SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 26s

it ny denotes the number of completed bulges in [0, T'? FE i
lim #np.=oc because there are infinitelv manv bul se =
T’>00
[0, oc]. Hence the choice of Ty such that ny >N/«- estaplishes
 Lemma 2 in case (49 c) holds. The proof from (4G 5) i.
similar.

A 6. PROOFS FOR A ZERO DISCOUNT RATE (.

Proof of (A). In (43 a) take
Then if we write u(x)Za, u’.

(54)

Uu

di =U + |.

y wu

. À

Aw

by (38), (40), regardless of T, T*, hence also for .
Proof of (B). We distinguish three cases regarding
asymptotic range [§, ©] of the given path (x, z,).
Case (1), {<Ç. In this case we have from Lemma 2 and
from (54) applied to (7%, 27), for anv N c

for an
r—

T> 1

waa — uly) dr -

ULX + » -

In this case. therefore. .

u. a

N +.

+ diverges to - \ a

a

. Koopmans - pag. 45