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 integrand
 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 domain.
 This requires £*(z) for almost every z to equal the solution
 x =x(z) of

‘61,

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Koopmans - pag. 49