562 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
favourably on any development of it, provided that this development
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 commodity
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 loglinear.
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 mathematics
as an analytical tool for the interpretation of economic phenomena,
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
