Structural Economic Dynamics, Markups, Real Wicksell Effects, And The Reverse Substitution Of Labor

I am being published in Structural Change and Economic Dynamics. Currently, this link is without my corrections to proofs, I guess.

Research highlights:

• Technical progress and variations in industry markups can change characteristics of the labor markets.
• A numeric example illustrates the theory of the choice of technique.
• In the example, switch points are created and destroyed with varying coefficients of production and varying markups.
• Around some switch points, higher wages are associated with greater employment, given the level of net or gross output
• Graphical displays are provided for visualizing these results.

Abstract: This article presents an example in which perturbations in relative markups and technical progress result in variations in characteristics of the labor market. Around a switch point with a positive real Wicksell effect, a higher wage is associated with firms wanting to employ more labor per unit output of net product. Around a switch point with a reverse substitution of labor, firms in a particular industry want to hire more labor per unit output of gross product. Technical progress and variations in markups can bring about and take away circumstances favorable for workers wanting to press claims for higher wages. This article presents specific fluke switch points in which variations in technology and markups change these circumstances, as well as novel diagrams for visualizing the effects of such variations.

No Such Thing As The Natural Rate Of Unemployment

I know that the idea of a "natural rate" of unemployment or a non-accelerating inflation rate of unemployment (NAIRU) makes no sense. I cite, for example, James Galbraith's 1998 book, Created Unequal: The Crisis in American Pay. I think Colin Rogers' 1989 book is related.

Jared Bernstein gives the idea of a natural rate of unemployment at the first of four examples of ideas that [mainstream] economists have gotten wrong for decades. This is not the first example of a case where Post Keynesians (and only Post Keynesians(?)) could explain an empirical phenomenon decades in advance.

Harrod-Neutral Technical Progress and Fluke Switch Points

Figure 1: A Pattern Diagram

I have put up a working paper with the post title.

Abstract: This article considers Harrod-neutral technical progress in the context of an analysis of the choice of technique. In a model of the production of commodities by means of commodities, neutral technical change is compatible with the reswitching of techniques, capital reversing, process recurrence, and the reverse substitution of labor. A taxonomy of fluke switch points is applied to an example, illustrating how these phenomena can arise and vanish in the course of neutral technical progress.

I get various fluke switch points, as is typical of my examples. By assuming Harrod-neutral technical change, I end up with the structure in Figure 2, in one slice of the parameter space.

Figure 2: A Two-Dimensional Pattern Diagram

Children, Dialectics, and Topology

"One of the curious things about our educational system, I would note, is that the better trained you are in a discipline, the less used to dialectical method you're likely to be. In fact, young children are very dialectical; they see everything in motion, in contradictions and transformations. We have to put an immense effort into training kids out of being dialecticians." -- David Harvey, Companion to Marx's Capital: The Complete Edition. Verso (2018).

I do not have children, and I am not sure I understand Harvey's claim. But one writer I liked was Jean Piaget. (I also want to mention Seymour Papert.)

I take from him that children think in a way that can be described by advanced mathematics. I think, in particular, of topology and modern algebra. The idea is children take time to learn certain invariants and conservation laws that many of us now take for granted. In topology, one asks what can be said about sets and functions when one does not have a distance function? If you rotate a disk, suppose, for example, the distance between two points cannot be assumed the same when you look in the east-west and north-south direction. Algebra investigates certain abstract structures, with as little as possible assumed about the properties of operations. A difference between mathematicians and children, however, is that the mathematicians (better than me) learn how to articulate and characterize such structures.

I do not think I am necessarily contradicting Harvey. J. Barkley Rosser, Jr. has a paper that perhaps can be used to draw connections between Piaget and Harvey's ideas about how children think.

On Milana's Purported Solution To The Reswitching Paradox

Carlo Milana has posted a paper on arXiv. I was prepared to accept this paper's claims. Economists have developed price theory. Referring to Sraffian "paradoxes" and "perverse" switch points is a matter of speaking. There does not exist separate Sraffian and neoclassical versions of price theory. For a result to be "perverse", it need only contradict outdated neoclassical intuition. But it is as much a part of the mathematical economics as any other result. (It is another matter that much teaching in microeconomics is inconsistent with the mathematics.)

In equilibrium, the price of the services of each capital good in use is equal to the value of the marginal product of that good, with all prices discounted to the same moment in time. This discounting implies that the interest rate appears in a formal statement of these equations. These equalities are very different from the claim that the interest rate equals the marginal product of (financial) capital. In limited cases, one can prove something like the aggregate equality. No such thing as a marginal productivity theory of distribution, however, is restored. Milana might cite Hahn (1982) on this background.

But Milana goes further. He claims that reswitching is impossible or, at least, examples up to now are erroneous.

I think Milana's basic mistake is exposed in Salvadori and Steedman (1988). (I go through one of their examples here.) The Samuelson-Garegnani model is not a model of two-(produced) goods. The model contains as many capital goods as there are techniques. Potentially, there can be a continuum of capital goods in the model. As such, it is meaningless to require the price of the capital goods used in each technique that is cost-minimizing at a switch point to be equal to one another. That is analogous to requiring the price of a ton of iron be equal to the price of a ton of tin.

For some reason, Milana does not discuss examples of reswitching in flow-input, point output models, such as in Samuelson (1966). Nor does he acknowledge, as I read him, valid examples in which the same n commodities are produced in all techniques, and all commodities are basic in all techniques. (Does he say anything at all about the distinction between basic and non-basic commodities?) At a non-fluke or generic switch point, in such a framework, the two techniques that are cost-minimizing differ in a process in exactly one industry.

Milana should read and reference Bharadwaj (1970), as well as Bidard and Klimovsky (2004) on fake switches in models of joint production. Other Linear Programming formulations are available for considering the choice of technique. Vienneau (2005) presents one. What does Milana have to say about the direct method for analyzing the choice of technique in Kurz and Salvadori (1995)? I briefly provide a survey of different analysis in Vienneau (2017), as well as an algorithm for finding the cost-minimizing technique? Are all these approaches in error?

References

• Khrishna Bharadwaj. 1970. On the maximum number of switches between two production systems. Schweizerische Zeitschrift fur Volkswortschaft and Statistik (4): 401-428. Reprinted in Bharadwaj 1989. Themes in Value and Distribution: Classical Theory Reappraised, Unwin-Hyman.
• Christian Bidard and Edith Klimovsky. 2004. Switches and fake switches in methods of production. Cambridge Journal of Economics 28:89-97
• Frank Hahn. 1982. The neo-Ricardians Cambridge Journal of Economics 6:353-374.
• H. D. Kurz and N. Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge University Press.
• Carlo Milano. 2019. Solving the Reswitching Paradox in the Sraffian Theory of Capital. arXiv:1907.01189
• Neri Salvadori and Ian Steedman. 1988. No reswitching? No switching! Cambridge Journal of Economics 12: 481-486.
• Paul A. Samuelson. 1966. A Summing Up. The Quarterly Journal of Economics 80 (4): 568–583.
• Robert Vienneau. 2005. On labour demand and equilibria of the firm. The Manchester School 73(5): 612-619.
• Robert Vienneau. 2017. The choice of technique with multiple and complex interest rates. Review of Political Economy 29(3): 440-453.