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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -
horizon is a mathematically explicit way of bringing the presence
of a mathematical limitation to ethical thought to our attention.
Professor HAAvELMO pointed out that sacrifices enforced at one
time may later be endorsed by public opinion, perhaps when the
oenefits from that earlier sacrifice become apparent. This would
re-enforce an idea I have expressed in my paper but not in my
presentation. Perhaps the discount rate p itself should be a function
of the level of consumption reached. I would expect that if we get
close to affluence p diminishes, It is conceivable that one could find
ways of making p depend on the consumption level in such a way
as to avoid the difficulties that I have encountered.
Several speakers have asked whether these strange results are
due to the assumption of a double commodity that can both be
eaten and used as capital. So far I do not know of more detailed
or elaborate studies directed to the same question; so I can only
state my hunches. 1 would think that essentially the same results
would be found with other forms of indefinitely continuing popu-
lation growth as long as the percentage rate of growth stays above
some positive percentage. I think one would find the same difficulty
even more strongly if one introduces technological progress in ad-
dition. It is possible, however, that resource limitations not ultimately
compensated by technological progress could work in the opposite
direction and would do away with the conclusion. If the single
social preference function is replaced by individual preference func-
tions and a market mechanism is introduced of the type that
Professor Arrais has stressed several times in the discussion, I
would not want to venture a guess as to whether the difficulty I have
encountered would remain or disappear.
As to Professor ALLAIS’ statement that there is no reason for
discounting, I started out with that idea myself. But I found that
for there to exist an optimum path, I had to either discount or
discriminate against people on the basis of how many there are in
a given generation.
51 Malinvaud - pag. 84
