Heterodox
The logical possibility of the reswitching of techniques is a devastating challenge to marginalism. But the Cambridge capital controversy does not depend on the presence of reswitching. I suppose I should have links for the possibilities listed below. None of these possibilities are fluke cases. One might make a distinction between the reswitching of techniques and the recurrence of techniques. In both cases a technique is cost-minimizing at two non-overlapping ranges of the wage. If only one technique is cost-minimizing at wages between these ranges, that is reswitching. If more than one technique is cost-minimizing between, then one should talk about the recurrence of techniques. I forget where I have seen this not very common and not very useful distinction. Capital reversing
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Robert Vienneau considers the following as important: Sraffa Effects, Vocabulary
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The logical possibility of the reswitching of techniques is a devastating challenge to marginalism. But the Cambridge capital controversy does not depend on the presence of reswitching. I suppose I should have links for the possibilities listed below. None of these possibilities are fluke cases.
One might make a distinction between the reswitching of techniques and the recurrence of techniques. In both cases a technique is cost-minimizing at two non-overlapping ranges of the wage. If only one technique is cost-minimizing at wages between these ranges, that is reswitching. If more than one technique is cost-minimizing between, then one should talk about the recurrence of techniques. I forget where I have seen this not very common and not very useful distinction.
Capital reversing can occur with neither the reswitching of techniques nor the recurrence of techniques occurring on the wage frontier. Reswitching and the recurrence of techniques, however, imply the existence of a switch point in which capital reversing occurs. With capital reversing, a lower rate of profits around a switch point is associated with a switch to a technique with a lower capital intensity and a lower net output per labor input. Capital intensity is measured by either the capital-labor ratio or the capital-output ratio, with capital valued at prices of production. Net output is of a given physical composition. I like to express the logical possibility of capital reversing by noting that around such a switch point, firms want to hire a greater quantity of labor at a higher wage, given net output.
A production process can be in cost-minimizing techniques at two non-overlapping ranges of the wage, with techniques not operating this process being cost-minimizing at intermediate wages. The recurrence of techniques implies process recurrence, but process recurrence can exist without the recurrence of techniques.
The reverse substitution of labor can occur without the recurrence of techniques, capital reversing, or process recurrence. The reverse substitution of labor occurs when around a switch point, the technique that is cost-minimizing at a higher wage results in the adoption of a process in some industry in which more direct labor is hired per unit of gross output in that industry.
The presence of fixed capital creates the possibility of additional effects. The analysis of the choice of technique includes the analysis of the economic life of machines. The recurrence of truncation occurs when the economic life of a machine in the cost-minimizing technique is the same at two non-overlapping ranges of the wage. Some other economic lifetime is in the cost-minimizing technique at intermediate wages.
In the theory of fixed capital, the adoption of a cost-minimizing technique around a switch point with an increased economic life of a machine can be associated with the choice of a less capital-intensive technique of production. I do not have a name for this phenomenon. As far as I know, nobody has explicitly pointed out this possibility before me, although I will not be surprised if somebody points out some text in Pasinetti (1980) or some work by Schefold.
I next turn to the theory of extensive rent, another special case of the theory of joint production. The order of fertility, also known as the order of efficiency, is the order of types of land, given the wage, from a high rate of profits downwards among wage curves. Alternatively, one can take the rate of profits as given and order lands downward by wages. These orders are not necessarily the same. The order of fertility shows the order in which lands will be cultivated as requirements for use expand. Anyways the order of fertility can vary with distribution.
The order of rentability is the order of types of land from high rent per acre to low rent per acre. The order of rentability can vary with distribution.
The order of fertility need not match the order of rentability. Whether or not these orders of types of land match can vary with distribution.
One can have the reswitching of the order of fertility. Given requirements for use, the order of fertility can be the same at two non-overlapping ranges of the wage. Some other order of fertility occurs at intermediate wages. One might note this possibility does not require any variation in the cost-minimizing technique. The same processes can be operated for industrial commodities, and the same types of land can be fully cultivated. The type of land that is only partially cultivated can be cultivated at the same level with these variations with distribution.
One can also have the reswitching of the order of rentability. Given requirements for use, the order of rentability can be the same at two non-overlapping ranges of the wage. Some other order of rentability occurs at intermediate wages. This possibility also does not require any variation in the cost-minimizing technique. As far as I know, I am the first to point out the possibility of the reswitching of the order of fertility and of the reswitching of the order of rentability.
The above descriptions of various results from the analysis of the choice of technique have all been about how cost-minimizing techniques vary around switch prices. I have not considered variations in prices of production for a single technique as distribution varies. Such variations are known as price Wicksell effects. Nor have I considered the general theory of joint production or the special case of intensive rent.
Prices of production reflect a different vision of political economy than marginalist theory.