**Summary:**

I have a research program that I have been pursuning for several years. And I seem to be able to go on for several more years. I have been looking at the analysis of the choice of technique in models of the production of commodities by means of commodities. Fluke cases are characterized as losing their qualitative properties with almost any perturbation of the parameters of the model. The parameter spaces in these models are partitioned by these fluke cases. Within a region formed by the partitions, qualitative behavior is invariant. I have been looking for regions in which such phenomena as reswitching, capital-reversing, the reverse substitution of labor, or the recurrence of processes occur. These models are open, with the functional distribution of income taken as exogenous to the

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I have a research program that I have been pursuning for several years. And I seem to be able to go on for several more years.

I have been looking at the analysis of the choice of technique in models of the production of commodities by means of commodities. Fluke cases are characterized as losing their qualitative properties with almost any perturbation of the parameters of the model. The parameter spaces in these models are partitioned by these fluke cases. Within a region formed by the partitions, qualitative behavior is invariant. I have been looking for regions in which such phenomena as reswitching, capital-reversing, the reverse substitution of labor, or the recurrence of processes occur. These models are open, with the functional distribution of income taken as exogenous to the model.

I think of my reseach as in agreement with Ian Steedman. The critique of marginalism coming out of the Cambridge Capital Controversy was too gentle. Prices of production are not to be explained by supply and demand. My hope is that if others take into account my sort of fluke cases, they will see that so-called 'perverse' cases are not strange at all. One can find statements in the literature about some cases being non-generic and other examples allowing for continuous variation in parameters to some extent. I suppose I ought to note such statements next time I come across them.

I have already achieved some publications from this research program:

- Normal forms for switch point patterns".
*Review of Behavioral Economics*5(2) 2018: 169-195. - Structural economic dynamics, markups, real Wicksell effects, and the reverse substitution of labor.
*Structural Change and Economic Dynamics*50 2019:216-226. - Fluke switch points in pure fixed capital systems.
*Centro Sraffa*CSWP 48 2021. - Characteristics of labor markets varying with perturbations of relative markups.
*Review of Political Economy*2023. To appear.

In addition, I have a forthcoming article in the *Bulletin of Policial Economy* presenting examples of
both
the reswitching of the order of fertility
and the reswitching of the order of rentability

I wonder if this approach can be used to continue to generate papers for some time. I have decided that describing a single fluke case, such as a real Wicksell effect of zero, is not interesting. Nor is a comprehensive partitioning of a part of a parameter space of interest. Some connection needs to be drawn to some propositions of interest for economic theory. I have a sort of survey article of perturbing fluke switch points. This article has been desk-rejected once, and I have yet to submit it elsewhere. I have a draft article demonstrating that extending the economic life of a machine has no necessary connection with increased capital-intensity.

I have more models in which to try to identify fluke cases. I am continuing to think about a model that combines intensive and extensive rent. A further extension could consider cases in which more than one process is known for producing the industrial commodity or in which more than one agricultural commodity can be produced. Kurz and Salvadori (1995) have a chapter on the joint utilization of machines, and one could perturb parameters in numerical examples in that chapter. I think pure fixed capital models with machines of constant efficiency can be combined with extensive rent and still retain simple properties of circulating capital. Of course, I would want to look for fluke switch points in models with machines of non-constant efficiency. And, one can look at models of pure joint production. All of these can be extended to include a kind of markup pricing.

My blog archives probably have fluke cases I have forgotton about. Some I vaguely remember, but probably will not do anything with. For example, I once considered a preturbation of an example in which two techniques have the same wage curve, that is, a continuum of switch points. I considered a case in which a continuum of wage curves are tangent at a switch point. Another case is indeterminacy arising with perturbing parameters for requirements for use in a model of joint production.

There are some directions one could take this research program that I probably will not pursue:

**Define a taxonomy of fluke cases:**At first, I thought that all of the fluke switch points created by varying coefficients of production would be a matter of combining four normal forms, in some sense. This was a failure of imagination.**Partition a multidimensional parameter space:**I have been confining myself to two-dimensional diagrams. But if one looks at the whole parameter space, one should talk about manifolds in higher-dimensional spaces.**Generic structures in parameter spaces:**I have at least a couple of suggestive examples. For the above two and this extension, it might be helpful to know more algebraic geometry or tropical geometry than I know.**Relate partitions to defined biases in technical change:**I am thinking about Harrod-neutral and Marx-biased technical change, for example. Perhaps this sort of research should deal with vertically integrated models rather than how I have typically addressed structural economic dynamics.**Relate partitions to short run dynamics of market prices:**I would like to see some connections drawn to bifurcation theory and explicit dynamic models. I am not sure the normal forms drawn in such a theory will correspond to my fluke cases.

I have tried to write overviews of my research program before:

- Start of a catalogue of fluke switch points (January 2018).
- Update to a start on a catalog of switch point patterns of high co-dimension (March 2018).
- A taxonomy of Wicksell effects (November 2009).
- normal forms for switch points patterns (October 2018).
- On my research program (June 2021).
- Summary of some conclusions from my research program (September 2021).
- Summaries Of my research program (January 2022).