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 equipment
 per worker may be completely erroneous.
Consider an economy in stationary equilibrium characterised
 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 preceding
 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 respectively
 by two values ¢; and ¢, of q with

(43% 2.

the values of X, and Xi remaining unchanged.

“r1] Allais - pag. 106