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 logarithmic- 
ally 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 unacc- 
eptable conclusion would follow that R would necessarily be zero if any 
one Rg were zero. 
?) Naturally, hypothesis (b) implies the more general hypothesis accord- 
ng to which there exists a valid index R. of the real national consumed 
income ($ 115, 119 and 211) 
Allais - pag. 121