I
Vienna, 18.9.1975
Dear Osiatynski,
In my opinion, Kaleckis exposition in the relenant pages
152 to 155 of Economic dynamics aontains a flaw. He discusses
the existence of real roots of the trend equation, using
linear approximations, such as in particular, e
which are valid only for small rates of growth v.
His arguments however, require that they should be valid for
all values of v. In fact, if we go back to an exact formulation,
using exponentials instead of the approximation, we find that
the straight line in the graphs (representing the left side of
equation 35 ) is in reality a curve which turns apwards for large
values of v, so that there is always a real root! Moreover,
in case II there are three roots instead of two, and the
discussion of stability is inadequate to prove that the third
root is ephamerial. My own solution to this difficulty would have
c'A£& JL
been to admit only the case flne as economically relevant solution,
4.e. to require 6^ m.
Now the new typescript version of these pages does
nothing decisive to remove these difficulties. In fadt, the
same approximations essentially are used again. If we use
exponentials^then we get in place of the equation 35 of the typesript
^ d  /yg. it t 'ir e ~t~«
which shows again that the caselll (no root) does not exist,
and that in case II there will be three roots.
I think that the new version is an improvement only in
relatively minor details of introducing the approximations ,
I think there is no reason why it should be introduced into the
edition of the works.
A very puzzling question is of course, what Kalecki
really thought whah he wrote it. Unless I am wrong myself
(which is never excluded) I find it surprising that , an reworking
the text, he was not struck with the difficulties mentioned.
He certainly felt unhappy about the argument; I think we can
be pretty sure that he was not satisfied with the typescript
dropped
version either. It is significant that he aja*n&$ x ti8S the whole
approach ( I mean, a trend term dependent on the capitalstock) ^
in his 1968 paper on the trend (regrettably, I think: the whole
approach deserves to be pursued ).
