Sunday, February 23, 2020

Update To Example In Vienneau (2019)

Maybe this post should be titled "Erratum" or "corrigendum". I have an example in my paper last year in which wage frontiers are supposed to vary with two parameters. One is the markup in the "iron" industry. And the other is σ t. The example should be as in Table 1. All the theory and the visualizations in the paper work out with this example.

Table 1: Technology for Producing Steel and Corn
Labora0,1 = 1aα,0,2(t) =
(5191/5770) e(1/10) - σ t
aβ,0,2 = 305/494
Irona1,1 = 9/20aα,1,2(t) = (1/40) e(1/10) - σ taβ,1,2 = 3/1976
Corna2,1 = 2aα,2,2(t) = (1/10) e(1/10) - σ taβ,2,2 = 229/494

Thursday, February 20, 2020


  • John Weeks presents Joan Robinson's contributions to the Cambridge Capital Controversy (CCC).
  • A discussion, from 2006, on Daily Kos, about one of my attempts to explain the CCC.
  • A post, from 2016, on Naked Capitalism about how the CCC shows microeconomics is all wet.
  • J. W. Mason has a handout explaining a definition of capital.
  • Doyne Farmer, Fotini Markopoulou, Eric Beinhocker, and Steen Rasmussen, in an essay in Aeon, Collaborators in creation, provide an overview of complexity economics.
  • An overview, from 2018, about how women were deliberately kicked out of software development in Great Britain.

Saturday, February 15, 2020

Universal Basic Income: Some Advocates And Analysts

"In fact, the realm of freedom actually begins only where labour which is determined by necessity and mundane considerations ceases; thus in the very nature of things it lies beyond the sphere of actual material production. Just as the savage must wrestle with Nature to satisfy his wants, to maintain and reproduce life, so must civilised man, and he must do so in all social formations and under all possible modes of production. With his development this realm of physical necessity expands as a result of his wants; but, at the same time, the forces of production which satisfy these wants also increase. Freedom in this field can only consist in socialised man, the associated producers, rationally regulating their interchange with Nature, bringing it under their common control, instead of being ruled by it as by the blind forces of Nature; and achieving this with the least expenditure of energy and under conditions most favourable to, and worthy of, their human nature. But it nonetheless still remains a realm of necessity. Beyond it begins that development of human energy which is an end in itself, the true realm of freedom, which, however, can blossom forth only with this realm of necessity as its basis. The shortening of the working-day is its basic prerequisite." -- Karl Marx, Capital, Volume 3, Chapter 48.

This post, I guess, is somewhat about current events. I claim no comprehensiveness for my impressions on the topic. I find my references are aspirational more than usual; some do not even seem to be in print. In this post, I do not compare and contrast UBI with a Job Guarantee, which seems to be argued about a lot on twitter.

Three properties define a UBI, according to Philippe Van Parijs. It is paid to individuals, not households. One obtains a UBI payment independent of need or any other sources of income. And it is not conditional on one's willingness to accept a job or on a requirement to have worked in the past or to work in the future.

I think a UBI is consistent with Keynes' vision in 1931 of "Economic possibilities for our grandchildren". Whether increases in productivity are broadly shared, including in increased leisure or non-work time seems not to be determined by technology. In some sense, the use of such progress for progressive ends is a result of collective choice. By the way, increased non-work time is part of a response to the global climate crisis. I have seen statistics about how less carbon is emitted during recessions. If we labor less voluntarily, and share time somewhat fairly, those trends would continue, I gather. So UBI could be one component of a green policy.

I always like to find those on the right stating their principles support supposed policies of the left. I find Hayek's ideas in The Road to Serfdom as inconsistent with UBI:

"There is no reason why in a society which has reached the general level of wealth which ours has attained the first kind of security should not be guaranteed to all without endangering general freedom. There are difficult questions about the precise standard which should thus be assured; there is particularly the difficult question whether those who thus rely on the community should indefinitely enjoy all the same liberties as the rest. An incautious handling of these questions might well cause serious and perhaps even dangerous political problems; but there can be no doubt that some minimum of food, shelter, and clothing, sufficient to preserve health and the capacity to work, can be assured to everybody." -- Hayek (1944, Chapter IX).

Hayek argues for too much, in that UBI proponents do not claim to be assuring, by this policy alone, that some necessary minimum will be achieved. He argues for too little, in that proponents of UBI do not want to even consider limiting the liberties of those who receive it. Nevertheless, the above quotation, and the chapter in which it is in, might be of interest to advocates of a UBI. From Hayek's perspective, a UBI does not seem to be a threat to the liberty of private property.

I have been reading Steve Wright about a much more radical movement that developed ideas close to a UBI. His book is an intellectual history of operaismo (workerism) and the area of autonomy in Italy in the 1960s and 1970s. Mario Tronti and Antonio Negri are two leaders of these tendencies, albeit they seem like the kind that are, in some sense, leaderless and spontaneous. I find some of the slogans and practices (for example, "the refusal of work" and "self reduction" (autoriduzione)) associated with autonomism intriguing. Workerists developed the concept of the social worker, the idea that the self-reproduction of the economy occurred not only in factories, but outside including by such non-waged individuals as students and housewives. The autonomists wanted to separate pay from productive labor, including a wage for housework. This social "wage" sounds a lot like an UBI to me.

I now turn to an author I know even less about. Philippe Van Parijs seems to be the most prominent academic advocate of UBI. He comes out of the tradition of analytical Marxism. I associate G. A. Cohen, Jon Elster, and John Roemer with this approach, although I knew that the September group had more members. Here Chris Bertram interviews Van Parijs. Van Parijs seems to have a number of books, more than I list below, in which others comment in his idea for UBI and in which he responds. Apparently, in discussing the impact of an UBI on work ethic, this literature also turns to a stereotype of surfers. (I was under the impression that the sunfish sailboat was also the product of a beach bum.)

My favorite approach to economics emphasizes questions of viability and what is needed to sustain human societies. Guglielmo Chiodi connects Sraffa's book with an UBI and normative concerns. No physical surplus is produced in the model in the first chapter of Sraffa's book. The inputs of production processes can be just reproduced from the outputs. Prices of production are determined by the need to redistribute these outputs, in accordance with a division of labor. One can consider these inputs as including commodities to sustain workers, just as they might include feed for horses. I think I take from Bertram Schefold the idea that the inputs might also include investment goods and capitalist consumption. Chiodi goes further. He suggests inputs include consumption by those who are neither capitalists nor working. And he reads Sraffa as emphasizing non-market institutions and non-market values. I am not sure I agree with this reading, but I find it of interest. I agree with Chiodi that Sraffa is more than an internal critique of neoclassical economics, but points to an alternative approach to economics. I do not think I have read anybody other Chiodi as connecting Sraffa to UBI. But I still have more to learn about the autonomist slogan of "the wage as the independent variable."


Saturday, February 08, 2020

Reswitching With Markup Pricing And Fixed Capital

Figure 1: Two Dimensional Pattern Diagram
1.0 Introduction

This post extends an example from Bertram Schefold. It presents markup pricing in an example with a machine that can be operated for two years or junked after one year. This is a case of joint production in which, unlike in some cases, the choice of technique can still be analyzed by the construction of the wage frontier. Also, I do not think the question of requirements for use enter in here, and all matrices are square. As usual, this is a proof that "the marginal productivity theory of distribution" (and the neoclassical theory of supply and demand) "is all bosh" (Robinson 1961).

2.0 Technology

Table 1 shows the coefficients of production for the three processes comprising the available technology. Inputs must be available at the beginning of the year, and outputs become available at the harvest at the end. In the first process, labor uses inputs of corn to produce a new machine. That machine is used by labor in the second process, with inputs of seed corn, to produce more corn and a one-year old machine. In the third process, labor uses inputs of seed corn and the one-year old machine to produce corn. (I did think of calling the machine a "tractor".) The machine varies in physical efficiency over the course of its lifetime.

Table 1: Coefficients of Production for The Technology
InputMachine IndustryCorn Industry
One ProcessAnother Process
Labora0, 1 = 1/10a0, 2 = 43/40a0, 3 = 1
Corna1, 1 = 1/16a1, 2 = 1/16a1, 3 = 1/4
New Machinesa2, 1 = 0a2, 2 = 1a2, 3 = 0
Old Machinesa3, 1 = 0a3, 2 = 0a3, 3 = 1
Cornb1, 1 = 0b1, 2 = 1b1, 3 = 1
New Machinesb2, 1 = 1b2, 2 = 0b2, 3 = 0
Old Machinesb3, 1 = 0b3, 2 = 1b3, 3 = 0

The technology is summarized by a row vector a0, the input vector A, and the output vector B. The example satisfies various assumptions that show the economy hangs together, in some sense, and that it is more than viable.

The technology also presents a choice of technique. Managers of firms in corn-production may want to truncate the use of the machine to one year, given certain configurations of prices. In the Alpha technique, the machine is used for two years. I call the technique in which the machine is only used for one year the Beta technique.

3.0 Prices of Production

The price equations for the Alpha technique are:

p A (I + r S) + w a0 = p B

where p is a row vector of three prices (the price of corn, the price of a new machine, and the price of a one-year old machine), w is the wage, and r is the scale factor for the rate of profits. In a common notation, I is the identity matrix. The square matrix S is a diagonal matrix. Its diagonal elements express persistent differences in the rate of profits among processes or industries. The rate of profits in the jth process is r sj.

I take corn as the numeraire. This can be expressed as:

p e1 = 1

where e1 is the first column of the identity matrix.

4.0 Some Visualizations of the Solution

Assume, without loss of generality, that the markup coefficient, s1, in the process producing new machines is unity. Figure 2 shows how the choice of technique varies with the wage in the case where the markup coefficients in corn-producing processes do not vary with the age of the machine. When barriers to entry in producing new machines ensure that the markups in corn production fall appreciably below the overall rate of profits, managers of corn-producing firms will operate the machine for its full physical life, whatever the wage. On the other hand, roughly, if the corn-producing industry maintains barrier to entries, the machine will be operated for its full life only at low and high wages. At intermediate wages, the use of the machine will be truncated after one year. As still higher markups in corn-production, the machine will only be operated for the full two years for high wages.

Figure 2: A Pattern Diagram

Figure 2 can be constructed in two ways. One is by constructing the wage frontier out of the wage curves for the two techniques. Figure 3 shows an example. This case is for what I call a reswitching pattern. The two wage curves are tangent at the single switch point. In finding the wage curve for the Alpha technique, one can also solve for the price of a one-year old machine. In the analysis of truncation with fixed capital, the machine is operated for only one year when this price turns negative. Switch points between the two techniques arise for wages in which the price of a one-year old machine is zero. I believe this analysis applies with the formulation of markup pricing in this post.

Figure 3: Wage Curves for a Reswitching Pattern

Figure 1, at the top of this post, generalizes the analysis to all values of the markups in the corn-producing processes. Regions are indicated in which the machine is operated for two years, whatever the wage; in which this is an example of reswitching; and in which the machine is operated for two years only for high wages. The dashed (45-degree) line shows the case in which the markup is the same in both corn-producing processes.

I wonder if it makes any economic sense to consider cases off the 45-degree line in Figure 1. In this simple example, the two corn-producing processes are in the same industry, in some sense. If one agrees with this limitation for economic sense, a question arises. How, in some formulation of markup pricing, should such constraints be formulated, in general, for prices of production in models of joint production? Could markups, for instance, vary between the production of mainly wool and mainly mutton? Since definitions of even basic commodities vary among analyses of joint production, I do not see how to identify such processes in general where you might want to raise the question. Maybe these questions could be partly addressed by considering the process of vertical integration.

5.0 Conclusions

This post has illustrated that the analysis of the choice of technique must be performed in models with fixed capital. Managers of firms always have the choice of truncation, of adopting a technique in which the economic life of a machine is shorter than its physical life. This presents a challenge to attempts to justify Marx's theory of value with Sraffa's standard commodity. I have not even gone into some of the complications raised by pure joint production and models in which multiple types of machines are used.

  • Luigi L. Pasinetti (ed.) 1980. Essays on the Theory of Joint Production. New York: Columbia University Press.
  • Joan Robinson. 1961. Prelude to a critique of economic theory. Prelude to a critique of economic theory 13: 53-58.
  • Bertram Schefold. 1980. Fixed capital as a joint product and the analysis of accumulation with different forms of technical progress. In Pasinetti 1980.

Friday, January 31, 2020

Precursors of Piero Sraffa

I want to consider contributions to economics after 1870 that reconsidered classical or Marxist economics, used input-output models and linear algebra, or bear a family resemblance to at least some points in Sraffa's 1960 book.

  • Vladimir K. Dmitriev. Used input-output analysis in an interpretation of Ricardo's theory of value.
  • Ladislaus Bortkiewicz. Had a simple three-good model, with one basic good, input-output model of prices of production. Sraffa and others argued against aspects of his interpretation of Marx's theory of value.
  • Georg von Charasoff. Apparently, around 1909 and 1910, he came up with the concept of "original capital". In a infinite series, much like Sraffa's reduction to dated labor, the capital goods needed more and more indirectly in producing some given net output converge to Sraffa's standard commodity.
  • Father Maurice Potron. A fairly conservative Jesuit priest and mathematician, writing in French. I know of him from this collection.
  • Wassily Leontief. His empirical work extends from the 1920s. I do not know that those building on his work often cite Sraffa.
  • Walter Isard. Applied Leontief input-output analysis to regional or spatial economics in 1951.
  • John von Neumann. I am thinking of the 1945-1946 translation of his A Model of General Economic Equilibrium. Kurz and Salvadori read this as a response to Robert Remak.
  • Jacob T. Schwartz. A mathematician whose 1961 Lectures on the Mathematical Method in Analytical Economics criticizes neoclassical and Austrian economics. Personally, I found his work not as rigorous as Sraffa's.

I do not know much about many of these authors, but other economists in the post Sraffian tradition have written about them.

Saturday, January 25, 2020

Why Does The Labor Theory Of Value Work Empirically As A Theory Of Prices?

Anwar Shaikh On The Transformation Problem

Lots of empirical work shows that prices tend to be proportion to the labor embodied in commodities. My references in this article document this claim. Furthermore, empirical wage-rate of profits curves tend to be close to straight lines. This is not what, say, Sraffa' mathematical economics would lead me to expect. What explains these surprising empirical findings?

Almost 34 minutes in, in the above video, Shaikh makes the above point about the contrast between theory and empirical findings. He concludes with speculation, including with comments on Bertram Schefold's work with input-output matrices formed out of random matrices.

I offer some speculations myself in this post. I do not have much theory to back these suggestions up.

The Leontief matrices obtained from National Income and Product Accounts (NIPAs) are still highly aggregated. The empirical results on the LTV are obtained with matrices that have on the order of, say, 100 industries. One of these industries, if disaggregated, might contain commodities that are produced with a high Organic Composition of Capital (OCC) and a low OCC. Their prices of production would deviate more from labor values than an average combining them both. The extremes would be cancelled out in forming an average.

In my examples of pattern analysis, I also suggest that Sraffa effects could be difficult to see, in that they arise in a transition from one very long run position to another. But I concoct those examples to make a point about possibilities. I do not want to insist on any empirical point here.

Technical progress, despite how I usually model it, is endogenous. If in process of production adopted in some industry, some input is noticeably more expensive than others, managers of firms will seek out and research processes in which that input is reduced or some other cheaper input is substituted for it. Perhaps after a couple of centuries of rapid technical change under these incentives, empirical Leontief input-output matrices will have the properties Schefold highlights for random matrices. I suppose one could confirm this by showing wage-rate of profits curves are closer to affine functions for more highly developed economies. I have done some empirical work along these lines.

Aside: Here is another YouTube video with Anwar Shaikh. He sounds a lot like he accepts Milgate and Eatwell's critique of "imperfectionism". Actually existing capitalism is to be analyzed by a theory that accepts empirical reality, not by deviations from a neoclassical utopia that could never exist in any conceivable world.

Saturday, January 18, 2020

Only The Super-Rich Can Save Us!

Neoliberals are hostile to labor unions and every other institution that would allow the vast majority of the population to have some effect on how we are ruled. And they have been so successful that only the super-rich can save us, as the title of a Ralph Nader novel a few years back had it. A couple of recent examples of journalism are about movements of the super-rich:

I suspect most of the super-rich, however, are vicious, reactionary fools. Apparently, Benjamin Page, Jason Seawright, and Matthew Lacombe provide evidence in their recent book, Billionaires and Stealth Politics. I've read and commented on their previous working paper.

In the United States and elsewhere, we had a progressive movement reacting to the terrible effects and excesses of the "roaring twenties" of a century ago. Of course, there was a fascist movement, too, that resulted in global war.

In the United States, prominent celebrities such as Henry Ford and Charles Lindbergh supported fascism. The super-rich did not step back. The business plot was an attempt by millionaires to stage a coup against Franklin Delano Roosevelt. They tried to get Major General Smedly Butler to act as a figurehead. I know of him for saying, war is a racket. I do not know if this falls in the politics of the super-rich, but I only recently learned about the Christian Front, a fascist organization inspired by the radio demagogue Father Coughlin. In 1940, their office in New York City was raided by the FBI for trying to overthrow the government. Seventeen members was arrested, but their prosecution was unsuccessful. (Caveat: I have not read the books and literature linked to in this paragraph.)

I think we need a better material basis than the well wishes and work of the super-rich to bring about hopeful change.

Saturday, January 11, 2020

Towards the Derivation of the Cambridge Equation with Expanded Reproduction and Markup Pricing

I have a new working paper.

Abstract: Does the Cambridge equation, in which the rate of profits in a steady state is equal to the quotient of the rate of growth and the savings rate out of profits, hold in an economy with widespread non-competitive markets? This article presents a multiple-good model of markup pricing in an attempt to answer this question. A balance equation is derived. Given competitive conditions, this model can be used to derive the Cambridge equation. The Cambridge equation also holds in a special case of markup pricing, with one capital good and many consumption goods being produced. No definite conclusions are reached in the general case.

Tuesday, January 07, 2020

The Factor Price Frontier In The Space Of Factor Rental Prices

Figure 1: Real Factor Price Frontier
1.0 Introduction

Carlo Milana has proposed a new way of visualizing the choice of technique, including in the case of reswitching. This way of describing what he has done is not neccessarily how he thinks of it. In this post, I describe his approach with a reswitching example, in a model of the production of commodities by means of commodities.

2.0 Technology

Table 1 shows the coefficients of production for this example. Coefficients of production specify inputs per unit output. Each process takes a year to complete. Inputs are totally used up in the production of the outputs. (This example is taken from one of my papers.)

Table 1: Coefficients of Production for The Technology
InputSteel IndustryCorn Industry
Labor1275/4641 Person-Yr
Steel1/10113/2322 Tons
Corn1/400(2/5) Bushels

Two techniques of production arise in this example. The Alpha technique consists of the Alpha process for producing steel and the corn-producing process. Both steel and corn are basic commodities, in the sense of Sraffa, for the Alpha technique. The Beta technique consists of the Beta process for producing steel and the corn-producing process. Only steel is a Sraffa-basic commodity for the Beta process. Suppose, however, corn is the only consumption good in this example. Then in the Beta technique, as with the Alpha technique, both steel and corn will be (re)produced for both techniques.

3.0 Prices of Production

If the Alpha technique is in use in a long-period position, prices satisfy the following two equations:

((1/10) pα,1 + (1/40) pα,2)(1 + r) + wα = pα,1
(2 pα,1 + (2/5) pα,2)(1 + r) + wα = pα,2

Prices are spot prices. The services of produced inputs are paid for at the start of the year, while wages are paid out of the surplus at the end of the year.

The corresponding equations for prices for the Beta technique are:

((113/232) pβ,1)(1 + r) + (275/464) wβ = pβ,1
(2 pβ,1 + (2/5) pβ,2)(1 + r) + wβ = pβ,2

At this point, I take a bushel corn as the numeraire. One can solve the Alpha system of equations, for example, to find (wα/pα,1) as a function of the interest rate. This is the wage curve for the Alpha technique and is shown below. The wage curve for the Beta technique is also graphed. The outer envelope of these curves, called the wage frontier, shows which technique is cost-minimizing at any given interest rate. Both techniques are cost-minimizing at the switch points, which arise for interest rates of 20 percent and 80 percent. Between the switch points, the Alpha technique is cost-minimizing. Outside the switch points, the Beta technique is cost minimizing.

Figure 2: Wage Curves and the Wage Frontier

4.0 Rental Prices for Factor Inputs

In marginalism, the choice of technique is often analyzed in terms of rental prices for factors of production. One can think of the example in terms of three factors: labor, steel, and corn. Steel and corn are capital goods.

Since a choice of production processes arises in the steel industry, I here take steel as numeraire. The rental price, also known as the factor price, for labor is the real wage:

wα,L = wα/pα,1

The rental or factor price for steel is the cost of a the services of a ton of steel when paid at the end of the year:

wα,Steel = pα,1(1 + r)/pα,1

Likewise, the rental or factor price of corn is:

wα,Corn = pα,2(1 + r)/pα,1

Using these definitions, the condition that, when in use, no extra profits are made and no extra costs are in incurred in producing steel with the Alpha process yields the following equation:

(1/10) wα,Steel + (1/40) wα,Corn + wα,L = 1

Notice that this is a linear equation in three variables. It is illustrated by the blue plane in Figure 1. The factor prices for the Beta process yield another linear equation:

((113/232) wβ,Steel + (275/464) wα,L = 1

The plane for Beta is shown in red in Figure 1.

At a switch point, both the Alpha and the Beta processes are eligible for adoption by cost-minimizing managers of firms. Accordingly, switch points must lie on the intersection of the two planes described above. The intersection, although difficult to see, is shown in black in the figure.

In discussing rental or factor prices, I have yet to take into account that corn must also be produced. If one substitutes, on the right-hand side in the three equations defining rental prices, the solution of the Alpha system of equations in Section 3, one obtains factor prices as a parametric function of the interest rate. This is the real factor price curve for the Alpha technique and is shown in blue above. The real factor price curve for the Beta technique, in red, is easier to see. (Each real factor price curve lies within the plane of the same color.) For each curve, when it lies on the real factor price frontier is indicated. And the switch points do indeed lie on the intersections of the real factor price curves.

5.0 Conclusion

Does the real factor price frontier in Figure 1 provide a mechanism for analyzing the choice of technique? Is the factor price curve for the cost-minimizing technique always furtherest from the origin?

The wage frontier, where applicable, can be drawn in a two-dimensional diagram for examples with any number produced of produced commodities. If n commodities are produced, Milana's diagram illustrates, roughly, the intersections of hyperplanes of dimension (n - 1). And those intersections will be themselves hyperplanes of dimension (n - 2). Switch points, if any, lie in those intersections. The factor price curves will still be one-dimensional curves, as I understand it, in the appropriate hyperplanes.

Obviously, this cannot be visualized in higher dimensions. Nevertheless, the mathematics still works out. Different valid approaches to finding the cost-minimizing technique in a long-period position, given an exogenous specification of the distribution of income, in some sense, will all yield the same answer. That is the case for the reswitching example presented here.

Thursday, January 02, 2020

Some People Who Have Shaped Economics

"The University [of Chicago] is the best investment I ever made in my life." -- John D. Rockefeller

Consider the following people and selected activities:

  • Lewis Brown founded the American Enterprise Institute, in 1938.
  • Jasper Crane cofounded the Foundation for Economic Education, in 1946.
  • Leonard Read cofounded the Foundation for Economic Education, in 1946.
  • Harold Luhnow, even before 1947, directed spending for the Volker Fund.
  • Sir Antony Fisher funded the Institute for Economic Affairs, around 1956.
  • Lord Ralph Harris, first general director of the Institute for Economic Affairs.
  • Arthur Seldon, first editorial director of the Institute for Economic Affairs.
  • F. A. Harper founded the Institute for Humane Studies, in 1961.
  • Charles Koch funded the development of the Virginia school, notably including James Buchanan's work.
  • Edwin Feuler, founded the Heritage Foundation, in 1973.
  • Edward H. Crane founded the Cato Institute, in 1977.
  • Eamonn Butler cofounded the Adam Smith Institute, in 1978.
  • Madsen Pirie cofounded the Adam Smith Institute, in 1978.

I've written on the influence of fundings sources on the development of economics before. A developing body of scholarly literature explores the impact of the above list of people. The above list is not complete. For example, John Blundell seems to be an important fellow in the world hinted at above.

I think funding sources have been concentrated on the right. I suppose you can try to make a list not so concentrated on the right. George Soros and the Institute for New Economic Thinking, John Reed of Citicorp and Santa Fe Institute, John Podesta and theCenter for American Progress (CAP) would all be in the list. I do not know where funding for the Economic Policy Institute comes from. It seems to me a distinction exists between investigating ideas and trying to publicize conclusions you already believe.