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)


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


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?