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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
KOOPMANS 
I share the beliefs expressed by both speakers, Prof. MAHALANOBIS 
and Prof. MALINVAUD, that the one-commodity study, one-commodity 
model does a service here in isolating just those problems that come 
from the open-endedness of the future. Considering those apart from 
or complications which arise in two- or more-commodity models, 
I used the term « belief » because I do not feel that a stronger term 
can be used at this point. One would want to go on to two- and 
more-commodity models to examine whether that belief is valid but 
this is my present state of espectation. 
On the question that Prof. MAHALANOBIS raised about flexibility 
in the ordering, that idea is merely mentioned at the end of my 
study. I have given some thought to the possibility of working from 
an ordering which has built into it the possibility of its own revision 
at a later time, and more particularly an ordering in which the 
decision maker is willing to make a present sacrifice of immediate 
satisfaction in order to leave open more doors in the future. He may, 
for instance, prefer to build a capital stock of such a nature that it 
can be applied to a wider range of different kinds of production, 
even though that kind of capital stock would not be the most econo- 
mical one if the composition of production in the future were already 
fully specified. For somewhat longer-range planning this seems to 
me a matter of practical importance. My speculations on this are in 
a reference at the end of my paper, identified by the year 1962, and 
‘hey did not carry very far. I believe that from the formal point 
of view it is a difficult matter to formalize this idea. I do find that 
the need for such an idea is strong enough to justify further forma- 
lizing effort in that direction. 
FISHER 
Prof. KooPMANS has as always presented us with an illuminating 
and beautiful piece of work. I am, however, disturbed a bit at the 
conclusions that he wants to draw from it. He has shown that there 
i4] Koopmans - pag. 74