MEMORANDUM

“There is another point I would like to mention. You say that the transformation
processes can be lumped together in such a way that all the f i
become equal. Of course
from the purely logical viewpoint this true, but if such a lumping together is done, we
may get results that have very little economic meaning. If the f
i
shall have economic
significance they must be interpreted as marginal costs or something of that sort
referring to concrete processes of the type we know from actual economic life, and if
they are defined in this way, they may of course turn out to have definite magnitudes.
But this is not all. Even from a purely logical viewpoint, there is something which
makes it perfectly artificial to assume all the derivatives equal; these derivatives
depend of course on the magnitudes of the various variables involved so that for one
set of values of these variables one would have to adopt one system of sub-division for
the process, and for another set of variables another kind of sub-division would have
to be adopted. The whole system of division would simply change continually as the
general system of general parameter (prices, quantities, etc.) changes in the market.
This leads to so much arbitrariness that I do not see how the idea of equality of
derivatives can help to shed light on the normal happenings.
There is, however, no need to assume these various derivatives equal. It seems
that your whole argument could be developed without making such an assumption. (…)
If you would like to work through your paper once more with these various things
in your mind, I should be very much interested if you would submit a new version of it
for consideration with a view to its being published in Econometrica. But some such
revision appears to me to be essential as I do not think we could accept the paper in its
present shape. Your manuscript is returned herewith.”
Three weeks later Leontief sent a revised version to Frisch with the title changed to
Vertical repercussions in a chain of production processes:
Leontief to Frisch, 26 January 1934.
“I am sending you a new version of my article on “Vertical Repercussions”
adjusted and brought in line with your requirements.
The assumption f
1
f
2
... f
n
is dropped and the mathematical treatment
changed accordingly. The problem of scale of measurements to [be] discussed in an
additional footnote on page 17 (addendum).
It would be rather difficult for me to make new computations and to redraft the
graphs, but one explanatory sentence in the text will, I hope, preclude any
misunderstanding in this respect.”
Leontief’s revision of the paper did not satisfy Frisch:
94