392 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
Analysis of a Simble Model 
432. These considerations can be illustrated by a simple 
model which shows that the conventional explanation of greater 
U.S. productivity as being due to the larger volume of equip- 
ment per worker may be completely erroneous. 
Consider an economy in stationary equilibrium character- 
ised by the three following relationships: 
452-1) 
"A=f [9X, E] 
E=g [¢X,] 
2 
A is the quantity of consumption good (A) produced during 
each period, E the output of an equipment good (E), X total 
labour input of which a part X, is absorbed by industry (A) 
while Xz represents the labour input of industry E. 
The quantity E of equipment goods produced during a pre- 
ceding period is assumed to be used completely during the next 
period. 
Finally, gq is a parameter indicating quality. 
The functions f and g are increasing functions of each of 
the variables and are assumed to be of first order homogeneity. 
We now consider two situations I and II characterised res- 
pectively by two values ¢; and ¢, of q with 
(43% 2. 
the values of X, and Xi remaining unchanged. 
“r1] Allais - pag. 106