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{(« adjusting preferences to opportunities »). Prof. KoopMANs has
found that the traditional approach to optimal growth (which con-
sists of maximizing utility over time, by accepting a certain rate of
discount of utility, called p, as given by individual preferences) can-
not always be applied. More precisely, he has found that it can be
applied only when the time horizon considered is finite. When time
is allowed to run from o to oo, then p<70 becomes impossible
calthough p>o still remains possible) because there simply would not
exist a utility function to be maximized,
Thus — Prof. Koopmans concludes — the open-endedness of the
future imposes limits on individual preferences. He seems to be
so surprised and even so afraid of this result as to prefer, at this
point, to begin to speculate on the meaning of all this.
I would suggest that the mathematical exercise should be com-
pleted, by allowing time to run from —oo to +oo (and not only
from 0 to +00). I may add perhaps that to consider time as running
from —oo to +oo does not mean allowing time to run in reverse.
It simply means putting ourselves in a slightly different position with
respect to the one Prof. KooPMANS has chosen. Instead of saying,
as he does: suppose we begin our process of maximization at time
zero, whatever happened before; we say: suppose that optimization
has been taking place since the beginning of time. (This, by the
way, appears to me a more logical approach to take in the context
of Prof. KooPMANS’ stationary society). Now, if we allow time to
run from —oo to +00, it is easy to see that, in a stationary economic
system, also p>>0 becomes impossible. The only value of p that
makes any process of utility maximization over infinity possible is
0=0.
Prof. KooPMANS might be even more surprised. For, by following
his arguments, we should conclude that individuals have not even
a limited inter-temporal preference choice: they have no choice at all.
But is it so? This conclusion — it seems to me — is fallacious,
although of course the mathematical results are correct. And the
fallacy stems from not bringing out explicitly the implications of the
following theorem: on the optimum growth path (by which I mean
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