Re: Participatory Planning

[FAC_BROSSER@xxxxxxxxxxxxxxxx]

Comment on Fel'dman and limit cycles:
     The mathematics of limit cycles was developed in the
nineteenth century by a variety of people to study celestial
mechanics.  By the time Poincare wrote in the 1880's limit
cycles were fully understood and Poincare was beginning to
move into what would eventually lead to chaotic dynamics.
     However prior to 1928, which memory serves me was the date
of Fel'dman's article, no economist had written about limit cycles,
although the Russian/Soviet mathematicians around Fel'dman were
among the world's leaders in studying such things.  It appears,
although I do not have my hands on the article, that Ragnar Frisch
may have discussed them in his 1936, "On the Notion of Equilibrium
and Disequilibrium," _Review of Economic Studies_, 3, 100-105
(perhaps the Norwegian mafia might weigh in here, especially if he
did).  But a definite reference is in Paul Samuelson's 1941, "The
Stability of Equilibrium: Linear and Nonlinear Systems," _Econometrica_
9, 97-120 (reprinted in modified form as Chap. 10 in his 1947
_Foundations of Economic Analysis_).  However the Kaldor trade cycle
model of 1940 is implicitly a limit cycle model as shown later by
Chang and Smyth in the _Review of Economic Studies_ in 1971.
     Also, there had been one discussion of economics involving
limit cycles prior to Fel'dman.  But it was in a book by the brilliant
biologist, Alfred J. Lotka, in 1925, _Elements of Physical Biology_,
published in the US, and which I do not think we can fault Fel'dman
for not being aware of.
Barkley Rosser
James Madison University