SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 817

Hypothesis {1

316. The assumption of logarithmic linearity is justified by
the results obtained in the research undertaken elsewhere on
production functions (1).
[t is further justified by the fact that a general property of
nature is that the empirically measured regularity of numerous
ohenomena can be expressed a wide range by logarithmically
 linear formulae. This explains, for example, the relative
stability of demand elasticities, the approximative constancy
of the rates of growth of population and production of dif-‘erent
 kinds, and the general applicability of the lognormal
statistical distribution.
It is worth stressing at this point that this hypothesis can
only be considered as valid in the context of a finite range of
variation of the parameters (?) (3).
The invariance of 3(8) over time is an assumption which
can have no a priori justification. It can only be justified by
its consequences.

Hypothesis (c): Stability of the Rate of Growth ¢ of Primary
Income R,,

317. The hypothesis of a constant value of the rate of growth
o> can be justified by the fact that if economic development is

(") ArLaIs (1960 A), $ 37.
‘?) In discrete notation if the production function (note 2, p. 45, $
R=a R,%» , Rt ,..., Ra’, ...
were considered valid for any value of primary input, the manifestly unacceptable
 conclusion would follow that R would necessarily be zero if any
one Rg were zero.
?) Naturally, hypothesis (b) implies the more general hypothesis accordng
 to which there exists a valid index R. of the real national consumed
income ($ 115, 119 and 211)

Allais - pag. 121