Brief von Josef Steindl an Jerzy Osiatyński
Josef
Steindl
1504170964703
Dr. J. Osiatynski
Polska Akademia Nauk
Vienna, 20th January 1978
ul. Nowy Swiat 72
Warssawa
Dear Dr. Osiatynski,
Thank you for your letter of Dec.28 and the photo copies of my
letters. I have nothin? against the publication of the passages
in question. The “countervailing power" does refer to Galbraith,
of course.
Instead of sending you my correspondence with Dr. Gomulka I have
written a few lines which contain practically all that is relevant
for the Kalecki edition, and which I enclose with this letter.
Whether you can include these remarks (without mentioning me of
course) in the edition depends,. I think, on whether Dr. Gomulka
agrees to it. He might also elaborate the last point of my note,
if it can be done in a limited space.
Z am sending him the note, and pending his agreement, it is only
for your information. Ultimately it depends of course, on you
whether you think it a suitable editoral comment.
With kind regards
yours
Kalecki's trade cycle theory in its first version (Econometrics 1935)
has been represented by a mixed difference - differential equation
with a backward argument:
I (t-o* - a l(t) - b I (t) (1)
This equation has been thoroughly investigated by Frisch and
Holme (Econometrics 1935) and holds no surprises.
All the later versions of Kalecki's theory have been represented
by an equation of the type
I (t + ©•) - a I (t) + bI (t) (2)
This was always written with a finite fa . Nonetheless many
readers have tended to regard it as an approximation to the mixed
difference - differential equation
I (t+o-) - a I (t) + b I (t) (3)
which in contrast to (1) has a forward argument.
Equations (2) and (3) have not been analysed in the same way as (1).
From unpublished work of Dr. Stanislaw Gomulka, London School of
Economics, it appears that the equation (3) yields explosive
cycles with a period smaller than the lag As a result the initial
conditions do not fade out in the solution and the process is not
ergodic.
This speaks against using equation (3). It appears that Kalecki
knew very well why he wrote finite differences and that he did it
on purpose. This can also be explained in economic terms. The last
term in (2) and (3) indirectly relates to the influence of a change
in profits on investment. Now business executives would hardly ob-
serve the change in profits from one second to the next, but
much rather from one year to the next, when they decide about invest-
ment. The equation (3),in other words, implies unreasonable economic
2
assumptions as well as absurd results and is not a proper inter-
pretation of Kalecki's theory.
Intuitively, it would seem that if the time unit in equation (2)
is sufficiently small the same troubles as in equation (3)
would arise also here. There exists a certain critical value
of the time unit in (2), which must be exceeded if explosive solu
tions are to be avoided. Dr. Gomulka has obtained results on this
which are as yet unpublished. In Kalecki's practical examples a
time unit of one year is assumed and it appears that this is
sufficient to avoid unsuitable solutions of the equation.
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