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may be severe conflicts between our ethical notions and the analysis 
of certain kinds of growth models. His conclusion is that we must 
change our ethical notions. My preference would be to say that there 
is something wrong with the model. In either case a good deal of 
further thought seems called for. More particularly, one frequently 
in the theory of optimization over time encounters peculiar difficulties 
when one uses an infinite time horizon. Now, in fact, the device of 
the infinite horizon was probably originally introduced because the 
choice of a finite horizon is an arbitrary one and because with a finite 
horizon one has difficulty in deciding what to do about terminal 
capital stock. Infinite horizons were, however, introduced primarily 
as a convenience. They have in several contexts now been shown 
to lead to difficulties all associated with divergence of the improper 
integral obtained in the problem. Now this suggests to me that 
infinite horizons are not in fact the convenience they appear. The 
obvious conclusion from KooPMANS’ paper, therefore, seems to me 
to be that one ought to abandon the use of infinite horizons — not 
that one ought to abandon certain ethical notions. 
Now, of course, this may be wrong. It may turn out — and 
Prof. KooPMANS assures me that it does — that even with a finite 
horizon one has similar problems which are not so severe. In that 
case, it may not be worth dropping infinite horizons. Still, the role 
of this sort of analysis is surely to tell us how one can best achieve 
one’s ethical and social ends. In the course of analyzing that, it 
may turn out that such ends are unachievable. In such a case, one 
has to moderate one’s ends. The usual circumstance, however, is 
that one’s ends are not achievable in the sense of being contradictory 
whereas Prof. KooPMANS has shown that our ends may be unachie- 
vable in the sense that no solution to the problem exists — that the 
whole analysis breaks down if one insists on certain kinds of ethical 
goals. This sort of circumstance does not persuade me to give up 
my ethical goals, but rather to refine the mode of analysis. I can 
understand that the end result may be that I will have to give up 
certain goals as unachievable, but the demonstration of that ought 
i Koopmans - pag. 75