SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC

LA

As explained already in Section 1, this simple integration
of an instantaneous utility flow u(x,) implies noncomplementarity
 between consumption in anv two or more parts of the
future.
We shall assume that the instantaneous utility flow is a
strictly concave, increasing and twice differentiable function
u(x) of the instantaneous consumption flow x. This function
does not change with time, and is defined for all x>0. Strict
concavity implies that we attribute greater weight to the marginal
 unit of per capita consumption of a poor generation as
compared with a rich one. To assume u(x) increasing rules
out saturation. Finally, instead of introducing a subsistence
minimum, we shall require that

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line ae.

a strong incentive to avoid periods of very low consumptio..
as much as is feasible.
Let #=u(£) denote the instantaneous utility flow derivec
from the consumption flow per worker of the path x, =x, ., .,
of the golden rule. We shall now work with the difference between
 the integral (14) for any given feasible path and its value
for the golden rule path, and study the behavior of this difference
 as T goes to infinity. The following propositions can be
proved (for proofs see Appendix).

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(A) There 1s a number U such

(ce ve

ha

u

dl ~~

for all feasible paths (x,, 2, and for all horizons T

‘al Koopmans - pag. 1°