326 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

derived from the exponential model appears to concord very
well with the results obtained from analysis of available data
on durable goods in all cases where a sufficiently large competitive
 market in these goods exists (1) (2).
An attempt to derive the fonction ¢(6) directly, at least
approximatively, can be made with the help of statistics of the
distribution of the working population. This analysis involves
major difficulties, but at first sight seems to produce results in
conformity with an exponential form of ¢(8) (3).
The length of the production period 6=y is of the order
of 3.5 years for the U.S.A. For the average amortisation period
® =vc, from (251-6)

(326-2)

&

B

— 60

Whence, for Ô=3.5 and p=1.7% (*), © is derived for
the U.S.A. as 3.72, i.e. a value which differs little from that
5

of

(1) Arras (1960 A), p. 22-23.
2) It may be objected that in a rigorous formulation, the composition
ot different exponential amortization functions cannot result in an expoaential
 global amortization function over the whole range of variation (0, oo)
of @. Nevertheless, over the useful variation interval (o, 100) of 0, use
of this type of function is certainly possible. as it involves a rather low
-elative error.
() Arrais (1960 A), § 45.
(*) Equal, as a first approximation. to the rate of population growth in
the T7.S A

11] Allais - pag. 130