Monday, January 15, 2018

Start of a Catalogue of Flukes of Fluke Switch Points

I claim that the pattern analysis I have defined can be used to generate additional fluke switch points. I am particularly interested in switch points that are flukes in more than one way (local patterns of co-dimension higher than one) and fluke switch points that are combined with other fluke switch points or some aspect of other switch points (global patterns). I have already generated some examples, not always with pattern analysis.

  • Fluke switch points of higher co-dimension
    • A switch point that is simultaneously a pattern across the wage axis and a reswitching pattern (a case of a real Wicksell effect of zero).
    • A switch point combining four three-technique patterns (due to Salvadori and Steedman).
  • Fluke switch points combined with other switch points
    • A reswitching example with one switch point being a pattern across the wage axis (another case of a real Wicksell effect of zero).
    • An example with a pattern across the wage axis and a pattern over the axis for the rate of profits.
    • Two switch points with both being reswitching patterns can be found from a partition of a parameter space where two loci for reswitching patterns intersect.
    • A pattern across the point where the rate of profits is negative one hundred percent, combined with a switch point, for the same techniques, with a positive rate of profits (of interest for the reverse substitution of labor).
    • An example where every point on the frontier is a switch point.

The above list is not complete. More types of fluke switch points exist. Some, like the examples of a real Wicksell effect of zero, I thought, should be of interest for themselves to economists. Others show examples of parameters where the appearance of the wage frontier, at least, changes with perturbations of the parameters. I would like to see that in at least some cases, short run dynamics changes qualitatively with such perturbations. But this seems to be beyond my capabilities.

Maybe I'll update this post some day, if I create more examples.

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