SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
ZI 
Let us assume that RAMSEY’s device can be used also in this 
case, and that it would again merelv result in addine the bor- 
derline value ç= te the set of discount rates defining a 
utility function for which an optimal path exists. Then a pre- 
dictable positive lower bound to the rate of technical progress, 
valid for an indefinite future period, precludes application of 
the ethical principle of timing neutrality in terms even of per 
capita utility — not to speak at all ot weighting generations by 
their numbers. 
Thus, if in the face of technological progress we want tc 
hold on to the idea of maximizing a utility integral such as (35, 
over time, we must invent a discount rate © satisfying (34), or 
its equivalent for another production function. Such a discount 
rate might just have to be a pragmatic one having no basis 
in a priori ethical thought. While it might well be a result, 
conscious or unconscious, of political processes or decisions, it 
would have to be revised upward if it is estimated that techno- 
logical progress will accelerate to such an extent as to « over- 
take it », and could be revised downward if it is expected that 
progress will slow down. 
One might instead conclude that the whole idea of maximiz- 
ing a utility integral is not flexible enough to fit the inequality 
of opportunity between generations inherent in modern techno- 
logy. Two alternative notions have been partially explored 
by the present author, using a discrete concept of time. In 
one of these [ KOOPMANS, 1960, see also KooPMANS, DIAMOND 
and WILLIAMSON, 1964], the utility function of a consumption 
path x, t—1, 4, .…, can be defined bv a recursive relation 
J(r,. x, 
== Viu(x,), U(x,, 3. y 
.1 Koopmans - pag. 3-