Brief von Josef Steindl an Stanisław Gomułka
Josef
Steindl
1504175156507
Vienna, 20th January 1978
Dr. Stanislew GOMULKA
Dept, of Economics
London School of Economics
Houghton Street
London WC2A 2AE
Dear Dr. Gomulka,
I am in correspondence with Dr. Osiatnynski in connection with
the Kalecki edition for which he prepares the second volume.
I think that certain formal results which you obtained in the course
of your work on Kalecki's equation are of sufficiently general inter-
est to be included in an editorial comment. To make clear what ex-
actly I mean I have written the enclosed note. The point of the
critical value could be elaborated, provided this is possible with-
out inflicting too much on the reader, (I am thinking of the analysis
referred to in your letter of Nov.16, 1976).
It depends on you whether you agree to this use of your results,
and on Dr. Osiatynski whether he wants to include it. I am only
trying to be an intermediate, in the interest of the edition.
With kind regards,
yours sincerely.
J. Steindl
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-<►) - a I(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) + b/1 I (t) (2)
This was always written with a finite A . Nonetheless many
readers have tended to regard it as an approximation to the mixed
difference - differential equation
I (t+®0 - 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From unpublished work of Dr.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 <r. 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.