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 noncomplemen- 
tarity 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 mar- 
ginal 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 be- 
tween the integral (14) for any given feasible path and its value 
for the golden rule path, and study the behavior of this diffe- 
rence 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°