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

28;

Proof of (K). We again distinguish the three cases with
regard to the asymptotic range of z,, used in the proof of (B).
Case (1), £<&. In this case Proposition (K) is equivalent
to Lemma 2.
Case (2), {=8=ty#2. For definiteness assume Ç<2 and
let 2-¢=3e. Since now lim z,=G we can choose T such that
ta

(71)

10r

A

and at the same time large enough for there to exist an attainable
 path (x}, 2;) on [o, T] such that z°=zr+e. For {=T we
choose (x3, 2) according to

(72)

x, + g(27) —2(z) for all t=T

Then, (x},2}) is attainable throughout, and from (42), (71),
for t=T,

(73) x" -

- g(a

ow LV ay a \~,

Ho 1878) * €

Hence for

(74) «Was (=,

p-WU...)



-U VUE)

rd 8

i (arty

(Xr —
£1

u(y) dt

On the other hand, by (36), (40 a), (71),

[4] Koopmans - pag. ,