Full text: Brief von Josef Steindl an Stanisław Gomułka

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From unpublished work of Dr.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
	        

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