SEMAINE D ETUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC.
679
have introduced many slight variations in these two models
but have left unchanged their basic features.
Let me begin by considering voN NEUMANN’s celebrated
model, which is built on a set of basic assumptions that may
be listed as follows: 1) there is a wide, well specified, and
invariable set of technical methods for producing separately
or jointly the various commodities; 2) there are constant re-
turns to scale in the employment of all inputs of production
(labour included, in the sense that labour is imputed a sub-
sistence wage rate and is treated — like any other commodity —
as an output which requires fixed coefficient inputs of subsist-
ance consumption); 3) the excess of the output of each com-
modity over the input of the same commodity in the production
process is accumulated. Given these assumptions, VoN NEU-
MANN shows that there exists a certain set of techniques and
of corresponding prices, and a certain proportion in which the
various commodities may be produced, at which a uniform
rate of growth of all products is maximum. At this rate of
growth, which is considered to be the optimum one, the system
grows uniformly in all its sectors, i.e., it multiplies all its sec-
tions in the same proportion and therefore keeps constant in
time the structure of prices and the relative composition of
production.
Professor LEONTIEF arrives at results which are very si-
milar to these, although he does not go into the problem of
choice of techniques and starts instead by immediately assum-
‘ng given production coefficients for each process. LEONTIEF
begins with his input-output flow matrix and adds to it a
matrix of capital coefficients. Then he shows that there is a
well defined proportion among the initial stocks of capital
(determined exclusively by the structural coefficients) which
yields a maximum uniform rate of growth for all sectors.
Even if the system does not start from this particular com-
position of the initial stocks of capital, it will all the same tend
10] Pasinetti - pag. 109
