Saturday, June 25, 2022

My Great-Great-Great-Great-Great-Great-Great-Great-Granduncle Babbitt Murdered a Native-American

The Babbitt family started in America with Edward Bobet, who died in 1675.

We have now come to that time of terror and disaster to the settlers the uprising of the Indians, known as King Phillip's War. It can easily be imagined how many anxious hours were passed by Edward and Sarah Bobet, so far removed from the garrison stockade, with their large family of children. Judging by the quantities of Indian relics found on his home farm it would seem that it was a peculiarly favorite haunt of the Indians before Bobet bought it. Finally their position became too dangerous to admit of further delay and being warned of the commencement of hostilities, on June 25, 1675, they took refuge in the garrison at Taunton, leaving behind the home which had been the fruit of so much labor in the wilderness. We must depend upon tradition for the account of Edward Bobet's last hours. This tradition has been so faithfully handed down from generation to generation and seems so fully confirmed by his place of burial that there is no reason to disbelieve it. According to this tradition Bobet returned to his house to secure some necessary article—perhaps the cheese hoop, as the story says: he was accompanied by his dog in the thought that perhaps warning of prowling savages would be given by it. He secured the needed article and was on his way back to the fort when he became aware of his pursuit by Indians; he climbed a tree and was effectually hidden, but his faithful dog disclosed his presence and his life was the forfeit of his hazardous adventure. His grave is in a private yard, near Berkley Bridge, and is thought to be the spot where he was killed. The spot was marked by a bronze Memorial Tablet in 1911 - its cost being defrayed by small contributions from his descendants, from all over the United States and Canada. (p. 23)

The family history has this bit about his son, also Edward Bobet (1655-1732):

He was a member of the 'train band' of Taunton and tradition relates that on one training day there appeared among the spectators one of the Indians who had killed Edward Bobet. This Indian who was perhaps intoxicated, boasted of this fact to Edward Bobet, Jr., who at a later date avenged his father's death. The Proprietors' records contain numerous entries concerning parcels of land which Edward added to his estate, and at the time of his death he owned many acres in both Taunton and the North Purchase…. (p. 27)

There is no suggestion of any arrest or any consequences.

Reference
  • Willliam Bradford Brown. 1912. The Babbitt Family History, 1643-1900. Taunton, Massachsetts.

Saturday, June 18, 2022

On Sraffian Methodology

I do not know if I will keep on, but I thought I might present a series of posts expanding on this one. By the way, I should have said there that the maximum rate of profits is the reciprocal of the organic composition of capital in Sraffa's standard system, not the actual system.

Sraffa's model is descriptive, based on objective data that can be observed for one production period. This data, at least through the first three chapters of The Production of Commodities by Means of Commodities, consists of:

  • The gross quantities produced over the production period, in physical units.
  • The proportion of labor employed in each industry.
  • The commodities that are used as inputs in each industry.
  • The wage, expressed as a proportion of the value of the net output produced in the period.

Assume that the same rate of profits is made in each industry. Evidently, this model is of a more or less competitive capitalist economy. Then, assuming a viable economy, prices of production are determined by the data.

Sraffa extends this approach to consider joint production, including fixed capital and rent. He often does not explicitly state assumptions or, if so, not in any detail. Furthermore, how this approach fits with a more thorough analysis of capitalist economies, at least, has been a subject of debate ever since the publication of his book.

Saturday, June 11, 2022

George Babbitt's Neighbor Is A Yale Economist

"On the other side of Babbitt lived Howard Littlefield, Ph.D., in a strictly modern house whereof the lower part was dark red tapestry brick, with a leaded oriel, the upper part of pale stucco like spattered clay, and the roof red-tiled. Littlefield was the Great Scholar of the neighborhood; the authority on everything in the world except babies, cooking, and motors. He was a Bachelor of Arts of Blodgett College, and a Doctor of Philosophy in economics of Yale. He was the employment-manager and publicity-counsel of the Zenith Street Traction Company. He could, on ten hours' notice, appear before the board of aldermen or the state legislature and prove, absolutely, with figures all in rows and with precedents from Poland and New Zealand, that the street-car company loved the Public and yearned over its employees; that all its stock was owned by Widows and Orphans; and that whatever it desired to do would benefit property-owners by increasing rental values, and help the poor by lowering rents. All his acquaintances turned to Littlefield when they desired to know the date of the battle of Saragossa, the definition of the word 'sabotage,' the future of the German mark, the translation of 'hinc illae lachrimae,' or the number of products of coal tar. He awed Babbitt by confessing that he often sat up till midnight reading the figures and footnotes in Government reports, or skimming (with amusement at the author's mistakes) the latest volumes of chemistry, archeology, and ichthyology.

But Littlefield's great value was as a spiritual example. Despite his strange learnings he was as strict a Presbyterian and as firm a Republican as George F. Babbitt. He confirmed the business men in the faith. Where they knew only by passionate instinct that their system of industry and manners was perfect, Dr. Howard Littlefield proved it to them, out of history, economics, and the confessions of reformed radicals." -- Sinclair Lewis. 1922. Babbitt pp. 21-22

Edward Erasmus Bobbit (1626-1675) has many descendants in America named Babbit(t). I do not know how Sinclair Lewis decided on the name of his protangonist.

Saturday, June 04, 2022

Elsewhere

Saturday, May 28, 2022

Selective Bibliography For The TSSI

is there a book with a focus exclusively on the TSSI more recent than the 2015 one in this list?

  • Armstrong, Phil (2020). Can Heterodox Economics Make a Difference? Conversations with Key Thinkers Cheltenham: Edward Elgar.
  • Potts, Nick and Andrew Kliman (eds.) (2015). Is Marx's Theory of Profit Right? The Simultaneous-Temporalist Debate. Lanham: Lexington Books.
  • Kliman, Andrew (2007). Reclaiming Marx's "Capital": A Refutation of the Myth of Inconsistency. Lanham: Lexington Books.
  • Freeman, Alan, Andrew Kliman, and Julian Wells (eds.) (2004). The New Value Controversy and the Foundation of Economics. Cheltenham: Edward Elgar.
  • Freeman, Alan and Gulielmo Carchedi (eds.) (1996). Marx and Non-Equilibrium Economics. Cheltenham: Edward Elgar.

I am not sure the first should be in this list. It is a collection of interviews with economists, including Kliman and Potts. The second has articles by such critics as Simon Mohun, Roberto Veneziani, and Robert Paul Wolff. The third includes articles by David Laibman and Paul Cockshott & Allin Cottrell, among many others. None have anything by Gary Mongiovi, as far as I can see. In general, I oppose the TSSI.

Saturday, May 21, 2022

Textbooks for Post-Sraffian Price Theory

This post provides a list of textbooks:

  • Syed Ahmad (1991). Capital in Economic Theory: Neo-classical, Cambridge, and Chaos, Edward Elgar.
  • Christian Bidard (2004). Prices, Reproduction, Scarcity, Cambridge University Press.
  • Duncan K. Foley, Thomas R. Michl, and Daniele Tavani.(2019). Growth and Distribution (2nd edition), Harvard University Press.
  • Richard M. Goodwin (1970). Elementary Economics from the Higher Standpoint, Cambridge University Press.
  • Steve Keen (2011). Debunking Economics: The Naked Emperor Dethroned? (Second edition). Zed Books.
  • Heinz D. Kurz and Neri Salvadori (1995). Theory of Production: A Long-Period Analysis, Cambridge University Press
  • Arrigo Opocher and Ian Steedman (2015). Full Industry Equilibrium: A Theory of the Industrial Long Run, Cambridge University Press.
  • Luigi L. Pasinetti (1977). Lectures on the Theory of Production, Columbia University Press
  • Fabio Petri (2021). Microeconomics for the Critical Mind, Springer.
  • Joan Robinson and John Eatwell (1973). An Introduction to Modern Economics, McGraw-Hill.
  • Alessandro Roncaglia (2006) The Wealth of Ideas: A History of Economic Thought, Cambridge University Press.
  • Ernesto Screpanti and Stefano Zamagni (2005) An Outline of the History of Economic Thought (Second edition). Oxford University Press.
  • Eric Sheppard and Trevor J. Barnes (1990) The Capitalist Space Economy: Geographical Analysis After Ricardo, Marx, and Sraffa. Routledge.
  • Yanis Varoufakis (1998). Foundations of Economics: A Beginner's Companion. Routledge.
  • Vivian Walsh and Harvey Gram (1980). Classical and Neoclassical Theory of General Equilibrium: Historical Origins and Mathematical Structure, Oxford University Press.
  • J. E. Woods (1990). The Production of Commodities: An Introduction to Sraffa, Humanities Press International.

Some of the above are out of print. I assume a reader who knows that one needs to read with paper and pen in hand. I deliberately do not include books by Christopher Bliss, Edwin Burmeister, or Avinash Dixit on growth theory, since I want to emphasize critics of mainstream economics. Nothing against them, and I could probably extend the above list with some thought. I have provided related lists before:

I suppose one might have other lists more Marxist than any of the above, a list for Leontief input-output analysis, a list for ecological economics, and a list with more emphasis on the history of economics.

Textbooks have been available for half a century that teach correct price theory.

Thursday, May 12, 2022

Value And Distribution

"It is the whole process of production that must be called 'human labour', and thus causes all products and all values. Marx and Ricardo used 'labour' in two different senses: the above and that of one of the factors of production ('hours of labour' or 'quantity of labour' has a meaning only in the latter sense). It is by confusing the two senses that they got mixed up and said that value is proportional to quantity of labour (in second sense) whereas they ought to have said that it is due to human labour (in first sense: a non-measurable quantity or not a quantity at all)." -- Piero Sraffa (D3/12/11:64, as quoted by Kurz and Salvadori)
"I shall begin by giving a short 'estratto' of what I believe is the essence of the classical theories of value, i.e. of those which incluce W. Petty, Cantillon, Physiocrats, A. Smith, Ricardo and Marx. This is not the theory of any one of them. I state it of course, not in their own words, but in modern terminology, and it will be useful when we proceed to understand their portata (delivery capacity) from the view of our present inquiry. It will be a sort of 'frame', a machine into which to fit their own statements in a homogeneous pattern, so as to be able to find what is common in them and what is the difference with the later theories." -- Piero Sraffa (D3/12/4:12 as quoted by Pasinetti and by Kurz and Salvadori and by )
1.0 Introduction

This post outlines a coherent theory to build on in trying to understand capitalist economies. I thought originally of trying to explain the unoriginal points in this post without any algebra. I wish I could be more terse. But I find that too difficult. No reason exists that all uses of this theory should be fully formalized.

This post contains an implicit criticism of other theories based on what is not here. The data are objective, and the approach is not that of methodological individualism. I do not draw any well-behaved supply and demand functions. Nor do I assume that the labor market, for example, clears. I do not calculate any marginal quantities. Unobservable preferences are not referred to, and no utility functions are maximized. I do not see why in extending this approach one needs to refer to such fictions.

2.0 Givens From A View From Outer Space

Consider a capitalist economy during a single production cycle, which I take as a year. One can observe the following:

  • A column vector, q, of the gross output of produced commodities. Each commodity is measured in physical units (tons, kilowatts, etc.), and is the output of some process of production.
  • The row vector, a0, of labor coefficients of the production processes. The coefficient a0,j is in physical units (for example, labor units per ton), where labor units are such that total employment over the year is unity. Different concrete activities are weighted by relative wages to reduce labor units to a common abstract labor unit. The product (a0,j qj) is the proportion of total employment allocated to the jth industry.
  • The square Leontief input-output matrix, A. Each element ai,j is in physical units (for example, kilograms per ton). The quantity (ai,j qj) is the physical units of the ith commodity used in producing the (gross) output of the jth process. The Leontief matrix is assumed to characterize a viable economy that can operate year after year at the same level. For simplicity, assume that each commodity enters directly or indirectly into the production of all commodities. That is, all commodities are Sraffian basic commodities.
  • The wage, w, where the wage is the proportion of the price of the net output obtained by the workers.
  • The column vector, d, of the commodities on which the wage is spent.

In this formulation, each industry produces a single commodity, and a single process is operated in each industry. Since the data is from a snapshot of the whole economy, in a sense, no assumptions are made on returns to scale. Each industry is operating at whatever scale is observed, with observed inputs being obtained from other industries.

Certain variables are implicit in these definitions of the givens. Net output is related to the the given technique and gross output:

y = q - A q = (I - A)q

where y is the column vector of net output, and I is the appropriately sized identity matrix. The net output is that part of gross output that can be consumed, while leaving available the reproduction of the capital goods used up in producing it so as to continue production in the next year at the same level and with the same technique. One can invert the above relation to find gross output from net output:

q = (I - A)-1 y

The assumptions ensure that the Leontief inverse exists.

The unit of measurement for labor is chosen such that total employment, at the observed level of gross outputs, is unity:

a0 q = a0 (I - A)-1 y = 1

The numeraire is the net output:

p y = 1

where p is a row vector of prices. The total wage is equal to the price of the commodities on which wages are spent:

w a0 q = p d

For what it is worth, the physical composition of wages by industry is d a0.

3.0 Social Relations Between Workers

The data reflect a certain allocation of labor over the industries comprising the economy. A notion of vertical integration is needed to think about how each commodity can be produced in a sustainable way.

For example, suppose a consumer buys one additional automobile of a specified make. To leave the production apparatus unchanged, workers will have to produce an automobile in Michigan, tires outside of Akron, steel from iron ore in Pittsburgh, and so on, with transport workers ensuring everything gets shipped appropriately. (Actually, this example probably reflects my understanding of the structure of production many decades ago.) This can all be expressed in algebra:

vj = a0 (I - A)-1 ej

where ej is the jthe column of the identity matrix. The integrated labor units per unit of the jth commodity, vj, is both an employment multiplier and the labor embodied in the commodity. I have explained it above as a matter of laborers working in parallel in the given year. But one can also think of it as a matter of notionally summing some labor in this year and over past years under the assumption that the observed technique has been used forever in the past at this scale.

One can also apply this algebra to certain collections of commodities. The labor embodied in commodities purchased out of wages, V, is:

V = a0 (I - A)-1 d

The labor embodied in the remaining commodities, S, which are produced by the workers but in the control of those owning the means of production are:

S = 1 - V = 1 - a0 (I - A)-1 d

The labor embodied in capital goods, C, is:

C = a0 (I - A)-1 A q

Certain ratios of these labor values have often been expressed. For example, the ratio, e, of the labor spent during the year to produce commodities not paid to workers to the labor spent to produce the commodities purchased out of wages is:

e = S/V

If one assumes wages are totally consumed, the above ratio has something to do with the maximum possible rate of growth. The ratio, occ, of the labor embodied in capital goods to the labor expended in the year is:

occ = C/(V + S)

4.0 Prices As Relations Between Things

Those making decisions about which processes to operate and at what levels have done so with certain expectations about being able to sell the produced commodities at certain prices. They also have expectations about costs. Observed market prices are almost certainly such that some of these expectations are being disappointed, and some will need to alter their plans. Such alterations include changing the scale at which certain processes are operated in some industries, disinvesting in some industries and investing in other industries, and replacing processes of production (perhaps with newly discovered processes) in various industries.

As a heroic simplification, consider what prices must be to be consistent with the data. Such prices of production are based on the assumption that the allocation of the labor force seen in the data is socially necessary. Perhaps, if the data were to be repeated year after year, market prices would circulate around prices of production or approach them in a 'gravitational' process.

Assuming competitive markets, in some sense, prices of production satisfy the following equation:

p A(1 + r) + w a0 = p

where r is the rate of profits. In this equation, wages are paid out of the product at the end of the year.

As a matter of mathematics, the assumptions in this model of circulating capital are sufficient to determine prices of production and the rate of profits. They still would be sufficient if one allowed for fixed capital and for land in a model of extensive rent. Likewise, one could allow for limitations in competition by assuming known ratios of the rate of profits among industries. Certain issues arise in determining prices of production and the rate of profits in models of intensive rent and of general joint production. More than one solution may arise in some cases.

These extensions to joint production require the modeling of the choice of technique. I am not sure how I can do this analysis without assumptions on returns to scale. I do see that I can restrict distribution such that the observed technique is cost-minimizing at the observed scale.

It is easier to solve for the wage as a function of the rate of profits:

w = 1/{a0 [I - (1 + r)A]-1 y}

The above is a monotone decreasing function. The maximum wage of unity occurs when the rate of of profits is zero. The maximum rate of profits occurs at a wage of zero, and that maximum is 1/occ. Prices of production are:

p = a0 [I - (1 + r)A]-1/{a0 [I - (1 + r)A]-1 y}
4.1 An Aside On Vertical Integration

I repeat the above equation for prices of production:

p A(1 + r) + w a0 = p

This can be rewritten as:

p Ar + w a0 = p(I - A)

Or:

p A(I - A)-1r + w a0(I - A)-1 = p

Or:

p Hr + w v = p

where I am going to call H the vertically integrated Leontief matrix. (Pasinetti probably has another name.) The row vector v is a vector of labor values. The solution of this system of equations is the same as above. When the rate of profits is zero, prices of production are equal to labor values.

5.0 Conclusion

The above has outlined a logical theory for describing a capitalist economy. The starting data are, in principle, observable and close to what can be obtained from the National Income and Product Accounts (NIPA).

This data allow one to examine how the labor force is allocated in a sustainable economy. The proportions of workers that are (re)producing certain aggregates (wage goods and the remainder) or embodied in certain aggregates (the capital goods used up in production) are noted. Presumably, individual commodities may be produced with extremes of labor-intensive methods, but these differences could come close to averaging out in the aggregate. One might want to extend wage goods to include, for example, commodities consumed by, for example, retired workers, students, the unemployed, and those unable to participate in the labor force. One might also want to look at other aggregates such as luxuries spent by those obtaining income produced by the workers but not paid out as (generalized) wage goods and investment goods used in expanding the economy.

These aggregates can also be evaluated with prices. I have drawn a few connections between prices of production and the labor embodied in these aggregates. The maximum rate of profits is the multiplicative inverse of the organic composition of capital. In formulating a system of equations for prices of production in vertically integrated terms, I find labor values useful. Otherwise, this post has drawn no connection between prices of production and the labor embodied in these aggregates. Can one pass easily between prices of production and labor values? The mathematics of eigenvalues and eigenvectors is useful for exploring the theory behind this question. Whatever you think of the answer, including difficulties arising with joint production and of empirical results, seems to be independent of the validity of anything in the above post.

I have talked about some of the conditions needed to sustain the operation of a capitalist economy, while only looking at the data for a single production period. Presumably, the gross output for the next year will be at a different level and mix. Such a change in scale in operation can be expected to alter the vector of labor coefficients and the Leontief input-output matrix.

Non-produced commodities that are available only as a finite stock that are used up in production (for example, oil, ores, and certain minerals) have been abstracted from. I have also ignored physical limitations imposed by bounds on throughput and sinks. The latter issue can be explored by the theory of joint production where one does not impose the assumption of free disposal.

Half a century ago, some economists demonstrated that economists a century and a half ago were mistaken. Jevons, Menger, and Walras made fundamental mistakes that cannot be fixed and are built into the work since then that builds on them. The political economy that had been developed in the century before them provides an alternative that is worth updating and building on.

Saturday, May 07, 2022

Axel Leijonhufvud, 9 June 1933 - 5 May 2022

I think it should be well-known that the Keynesian economics in Paul Samuelson's textbook, for example, does not capture a lot of the theory in Keynes General Theory. Axel Leijonhufvud, along with Robert Clower, raised this point in the 1960s from a standpoint outside of the emerging Post Keynesianism of Sidney Weintraub, Paul Davidson and Keynes' immediate colleagues at Cambridge.

I do not recall Leijonhufvud's book well. As I recall, much discussion occurred over the previous few decades around which selection of a few markets would be good to organize macroeconomics around and whether it mattered. Candidate markets were for goods, bonds, stocks, money, and labor. Leijonhufvud thought that Keynes organized his theory around a different selection than that selected by Keynesian economists. In the General Theory, Keynes insists that the line between bonds and money is not sharp. I think Leijonhufvud emphasized also that Keynes was a Marshallian, not a Walrasian. Clower suggested that the budget constraint for consumers should, in disequilibrium, be based on actual prices, not prices that would prevail after the completion of some sort of tâtonnement process. Leijonhufvud, I guess, emphasized interest rates and the discoordination possible with savings and investment. A decision to defer spending is not a decision to order consumption goods at a definite future date.

In later work, Leijonhufvud explored Wicksell's macroeconomics. (By the way, Gunnar Myrdal developed a macroeconomics much like Keynes from an immanent critique of Wicksell.) Leijonhufvud developed the difficult-to-formalize notion of the corridor. There is a range of prices, wages, and interest rates in which markets act normally and tend to fall back into equilibrium. If markets fall outside that range, expectations will be so upset that one cannot expect the economy to fall back onto a full-employment equilibrium path without some guidance.

I suppose I ought to mention Leijonhufvud's interest in Hayek too.

Selected Works by Leijonhufvud
  • Keynes and the Keynesians: A suggested interpretation. American Economic Review 57(2) 1967: 401-410.
  • On Keynesian Economics and the Economics of Keynes: A Study in Monetary Theory , Oxford University Press, 1968.
  • Life among the econ, Western Economic Journal 1973.
  • Information and Coordination: Essays on Macroeconomic Theory , Oxford University Press, 1981.

Sunday, May 01, 2022

Mark Levin's American Marxism: Worse Than Worthless

Authortarians in the United States are currently competing to see who can publish the most stupid book. Mark Levin is a strong contender. Much more drivel exists in the book under review in this post than described here.

Levin goes on about selected philosophers in odd ways. I haven't seen others point out his curious grouping of Rousseau, Hegel, and Marx. They supposedly "argue for the individual's subjugation into a general will, or greater good, or bigger cause built on radical egalitarianism - that is, 'the collective good'" (p. 18). He has the usual misassignment of utopian schemes to Marx. I do not claim to understand Hegel, but I do not see why holding up the Prussia of his day is a matter of advocating egalitarianism.

The 1619 Project, created by Nikole Hannah-Jones, was originally published in the New York Times. Levin insults his readers by suggesting that the naivety of Walter Duranty, the Times Moscow bureau chief from 1922 to 1936, and Herbert Matthews 1950s' scoop interview with Fidel Castro are relevant to the validity of the 1619 project (pp. 110-111). This fallacy is called poisoning the well. But what does the 1619 project have to do with Karl Marx?

Levin is big on arguing strawpersons. He tells us that Marx does not appreciate the industrial revolution and "the technological and other advances" with which "capitalism has created unimaginable and unparalleled wealth for more people in all walks of life than any other economic system" (p. 4). "Longer workdays do not ensure wealth creation or growth" (p. 4). Levin is probably incapable of reading volume 1 of Capital or even noting the existence of part IV, on the production of relative surplus value. Finally, in arguing against supposed Marxist environmentalists, who critize Marx for emphasizing economic growth, he manages to quote (p. 157) Marx's praise for the bourgeois from The Communist Manifesto near where Marx writes "All that is solid melts into air."

Despite the above, Levin has very little to say about Marxism. Some of his rants are quite curious. A 1909 book by Herbert Croly, an author associated with the founding of The New Republic, provokes a numbe of pages (pp. 45-48). He is curiously obsessed with John Dewey's impact (p. 54 and p. 204) on education. Levin goes on about (pp. 32-39) a 1966 essay in the Nation, by Francis Fox Piven and Richard A. Cloward. I happen to recognize Piven and Cloward, but what this has to do with Black Lives Matter, Antifa, Critical Race Theory, or whatever else is unexplained.

Levin quotes Ayn Rand (pp. 153-158) and George Reisman as 'experts' when denying global warming. But let me turn from inappropriate arguments from authority back to strawpersoning. As others have noted, much of this book is long chunks of quotations from others. Sometimes he even manages to find somebody on his side who is worth studying. (I would not cite Hayek's The Fatal Conceit too much myself, given disputes about its authorship.) So he has many long passages from various academics. Although these passages are often long-winded academic prose with many polysyllabic passages, they are usually quite reasonable. Levin will then have a short passage supposedly saying what they say in other words. Rarely does his rephrasing have much basis in the quoted text. Sometimes it is a complete non sequitur.

But maybe Levin is just illiterate and can neither say what he means nor mean what he says.

"American Marxism exists, it is here and now, and indeed it is pervasive, and its multitude of hybrid but often interlocking movements are actively working to destroy our society and culture, and overthrow the country as we know it. Many of the individuals and groups who collectively make up this movement are unknown to most Americans, or operate in ways in which most Americans are unaware. Thus, this book is written to introduce you to a representative sample of them, some perhaps, more familiar than others, and to provide you with specific examples of their writings, ideas, and activities, so you can know of them and hear from them." (p. 12)

So he claims he is presenting a "representative sample of them", thus the strawpersons. This is supposedly a representative sample of "the individuals and groups who collectively make up this movement", where "the movement" is a "multitude of hybrid but often interlocking movements". Presumably, he took some care over this circular, vague, non-definition.

Here he says Critical Theory started in American universities in 1989:

"Indeed, in 1989, ... the seeds of a radical-fringe ideology, Critical Theory, which I discuss at length ..., and the unraveling of the existing society by weaponizing the culture against itself, began their early bloom throughout the American landscape, but with little public notice." (pp. 43-44)

Others have noted that Levin cannot even get his Nazi conspiracy theories right. As near as I can parse this non-sentence, Levin here says that higher education in science, technology, engineering, and mathematics are highly relevant for the degrowth movement (that is, the belief in their irrelevancy is expendable):

"Inasmuch as the purpose of this movement is to regress back to nature and a mere subsistence economy, where the communal psyche is anti-growth, anti-technology, anti-science, and anti-modernity, ironically the irrelevancy of higher education, graduate studies, and doctoral degrees, and the colleges and faculties themselves, particulary in the teaching of hard sciences, technology, engineering, and mathematics, are expendable." (p. 158)

This book fails at the level of the sentence, the paragraph, the chapter, and overall. It has no index.

Ignorance, incoherency, disdain for his reader - on which criteria is Levin the greatest?

Thursday, April 28, 2022

Characteristics of Labor Markets Varying with Pertubations of Relative Markups

My article with the post title is now available at the Review of Political Economy. The abstract follows:

Abstract: This article examines a model of long-period positions with markup pricing. The variation in certain characteristics of the wage frontier with perturbations of relative markups is illustrated. This analysis provides a demonstration of the emergence of the reswitching of techniques and of capital reversing, for example, in non-competitive markets.

Saturday, April 23, 2022

Elsewhere

Paul Krugman's Godley-Tobin Lecture

Saturday, April 09, 2022

An Indeterminate Solution In An Example Of Extensive Rent

Figure 1: Extra Profits with Given Rent On Type 2 Land
1.0 Introduction

This post revisits this example of extensive rent. I repeat quite a lot from that post.

Prices of production are defined, in models of circulating capital alone, from a given technology, requirements for use, and either the wage or the rate of profits. I usually take requirements for use as given by net output and assume constant returns to scale. Since I am concerned with a choice of technique, I am not disagreeing with Sraffa in assuming constant returns. These givens also determine prices of production in models of pure fixed capital.

The example shows that these givens are insufficient to determine prices of production in special cases in the theory of extensive rent. The givens can be compatible with a continuous range for prices of production. As I understand it, this indeterminacy, however, only arises in the parameter space for models of extensive rent for a set of Lebesque measure zero. In this sense, the properties of the circulating capital model emphasized above extend to models of extensive rent. Some properties do not. In particular, prices of production can vary with sufficiently large variations in requirements for use. Nevertheless, I think fixed capital and extensive rent (both together?) are compatible with the Sraffian reconstruction of the theory of value and distribution in classical political economy.

Problems arise, though, with models of intensive rent and general joint production. The sort of indeterminancy illustrated in this post can exist in those models in a set in their parameter space with a positive Lebesque measure.

2.0 Technology and Requirements for Use

Consider a capitalist economy in which two commodities, iron and corn, are produced. One process is known for producing iron. In the iron industry, workers use inputs of iron and corn to produce an output of iron. The output of the iron industry is one ton with the inputs shown in Table 1. Two processes are known for producing corn. Each corn-producing process operates on a specific type of land. The coefficients of production shown in Table 1 are for an output of one bushel corn. These processes can be thought of as examples of joint production. Their outputs are corn and the same quantity of land used as input, unchanged by the production process. Presumably, some of the labor in these processes is used to maintain the land in a given state. For this post, I assume σt is 17/100.

Table 1: The Coefficients of Production
InputIron IndustryCorn Industry
IIIIII
Labora0,1 = 1a0,2 = 5191/5770a0,3 = (305/494) e(3/20) - σt
Type 1 Land0c1,2 = 10
Type 2 Land00c2,3 = e(3/20) - σt
Irona1,1 = 9/20a1,2 = 1/40a1,3 = (3/1976) e(3/20) - σt
Corna2,1 = 2a2,2 = 1/10a2,3 = (229/494) e(3/20) - σt

The specification of technology is completed by noting the values of parameters for the quantities available of non-produced means of production. For this numerical example, let there be 100 acres of type 1 land and 100 acres of type 2 land. The iron-producing process and each corn-producing process exhibits constant returns to scale, up to the limits imposed by the endowments of land.

I consider stationary states with a net output consisting solely of corn. A bushel corn is the numeraire. Any one of four techniques can be used to produce corn, depending on the requirements for use. The process for producing iron is part of each technique. Table 2 specifies which types of land are fully or partially farmed in each technique. In the Alpha and Beta techniques, both types of land are cultivated, with one type only partially farmed. In the remaining two techniques, one type of land is left totally farrow. Which techniques are feasible depends on the endowments of the land and on the requirements for use.

Table 2: Techniques
TechniqueType of Land
Type 1Type 2
AlphaFully farmedPartially farmed
BetaPartially farmedFully farmed
GammaPartially farmedFarrow
DeltaFarrowPartially farmed

I pick a point in logical time, where σ t is 17/100, to fix the technology. Suppose requirements for use are such that they can be satisfied by totally cultivating type 2 land and leaving type 1 land farrow. That is, net output is approximately 55.112 bushels. The common limiting case of the Beta and Delta techniques is feasible.

3.0 Prices of Production

Under the assumptions, requirements for use can also be satisfied by partially cultivating type 1 land, and leaving type 2 land farrow. When the Gamma technique is adopted, neither type of land is scarce and their rents are zero. Prices of production, for a given rate of profits, for the Gamma technique, solve the following system of equations:

(p a1,1 + a2,1)(1 + r) + w a0,1 = p

(p a1,2 + a2,2)(1 + r) + w a0,2 = 1

One can find the difference between the revenues and the costs for each process, where the value of capital goods are found at the going rate of profits. For example, extra profits for the third process operated at a unit level at Gamma prices, sγ,3(r), are specified as follows:

sγ,3(r) = 1 - ((pγ(r) a1,3 + a2,3)(1 + r) + wγ(r) a0,3)

The notation emphasizes that the price of iron and the wage are functions of the rate of profits. Since under Gamma rents are zero, no coefficient of production for land appears in the above equation. Figure 2 displays extra profits for each process at a unit level. One can see that the Gamma technique is cost-minimizing only at an intermediate range of profits.

Figure 2: Extra Profits with Gamma Prices

Return to the case in which type 1 land is farrow and all type 2 land is farmed, the limiting case for both the Beta and Delta techniques. Suppose the rent on type 2 land, ρ2, is given. It is between zero and the bound from the Beta technique, inclusive. For the Beta technique, rent and prices of production, as functions of the rate of profits, are found by solving the system of equations specified by the first two equations above and the following equation:

(p a1,3 + a2,3)(1 + r) + ρ2 c2,3 + w a0,3 = 1

For rent on type 2 land in the interior of this range, prices of production are found, given rent and the rate of profits, by solving the system of two equations given by the first and last equations above.

From these prices of production, one can find extra profits obtained in operating each of the three processes specified in the technology. Extra profits are zero in operating the first and third process. Figure 1 graphs extra profits, sδ,2(r, ρ2), against the rate of profits for four levels of the rent per acre for type 2 land, in operating the second process to produce a bushel corn. The rent per acre for type 2 land is zero or negative between the switch points. Outside the switch points, rent per acre for type 2 land ranges between zero and a positive upper bound. The technique associated with this continuum for prices of production is cost-minimizing in these ranges outside the switch points.

4.0 Conclusion

Any lower requirements for use can be satisfied by cultivating type 2 land alone, with some of type 2 land remaining farrow. The rent on type 2 land is then zero. Given the rate of profits, the system of linear equations for the Delta technique have a unique solution for the wage and the price of iron. Any higher requirements for use necessitate the cultivation of at least some type 1 land. A system of three linear equations can be solved, given the rate of profits, for the wage, the rent on type 2 land, and the price of iron. In either case, prices of production are determinate.

I call this fluke case a pattern for requirements for use. I think I have not previously noted this indeterminancy in models of extensive rent.

Thursday, March 31, 2022

Elsewhere

  • An applet for Marx's schemes of simple and expanded reproduction.
  • Eli Cook, in The American Prospect says mainstream economists need to talk about profits.
  • Simon Torracinta, in the Boston Review, decries bad (micro)economics.
  • I should have mentioned Abraham Robinson and non-standard analysis in a previous post.
  • Paintings by the economist Willaim Baumol.
  • A painting by the economist Richard Goodwin. Apparently, he had a book.

Monday, March 28, 2022

I Was Taught That Boys Need Girls And Girls Need Boys; You Say That's Not True

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 References
  • Judith Butler. 1990. Gender Trouble.
  • Anne Fausto-Sterling. 2000. Sexing the Body: Gender Politics and the Construction of Sexuality.
  • Deidre McCloskey. 1999. Crossing: A Memoir.
  • Flannery O'Connor. 1955. A temple of the holy ghost.

Saturday, March 19, 2022

Some Stories About Math And Science

I 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.

References
  • David Asperó and Ralf Schindler. 2021. MM+ implies (*).
  • J. S. Bell. 1964. On the Einstein Podolsky Rosen paradox. Physics 1(3): 195-200.
  • Stephen Budiansky. 2021. Journey to the Edge of Reason: The Life of Kurt Gödel W. W. Norton.
  • Paul J. Cohen. 1963. The independence of the continuum hypothesis IProceedings of the U.S. National Academy of Sciences 50(6):1143-1148.
  • Paul Cohen. 1964. The independence of the continuum hypothesis IIProceedings of the U.S. National Academy of Sciences 51(1):105-110.
  • Torkel Franzen. 2005. Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. Peters.
  • Kurt Gödel. 1936. On formally undecidable propositions of Principia Mathematica and related systems I. Monatsheft für Mathematik und Physik 38:173-198.
  • Kurt Gödel. 1938. Consistency-proof for the generalized continuum-hypothesis. Proceedings of the U.S. National Academy of Sciences 25: 220-224.
  • Kurt Gödel. 1940. The consistency of the axiom of choice and the generalized continuum hypothesis with the axioms of set theory. Annals of Mathematic Studies 3.
  • Kurt Gödel. 1949. An example of a new type of cosmological solutions of Einstein's field equations of gravitation. Review of Modern Physics 21: 447-450.
  • Joel David Hamkins. 2011. The set-theoretic multiverse
  • Morris Kline. 1982. Mathematics: The Loss of Certainty. Oxford University Press.
  • Calvin Leung et al. 2018. Astronomical random numbers for quantum foundations experiments
  • Edwin E. Moise. 1963. Elementary Geometry from an Advanced Standpoint. Addison-Wesley.
  • Piero Sraffa. 1960. Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory. Cambridge University Press.
  • Robert A. Wilson. 2009. The Finite Simple Groups. Springer.

Wednesday, March 16, 2022

The Spread Of Marxism: A Riddle

Karl 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.

Saturday, March 12, 2022

A Theorem for Capital-Reversing

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.

Tuesday, March 08, 2022

Elsewhere

The Italian Post Keynesian Seminar on Garegnani
  • The Problem with Jon Stewart interviews Stephanie Kelton and Rohan Grey.
  • Samuel Fleischacker explains Adam Smith was not a propertarian.
  • Jania on econophysics.
  • A seminar on Stephen Marglin's Raising Keynes.

Wednesday, March 02, 2022

Reminder: Wages, Employment Not Determined By Supply And Demand For Labor

Figure 1: The Wage as Functions of Employment by Industry
1.0 Introduction

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 Technology

Consider 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.

Table 1: The Technology
InputIron
Industry
Steel
Industry
Corn
Industry
abcdef
Labor1/31/105/27/2013/2
Iron1/62/51/2001/10010
Steel1/2001/4001/43/1001/4
Corn1/3001/3001/300000

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
TechniqueProcesses
Alphaa, c, e
Betaa, c, f
Gammaa, d, e
Deltaa, d, f
Epsilonb, c, e
Zetab, c, f
Etab, d, e
Thetab, 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 System

Prices 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 Technique

Figure 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.

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.

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 Markups

In 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.

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 Conclusion

As 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?

Monday, February 21, 2022

A Theorem For The Reverse Substitution Of Labor

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) et

The corresponding labor coefficient for the Beta technique declines at the rate σ:

aβ0, n(t) = aβ0, n(0) et

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.

Saturday, February 19, 2022

New York City Subway: A Parable

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.

Tuesday, February 15, 2022

What Paul Krugman Could Learn From The Post Keynesian Roots Of MMT

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.

References
  • Zachary D. Carter. 2020. The Price of Peace: Money, Democracy, and the Life of John Maynard Keynes. Random House.
  • Paul Davidson. 2007. John Maynard Keynes. Palgrave Macmillan
  • John Hicks. 1981. IS-LM: an explanation. Journal of Post Keynesian Economics 3(2): 139-154.
  • Stephamie Kelton. 2020. The Deficit Myth: Modern Monetary Theory and the Birth of the People's Economics. Public Affairs.
  • John Maynard Keynes. 1936. The General Theory of Employment, Interest, and Money. Harcourt-Brace.
  • Stephen A. Marglin. 2021. Raising Keynes: A Twenty-First-Century General Theory., Harvard University Press.
  • Hyman Minsky. 2008. John Maynard Keynes. McGraw-Hill.
  • Franco Modiglani. 1944. Liquidity preference and the theory of interest. Econometrica 12(1): 45-88.