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In the derivation of these conditions, inequality (21), 
page 20, plays an essential role. It permits a comparison be- 
tween a feasible program # and another feasible program 
fo+¢ : it might be written as: 
SU. 
= Apr at LS ; 
Lon trang veo Ngo - 72, 2S, 
T_ 
%, 8; and Ar depending on the values of the variables in M. 
The coefficient Jr being non-negative, / is optimal if the 
2's and B,’s are equal to zero and if & S,=o for any T and 
any feasible program #+¢ Æ such that t>T would imply 
> U,zo. 
This is essentially what proposition 1 amounts 2. I first 
define as « regular » a feasible program for which the &,s 
and $s are all zero; this is equivalent to requiring that the 
equations (22) be fulfiled. I then specify a condition 1 that 
automatically implies the condition quoted at the end of the 
preceding paragraph. Condition 1 requires that, in Æ, the 
marginal utility of consumption be positive at all times and 
that there exist a number % larger than 1 such that, at least for 
large ¢: 
2 
> 
fx being the marginal productivity of capital at time ¢ Fro- 
position 1 states that a regular program that satisfies condi 
tion 1 is optimal. 
Let me point out here that any regular program would ap- 
pear as optimal if time were restricted by a finite horizon T and 
if the values of both S, and S- were taken as boundarv cons 
Yi 
Malinvaud - pag. 
37