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favourably on any development of it, provided that this develop-
ment goes in the direction of a more practically relevant type of
analysis, by relaxing some of the unrealistic assumptions.
Now, my question is: does Professor MORISHIMA move in this
direction? If I understand him correctly, I must say he does not.
By considering technical change — and thus increasing per-capita
ncomes — he has been compelled to introduce specific assumptions
on consumers’ preferences. He has assumed that all individual
utility functions, besides being « identical », are « log-linear in the
quantities of the commodities consumed. » This means that, when
per-capita incomes increase, each consumer — if relative prices do
not change — is supposed to increase his demand for each com-
modity in exactly the same proportion.
These are further assumptions with respect to vON NEUMANN’S.
And what is unfortunate is that these additional assumptions are
not only unrealistic; they postulate a behaviour which we know to
be impossible, at least among human beings. As ERNST ENGEL
pointed out more than a century ago, when per-capita incomes
increase, the demand for each commodity does not tend to increase
proportionately; which means that utility functions are not log-
linear.
To postulate a consumers’ behaviour which goes against one
of the strongest empirical laws of economics (ENGEL’S law) makes
Professor MORISHIMA’S analysis more — instead of making it less
— artificial than that of voN NEUMANN. I have been wondering
why Professor MoriSHIMA has made such assumptions; and the only
reason that occurs to me is that they are the only ones that allow
a model with technical change to keep the mathematically elegant
property of proportional economic growth.
If this is the case, I must confess to be very disturbed. I feel
that this is just the way in which mathematics can do economics
a great disservice, For, in this direction, instead of using mathe-
matics as an analytical tool for the interpretation of economic phe-
nomena, we risk developing elegant mathematical models for their
own sake, and then making whatever assumption may be necessary
to give them an economic interpretation.
9] Movishima - pag. 34
