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

Input	Industry
	Iron	Corn
		Alpha	Beta
Labor	a0,1 = 1	aα,0,2(t) = (5191/5770) e(1/10) - σ t	aβ,0,2 = 305/494
Iron	a1,1 = 9/20	aα,1,2(t) = (1/40) e(1/10) - σ t	aβ,1,2 = 3/1976
Corn	a2,1 = 2	aα,2,2(t) = (1/10) e(1/10) - σ t	aβ,2,2 = 229/494

• Vienneau, Robert L. 2019. Structural economic dynamics, markups, real Wicksell effects, and the reverse substitution of labor. Structural Change and Economic Dynamics 50: 216-226.

Elsewhere

• 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.

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."

References

• Rutger Bregman, Utopia for Realists: How we can build the ideal world, 2018.
• Guglielmo Chiodi. Beyond capitalism: Sraffa's economic theory. In Sraffa or an Alternative Economics (ed. by Guglielmo Chiodi and Leonardo Ditta), Palgrave Macmillan, 2008.
• Guglielmo Chiodi. Sraffa and the universal basic income: some notes. In The Evolution of Economic Theory: Essays in honour of Bertram Schefold (ed. by Volker Caspari). Routledge, 2011.
• Guglielmo Chiodi and Leonardo Ditta. Sraffa and Keynes: Two ways of making a 'revolution' in economic theory. In Sraffa and the Reconstruction of Economic Theory: Volume 1 (ed. by Enrico Sergio Levrero, Antonella Palumbo and Antonella Stirati), 2013.
• Mariarosa Dalla Costa and Selma James. The Power of Women and the Subversion of the Community. 1973.
• Phil Edwards. 'More Work! Less Pay!' Rebellion and Repression in Italy, 1972-7. Manchester University Press, 2009.
• David Frayne. The Refusal of Work: Rethinking Post-Work Theory and Practice. 2015.
• F. A. Hayek, The Road to Serfdom, 1944.
• John Maynard Keynes, Economic possibilities for our grandchildren. In Essays in Pursuasion, 1931.
• Philippe Van Parijs (ed.). Arguing for Basic Income: Ethical Foundations for a Radical Reform., Verso.
• Philippe Van Parijs. Real Freedom for All: What (if Anything) Can Justify Capitalism? Oxford University Press, 1997.
• Philippe Van Parijs et al. What's Wrong with a Free Lunch, Beacon Press, 2001.
• Philippe Van Parijs and Yannick Vanderborght. Basic Income: A Radical Proposal for a Free Society and a Sane Economy, 2019.
• Steve Wright. Storming Heaven: Class Composition and Struggle in Italian Autonomist Marxism, 2nd edition. 2017.

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

Input	Machine Industry	Corn Industry
		One Process	Another Process
Labor	a0, 1 = 1/10	a0, 2 = 43/40	a0, 3 = 1
Corn	a1, 1 = 1/16	a1, 2 = 1/16	a1, 3 = 1/4
New Machines	a2, 1 = 0	a2, 2 = 1	a2, 3 = 0
Old Machines	a3, 1 = 0	a3, 2 = 0	a3, 3 = 1
Output
Corn	b1, 1 = 0	b1, 2 = 1	b1, 3 = 1
New Machines	b2, 1 = 1	b2, 2 = 0	b2, 3 = 0
Old Machines	b3, 1 = 0	b3, 2 = 1	b3, 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 s_j.

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.

References

• 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.