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

267

For the proof of Lemma 2 we must strengthen (46) to
obtain a positive lower bound on the gain Us (gp) associated
with the « straightening out » of a bulge [T, T*]. For this
purpose we choose an interva. "2. 7 such that

(49) (a) &

~ Ba e

C and either (b) 2(p)<z, or (c) 2* 2

which is always possible. If for definiteness we assume (49 €,
we have from Assumption (c) of Section A 2

(50) g'(2

— v

0]

for

Now 2, has infinitely manv bulges

ww"

[T, T*' with the

pre

perties

(SI)

iN

for some ?.

Because of the c --tinuitv of z, we can for each ot ‘hes
an interval “we write

1

hoc.

(52)

7/0

Koopmans - pag. 43