A-=1103 Wien Postfch 91
13th June 1976
Dear Dr Gomulka,
Thankyou very much for your letter and the manuscript.
In the meantime I have come to see a new aspect of the matter.
In fact, Kalecki never used the mixed difference-differential
equation with the forward argument which you attribute to him
After the first version of 1935 he always used finite differences only.
Now you may say this comes to the same if the differences are small
( the unit of time, that is ). However, I have come to the conclusion
that he did not mean the differences i.e. the unit of time, to be small.
This is perfectly clear just in the paper which you use as a starting
point for your discussion, the 1962 paper. The unit of time is there
equal to the lag, and he writes
I,,, = alt + bAI,
3ince we must reasonably interpret
the equation will be
I ,o - (a+b) Ig4yq +B Ig =
This is no dout a simplification, and the time unit more generally
may be different, but i$ is clear that it should be not small.
ln fact, it would be absurd to assume anything else;
it would mdan assuming that the changes in profit from one day to the
other influence the investment dgcisions. Realisticlaly you must assume
that the investor wall wait zmzx some time and decide then only whether
ond how much profits have increased; this time may be a year or 1t
may be less, hardly less then half. or a quarter of a year.
If you assume such a finite differencefor the increase in
profits, all the absurdities which I talked about in my last two letters
do not exist any more. The short time ups and downs of profits will
anter the investment decision only after they have been smoothed out.
The minor cycles which will exist to take account of a finiet span
of initial conditions cannot have, in the case of the difference
squation . an anti-damping if the major cycle is damped.