Profits Not Explained By Merit, Increased Risk, Increased Ability To Compete, Etc.

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 supports the illusion that returns to capital can come from markups over costs. The circular model demonstrates that profits come from the ability of a surplus product to be generated in production. It is not a matter of prices.

"Finally, when production is circular, profits depend first and foremost on the ability of the economic system to generate a surplus, that is, the possibility to produce commodities such as corn, cloth, wood, steel and chips to a greater degree than required, and secondly on the capitalists' power to appropriate a part of it (if workers also get a share of the surplus) or all of it (if workers earn only the subsistence wage). Profits thus emerge in the sphere of production and in the relative bargaining strength of capitalists in fixing real wages. They are not the merit of a particular input, firm, or industry. The profits of an individual are a claim on the surplus, a claim which is independent of the risk taken, the ability to compete, or the sector in which it produces. These qualities may explain why one capitalist can get more than others, but not why there are profits in the economic system. In a circular system, the generation of surplus is a necessary condition for the existence of profits. [Footnote]

[Footnote:] Saying that profits depend on the economy's capacity to generate a surplus does not deny the possibility that, at an individual level, a capitalist may attempt to increase their profits by raising prices. However, such increases can only be temporary under competitive conditions. The daring capitalist will eventually lose market share since they will attract other competitors, making their rate of profit converge to the general one..." -- Bellino and Brondino

I have a question about the history of economic thought. Ricardo had examples of the one-way model of production, for example, in his first chapter showing why a simple labor theory of value. The Ricardian socialists, as I understand it, often explained profits by capitalists being able to exert force to markup prices over costs. Does Bellino and Brondino's argument illustrate a superiority of Marx over the Ricardian socialists?

Another Hayekian Triangle Not Supporting The Austrian School

Figure 1: Hayekian Triangles for The Two Techniques

1.0 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

Input	Corn Industry		Ale Industry
	Process I	Process II	Process III
Labor	1 person-yr.	275/464 person-yrs.	1 person-yr.
Corn	1/10 kilo-bushels	113/232 kilo-bushels	2 kilo-bushels
Ale	1/40 kilo-liters	1/200 kilo-liters	2/5 kilo-liters
OUTPUTS	1 kilo-bushel	1 kilo-bushel	1 kilo-liter

Each column in the Leontief matrix and corresponding direct labor coefficient defines a production process. Each process exhibits constant returns to scale and requires a year to complete. Each of the produced commodities are available at the end of the year. All commodities enter, either directly or indirectly, into the production of all commodities and the economy is productive. Labor is directly required to operate each process.

This analysis takes the proportions in the net product as given. These proportions are specified by a column vector, as in Table 2. This numeraire is the net product or net output of Sraffa's standard system for the Alpha technique. This special case has implications for the shape of Hayekian triangles, as seen below.

Table 2: The Numeraire

Commodity	Amount
Corn	d1 = (337 - 29 (29)1/2)/455 kilo-bushels
Ale	d2 = (17 + 25 (29)1/2)/1,820 kilo-kiters

3.0 The Choice Of Technique And Hayekian Triangles

The usual analysis of prices and production and the choice of technique yields the wage curves in Figure 2 below. The Beta technique is cost-minimizing for a low interest rate. The Alpha technique is cost-minimizing for a higher interest rate.

Figure 2: Wage Curves for the Two Techniques

Figure 1, at the top of this post, shows the Hayekian triangles at the single switch point. Around this switch point, a lower interest rate does extend the structure of production. But it does not require more savings to achieve that extension.

4.0 Conclusion

The above has constructed Hayekian triangles not consistent with Austrian business cycle theory. A coordinated state does not necessarily rotate the Hayekian triangle to have a longer structure of production with less consumption (more savings).

Paul Kengor's The Devil and Karl Marx

Paul Kengor's The Devil and Karl Marx: Communism's Long March of Death, Deception, and Infiltration is a stupid and ignorant book. Kengor is particularly keen to chronicle atheist attacks from Marx and communists on religion.

Juvenile Literary Works from Marx

Kengor starts with a poem that Marx wrote when he was 19. Marx envisions himself, I guess, as a ferocious violin player, inspired by the devil. Apparently, Marx was a fan of Goethe. Kengor never uses the phrase 'sturm und drang'. He goes on about some other poems and a play of Marx's. Kengor thinks that Marxists unjustly ignore these early works. They are in the first volume, though, of the Marx-Engels Collected Works.

Some Bits and Pieces from the Lives of Marx and Engels

The second section, after this prelude, is about Marx and Engels. It has little to say about Marx's ideas. He calls Marxism utopian, seeking a heaven on earth. He says nothing about distinction between scientific and utopian socialism.

Kengor, in this part of the book has a lot to say about Marx's life. When discussing his movement among countries, he does not even mention that nations kept on kicking him out. Kengor hops around in chronology. He is big on Marx not earning a living while studying and agitating. Also, Marx had poor bathing habits.

He brings up Bruno Bauer several times. But he does not mention that The Holy Family mocks Bauer. When bringing up Mikhail Bakunin, Kengor does mention the later falling out of Bakunin and Marx. Does Marx's intolerance in splits in the First International have something to do with Lenin's behavior? With Stalin?

Inasmuch as Kengor even discusses Marx's work, he stops at 1848, with the Communist Manifesto. The quotation about religion as the "opiate of the people" is from Marx's Critique of Hegel's Philosophy of Right, from 1944. Marx's argument is for changing material conditions so that religion will no longer be needed as "the sigh of the oppressed creature". This idea is not inconsistent with arguments for atheism. Such idealist, superstructural arguments are beside the point, though. The context of this well-known phrase from Marx is over Kengor's head.

Here is all Kengor has to say about Capital:

"Marx had wasted over two decades writing Das Kapital, a long, ridiculous tome, a waste of money as well as time. He had initially received a three hundred dollar advance for the book, but extended over twenty-three years of drawn-out writing, it equated to a little over a dozen dollars a year.

The Bolshevik War on Religion

Kengor does not connect the ideas of Marx to Lenin and events in the Soviet Union. At a more personal level, I do not know that Marx was responsible for what happened to his children after his death, including the suicides of two daughters. I had not known Lenin spoke at Paul Lafarge's funeral. Kengor brings up Bukharin several times, but does not mention that he was a victim of Stalin's show trials. I do not think Engels not getting married to the women that he slept with is on the same moral plane as the tortures in communist prisons in eastern and central Europe.

Excerpts from the House Un-American Activities Committee

I do not know why I should care about testimony in the 1940s and 1950s to the House Unamerican Activities Committee. I was under the impression that a united front and a popular front are different concepts. The former is all non-facist forces, while the latter is all leftist forces. Anyways, Kengor does not discuss this distinction or even why it is a proplem for the Communist Party to work with Christians, and specifically Catholics, for specific reasons. Yes, the Communist Party was atheist. Kengor barely mentions the relationship of Catholics to Franco, and only in the context of what communists say. He only mentions Hitler in the context of turns in the communist party line with the Hitler-Stalin pact and then the German invasion of the Soviet Union. He has nothing to say about how this has anything to do with Marx's ideas. And he doesn't really discuss communist sectarian activities in taking over front groups. I am not surprised that communists were sometimes deceitful.

Various Intellectuals

The fifth part consists of two chapters. Kengor writes a bit about the life of the occulist Aleister Crowley, the New York Times's reporter Walter Duranty (who believed what the Soviets told him in the 1930s), the gay activist Harry Hay, Wilhelm Reich, Walter Benjamin, and Kate Millett. Why this selection? Perhaps because snippets of their lives are suitable for ad hominem. Kengor is fairly candid that Crowley does not have much to do with Marxism or communism, for example.

We have another time Kengor says he does not know what he is talking about:

"Trying to discern the inane and impentrable ideas of the men of the Frankfurt School is a soul-crushing exercise in futility. One must spend years scouring pages and footnotes of thick volumes (mostly in untranslated German) trying to arrive at a vague flickering of understanding at what in the devil's name these madmen were thinking about. It would be bad enough if this venture was simple a waste of one's time - especially given the sacrifice of more edifying reading - but what is worse is the strain and toxicity to the intellect and the soul. One is struck again and again at how some Godless intellectuals (especially German ones) can descend into such rank intellectual vacuity, ambiguity, and downright stupidity..."

If I thought Kengor was a person of good-will, I might emphasize here.

Conclusion

The single chapter in the conclusion section neither summarizes the book nor follows from what comes before. We get complaints about Obama's totalitarianism, gay marriage, the Frankfurt school, critical theory, Gramsci, relativism, and cultural Marxism. We also get echos of Fulton Sheen and Pope Pius X's 1907 encyclical on modernism. Apparently, Kengor has never heard of post-modernism. Kengor does not even know what he has covered in the book:

"In this book, we have looked at key figures of the Frankfurt School, including Georg Lukacs, Walter Benjamin, The Sexual Revolution's Wilhelm Reich, and (among others) Herbert Marcuse..."

No, he has not discussed Lukacs or Marcuse, even to the extent of saying something about some moments in their lives.

Some Overall Comments

The book has lots of redundancy. Kengor distinguishes between socialism and communism. I do not see why the book should go through the same quotations from the same papal encyclicals again to see that the Catholic Church opposed both communism and socialism.

The references are odd. For example, if I see a discussion of Darkness at Noon, I expect a reference to Koestler's novel, not a book by a historian. I would hope for more than extracts from Wikipedia and from the "About" section from certain web sites.

It fails at the level of the individual sentence. Consider, "Sheen noted that whereas Karl Marx called religion 'the sigh of the oppressed creature, Sheen saw communism as the sigh of the oppressed creature." Is Sheen noting how Sheen saw communism? At one point, Kengor has Manning Johnson testifying to the HUAC that "this was 'the extension of the hand of friendship and cooperation to the church, while in the other hand holding a dagger to drive through the heart of the church.'" But then, "the outstretched hand concealed a knife." Which metaphor do you want?

Adam Smith, David Ricardo, And The Labor Theory Of Value

1.0 Introduction

I resolutely am not commenting on unhappy current events.

Smith and Ricardo thought a (simple) LTV was not applicable to capitalism. Prices do not tend to or orbit around labor values. At least that is their claim.

Ricardo had more to say about the LTV.

This argument is not new. Smith confined the LTV to a supposed "early and rude state of society which precedes both the accumulation of stock and the appropriation on land" (WoN, book 1, chapter 6; see also book 1, chapter 8). Ricardo thought this was sloppy reasoning. The LTV does not become nonapplicable merely because of the accumulation of capital and of the division of society into capitalists and workers (Principles, 3rd edition, chapter 1, section III).

2.0 Technology

A simple model of circulating capital can be used to make Ricardo's point. Let a₀ be a row vector of direct labor coefficients. Let A be the Leontief input-output matrix. An element of a₀ and the corresponding column of A specify the labor time and the capital goods needed to operate a process to produce one unit of the output of that industry. The technology satisfies the following common assumptions:

• Some labor is needed to operate every process in each industry.
• Constant returns to scale prevail.
• Each commodity enters, directly or indirectly, into the production of every commodity. Iron, for example enters indirectly into the production of automobiles if iron is needed to produce steel and steel is needed to produce cars.
• The technology is productive. For some level of operation of the processes for each industry, some commodities are left over after reproducing the capital goods used in producing them.

Now for the unusual special case. Let λ be the largest eigenvalue of the Leontief matrix. This eigenvalue is also known as the Perron-Frobenius root of the Leontief matrix. Assume that the vector of direct labor coefficients is a corresponding left-hand eigenvector:

a₀ A = λ a₀ (Display 1)

3.0 Labor Values

Let v be the row vector of labor values. By definition, labor values satisfy the system of equations in Display 2:

v A + a₀ = v (Disp. 2)

The total labor to produce a commodity is the sum of the labor values of the capital goods used in that industry and the direct labor coefficient.

Under the special case assumption, labor values are a multiple of direct labor coefficients:

v = (1/(1 - λ)) a₀ (Disp. 3)

One can check this solution by merely plugging it into the solution in Display 2:

(1/(1 - λ)) a₀ A + a₀ = (λ/(1 - λ)) a₀ + a₀ = (1/(1 - λ)) a₀ (Disp. 4)

Since the above is a one-line proof, I thought I would include it. Labor values are also an eigenvector of the Leontief matrix.

4.0 Prices

Under the usual assumptions, the row vector p of prices satisfies the system of equations in Display 5:

p A (1 + r) + w a₀ = p (Disp. 5)

The scalar w is the wage, and r is the rate of profits.

Let R be the maximum rate of profits, obtained when the wage is zero, and the workers live on air. For the special case, the solution to the price system is quite simple:

R = (1/λ) - 1 = (1 - λ)/λ (Disp. 6)

r = R (1 - w) (Disp. 7)

p = v (Disp. 8)

One can check this solution by plugging it into the system of equations in Display 5.

So Ricardo was correct. The LTV could apply to capitalism under a special case. The failure of the LTV to apply in general is because those special case conditions cannot be expected to arise.

5.0 Conclusion

Ricardo had a point. As any ent would tell you, Smith was too hasty. The simple conflict between the wage and the rate of profits in Display 7 applies more generally than the above special case. The LTV, even when it is not valid, points to theories of the returns to capital.

I suppose reconstructing arguments between Ricardo and Smith with modern economics may conflict with how some historians do history. Even saying that Smith was analyzing capitalism could be considered an anachronism.

Roger Garrison On The Inadequacy Of Hayekian Triangles

Hayek introduced his triangles in his lectures for his book Prices and Production. The first edition was in 1931 and the second in 1935. He attempted a more general treatment of capital theory in his 1941 book, The Pure Theory of Capital. I want to claim that Hayek knew that he could not draw his triangles under these more general assumptions. And that he knew that capital theory needed more development than he was able to give.

Jack Birner knows this, although I do not know a reference off-hand. I want to say that Roger Garrison knows this too, that he presents his diagrams of trianlges in his 2001 book, Time and Money: The Macroeconomics of Capital Structure, mainly for their heuristic and pedagogical value. He says something like this in the following:

"...The widely recognized but rarely understood Hayekian triangle, introduced in his 1931 lectures at the London Schoold of Economics, were subsequently published (in 1931 with a second edition in 1935) as Prices and Production. The triangle, described in the second lecture ... is a heuristic device that gives analytical legs to a theory of business cycles first offered by Ludwig von Mises... Triangles of different shapes provide a convenient but highly stylized way of describing changes in the intertemporal pattern of the economy's capital structure.

In retrospect, we see that the timing of Hayek's invitation to lecture at the London School of Economics takes on a special significance. We learn from the preface of the subsequent book that had the invitation come earlier, he couldn't have delivered those lectures; had it come later, he probably wouldn't have delivered them.

(The invitation) came at a time when I had arrived at a clear view of the outlines of a theory of industrial fluctuations but before I had elaborated it in full detail or even realized all the difficulties which such an elaboration presented. (Hayek, [1935] 1967: vii)

Hayek mentions plans for a more complete exposition and indicates that his capital theory would have to more developed in much greater detail and adapted to the complexities of the real world before it could serve as a satisfactory basis for theorizing about cyclical fluctuations.

A decade after the London lectures, the more complete exposition took form as The Pure Theory of Capital (1941). In this book Hayek fleshed out the earlier formulations and emphasized the centrality of the 'capital problem' in questions about the market's ability to coordinate economic activities over time. The 'pure' in the title meant 'preliminary to the introduction of monetary considerations.' Through some 450 pages in length, the book only achieved only the first half of the original objective. The final sixty pages of the book did contain a 'condensed and sketchy' (p. viii) treatment of the rate of interest in a monetary economy, but the task of retelling the story in Prices and Production in the context of the Pure Theory was put off and ultimately abandoned. The onset of the war was the proximate reason for cutting the project short; Hayek's exhaustion and waning interest in business-cycle issues - and his heightened interest in the broader issues of political philosophy - account for his never returning to the task. In later years, he acknowledged that Austrian capital theory effectively ended with his 1941 book and lamented that no one else has taken up the task that he originally set for himself (Hayek, 1994: 96).

More fully developing the Austrian theory of the business cycle came to be synonymous with writing the follow-on volume to Hayek's Pure Theory. Many a graduate student has imagined himself undertaking this very project, only to abandon the idea even before the enormity of the task was fully comprehended. Thus, while the comparatively simple relationships of capital-free Keynesian theory captured the attention of the economics profession, the inherently complex relationships of Austrian theory languished.

Time and Money is not the sequel to Hayek's Pure Theory. Rather, the ideas and graphical construction in the present volume take the original Hayekian triangle of Prices and Production to be the more appropriate point of departure for creating a capital-based macroeoconomics. The trade-off between simplicity and realism is struck in favour of simplicity. Hayek's triangles allow us to make a graphical statement that there is a capital structure and that its intertemporal profile can change. This statement enables the Austrian theory to make a quantum leap beyond the competing theories that ignore capital altogether or that treat capital as a one-dimensional magnitude." -- Roger Garrison (2001: 10-11).

I think J. R. Hicks' Value and Capital is an attempt to formalize some ideas from Hayek's capital theory. Garrison does not mentioned the possibility that maybe the formalization of a general theory along Austrian lines is impossible.

Anyways, here is an attempt to fairly shorten the quotation:

Hayek ... indicates that his capital theory would have to more developed in much greater detail ... before it could serve as a satisfactory basis for theorizing about cyclical fluctuations... The final sixty pages of [Hayek 1941] did contain a 'condensed and sketchy' (p. viii) treatment of the rate of interest in a monetary economy, but the task of retelling the story in Prices and Production in the context of the Pure Theory was put off and ultimately abandoned... More fully developing the Austrian theory of the business cycle came to be synonymous with writing the follow-on volume to Hayek's Pure Theory... Time and Money is not the sequel to Hayek's Pure Theory. Rather, the ideas and graphical construction in the present volume take the original Hayekian triangle of Prices and Production to be the more appropriate point of departure... -- Roger Garrison (2001: 10-11).