I am not a biologist. In this world of 8 billion people, not all are men or women, where a man has XY chromosomes and a woman has XX chromosomes.
When fraternal twins are conceived, these two balls of cells may clump together, and one person develops. Such a human chimera may have a mixture of cells that are both XX and XY.
The SRY gene may cross over from a Y to an X chromosome. And so some men may grow up with XX chromosomes.
Klinefelter syndrome occurs in men with XXY chromosomes. Men can also have XYY or XYYY chromosomes. Women can have XXX chromosomes.
But genetics is not destiny. A long road is traversed in growing up. Sports, such as the Olympics, is about finding exceptional people who can delight us with their performances. Caster Semenya is one example, who apparently is a woman with androgen insensitivity. As I understand it, she is only one case in which the International Olympic Committee has wrong-footed itself.
In Las Salinas, in the Dominican Republic, some girls grow up to be men. Basically, some physical developments that occurred for me in the womb occur there during puberty. For some reason, this condition is more common there than elsewhere.
This post is inspired by sad current events in the United States. I have tried to concentrate above on biology. One can read Flannery O'Connor to get a Catholic sensibility on another possible complication. Deidre McCloskey is an economist who has an interesting memoir. Judith Butler supposedly is clearer in lecturing or talking about the complexities of gender than she is in her writing.
Selected ReferencesI find certain stories of achievements in mathematics and science intriguing. In some of those I select, much that came before was overthrown. At any rate, these are stories about creations of the human mind that are tough to wrap your head around. I only claim to understand the last story.
Fermat's last theorem lacked a proof for three and a half centuries. When he first saw the theorem as a school boy, Andrew Wiles decided he was going to be a mathematican when he grew up and prove it. And he did.
I have written about the classification of finite simple groups before.
The twentieth century saw some amazing results in logic, set theory, and model theory. Gödel's incompleteness theorem, computability, the axiom of choice, the (generalized) continuum hypothesis, and the Löwenheim-Skolem theorem are very puzzling topics. Perhaps the question of the truth of the continuum hypothesis is, after last year, closer to being solved, whatever that might mean. As I understand it, both the assertion and denial of the continuum hypothesis are consistent with the axioms of Zermelo Fraenkel set theory. So its resolution would take agreement on additional axioms. Apparently, David Asperó and Ralf Schindler showed last year that one such proposed axiom implied another. I doubt I will ever understand this. I suppose perplexity at how maths mean goes back to, at least, the invention of non-Euclidean geometry.
In physics, quantum mechanics and the theory of relativity provide amazement. Their very existence is a surprise. Newtonian mechanics seemed to be the most empirically well-confirmed theory in all of science. Then, in the first couple of decades of the twentieth century, Newton was shown to be incorrect in his basic picture of the universe. At least, this is something like how Karl Popper saw it. Relativity has the surprising implication that time travel is possible in a rotating universe. Gödel showed this when he wanted to provide something for a festschrift for his friend Albert Einstein. I gather Bell's theorem shows that quantum mechanics and a limitation imposed by general relativity cannot both be right. I gather that Bell has been experimentally verified by astronomers looking at radiation passing through gravitational lenses formed from intermediate galaxies.
Political economy provides at least one story like the above. I refer to Sraffa's disproof of marginalism half a century ago.
ReferencesKarl Marx died on 14 March 1883. Less than 15 people attended his funeral, and Engels gave an eulogy. Marxists existed, a century later, in every country on the face of this planet, and most had political parties, some powerful, that claimed to follow Marx. How did this change from obscurity to world-wide recognition come about? What did Marx have to say that was so persuasive?
If economics were a serious subject, these questions would be explored within academic economics departments. And some universities in the United States can be taken seriously. But, as I understand it, one cannot expect mainstream economists in North America to be able to discuss these questions. One would need to be interested in economic history and the history of economics, for example, to have an informed take. Mainstream economics, I gather, are trained to deprecate such subjects. Following on the work of such economists as Donald Harris, Michio Morishima, and John Roemer, I would like those exploring Marx's economics to know some linear algebra, as well.
I suppose some might justify this incapacity and ignorance by asserting that Marx just did not have an impact on academic economics, at least in the leading schools. I am not sure this is true. Mainstream economists had to re-invent some of Marx. Consider Michal Kalecki's independent development of Keynesianism. Compare and contrast growth models, such as the Harrod-Domar and von Neumann models, with Marx's schemes of simple and expanded reproduction at the end of volume two of Capital. Employment multipliers in Leontief input-output analysis are labor values.
One can also argue the importance of Marx in the promulgation of marginalism. Eugen von Böhm-Bawerk and Philip Wicksteed explicitly argued against Marx in promoting their theories. John Bates Clark stated that his theories showed the possibility of classes living in harmony. In this sense, the erroneous doctrines that are taught today are strongly influenced by Marx, albeit in a reactionary way.
If Marx is not important to economics, why must we keep on having these purges of economics departments? Of course, those doing the purges, in their wide and deep ignorance, cannot identify a Marxist, no matter how often they look for ghosts under their bed at night.
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| Figure 1: The Wage Frontier for a Numeric Example of a Real Wicksell Effect of Zero |
Theorem: Consider a model of an economy in which n commodities are produced by means of commodities. Let Alpha be a technique in which each of the n commodities is produced by a fixed-coefficients, constant-returns-to-scale process. Suppose the Beta technique differs from Alpha only in the process operated in the nth industry. For simplicity, assume all n commodities are Sraffian basics in both techniques. Let both techniques undergo technical change, with only labor coefficients varying through time. The labor coefficients for Alpha decrease at the rate σ1 or σ2, while the labor coefficient for the nth industry in Beta decreases at the rate σ2. Then the wage curves for Alpha and Beta intersect at a rate of profits of zero at time t1 if
σ2 t1 = σ1 t1 - ln[ -z1/z2]
where z1 is a linear combination of the values of the labor coefficients at time zero in the Alpha technique that decrease at rate σ1, and z2 is a linear combination of the remaining labor coefficients at time zero in the Alpha technique and of the labor coefficient at time zero in the Beta technique for the process producing the nth commodity.
Proof: Left as an exercise for the reader.
I consider my proof to be inelegant. This theorem is related to my previous theorem. (I've updated that post.)
Thee theorem gives an explicit condition for the wage curves for the Alpha and Beta techniques to intersect at a rate of profits of zero percent at time t1. Suppose a switch point also exists at this time at a positive rate of profits that is less than the minimum of the maximum rate of profits for the Alpha and Beta techniques.
Around the switch point, a variation in the rate of profits or the wage is associated with no change in the quantity of labor hired per unit of net output economy as a whole.
The wage frontier illustrates for a numeric example with three produced commodities and two processes available in each industry. The techniques mentioned in the theorem are labeled "Gamma" and "Delta" in this example. Before the illustrated time in the example, this switch point is associated with a negative real Wicksell effect. Less labor is employed, per unit output of net product, at a higher wage around the switch point. After this time, it is associated with a positive real Wicksell effect. More labor is employed in the economy as a whole, given net output, at a higher wage around the switch point. The theorem gives conditions for capital-reversing to emerge, given another switch point on the frontier for the mentioned techniques.
| The Italian Post Keynesian Seminar on Garegnani |
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| Figure 1: The Wage as Functions of Employment by Industry |
This post repeats a common theme of mine. It builds on an example I have previously gone on about. I use this example to graph, given the wage, the amount of labor firms would like to employ in each industry, per unit of gross output in each industry. These graphs are derived for an economy in which three commodities are produced: iron, steel, and corn. I also graph the amount of labor firms would like to employ across all industries, given that the net output of the economy consists of a unit quantity of corn. The value of this function is called an employment multiplier.
No doubt, in actual capitalist economies, some firms in some places have market power in hiring workers. Workers incur search costs in trying to find jobs whose requirements match well with their skills. Owners and managers of firms face principal agent problems. Owners, managers, workers, etc. have their own information sets at any given instant, and doubtless they are not all identitical. But, before exploring these complications, if would be nice if so many leading mainstream economists were not clueless about price theory. One might be more interested in institutions and the history of the labor movement.
2.0 TechnologyConsider an economy in which three commodities, iron, steel, and corn, are produced. Two processes, as seen in Table 1 are available to produce each commodity from inputs of labor, iron, steel, and corn. Each process exhibits constant returns to scale and takes a year to produce. Each column in Table 1 specifies the inputs needed to produce a unit quantity of the commodity produced by that process. This is a model of circulating capital. All physical inputs in each process are used up in the course of the year in producing the commodity output by that process.
| 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.
| 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 |
Each technique is represented by coefficients of production. For the Alpha technique, let a0, α be a three-element row vector representing the labor coefficients, and let Aα be the 3 x 3 Leontief matrix for this technique. The first element of a0, α, (1/3) person-years per ton, represents the labor input needed to produce a ton of iron. The first column of Aα represents the inputs of iron, steel, and corn needed to produce a ton of iron. A parallel notation is used for the other seven techniques.
Suppose the net output of the economy is a bushel corn. A bushel corn is also the numeraire.
3.0 The Price SystemPrices of production are defined to be constant spot prices that allow the smooth reproduction of the economy. Suppose Alpha is the cost-minimizing technique. Let p be the three-element row matrix designating the prices of iron, steel, and corn. I make the assumption that markets are such that the rate of profits in the iron, steel, and corn industries are (r s1), (r s2), and (r s3), respectively. Suppose S is a diagonal matrix with the obvious elements along the diagonal, and I designates the identity matrix. Then prices of production satisfy the following system of equations:
pα Aα (I + r S) + wα a0, α = pα
I choose a bushel of corn to be the numeraire. If e3 is the last column of the identity matrix, the following equation specifies the numeraire:
pα e3 = 1
As is not surprising, the above system of equations has one degree of freedom. One can solve for the wage, wα(r), as a function of the scale factor for the rate of profits, r. The wage curve is a downward-sloping curve that intercepts both the axis for the wage and the scale factor at positive values. A similar function can be derived the other techniques, and they can be graphed in the same diagram.
4.0 The Choice of TechniqueFigure 2 graphs the wage curves for the techniques that are cost-minimizing for some feasible wage, given markups by industry. The outer envelope is the wage frontier. The cost-minimizing technique at a given wage is the technique with the right-most wage curve at that wage. The cost-minimizing techniques at each wage and the switch points between techniques are noted on the figure.
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| Figure 2: The Wage Frontier |
5.0 Wages and Employment
For each technique, one can calculate the employment required across all three industries to produce a net product of a bushel corn. In these calculations, the processes in a technique are operated at a level so as to replace the iron, steel, and corn used up in producing that bushel of corn. Since which technique is cost-minimizing at a given wage is shown above, one can plot the wage against employment, as in Figure 3. In some sense, this is a macroeconomic labor demand function. On the other hand, if one does not get well-behaved supply and demand functions for labor, one might want to say that supply and demand does not apply here. Notice the switch point between the Gamma and Delta techniques. Around this switch point, a higher wage is associated with firms wanting to employ more workers.
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| Figure 3: The Wage as a Function of Employment Across Industries |
The labor coefficient in each industry is specified along with each technique. Figure 1, at the top of this post, graphs employment in each industry per unit gross product. Here, a higher wage around the switch point between the Gamma and Delta techniques is associated with firms wanting to employ more labor per bushel corn produced as gross output in the corn industry. This reverse substitution of labor can occur around a switch point in which capital-reversing does not occur and vice versa.
6.0 The Effects of MarkupsIn the above story, the markup in the steel industry is less than the markups in the iron and corn industries. One might think of this as a deviation from competitive markets. In this conception, markets are competitive when markups are unity in all industries.
Figure 4 illustrates how the sequence of techniques along the wage frontier varies with the markup in the steel industry. The result of the specific markups used above is that the Beta technique is cost-minimizing at a low enough wage. That is the second process in the corn-producing industry recurs. The first corn-producing process also recurs.
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| Figure 4: The Variation of the Wage Frontier with the Markup in the Steel Industry |
If those investing in the iron and corn industries are able to persistently impose even greater barriers to entry, the markup in the steel industry would be even lower. Evenually, the Alpha and the Gamma techniques would not be cost-minimizing at any wage. Neither process in the corn industry would recur. The instance of capital-reversing would also be destroyed. The same follows if the markup in the steel industry exceeds the markups in the iron and corn industry sufficiently.
7.0 ConclusionAs far as I know, mainstream economists have been teaching what has been known to be, at best, incorrect for half a century. Are they fools or knaves? What accounts for this extraordinary intellectual bankruptcy?
| Bob Murphy On Infinity |
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| Figure 1: The Wage Frontier for a Numeric Example |
Theorem: Consider a model of an economy in which n commodities are produced by means of commodities. Let Alpha be a technique in which each of the n commodities is produced by a fixed-coefficients, constant-returns-to-scale process. Suppose the Beta technique differs from Alpha only in the process operated in the nth industry. For simplicity, assume all n commodities are Sraffian basics in both techniques. Let both techniques undergo technical change, with only labor coefficients varying through time. The labor coefficient for the nth industry declines at the rate ρ for the Alpha technique:
aα0, n(t) = aα0, n(0) e-ρ t
The corresponding labor coefficient for the Beta technique declines at the rate σ:
aβ0, n(t) = aβ0, n(0) e-σ t
Then the wage curves for the Alpha and Beta techniques intersect at time t0 at a rate of profits of -100 percent if the following condition holds:
σ t0 = ρ t0 - ln[ aα0, n(0)/aβ0, n (0)]
Proof: Left as an exercise for the reader.
I arrived at this theorem from a somewhat more general setting. Assume that in each industry, M processes are available to produce the corresponding commodity, at each instant in time, and that each of these processes has constant returns to scale. Each of these processes requires a positive input of labor. Consider the M techniques (out of Mn techniques) in which each commodity is produced, and the mth process in each industry is operated for the mth technique. Suppose Harrod-neutral technical change occurs for each one of these techniques, with the rate of increase of labor productivity varying among the techniques.
The theorem gives an explicit condition for the wage curves for the Alpha and Beta techniques to intersect at a rate of profits of -100 percent at time t0. Suppose a switch point also exists at this time at a positive rate of profits that is less than the minimum of the maximum rate of profits for the Alpha and Beta techniques. At that time, one has:
aα0, n(t0) = aβ0, n(t0)
Around the switch point, a variation in the rate of profits or the wage is associated with no change in the quantity of labor hired per unit of gross output in the nth industry.
The wage frontier illustrates for a numeric example with three produced commodities and two processes available in each industry. The techniques mentioned in the theorem are labeled "Gamma" and "Delta" in this example. Before the illustrated time in the example, this switch point is associated with a forward substitution of labor, in which less labor is employed in the nth industry per unit output of gross product of that industry. After this time, it is associated with a negative substitution of labor, in which increased employment per unit of gross product is associated with an increased wage around the switch point.
The ability to explicitly state mathematical theorems is a step forward for my approach of using fluke cases to partition parameter spaces associated with models of prices of production.
A number of years ago, I was in the subway station under Times Square in New York City. I must have looked lost, because this fellow came up to me and asked me where I was going.
I said, "A bookstore, The Strand. I like to see what they have in their economics section. I am trying to decide if I should take the cross-town shuttle and go south from Grand Central."
He said, "I am an economist myself. You can have this subway map." And he handed me a map of the tube in London.
"This map is inaccurate."
"Of course. A map on a one-to-one scale would not be useful."
"I don't mean that. Here in New York, there is no circle line."
"It's called 'abstraction'. We don't care about curves between stations that do not matter."
"But this is just wrong for here."
"All models are wrong. Some are useful."
I finally saw I should just thank him, take the map, and back away. As I did, I heard him mutter to himself, "That guy does not understand scientific methodology."
I trust mainstream economists to help gather data for, for example, Simon Kuznets' National Income and Product Accounts and, for some, to provide guidance among data sources.
To the common reader, the distinctions among old Keynesianism, new Keynesian, and Post Keynesianism might seem confusing. You might find these are political doctrines, with broad agreement among their followers. Governments should run deficits in periods of sustained unemployment. Maybe sometimes fiscal policy should be more emphasized over monetary policy. After all central banks cannot stimulate the economy by lowering interest rate when it is zero. In an inflationary period, central banks can fight it by raising interest rates, although this is a blunt, crude tool. What is there to argue about?
Yet economists argue. Kelton (2020) has a popular book emphasizing that, given how money and banks work, governments need not be concerned with balancing their budgets because of a fear that the money to pay for it will not be there. And then Clinton's Secretary of the Treasury and Obama's director of the National Economic Council responds to Kelton getting publicity:
"I am sorry to see the [New York Times] taking MMT serious as an intellectual movement. It is the equivalent of publicizing fad diets, quack cancer cures or creationist theories" -- Larry Summers
Those who follow MMT have seen the claim that it is revolutionary and that mainstream economists do not understand money. Paul Krugman, a leading mainstream economist, reacts:
"...And I will say that I am, to use the technical term, pissed at this kind of thing. I spent years after the 2008 financial crisis arguing against austerity and the obsession with debt, taking a lot of abuse in the process.." -- Paul Krugman
What is going on here? Is this just pettiness about who should have more influence in the public square?
I have said before that what is being argued is not the desirability of certain policies. Keynes stated that his book was about something else:
"This book is chiefly addressed to my fellow economists. I hope that it will be intelligible to others. But its main purpose is to deal with difficult questions of theory, and only in the second place with the application of this theory to practice." -- Keynes (1936) [first three sentences]
Keynes' attempt at revolution failed. Mainstream economists, after Keynes and maybe before, argued that sometimes governments should spend more and tax less in a recession to prod the economy toward a long run equilibrium.
The background theory is that of an economy that is always approaching an equilibrium, in the long-run. The current "saltwater" school, also known as new Keynesianism, argues that this approach is too slow to be relied on for policy. Monopolies and limitations to competition, information asymmetries, sticky wages and prices are just too large. Government policy should focus on removing these limitations or somehow getting the economy to simulate a desired equilibrium path. I do not know that Joseph Stiglitz, for example, would argue that some these hindrances to equilibrium could ever be removed.
The "freshwater" school, once known as new classical economics, argues that, empirically, modern economies function close enough to the ideal competitive model that any such government policies should be looked on with great suspicion. Their simple macroeconomic models are the baseline with which both schools operate.
The names come from historical associations. Freshwater economists came out of the University of Chicago, the University of Minnesota, and the University of Rochester, all near one of the Great Lakes. Saltwater economists tend to be nearer ocean coasts, such as at Harvard and the Massachusetts Institute of Technology.
New classical economists, such as Robert Lucas and Thomas Sargeant, overthrew, in the 1970s, the Neokeynesianism or Old Keynesian of Alvin Hansen, Paul Samuelson, and Robert Solow. In the 1960s, Old Keynesian was known as the "New Economics" and the neoclassic synthesis. There is good reason for the common reader to be confused.
MMT builds on Post Keynesianism, and I am going to take it for granted that their proponents accept a Post Keynesian take on the above. (Which is not to say that Post Keynesians do not argue, sometimes vehemently, among themselves.) Joan Robinson called the neoclassical synthesis "bastard Keynesianism". Both freshwater and saltwater economists are pre-Keynesian. Carter (2020) provides an interestingly structured popular presentation of the unjustified rejection of the economics of Keynes
I find it hard to locate the logic in arguments that labor markets, good markets, and money markets tend to clear in any run. Some, such as Davidson (2007) emphasize money and uncertainty. Minsky (2008) and Marglin (2021) note the dynamic setting of Keynes' theory. In a model of the United States economy, it should not matter whether one calculates prices in dimes or dollars. This is a far cry from arguing that money is neutral, that the same real equilibrium would be approached if prices fell to 10 percent of their current nominal values.
I tend to emphasize microeconomics, following Sraffa. The theory of prices of production does not provide a logical foundation for the substitution mechanisms marginalists require for their ideas to make sense. Well-defined supply and demand functions do not exist in the long run.
Mainstream economists are apparently not taught any of this:
"...This article aroused the anger of just about every macroeconomist on Twitter..."
"...The brief description of freshwater and saltwater economics is fine, but to describe MMT as being 'brackish' — i.e., some sort of fusion of freshwater and saltwater, or a middle ground between the two — is absurd..."
-- Noah Smith The NYT article on MMT is really bad
I suspect many economists on twitter were not angered by this article. As far as I know, James Galbraith came up with the metaphor of brackwater economics. As seen above, it is not intended to be a fusion or middle ground. Rather it is a matter of rejecting both freshwater and saltwater economics. The nonexistence of an intertemporal budget constraint is another aspect of macroeconomics that Noah Smith seems to be confused about. Mainstream macroeconomists absurdly postulate that governments must always pay off their debts as time approaches infinity.
But why should Noah Smith be any different? Larry Summers ignorantly cited James Galbraith, who is a proponent of MMT or, at least, theories of endogenous money. I doubt that Summers believes this:
"I am all for intellectual diversity and wish that the NYT would give more attention to Marxist scholars like Steve Marglin, whose book Raising Keynes deserves extensive debate, or other left scholars like Tom Palley, Dean Baker or Jamie Galbraith." -- Larry Summers
You can find a post-2008 YouTube video, where Marglin says something like that his colleages are polite to him at holiday parties, but they have nothing to say about his research. Anyways, his long tome, which I have barely started, is clear that Keynes was arguing about more than government policy. He argues that models like the Keynesian cross and IS/LM are only a first pass description of the General Theory. The dynamic setting has to be taken into account in further passes. According to one review I stumbled upon Marglin's book could be improved in its account of money. Keynes' Treatise on Money contains a theory of endogeneous money. I can see reading the General Theory as assuming the central bank can set the stock of money, as a concession to the view he was arguing against, even though others say otherwise.
One could pursue political economy because one is interested in advancing political means that improve the lives of the vast majority of the population. One might make a compromise here. One might think one's policies are more likely to be enacted if one does the least to challenge hegemonic ideas about how the world works. As I understand it, Krugman has said somewhere that his academic strategy is to think in terms of simple models, like IS/LM, and then recast the argument into a publishable model of a Representative Agent, Rational Expectations (RARE) economy, also known as Dynamic Stochastic General Equilibrium (DSGE) model. In this approach, one puts forth arguments that one correctly believes have nothing to do with how actually existing capitalist economies function. One ignores some conclusions of the model. And it is doubtful that this approach will ever approach an useful description of a capitalist economy. I think Brad DeLong has said somewhere that this approach of boring from within is wasted time. (I welcome explicit links for the above.) It would seem that however politically useful such attempts have been, maybe after a half century of scientific failure by mainstream economists, heterodox approaches should be taken more seriously.
ReferencesSuggestions for more? There are other feeds from scholars just starting out. One can also find mainstream economists on twitter who do not know that almost everything they say was shown to be, at best, wrong more than half a century ago.
Updated 14 and 15 February 2022
Engels had a lot to do with formulating orthodox interpretations of Marx in the period after Marx's death. So it is interesting to see what he says. I have transcribed another letter before, about the law of value. The following is about historical materialism and the relation of the superstructure to the economic base:
According to the materialist conception of history, the ultimately determining element in history is the production and reproduction of real life. Other than this neither Marx nor I have ever asserted. Hence if somebody twists this into saying that the economic element is the only determining one, he transforms that proposition into a meaningless, abstract, senseless phrase. The economic situation is the basis, but the various elements of the superstructure - political forms of the class struggle and its results, to wit: constitutions established by the victorious class after a successful battle, etc., juridical forms, and even the reflexes of all these actual struggles in the brains of the participants, political, juristic, philosophical theories, religious views and their further development into systems of dogmas - also exercise their influence upon the course of the historical struggles and in many cases preponderate in determining their form. There is an interaction of all these elements in which, amid all the endless host of accidents (that is, of things and events whose inner interconnection is so remote or so impossible of proof that we can regard it as non-existent, as negligible), the economic movement finally asserts itself as necessary. Otherwise the application of the theory to any period of history would be easier than the solution of a simple equation of the first degree.
We make our history ourselves, but, in the first place, under very definite assumptions and conditions. Among these the economic ones are ultimately decisive. But the political ones, etc., and indeed even the traditions which haunt human minds also play a part, although not the decisive one. The Prussian state also arose and developed from historical, ultimately economic, causes. But it could scarcely be maintained without pedantry that among the many small states of North Germany, Brandenburg was specifically determined by economic necessity to become the great power embodying the economic, linguistic and, after the Reformation, also the religious difference between North and South, and not by other elements as well (above all by its entanglement with Poland, owing to the possession of Prussia, and hence with international political relations - which were indeed also decisive in the formation of the Austrian dynastic power). Without making oneself ridiculous it would be a difficult thing to explain in terms of economics the existence of every small state in Germany, past and present, or the origin of the High German consonant permutations, which widened the geographic partition wall formed by the mountains from the Sudetic range to the Taunus to form a regular fissure across all Germany.
In the second place, however, history is made in such a way that the final result always arises from conflicts between many individual wills, of which each in turn has been made what it is by a host of particular conditions of life. Thus there are innumerable intersecting forces, an infinite series of parallelograms of forces which give rise to one resultant - the historical event. This may again itself be viewed as the product of a power which works as a whole unconsciously and without volition. For what each individual wills is obstructed by everyone else, and what emerges is something that no one willed. Thus history has proceeded hitherto in the manner of a natural process and is essentially subject to the same laws of motion. But from the fact that the wills of individuals - each of whom desires what he is impelled to by his physical constitution and external, in the last resort economic, circumstances (either his own personal circumstances or those of society in general) - do not attain what they want, but are merged into an aggregate mean, a common resultant, it must not be concluded that they are equal to zero. On the contrary, each contributes to the resultant and is to this extent included in it.
I would furthermore ask you to study this theory from its original sources and not at second-hand; it is really much easier. Marx hardly wrote anything in which it did not play a part. But especially The Eighteenth Brumaire of Louis Bonaparte is a most excellent example of its application. There are also many allusions to it in Capital. Then may I also direct you to my writings: Herr Eugen Dühring's Revolution in Science and Ludwig Feuerbach and the End of Classical German Philosophy, in which I have given the most detailed account of historical materialism which, as far as I know, exists.
Marx and I are ourselves partly to blame for the fact that the younger people sometimes lay more stress on the economic side than is due to it. We had to emphasise the main principle vis-a-vis our adversaries, who denied it, and we had not always the time, the place or the opportunity to give their due to the other elements involved in the interaction. But when it came to presenting a section of history, that is, to making a practical application, it was a different matter and there no error was permissible. Unfortunately, however, it happens only too often that people think they have fully understood a new theory and can apply it without more ado from the moment they have assimilated its main principles, and even those not always correctly. And I cannot exempt many of the more recent "Marxists" from this reproach, for the most amazing rubbish has been produced in this quarter, too.... -- Engels to J. Bloch, 21 September 1890
I expected to see the phrase, "In the last instance" here. I guess that is how Lenin phrased the idea that the material base ultimately explains or determines the course of history. If you read Lenin as not so determinist, is Engels' letter consistent with Gramsci's ideas? One can see that Engels is almost quoting the second paragraph of The Eighteenth Brumaire of Louis Bonaparte:
"Hegel remarks somewhere that all great world-historic facts and personages appear, so to speak, twice. He forgot to add: the first time as tragedy, the second time as farce...
Men make their own history, but they do not make it as they please; they do not make it under self-selected circumstances, but under circumstances existing already, given and transmitted from the past. The tradition of all dead generations weighs like a nightmare on the brains of the living..."
As I understand it, Engels' Anti-Dhüring was easier to obtain than even most of Marx's published writings during the period of the Second International and the founding of German social democracy. Engels has something to say about the application of dialectics to natural sciences in this book, an idea I find questionable. He does say that he needs to address a broad range of topics because "Herr Dhüring ... dealt with all things under the sun and then a few more." What should one make of Engels' mechanical analogy about about a parallelogram of forces? I like the idea that the result is not something anybody is necessary conscious of willing.
I also like the first three chapters of the last part of Anti-Dhüring, in which Engels (I gather with Marx's help) writes about the distinction between utopian and scientific socialism. These chapters were published as a stand-alone pamphlet. My take is that the experience of the Soviet Union, of no-longer-actually existing socialism, cannot discredit Marx's plans for a post-capitalist society, not because it was not "true communism", but because he refused on principle to draw up such plans. I suppose I ought to have a caveat about The Civil War in France and Critique of the Gotha Program. You might think those who want to abolish or transcend capitalism should draw up such plans, especially after these terrible experiences. And Marx and Engels do have somewhere, I guess, some naive comments about all that is needed for successful economic planning is widespread knowledge among the workers of arithmetic and accounting, and these comments should be criticized. I do not necessarily take issue with some criticisms. But, still, the position of Marx and Engels was not to draw up such plans.
An analysis of structural economic dynamics in post-Sraffian models shows how reswitching and capital-reversing, for example, can be brought about or taken away by technical change, variation in relative markups among industries, or variations in requirements for use.
2.0 Descriptive KeywordsResearchers in post-Sraffian price theory have constructed models for the analysis of the choice of technique. Fluke switch points can be identified by considering perturbations of parameters in such models. Parameters considered here characterize technology, relative rates of profits among industries, and requirements for use - also known as net output or final demand. Parameter spaces are partitioned by fluke cases. This analysis identifies how reswitching, capital-reversing, the recurrence of processes comprising a technique, and the reverse substitution of labor, for example, can appear and vanish. Single production, fixed capital, extensive and intensive rent, and joint production in general are explored. Results are presented by means of numerical examples, with many tables and figures.
4.0 Summary In Multiple ParagraphsIf workers successfully push for higher wages, will firms tend to hire less labor? Is land that receives a higher rent per acre more fertile? If firms extend the economic life of machinery, are they adopting a more capital-intensive technique? If firms in some industry impose barriers to entry and achieve rates of profits persistently higher than others, will the answer to these questions change?
Researchers in price theory, in the tradition of the pioneering work of Piero Sraffa, have found surprising answers for these questions and more, in a rediscovery of the classical theory of value and distribution. My work extends such work by examining the effects of perturbing model parameters. Innovation in technology is represented by decreases in coefficients of production. Changes in market structure are depicted by persistent variations in relative rates of profits among industries. Variations in final demand are explored in models with long-lasting machinery, non-produced means of production, and general joint production.
Fully-specified numerical examples illustrate how parameter spaces are partitioned into regions among which qualitative behavior changes, while remaining invariant within each region. Many graphs provide unique transparency and visualization into aspects of price theory.
5.0 CommentsI have tried to summarize what I have been doing several times before.
| Mirowski On Markomata |
In the title of this post, I introduce a new technical term. Consider a Leontief input-output matrix characterizing the technique in use, in physical terms. Suppose n industries are producing n commodities. If an alternative process is available in one industry, then a problem of the choice between two techniques arises. If two processes are available in each industry, the choice is among 2n techniques. If three processes are available in each industry, 3n techniques exist.
Some researchers are quite aware of the challenges posed by combinatorics. Christian Bidard has what he calls a market algorithm. I have written a bit about a similar algorithm in my 2017 Review of Political Economy article. I think Yoshinori Shiozawa, Masashi Morioka, and Kazuhisa Taniguchi's 2019 book Microfoundations of Evolutionary Economics also has something about this sort of algorithm. By the way, D'Agata's example of the non-existence of a cost-minimizing technique is an example of an infinite loop in this market algorithm.
When analyzing the analysis of the choice of technique, Bidard champions Lemke's algorithm so that the observing economist can avoid looking at all combinations and permutations. Stefano Zambelli, Bertam Schefold, and each of their collaborators had to address combinatorial challenges in obtaining their empirical results.
Kumaraswamy Vela Velupillai, for example, in his Computable Foundations for Economics is another post-Sraffian addressing these issues. If you want to fully understand this stuff, which I do not, you might want to study algorithmic game theory, Norbert Wiener on cybernetics, Claude Shannon on information theory, the Chomsky heirarchy, and so on. I think those building on Sraffa have a contribution to make here.
I have not read a lot of the above. One might think of 'the' market as a distributed system. Markets with different rules for settling transactions can be thought of as types of automata. Somehow, many of these interacting automata comprise a capitalist economy.
Social norms exist about what wages can be expected from various types of jobs. And norms also exist for what the rate of profits or markups will be. Inflation arises when these norms conflict and institutions exist to fight about these norms.
There is no single rate of profits or a single wage for all jobs. In some jobs, you can expect to have a standard work week, weekends off, benefits, some asurance that your job will exist next week, and so. And in other jobs you cannot expect such. Here I am alluding to the theory of dual labor markets.
By the way, whether a job is in the formal or informal sector is not a matter of 'skill'. "The suggestion that any job is 'low skill' is a myth perpetuated by wealthy interests to justify inhumane working conditions, little/no healthcare, and low wages". A lot of struggle led to some jobs being considered 'skilled', and a reactionary counter-struggle resists such. Gender and race goes into this, of course. I doubt programmers were well-payed when a computer was a 'girl'. For example, I've read Richard Feynman's memoirs about how the 'computers' at Los Alamos implemented a time-sharing operating system (not his terminology). Do taxi drivers and Uber drivers face the same expectations? Bartenders at high-end restraurants in trendy parts of town and elsewhere?
How those with power understand what is going on matters. Suppose a certain set of hegemonic beliefs includes the incorrect idea that labor 'markets' tend to clear, maybe if only they could be made more 'flexible' and obstacles, such as labor unions, minimum wages, and so on are removed. And those running a country's central bank think their primary job is to fight inflation by raising interest rates whenever real wages show a slight increase. If the economy is run 'cold' for decades, much bad can result.
Consider a country where the workforce is highly unionized and collective bargaining is widely accepted, including with backing in law. Suppose contracts are staggered. Different sectors negoiate at different times. Suppose, by contrast, that the employers and employees are all expected to come together at one time. Inflation will be different in these two setups.
Another set of conventions involves families and households. Is co-habitation, without marriage, common? If you work in the formal sector, can you put your partner and non-biological children on your benefits? How many are expected, in the typical household - whatever that is - to work full or part time? What do you need for commuting? What kind of non-wage support can you expect? Have these norms varied recently? Have you tried following different conventions lately, and did you prefer it? The answer to these questions might have something to do with fluctuations in the labor force participation rate. With low unionization, a different set of institutions will resist attempts at the casualization of the work force.
Another set of expectations involves firms, their suppliers, and their customers. What proportion of restaurants and grocery stores do those who process agricultural products expect to be among those providing final demands? What level of capacity do firms expect to operate at? Does a different mode of operations change this? For example, I suspect a number of firms have realized they could double their office staff, if they had the demand and need, perhaps with an increase of support from their Information Technology support staff. If those running firms have highly uncertain or incorrect expectations, bottlenecks in some sectors can be expected to result.
I probably would not have written the above two paragraphs - maybe the whole post - without the prompting of current events. I look backwards to Joan Robinson's explanation (prediction) of stagflation and other literature.
Selected References |
| Figure 1: Variation of the Wage Frontier with Technical Progress |
I continue to explore perturbations of an example from Antonio D'Agata. I have found a new type of fluke switch point, in models of intensive rent. Here I explore structural dynamics along a path in which technical change overwhelms the scarcity of land.
In this post, I repeat the data on technology, with a specific parameterization. Table 1 presents the available technology. Iron and steel are produced in processes with inputs of labor and circulating capital. Corn is grown on homogeneous land, and three processes are available for producing corn. One hundred acres of land are available, leading to the possibility of two processes being operated side-by-side with positive rent.
| Input | Industries and Processes | ||||
| Iron | Steel | Corn | |||
| I | II | III | IV | V | |
| Labor | 1 | 1 | 1 | (11/5) e(5/4) - σt | e(1/20) - φt |
| Land | 0 | 0 | 1 | e(5/4) - σt | e(1/20) - φt |
| Iron | 0 | 0 | 1/10 | (1/10) e(5/4) - σt | (1/10) e(1/20) - φt |
| Steel | 0 | 0 | 2/5 | (1/10) e(5/4) - σt | (1/10) e(1/20) - φt |
| Corn | 1/10 | 3/5 | 1/10 | (3/10) e(5/4) - σt | (2/5) e(1/20) - φt |
Requirements for use are 90 tons iron, 60 tons steel, and 19 bushels corn.
Table 2 shows the processes operated in each of the six techniques available. (All three corn-producing processes are operated only at a switch point where the Delta, Epsilon, and Zeta techniques are simultaneously cost-minimizing. Iron, steel, and corn are basic commodities in all techniques. Land is never a basic commodity.
| Technique | Process |
| Alpha | I, II, III |
| Beta | I, II, IV |
| Gamma | I, II, V |
| Delta | I, II, III, IV |
| Epsilon | I, II, III, V |
| Zea | I, II, IV, V |
Suppose the coefficients or production in process IV decrease at the rate specified by setting σ to 5/4. And the coefficients of production in process V decrease, with φ set to 1/20.
Figure 1, at the top of the post, illustrates the evolution of the wage frontier with time in this scenario. Table 3 summarizes how the cost-minimizing technique varies with the rate of profits in each region. A discontinuity occurs at the pattern for requirements for use. Alpha, Delta, and Epsilon can satisfy requirements for use in Regions 1, 5, 10, and 11, while Alpha, Beta, Epsilon, and Zeta can satisfy requirements for use in Regions 12, 13, and 4. Finally, Alpha, Beta, and Gamma can satisfy requirements for use in Region 20, which is not shown in Figure 1. Region 20 is an example of a model of circulating capital. Land is in excess surprise, and rent is zero.
| Region | Range | Technique | Notes |
| 1 | 0 ≤ r ≤ Rα | Alpha | No rent. |
| 4 | 0 ≤ r ≤ Rβ | Beta | No rent. |
| 5 | 0 ≤ r ≤ r1 | Alpha | Rent per acre, when Epsilon is adopted, increases with the rate of profits and decreases with the wage. |
| r1 ≤ r ≤ Rε | Epsilon | ||
| 10 | 0 ≤ r ≤ Rε | Epsilon | Rent per acre increases with the rate of profits and decreases with the wage. |
| 11 | 0 ≤ r ≤ r1 | Epsilon | A range of the rate of profits exists for which no technique is cost-minimizing. The wage frontier is a non-unique function of the rate of profits. The wage curve for Delta slopes up on the frontier. |
| r1 ≤ r ≤ r2 | Delta and Epsilon | ||
| 12 | 0 ≤ r ≤ r1 | Epsilon | Rent per acre is a non- monotonic function of the rate of profits or of the wage. The wage curve for Zeta slopes up. |
| r1 ≤ r ≤ r2 | Zeta | ||
| r2 ≤ r ≤ Rβ | Beta | ||
| 13 | 0 ≤ r ≤ r1 | Epsilon | Rent per acre is a non- monotonic function of the rate of profits or of the wage. The wage curve for Zeta slopes down. |
| r1 ≤ r ≤ r2 | Zeta | ||
| r2 ≤ r ≤ Rβ | Beta | ||
| 14 | 0 ≤ r ≤ r1 | Zeta | Rent per acre, when Zeta is adopted, decreases with the rate of profits. The wage curve for Zeta slopes down. |
| r1 ≤ r ≤ RΒ | Beta | ||
| 20 | 0 ≤ r ≤ Rβ | Beta | No rent. |
D'Agata's example arises when t is one. As shown in Figure 1, there is a range of the rate of profits in Region 11 in which both Delta and Epsilon are cost-minimizing. Regions 12 and 13 vary in that the wage curve for Zeta slopes up in Region 12 and down in Region 13. The cost-minimizing technique is not a unique function of the wage in Region 12.
Anyways, my approach of partitioning parameter spaces based on fluke cases applies to this example of intensive rent.
ReferencesMoney is a medium of exchange (or means of purchase), a unit of account, and a store of wealth. I think Sraffa (1960) implicitly assumes an economy in which money is used. How would one explicitly and formally introduce money into Sraffa's scheme? I think one would want a theory of endogenous money, maybe as in a circuitist theory. How should the references below be extended? Which should I make an effort to read? I am aware that Sinha (2021) has a couple of other chapters about money and that Bellofiore and Passarella (2016) and Giuseppe and Realfonzo (2017) are introductions to special issues of ROKE and Metroeconomica, respectively. Any guidance to the literature, including these pointers, would be useful.
Reference |
| Figure 1: The Wage Frontier And Rent |
I continue to explore perturbations of an example from Antonio D'Agata. I have found a new type of fluke switch point, in models of intensive rent. In this post, I repeat the data on technology, with a specific parameterization.
Table 1 presents the available technology. Corn is grown on homogeneous land, and three processes are available for producing corn. One hundred acres of land are available, leading to the possibility of two processes being operated side-by-side with positive rent.
| Input | Industries and Processes | ||||
| Iron | Steel | Corn | |||
| I | II | III | IV | V | |
| Labor | 1 | 1 | 1 | (11/5) e(5/4) - σt | e(1/20) - φt |
| Land | 0 | 0 | 1 | e(5/4) - σt | e(1/20) - φt |
| Iron | 0 | 0 | 1/10 | (1/10) e(5/4) - σt | (1/10) e(1/20) - φt |
| Steel | 0 | 0 | 2/5 | (1/10) e(5/4) - σt | (1/10) e(1/20) - φt |
| Corn | 1/10 | 3/5 | 1/10 | (3/10) e(5/4) - σt | (2/5) e(1/20) - φt |
Table 2 shows the processes operated in each of the six techniques available. (All three corn-producing processes are operated only at a switch point where the Delta, Epsilon, and Zeta techniques are simultaneously cost-minimizing. Iron, steel, and corn are basic commodities in all techniques. Land is never a basic commodity.
| Technique | Process |
| Alpha | I, II, III |
| Beta | I, II, IV |
| Gamma | I, II, V |
| Delta | I, II, III, IV |
| Epsilon | I, II, III, V |
| Zea | I, II, IV, V |
Requirements for use are 90 tons iron, 60 tons steel, and 19 bushels corn. Alpha, Delta, and Epsilon can meet requirements for use. That is, one can find levels of operation of the processes comprising these techniques such that the net output of the economy is the previously specified vector and no more than 100 acres of land are farmed. Beta, Gamma, and Zeta are infeasible.
At the specific parameter values illustrated at the top of this post, the switch point between the Alpha and Epsilon techniques occurs at the rate of profits at which the wage curve for the Delta technique intercepts the axis for the rate of profits. This fluke condition arises for a locus in the parameter space in which (φt) is a function of (σt). It reminds me of a fluke case for the order of fertility in models of extensive rent.
At a slightly lower value of (σt) or a higher value of (φt), no range of the rate of profits exists in which both the Alpha and Delta technique are cost-minimizing. A range of the rate of profits does exist in which the Epsilon technique is uniquely cost-minimizing. On the other hand, at a slightly higher value of (σt) or a lower value of (φt), a range of profits exists in which both the Alpha and Delta technique are cost-minimizing, and Epsilon is not uniquely cost-minimizing for any rate of profits. In both cases near this fluke case, a range of profits exists in which Alpha is uniquely cost-minimizing. And a range of the rate of profits exists in which both the Delta and Epsilon techniques are cost-minimizing.
So this fluke case is associated with a variation in the details of of an example in which the cost-minimizing technique is non-unique, and in which no cost-minimizing technique exists even though feasible techniques with positive prices, wages, rate of profits, and rent exist.
References
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