Abstract
We shall not attempt here any final, or even penultimate, resolution of the capital theory controversies that have raged and sputtered with varying degrees of intensity over the last several decades. We are referring here to those labeled “Cambridge controversies,” (Harcourt, (1972)) after Cambridge, England and Cambridge, Massachusetts, the respective locations of several of the principal participants. However, we shall attempt to explicate the role played by discontinuity in certain aspects of these controversies and perhaps to the continuing lack of any such ultimate resolution of these controversies.
“Time is a line that eats itself”
Michael Friedman, 1977, First Blood
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Notes
Prince and Rosser (1985) argue that delayed environmental costs associated with certain techniques can be the source of such an effect. Asheim (1980) presents a model of “paradoxical consumption behavior ” based on a similar argument regarding delayed environmental costs.
An unusual response to Steedman was by Farjoun and Machover (1983) who argue that the probabilistic nature of economic outcomes undermines the neoRicardian critique and supports the usefulness of Marxian labor values in long-run analysis.
Assuming that technology is neoclassical will not bring about this condition if inputs to production are complementary Matta, 1976 ). Such complementarity has been allegedly found in four factor aggregate production functions between energy and capital (Berndt and Wood, 1979).
These techniques are all constant returns to scale, as in the von Neumann (1937) model. A more complex description would be necessary otherwise unless we assume constant levels and composition of output. Sraffa (1960) assumed these latter two points thus allowing the hotly disputed claim that his model did not assume constant returns to scale (Levine, 1974 ).
The image of a “book of blueprints” suggests a countably infinite set of techniques. However since techniques are representable by curved lines, the set may be as great as ti2 i the level of infinity above the continuum. Indeed there may be more techniques passing through a single point on the WPF than there are points on the WPF.
This concept has been used previously to describe related micro techniques, i.e. TV and VCRs. To my knowledge this is the first use of it for whole-economy techniques.
It could be that a technique cluster represents a set of related neoclassical production functions for the respective commodities. A different cluster would be an alternative such set. Thus we can subsume neoclassical technologies within the book-of-blueprints approach.
Much of this literature talks loosely about “neighboring techniques” when they are infinite in number. If they are countably infinite it may be possible to identify specific “neighbors,” much as the integers 3 and 5 are the“neighbors” of 4. However if the WPF is a continuum and the number of techniques is also (or greater), then all talk of “neighboring techniques” is essentially empty and at best highly metaphorical.
We shall assume the capital good is homogeneous and physically measurable. It has often been argued (Harris, 1973; Yeager and Burmeister, 1978) that a change of capital-intensity in the capital-good implies a different capital good. The author has always disagreed with this, believing that a commodity is defined by what it is, not how it was produced.
Salvadori and Steedman (1988) and Woods (1988) have shown for a two-sector, two technique world that if sectors have equal capital intensities (equal “organic compositions of capital” and hence straight-line wage-profit curves), and the two techniques share at least one process, then there are no switch points between them. Assuming a common process was part of the failed effort by Gallaway and Shukla (1974) to sharply limit reswitching possibilities, critiqued by Garegnani (1976), Sato (1976), and by Laibman and Nell (1977).
Joan Robinson would certainly consider such assumptions to amount to “putting the rabbit in the hat in full view of the audience before taking it back out again with great drama.”
Albin (1975) claimed to have discovered such a case in the Northwest US lumber industry where horse technology was used at low wage rates in the nineteenth century and at high wage rates in the late twentieth century whereas mechanized technology was used at intermediate wage rates. Prince and Rosser (1983) argue that this is not actual “historical reswitching” because the high wage horse technique involves environmental cleanup whereas the low wage one did not. We-could say that what “recurred” was the horse-related “technique cluster” rather than the exact same technique.
Emphasis upon both technological as well as financial uncertainty has been a major theme of Post Keynesian analysis (Davidson, 1982–83).
Schumpeter’s model included shorter cycles, Juglars and Kitchins, within the longer Kondratieffs. Goodwin (1986) has developed such a model exhibiting short-term fluctuations within longer-term technological shifts. Similar efforts have been made by Medio (1984) emphasizing synergetics and by Silverberg (1984) emphasizing self-organization as bases for major structural shifts.
The Day-Walter model was originally motivated by a multi-disciplinary conference on the causes of the Classic Mayan collapse (Sablov, 1980). Prince (1985) shows the possibility of that collapse as arising from the interaction of nonconvexities and externalities in a neoclassical production function.
And as Joan Robinson would point out, true reswitching involves steady-state equilibirum comparisons in logical time rather than transitions in historical time.
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Rosser, J.B. (2000). Discontinuity and Capital Theory. In: From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1613-0_8
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