont (1982) for some related macroeconomic arguments. Finally, Hildenbrand (1994) provides a sobering corrective to first-year demand theory.

² I leave aside the deeper concern that the primary role of mainstream economics in our society is to provide an apologetics for a criminally oppressive, unsustainable, and unjust social order.

The above quote is from a paper about inflations expectations. I wondered how far and on what grounds Rudd thinks this arrant nonsense extends. The talk in the video linked to the top of this post helps answer this question.