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

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In the derivation of these conditions, inequality (21),
page 20, plays an essential role. It permits a comparison between
 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 ¢ Froposition
 1 states that a regular program that satisfies condi
tion 1 is optimal.
Let me point out here that any regular program would appear
 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.

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