362 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

the value of A is found as

A =0.40

This figure is of the same order of magnitude as the 0.316
found in § 333-6. Here again, the divergence can be attributed
‘0 the approximative nature of the hypothesis (H”), on the
assumption that the exponential model is valid. But if this
approximation is admitted, the concordance of orders of magnitude
 indicates that, if hypothesis (H"”) is taken to be approximately
 true, the exponential model can be considered as not
departing very far from reality.
This reasoning shows, at least intuitively, how the assumption
 of exponential amortization of primary income is justified.
If the general formulation of the exponential model is taken
as exact, it also supplies an estimate of the order of magnitude
of the proportion A of primary income incorporated in investment,
 which agrees with observed data (1).

(!) Of course it would be of the greatest possible interest to generalise
‘he above reasoning to the case in which the lengths of the production
ind amortisation periods of different types of investment are no longer
considered as uniform, but the frequency of a production period extending
irom § to 6+ df would be (6) de, and the frequency of an amortisation
period for primary inputs extending from 6 to 0+d6 would be ¢(6)d6,
with the discrete model becoming continuous (See § 333-2 above). Up to
now, I have been unsuccessful in making a calculation of this kind. If it
could be done, it would doubtless enable the validity of the exponential
model to be verified efficiently, by determining the relations between the
quantities A, x and @ and the data Rc, C et p, using this model.
In present circumstances, and in the absence of a calculation of this
kind progress can onlv be made on the basis of rough estimates

11] Allais - pag. 166