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

the exponential amortization which is a characteristic oi th
exponential model (1).
It is shown in the Appendix to the present study that under
the very general hypothesis that the function [3(8)e*’ can be
developed as a Taylor series, at least for a certain value of p,
the coefficient A (which is equal to 1 in the exponential model)
will not differ generally from unity by more than +o.5, for
hypotheses which can reasonably be accepted.
It follows from this that while the exponential model clearly
may not offer a perfect portrayal of real conditions, it doubtless
does not differ therefrom all that much, so that, at least in
terms of a first approximation, it is capable of depicting the
essential features of reality quite correctly.
If this approximation is deemed insufficient, the develop
ment of the function 3(6)e*’ as a Tavlor series of which the very
first terms only are retained, provides as far as can be judged
a reasonable representation of actual conditions (#

The Value of the Model

337. It follows from the preceding dimission that.

a) the model is consistent with the information which ca..
obtained from available statistical data:
b) it cannot be proved that the assumptions made are the only
ones which would give results consistent with available data

y From relation (z:zc

x

Thus if (0) declines more rapidly than

© © we have

since

for (60)=e ©/v.
(3) See Appendix

.| Allais - pag. 179