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