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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2¢

These are the various relations for a stationary process given
in my 1947 book « Economy and Interest » (!) (3).

Primary Capital

I4I. In a stationary process, the average amortization period
 is equal to the quotient derived by dividing capital by
amortization, whatever the amortization rules. It follows that
for primary capital C, we have

(I4I-I)

C.=0R,.

From the earlier expression for C (3) and for a given funcfon
 ¢(0), C, can be derived by putting i=0. Thus we have

(I41-2)

Co lim P elr
=m € -Tw(e)do

rr 0¢(6)d6

and this is effectively relation (141-1), (relation 112-I).
Thus ® can be regarded as the average amortization period
of primary capital (4).

(!) « Economy and Interest », pp. 127, 128, 132, 133, 187 and 188.
(3) The hypothesis that k=1 is made implicitly in this study; the function
 (6) there considered is the same as Rw ©(A) in the notation of the
present paper.
(3) Relation (140-7).
(*) Of course this equality also holds as a first approximation for small
values of n (relation 126-10)

111 Allais - pag. 72