SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 275 
where #(z) denotes the inverse of z, on [o, T], and x(2)=x,,. 
The unknown function is now x(z), defined, like #(z), on the 
interval 2,<z<{2, or on 2<z=z, as the case may be. The 
advantage from the change of variables lies in the fact that 
only x(z) itself, and no derivative thereof, occur in the inte- 
grand in (60). Hence (60) is maximized on the set of superior 
paths if and only if x(z) is given a value £*(2) such that the 
integrand is maximized for almost every value of z in its do- 
main. This requires £*(z) for almost every z to equal the solu- 
tion x =x(z) of 
‘61, 
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21H 
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Koopmans - pag. 49