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From unpublished work of Dr.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